Hamburg Music Notation Poster

Dear friends of music,
during the last 20 years we have been working on the development of Hamburg Music Notation, which aims at simplifying the reading and writing of music in such a way that it becomes as easy to handle as in the field of language.
We are convinced that so-called Western music, which consists of twelve tones, can best be represented by the Duodecimal System.
Also written representation on five lines can be radically simplified by the use of two differently shaped note heads analogous to two colors on the keyboard and the principles developed by Bach for the well-tempered piano.
A detailed account of our considerations can be found on our website.
A software that can be used as an addon ( for the free music software MuseScore is available to convert the usual notation into Hamburg music notation.
On a poster ( , which is generally available, we have displayed all keys in major and minor.
Also the most important chords are shown there.
Music is a language in which reading and writing should be easy to learn.
The currently used method does not meet these requirements.
We propose to teach the method we have developed in addition to the common method as a second clef.

Poster HMN

DS66 Music Notation

This experimental system combines a diatonic staff with a 6-6 solid/hollow note head pattern. (“DS” for Diatonic Staff, “66” for 6-6 note head pattern.)

The 6-6 solid/hollow note head pattern helps musicians identify intervals and read music relatively (by interval). It also reminds them when notes are sharp or flat due to the key signature (or accidental signs).

The staff’s line pattern ‘cycles’ every two octaves. You can think of it as a 6-line staff except the third line from the top is a ledger line. Two separate groups of two and three lines are arguably easier to learn and to read than a staff of six. Also, the groups of lines are inversions of each other since both are centered on the note G.  (The middle line of the three line group is G, and the space between the two lines of the two line group is G.) This inverse relation helps with learning and remembering the lines and spaces of the staff.

The line pattern also follows the traditional treble and bass clefs. The lower part of the staff (the three line group) is the same as the bottom of the treble clef staff and the upper part (the two line group) is the same as the top of the bass clef staff.  This means the notes of the DS66 staff covers the notes of the bass and treble clefs, and thus can be used as a direct replacement with music written on those traditional clefs.  The similarity with the traditional staff and clefs also makes it easier to learn DS66 along with the traditional system.

DS66 offers a lot of continuity with the traditional system, while addressing some of its shortcomings.  Traditional key signatures and accidentals are used. Traditional rhythm symbols are used except half notes are indicated by double stems.

This system is similar to Classic Nydana ( except it prioritizes consistency of interval appearance over consistency in the appearance of individual notes.  Thus it maintains a consistent line-space alternation and cycles every two octaves rather than every octave.  (Classic Nydana has two adjacent space notes, A and B, to achieve a diatonic staff that cycles every octave.)

Originally introduced by Paul Morris in this post on the MNP forum (google group) in March 2017.


Concerns with Traditional Rhythm Notation

Although rhythm notation has not received as much attention as pitch notation, there are a number of complexities and inconsistencies in tradtional rhythm notation that present opportunities for improvement or alternative approaches.

1. There is a multiplicity of graphical representations for relative duration:
– stems or not
– solid or hollow noteheads
– flags (various numbers)
– beams (various numbers)
– dots (various numbers)
– ties
– super/sub-script digits with arcs for tuplets
– a whole set of different symbols for rests (duration of silence)
– same symbol used for whole note rest (4 counts) and entire measure rest (various durations).
Aside from the sheer multiplicity and inconsistency of graphical schemes,
this practice preempts too many graphical distinctives that could be used for other notational purposes.
For example, some pitch proposals use solid/hollow noteheads to distinguish whole-tone rows, which then requires an alternative notation to distinguish whole and half-notes from quarter notes, etc.
2. Rhythms are notated by duration instead of “beat” or “count”
This is a particular problem for notation software, since it makes note position dependent on cumulative durations,
making it difficult to do editing without global side-effects.  Perhaps as a consequence,
notation software often resorts to a Procrustean “tyranny of the bar”, making it difficult to edit passages that don’t begin and end at bar lines.
Musical “sense” and performance, however, is characterized by regular patters of beats (stress) similar to the “poetic feet” patterns of stress in spoken poetry.  Moreover, music students routinely learn “counting” pattern, such as 1 & 2 & 3 & 4 &, , and often amend their scores to include this essential information.
3. Notation of syncopation
In syncopated music, when notes are sustained across a beat, there is a convention of tying notes across the bar and even the half-bar.
This results in inconsistent notation for the same duration,
e.g. a quarter-note vs. two tied eighth-notes,
but it is perhaps a nod to the idea that “beat” takes precedence over duration.
4. Encoding of up-beats or “soft” feet is “backwards”.
In traditional notation, it is customary in to have notational rhythm units start on a beat. So, for example,  a dotted eighth note may be beamed to a subsequent sixteenth note, or a half-note may be followed by a quarter-note in the same measure, Often, in “compound meter” especially, the sustained note is perceived as the “end” of phrase or motif, and the following unstressed note is perceived as a  “pick-up” to the next phrase or motif, not as an extension of the previous one. But the visual connection between the two, via a beam or inclusion in the same measure, obscures the break.  This problem is exacerbated by the practice of breaking lines only at bars. This can result in the beginning notes of one phrase being “orphaned”  at end of a line ending one phrase, separated from the bulk of the phrase on the next line or even next page.
5. Music is “poetry”, but it is traditionally printed as “prose.”
This observation actually encompasses “form” as well as rhythm.
Music is traditionally printed in a way that minimizes the number of pages at the expense of formal clarity or even page-turniing convenience.  Furthermore, typically printed lines break only at bar lines, even though, as noted previously, musical phrases often end mid-bar.  This carries over into conventions for repeats and alternative endings, requiring duplication  of “beginnings” of initial passages after the “end” of final passages to notate a “repeat”, or repeat of “ends” of common material at the beginning of each alternative ending.
These practices are analogous to printing poetry as prose, newspaper style, vs. printing in “lines and stanzas” to expose the formal structure of the piece.

SLING guitar notation by Ole Kirkeby

SLING, by Ole Kirkeby, is an  acronym for “Schoenberg-Lyrebird Isomorphic Notation for Guitar.” It is closely related to Lyrebird by Jan Braunstein, Clairnote by Paul Morris, and MSG by Ole Kirkeby. Staff lines, from bottom to top, are E2 – C3 – E3 – C4. The notation is designed for the major-thirds tuning for six-string guitar, in which the pitches of the strings are, from bottom to top, E2 – Ab2 – C3 – E3 – Ab3 – C4. Kirkeby maintains a web site with information about how to play a guitar tuned in major thirds.


A Lilypond file for the above 3-octave example is provided. (See LilyPond.) The file requires a Lilypond template for Lyrebird and another for MSG to be present as well.


Dozenal Conventional Music Notation DCMN

Dear reader,

We will present this letter under the category Music Notation on the website of and on the forum of with the request to the governing body of that organisation to move this new type of dozenal notation see Annex 1

from the wiki section to the 7-5 Pitch pattern section. There are more then 100 other graphic solutions possible for this type of notation than the one proposed by me.

Several members of the community know that I am advocating for some years now as well as others that Western music can be best represented by the duodecimal number system and a proposal was made to change the nomenclature in such a way that twelve single digits are used for each semitone eg as I have done it in Hamburg Music Notation. Together with Arpegemusic we developed the software Pizzicato Alternative Notation that corresponds to the pictorial representation of Numbered Notation (Jianpu) , which is commonly used in Asia where almost all beginners learn this method.

I myself even could read this notation only at limited speed despite intensive efforts.

Now I developed in October 2015 the Dozenal Conventional Music Notation (DCMN) for which I have applied the following other names Hamburg Music Pianotype Notation (HMPN) or Hamburg Music Emoji Notation (HMEN) as well but prefer the one highlighted in bold. This notation uses single dozenal digits as note names and a 7- 5 pitch pattern (Pianotype Notation) that closely resembles conventional notation but each tone is placed in such a manner on four lines that it has its own picture and therefore could be called Emojitype Notation (HMEN).

It is easy to learn, write and read, preserves the conventional diatonic structure and enriches it by opening it to dozenal mathematics. I try to get people interested from the educational and scientific field and try to raise funds to have my hypothesis tested.

It will be presented in detail on my website with examples. It uses five lines as in conventional music notation but places the noteheads in a way that eliminates the need for additional clef. The method requires three ledger lines between 5-line systems and enables easy depiction of all audible sounds as continuous system.

The use of two different forms of note heads within an octave allows like the piano, the realization of all scales. The use of accidentals is unnecessary.

The proposed notation can be represented with almost any currently in-use music software. Unfortunately, however, not the correct MIDI is played. A few other changes are necessary in order to achieve a correct image of music. The input of musicnotation of this type into existing software is currently very cumbersome.

Therefore Harry Schreiber and myself created a specification open to all programmers, who want to implement it, to facilitate this task.

Annex 2

Specification to integrate Dozenal Conventional Music Notation (DCMN) into existing software

We place it under the

Creative Commons Attribution-Share Alike 3.0 License 3.0

That is free for any noncommercial use.

Commercial use has to obey copyright laws and requires our express permission.


Christian Pörksen alias Robert Elisabeth Key

DCMN Dozenal Conventional Music Notation

DCMN Dozenal Conventional Music Notation

Hamburger Musik Pianotyp Notation = Hamburg Music PianoType Notation (HMPN)
Hamburger Musik Emoji Notation = Hamburg Music Emoji Notation (HMEN)

Preliminary information ( more detailed information coming soon)

see also for more

HMPN-1-chromatisch-7-diatonisch HPMN-2-chromatisch-8-diatonisch-W-L

Untitled by Johann Ailler


A chromatic scale from C to C.

Johann Ailler’s untitled 4-line system (introduced in 1904) is the earliest of the four-line-staff designs, although Albert Brennink was not aware of its existence until after he had designed his 4-line system.

Ailler’s system does not cycle on the octave as Brennink’s and Parncutt’s do.  (See criterion 9.)  One of Ailler’s illustrations of his system shows that when two staves are stacked vertically he only placed one ledger line between them, as shown above.  So the bottom line of the lower staff is E, as with the traditional treble clef, but the bottom line of the upper staff is D.

The Music Notation Project (following in the footsteps of the MNMA) presented Ailler’s system as if it did cycle at the octave, with two ledger lines between stacked staves, until this error was pointed out by Albert Brennink, and corrected in December 2015.

Earliest documentation: 1904

Source: Directory of Music Notation Proposals, section/page: 10/7, 11/3, 13/13

Similar Notations: Untitled by Franz Grassl

Manuscript Paper: Discontinuous Staves Continuous Staves

Principles of Rhythm Notation

Principles of Rhythm Notation

This section is to propose principles to guide the development of rhythm notation.

What is Rhythm

  • rhythm is a pattern in time
    • pattern is characterized by repetition, period
    • pattern is discerned holistically—the forest, not the trees
    • therefore layout is crucial to discerning visual patterns
    • analogy: poetry: layout in stanzas, lines, feet
  • rhythm is a “conversation” among multiple parts
    • it is inherently polyphonic,
      • separate parts may be represented by un-pitched timbres
      • as well as pitched voices
    • syncopation implies a regular background beat
      against which foreground melodies contrast
  • _


  • Music is poetry;
    It should not be formatted as prose
  • music should be laid out on a page in lines and stanzas
  • each line is a musical phrase
  • line breaks should match phrase breaks
  • page breaks should match section breaks
  • corresponding beats of consecutive lines should be aligned
  • _


  • elemental units (“letters”): contrasting stresses (unstress, stress)
    • duration: short, long
    • amplitude: soft, loud
    • timbre, e.g. drum, cymbal
  • “meaningful” units (“words”): beat-unit
    • contains one strong beat
    • analogous to poetic feet
    • notation should not connect (tie, beam) units of different “feet”
  • musical phrases consist rhythmically of integral beat-units
    • may or may not correspond to measures
  • _

Rhythmic Structure

  • Anacrusis is a symptom of beat-units that start on an un-stress:
    iambic, anapestic.

    • “anacrusis” is not just a property of the first measure
      but of every phrase
    • 3-time (compound meter) music typically begins phrases on an un-stress
  • phrase breaks will not necessarily occur at measure bars!
  • _



Rhythmic Patterns

  • the two “natural” rhythmic patterns are:
    • cadence of walking, marching: Left, Right, Left, Right
    • g. | q q q q | q q q q |
    • heartbeat: lub DUB – lub DUB –
      g. q | h – q | h –
      where q = quarter note, h = half-note
  • n-tuplets
    • “tuplet” rhythm inserts additional note incidence points into the typical beat interval,
      dividing the original interval into equal sub-intervals.

      • triplets: insert three incidences in the time-value normally filled by two
        example: e e with incidences 2/8, 3/8 (6/24, 9/24)
        replaced with 3(e e e) with incidences 6/24, 8/24, 10/24
    • syncopation
      • syncopation: a note incidence occurs before a beat or sub-beat
        and the note is held through the beginning of the beat
        example: typical incidcents 3/4, | 0/4, 1/4
        replaced with 3/4 , 7/8 | 1/4
      • swing: variation of syncopation in which the second half of a count
        is regularly delayed from the nominal rhythm,
        typically by 1/3 to ½ of it’s duration.
      • incidences notated as:
        0/8, 1/8, 2/8, 3/8,… (0/24, 3/24, 6/24, 9/24,…)
        played as: 0/24, 4/24, 6/24, 10/24,…


  • ISSUE: swing, being a global style, is typically not notated in TN.
    For otherwise complex rhythms, such as including syncopation and triplets, sophisticated calculation may be needed to convert the nominal rhythm into the performed rhythm.
  • mixed rhythm
    • clave is the basis of many “Latin” rhythms, consisting of alternating beat-groups, one counted in “two” and one counted In “three”.
      example: 0/12, 6/12; 0/12 4/12, 8/12; etc. or vice versa.
      In typical music, the actual incidences are distributed unevenly among these nominal incidence points.
  • _

Absolute vs. Relative

  • for sensing rhythm, occurrence relative to the beat-pattern (absolute time)
    is more important than “duration” (relative or differential time).
  • rhythm notation should primarily identify the beats and counts on which notes are struck (incidence)
  • duration is less effective for notating rhythm
    • requires calculation of cumulative sums to determine the count and beat
    • duration irregularly modified by dynamics of instrument and style
  • _

Mathematical Interpretation

  • An issue: “compound-meter” music is usually said to consist of “three quarter notes” per measure
    • This is mathematically untenable
    • Three counts in a measure should be called “three third-notes”,
      not “three quarter-notes”
    • (MIDI “solves” the problem by considering the “quarter-note” the unit)
  • TN names the counts of a measure starting with “one”:
    ”one, two, three; one, two, three.”

    • it would be more computationally convenient to start with “zero”;
      “zero, one, two, zero, one, two
    • then we could use standard modular arithmetic.




Minimal 6-6 Notation System by Paul Morris





What? Why? and for Whom?

This system is a minimally radical 6-6 music notation system designed for those who are averse to adopting an alternative notation system or who do not like the chromatic staff approach.  It provides the advantages of the 6-6 approach with as little divergence from traditional notation as possible.

6-6 Pitch Pattern

The 6-6 pitch pattern (i.e. the two whole-tone scales) is represented by note heads that either have a dot in their center or do not have a dot.  Solid/black note heads have white dots and hollow/white note heads have solid dots.  Because this 6-6 system simply adds this visible 6-6 pattern to the traditional one, the existing semantics of the traditional system are not altered or disrupted.  If you can read this system you can read traditional notation, and vice-versa.  There is very little reason not to use this system since you can easily switch back to traditional notation, or use them both interchangeably.  One could say that this system offers full “backwards compatibility” with the traditional system.

Of course, the 6-6 pattern is especially relevant if one is playing a janko keyboard, a 6-6 Colored Traditional (7-5) Keyboard, or is simply approaching one’s instrument in 6-6 terms.

(Some other possibilities for the 6-6 pattern are to use different note head colors or shapes like ovals and rectangles, or ovals and diamonds.  These shapes were tried and the notes with dots seemed preferable.  Similarly, a “4-4-4” or tri-chromatic pattern could be implemented with three note head shapes or colors, etc.)


Even with the traditional diatonic staff (as opposed to a chromatic staff) having note heads that reflect the 6-6 pitch pattern makes it much easier to identify intervals quickly and fully.  It makes it possible to see the difference between major and minor seconds, major and minor thirds, major and minor chords – to see the interval patterns that make up scales, chords, melodies, etc.  None of this is possible in traditional notation.

See the Demo File (PDF) for illustrations of intervals.  Notice how, assuming there are no accidental signs (only a key signature)… Minor 2nds will always be one dot-note and one regular note.  Major 2nds will always be two regular notes or two dot-notes.  Minor 3rds will always be one dot-note and one regular note.  Major 3rds will always be two regular notes or two dot-notes, etc.

Key Signatures

Once musicians gain some familiarity with the 6-6 pattern it will also help them learn to play in different keys / key signatures.  If a note is sharp or flat because of the key signature it will have a different appearance than if it were a natural note – a direct visual reminder to play it as a sharp or flat.  One simply needs to remember whether the key signature contains sharps or flats.

Additionally, the intervals between a given note and the surrounding notes also indicate whether to play it sharp or flat (especially when there are no accidental notes / accidental signs involved).  Basically, because the intervals between notes are easy to see, making it possible to “read by intervals“, this will help prevent “forgot the key signature” mistakes.


The difficulty of reading multiple clefs in traditional notation could be addressed in one of several ways, in keeping with the “minimally radical” approach.  The goal is to make orientation in different clefs easier without breaking with the traditional five-line pattern for each clef.  (This aspect is optional and experimental.  One possibility is to use it as a temporary educational aid for teaching different clefs to beginners.)

One possibility is to make the bottom line of the treble clef (E) and the top line of the bass clef (A) dotted or dashed.  That way the four remaining solid lines represent the same notes in both treble and bass clef (G, B, D, F).

A second possibility is that the staff line representing a given note (i.e. G, B, D, or F) could be a dotted or dashed line in both bass and treble clefs.  This could be extended to other clefs as well – the Alto clef has G and F lines, and the Tenor clef has an F line.  So a dotted F line would appear in all four of these clefs.

A third possibility for piano music is to simply write the music in the left hand staff in a transposed treble clef – transposed down so that there are two ledger lines between the left and right hand staves instead of one.

Finally, in any case the 6-6 note head pattern would also make it easier to read music in different clefs since the same note in different octaves and in different clefs would always have the same kind of note head (dot-note or regular non-dot-note).

Meta Data

This system was introduced in August of 2015 by Paul Morris (although he still prefers Clairnote).  See also Classic Nydana a somewhat similar system that also has a diatonic staff and a 6-6 note head pattern.


The names for the black notes Va Wu – Xe Yu Ze have initials that can coexist with the  main note name systems ABCDE…AHCDE..  Do Re Mi…and Sa Re Ga.. The vowels  contrast with solfa note names within a range of three frets.

…………………Va     Wu          Xe        Yu     Ze

………..Do=Ut     Re     Mi  Fa     Sol     La     TSi

These five syllables can be integrated with Fixed Solfa and movable solfa as will be shown in the examples that follow  that are suitable for beginners, casual readers and late starters. The notes are easily identifiable, bypassing the complications of clef, signature and accidental. The scores follow in all other respects the conventions of traditional sheet music. A note that has been tied is shown as a normal note head.

The first example places VaWu among Fixed Solfa in this Minuet from the Notebook of Anna Magdalena Bach. To give unique initials with each note Si has been shown as TSi which can be sung as Si, Ti or indeed TSi..  The initial  of Do could easily be confused for its neighbour, the lettername D. So instead the initial of the older name Ut is used. It can still be sung as Do. To view click on the following title Minuet in Fixed Solfa

When the letters have lower case initials they represent movable solfa as in the next example. Following the tradition of Kodaly music education the minor tonic is here shown as la. It can be seen that between bars 13 and 16 the piece modulates to the relative major cadencing on do=ut. Minuet in movable solfa

The next example shows how movable solfa can display the relationship of both melody and harmony to the key. In the Swan from Saint-Saens’ Carnival of the Animals, the melodic notation runs parallel with chord symbols built on movable solfa initials.The conventions of chord symbols are followed with a few adjustments. The symbol s3 represents a major chord built on so in order to distinguish it from a melody note to be sung.. The 3 is dropped when there are other clues to identify the letter as a chord symbol. Following a jazz convention the minus sign indicates a minor chord (rather than m which could be confused for the note mi). The note after a slash is single note in the bass. Occasionally as in bar 19 a separate chord is in the bass. Click on the following title to see the score: the Swan Saint Saens

In all these example the key signatures are redundant but can be included as an option. The staves are adapted to make the characters stand out being grey with slightly broader lines. On manuscript the dotted lines replace leger lines whereas on a final printed version grey leger lines can be used. Click the following link to see and print grey staves. grey lines5leger

Pronunciation of the solfa syllables varies between language groups, however  contrast between adjacent consonants can be achieved by pronouncing the Xe as in Greek that is with the German /Scottish ch, and Ze as in Castilian Spanish as in the English th. .

These usages are public domain. The letters VW XYZ were proposed by Robert Stuckey and Richard Parncutt in 1987.The vowels  were added in 1995. Computer program to convert from MusXML or MIDI files into the users preferred output..

Color Coded Music

Color Coded Music (CCM) uses a four line three space staff to represent the seven white keys, A, B, C, D, E, F and G.


There are 8 groups of keys on the piano and these are represented by coloring each group in the order of the colors of the rainbow.  Starting with red on the left, and moving across the piano to the right, orange, yellow, green, blue, purple pink, and then ending with white in the smallest group of keys on the far right.


Each group of keys has its own staff.

The staffs for the whole piano are below. Each staff is lettered the same for the whole piano.  They will not all be displayed in a piece of music.  Only the staffs used in a piece will be present. Sometimes partial staffs will be used to conserve space.  See example below.


The black key notes are diamond shaped and renamed, H, I, J, K, and L. They are located on the space and over the line of the white keys they come between.  The H is located between the A and B keys, therefore the H note is on the B space and over the A line.  All other music terminology will remain the same for eighth notes, quarter notes, half notes, etc.


Colored lettered stickers are available to label the piano, much like our computer keyboards and phones are labeled.

Example of “Be Thou My Vision” in CCM.


Color Coded Music website:

Numbered Notes by Jason MacCoy

Numbered Notes is an alternative music notation system introduced by Jason MacCoy in 2009.  It uses the numbers from 1 to 12 to designate notes.  There have been two major versions of the system.  The first version (2009-2012) places the notes on a chromatic staff, while the second version (2012-) uses a flat staff.

Version 1 (Chromatic staff)

This version was presented at from 2009 to 2012.  It uses a chromatic (12-note) staff with lines placed three semitones apart, and features a “counts per measure” timing system in which notes are modified to be “fractional” or “multiple” in a consistent way.  Details can be found in this post.  See also this page on our main site. Below is the start of Mozart’s “Rondo Alla Turca” rendered in Numbered Notes. The full piece is available here.


To render a LilyPond file (.ly) in this version of Numbered Notes, follow the instructions at our LilyPond page, using “StaffNumberedNotes” from the provided file.

Version 2 (Flat staff)

This version was introduced in 2012 and features a text-based notation in which notes are laid out in a row and apostrophes next to a note are used to show range instead of vertical position on a staff.  Details can be found at

Other Sheet Music Sources

This wiki contains a selection of sheet music in various alternative notation systems organized by composer. Below is a list of other sources of sheet music for particular alternative music notation systems.

Ambrose Piano Tabs

Clairnote Music Notation

Klavar-Foundation in the Netherlands (Klavarscribo)

Klavar Music Foundation of Great Britain (Klavarscribo)

(The Chroma Institute website previously sold music for Albert Brennink’s A-B Chromatic Notation, but the site is no longer available.)

Tri-Chromatic Keyboard Layout

Roy Pertchik designed a “Tri-Chromatic Keyboard” layout that he uses on a custom-built vibraphone.  It has an isomorphic, symmetrical, 6-6, Janko-style, layout and a rotating three-color pattern that highlights minor thirds and diminished chords.  He also has a note naming system along similar lines.  The instrument layout and note names were inspired by Barry Harris’ approach to Jazz theory and harmony and are designed to complement it.

Here is an image showing the isomorphic 6-6 layout with its rotating three-color pattern.


The green outlines highlight one of the two scales that are central to the Barry Harris approach: the Maj6th/Diminished. It is formed by interlacing a Major 6th chord with a Dimininished chord, which yields a traditional major scale with a chromatic note added between the 5th and 6th scale degrees.  (For example, a C major scale with a G-sharp/A-flat note added.)  In this image the red circles are the Diminished chord and the other circles inside the green outlines are the Major 6th chord.

Here are a couple of videos where Pertchik presents his vibraphone:

Shorter 6 minute introduction:

Longer presentation at Stanford University:

Here are two handouts (PDFs) from the Stanford presentation:
CCRMA Outline 02
I-IV-V in Bb

More on the Barry Harris approach to jazz harmony can be found in these two articles:

Contributing to the Wiki

This wiki is a companion to the Music Notation Project’s main website and Forum (Google Group). It is powered by WordPress — free/open-source software that lets contributors collaboratively edit and add informative content to the wiki. (See this blog post for more on why we are using WordPress for the wiki.)

If you would like to contribute to the wiki by editing or adding content to it, contact us so we can set up an account for you. Once your account is set up, log in by clicking “Log in” at the top right corner of any wiki page. This will take you to the WordPress editing interface, where you can edit existing pages, add a new page, or add images, PDFs, or other files.

Details about editing the wiki:

  • Save a draft of a new page before publishing it by clicking the “Save Draft” button.
  • Preview any changes you have made before publishing a page or updating it by clicking the “Preview” or “Preview Changes” button on the right.
  • Publish a new page or update an existing page by clicking the “Publish” or “Update” button on the right.
  • For a wiki page to appear in the main navigation sidebar on the left side of the wiki it needs to be assigned to one of the top-level parent pages (like “Notation Systems,” “Sheet Music,” “Music Theory,” etc.).  When editing a page you can select its parent page on the right under Attributes > Parent.
  • It may seem that the content of the top-level parent pages is editable, but their content is never shown on the wiki. These pages are set up to simply show a list of their “child” pages.  (For example: )
  • To create a link select some text that you want to make a link, and click the link button in the top row of formatting buttons (it looks like a chain), then follow the instructions.
  • To add an image or a file (like a PDF or LilyPond file) to a page click the “Add Media” button.
  • You can edit a page in “Visual” or “Text” mode using the tabs with those names towards the top and right.  Normally you would use the Visual tab.  The Text tab corresponds to the underlying HTML code that is used to display the page.

If you have questions, ask on our Forum (Google Group), or contact us.

WordPress Documentation

The WordPress site has great documentation on using WordPress.  Here are some pages to help with getting started:

More Composers

Works by various composers in alternative music notation systems.

The following sheet music for piano is now available in Express Stave (PDF format).  They were created by John Keller using Finale.

J.S. Bach

Works by Johann Sebastian Bach in alternative music notation systems.


Two Part Inventions

The following sheet music for piano is available in Express Stave (PDF format) and was created using Finale:


Prelude 1 (Book 1) from the Well-Tempered Clavier

Here is the J. S. Bach Prelude 1 (Book 1) from the Well-tempered Clavier, transposed into all 12 keys and notated in Express Stave (ES) by John Keller using Finale.

This famous piece is originally in C major. Here it is presented with exactly the same layout on all 12 pages, but starting in F major (a perfect 4th or 5 semitones higher than C) and progressing successively downward by semitones. The original key of C major is on page 6.

By viewing the PDF file and using Page Down and Page Up controls, you can see how the intervals comprising each chord are invariant while the black/white notehead color fluctuates, according to the key signature. (Page Down takes you down in pitch.)


Two Part Invention 9

The next file was created using John Keller’s Finale method, and it shows Bach’s Two Part Invention 9 (F minor, BWV 780) in the following five notation systems:

  • Express Stave (Keller)
  • Black Triangle Twinline (Reed, var Keislar)
  • 6-6 Tetragram (Parncutt)
  • Quasi-Isomorph (Wojcik, var Keller)
  • Traditional Notation

The files below were created by Kevin Dalley using Lilypond notation software, and in some cases are first-step approximations towards their respective notation systems.

See Kevin Dalley’s LilyPond Code and his website for more info.

Z-Extended Nashville Chord Root Names

SquiggleZM-Nash onwhite@72.png

Presentation courtesy of Squiggle Theory


“Nashville” numbering for chords amounts to a movable solfege, in that it is key-free, key-agnostic, key-generalized. Studio musicians and multi-instrumentalists typically are familiar with using numbers 1..7 as chord root designators, inflected as necessary with sharp or flat. What with added degrees and characterizations superscripted (min, m, maj, ma, aug, dim, sus, …) and slash chords, this makes for some wordy chord indications.

This proposed convention erects five single-letter main designators to stand for the inflected forms. It eliminates such complexities as “flatted .3” in A not being a black keyboard note.

Z-Modal Music

Since Nashville departs from Rameau floating modal tonic convention (6 tonic for minor, 5 tonic for mountain, e.g.) by treating tonic as 1 regardless of mode, the designations 1mi, 1m and 1 for 1-minor are seen (minor, dorian, phrygian).

In much music, the flatted seventh degree is prominent in practical chord-root use. It arises in mountain (mixolydian), dorian and natural minor (aeolian), as well as the less frequent phrygian. (Lydian and locrian are “right out” [Monty Python or somebody].) Indeed, in folk music such as ballads, sea chanties, and modern compositions in their genres, a bi-centric chord structure of tonic and sub-tonic is seen in contrast to more modern tri-centric 1-4-5. There is a large body of bi-centric music with 1-Z (mountain: Old Joe Clark) or 1m-Z (dorian: Scarborough Fair, Shady Grove, Drunken Sailor) or 1m-Zm (phrygian) chord structure. The quickly recognizable similarity in sound from this simpler chord root alternation comes from their being Z-modal.


Z-Nash Example 1.png

The example is in slantnote-on-rails. Rails are tonic and dominant; leger lines likewise. Tonic top and bottom is authentic lie, as here. Plagal lie puts tonic rail between two dominant rails The “Three Blind Mice” 3-2-1 footprint indicates the mode.


The glyph for 7-flat is Z, visually related to the numeral. The other glyphs are likewise chosen for mnemonic convenience. The J for 6-flat/5-sharp is a hook mirror-imaging 6. The Q between 4 and 5 reflects the Latin words for those numerals (quartus, quintus). Also, imagining Q as “split O” evokes splitting the “full circle” Octave quite in half, for that “Queer” tritone sound.

The degree between 2 and 3 is more usually related to 3 (blues, e.g.), so M is proposed: 3 rolled over onto its legs (with its joints angularized). A further mnemonic hook is that the alteration creates a Minor tonality. For european-trained musicians, M bespeaks moll (minor). Such a musician is apt to say “soft” in English instead.

For the 2-flat/1-sharp degree I chose T. “Tea for Two-flat” or, for the other context, 1 with “something extra” on it. Constraining these choices was a concern for avoiding conflict with musical directions that may likewise appear above a staff, such as P, V (up-bow), X (pitchless note), and so on.

Squiggle Schema Above

The squiggle diagram above, on which these extensions and the 1..7 main chord designators are schematized, is the basis for Slantnote, an alternative music notation system.

— “Slantnote” (David Zethmayr), 22 November 2011

TwinNote by Paul Morris

TwinNote Music Notation by Paul Morris was designed in December of 2009 when it was first introduced on this wiki page. For more complete documentation of TwinNote, see the TwinNote Music Notation website and also this page on the Music Notation Project’s website.

TwinNote was inspired and influenced by Twinline notation in its various versions by de Vries, Reed, and Keislar (as well as Bilinear notation by Sotorrio). When compared to Black-Oval Twinline (Morris’ version of Twinline and previous notation system of choice), TwinNote is simpler, using two note shapes, triangles pointing either up or down. The two orientations of the triangles highlight the 6-6 pitch pattern. In one whole tone scale all the triangles point upwards, and in the other they all point downwards. In a chromatic scale there is a regularly alternating pattern of triangles pointing upward and downward. This way of representing a 6-6 pitch pattern gives intervals a more clear and consistent appearance (than is found in Black-Oval Twinline notation, for example).

Below is a chromatic scale with alternating solid and hollow noteheads.  This was the original note layout, but it is no longer accurate.  In March 2011 Morris shifted the notes up a semitone so that the notes C D E F G A B would correspond to the lines and spaces of the traditional treble clef staff. The images below show the previous note assignments (with only C D E corresponding with the treble staff).


 Chromatic scale with original note layout (no longer accurate).


Interval Profile

Below is an llustration showing TwinNote’s complete “interval profile.” You can see that the intervals in this system have a more consistent appearance compared to intervals in Black-Oval Twinline. (See also this discussion of influences on TwinNote.)

TwNt Intervals from PDF.png



Below is an illustration showing how TwinNote is “pitch-proportional,” having a proportional vertical pitch axis:


The distance between the centers of any two noteheads is always proportional to the musical interval between them. See the MNP’s 8th criterion for alternative notation systems: “The notation possesses a fully proportional pitch coordinate, where each of the twelve common pitches is spaced in a graphic manner, so that progressively larger pitch intervals have progressively larger spacing on the coordinate, providing a visual representation of each interval that is exactly proportional to its actual sound.”

In the image above the centers of the triangles are shown at 3/8 of the triangle’s height (the distance from its base to its tip). In geometry there are various kinds of centers for any given triangle, for example: Incenter, Circumcenter, Centroid, and Orthocenter. The most relevant center in this case is arguably the centroid, also known as the triangle’s “center of gravity”.

For an isosceles triangle like the ones used in TwinNote, the centroid is located at 1/3 (0.333…) of the triangle’s height. (Interestingly enough, changing the width of an isosceles triangle does not affect the centroid’s position on the vertical axis.) 1/3 of the height is only slightly less than the 3/8 (0.375) shown in the image above.

To find the difference: 0.375 minus 0.333… equals 0.041666… of the height of the triangle. The triangle’s height is the same as the distance between two staff lines which are commonly spaced about 1/16 (0.0625) of an inch apart. So 0.0416 times 0.0625 is only 0.0026 of an inch in terms of actual real-world difference between the centroid and the 3/8 point.

This is so miniscule that it is effectively negligible, and could be easily negated by small adjustments in musical fontography and engraving. Consider also that the notes as perceived on the page are not pure, ideal, abstract geometric objects, and are subject to the vicissitudes of human perception. (How does the line thickness of hollow notes affect the perception of their center? How does the thickness of the staff lines come into play? Is the base of the triangle the top or bottom edge of the staff line it rests on?  How important are the positions of the top and bottom edges/points of two triangles relative to each other, as compared with their centers, when determining relative vertical position?)

The following image illustrates the difference between the centroid at 1/3 and the 3/8 point used in the image above. Even at this large magnification, the difference is quite small.


Shape Note Notation

Shape notes are a music notation designed to facilitate congregational and community singing. Links to more information on shape note are available on the More Notation Systems Page, under the heading “Systems that use the traditional diatonic staff”.

To understand shape note, consider that there are three things related to a note’s pitch that can be represented:

  • A note’s absolute pitch
  • A note’s relative pitch / interval relationship to other notes
  • A note’s scale degree or position in the current key

In shape note the shape of a note and its position on the staff indicate its position within the key or scale, rather than its absolute pitch, which is not indicated. It works like a moveable-do system. This works well for singing because with the voice it is easy to pitch a song at any key, with no transposition difficulties like with most instruments.  The voice is the relative pitch instrument par excellence.

Most instruments are played by absolute pitch rather than by relative pitch/intervals, or scale/key degree, at least at first. Clearly shape note notation would work much better with isomorphic instruments, since they’re closer to the voice’s relative-pitch intuitiveness. You would presumably have to internalize the diatonic scales/keys on a given instrument to be able to play by scale degree rather than absolute pitch.

Combining Shape Note and Chromatic Staff Notation Approaches

One way to use a shape note approach in an alternative notation system would be to have the staff position represent the absolute pitch value and then have the note shape represent the note’s scale/key degree. This would provide both absolute pitch info and scale degree info.

This would work well for music that stays in one key, or switches cleanly at once from one key to another. It would impose the diatonic scale/key framework on the representation of music, hard-wiring it into the notation (as is the case with traditional notation). So it would impose a meaning on notes that may not be there, say if the music is drifting from one key to another such that the scale degree/position of a series of notes is ambiguous. In other words, this approach would be less neutral than just representing the intervals and absolute pitch values.

Traditional Music Notation

There are many resources available for Traditional Notation, known also as Western Notation and simply as “music” writing. The Music Publishers Association has created a valuable document:

Standard Music Notation Practice (PDF)

It offers in one document the list of implemented and accepted practices used by music publishers for decades. In many instances, designers of alternative notation systems will find guidelines that apply to their systems.

A professor at Indiana University has a Web page listing many borderline cases in traditional music notation: Extremes of Conventional Music Notation. This can be useful to notation inventors in considering various limits that they might want their new systems to handle. Don’t overlook the illustrations.

Modified Schoenberg notation for Guitar (MSG) by Ole Kirkeby

MSG is the acronym for “Modified Schoenberg notation for Guitar,” by Ole Kirkeby. It is closely related to Chromatic Lyre Notation by Jan Braunstein and Clairnote by Paul Morris, as well as to Kirkeby’s newer SLING notation. The system spans 3 octaves, and staff lines are 4 semitones apart, so from bottom to top the lines are at E2 – Ab2 – C3 – E3 – Ab3 – C4 – E4 – Ab4 – C5 – E5. The E lines are full, whereas the Ab and C lines are dashed. (In an earlier version, the top three lines were dashed, all other lines were full, and the E2, E3, and E4 lines were bold.) The notation is designed for a 7-string guitar with strings all tuned 4 semitones (a major third) apart, so that each open string corresponds to a staff line. However, it might also appeal to guitarists who play in conventional tuning, since the full staff lines E2 (open 6th string), E4 (open 1st string), and E5 (1st string 12th fret) are strong visual anchors on the instrument. Kirkeby maintains a web site with information about how to play a guitar tuned in major thirds.


A Lilypond template for MSG is provided. (See LilyPond.) The template requires a Lilypond template for Chromatic Lyre Notation to be present as well.

I-Accord Music Notation by Saieb Khalil

The “I-Accord” (First accord or Iraq Accord) is a music notation system with 3 lines per octave designed by Saieb Khalil. (The first version of the text and images on this page came from his documentation of this system that he shared with the MNP. The name “I-Accord” is apparently a pun; “accord” is French for “chord.”)


1. It is based on relative values. The notes represent the relative value depending on its position w.r.t. the root note (I), which can be any note.

2. Like other notation systems of this category, it is motivated by the fact that the relative position of the note has more a musical meaning than its physical measure of frequency.

3. The lines in this system are assigned for the notes of the tonic, i.e., root chord (I chord) (I, III, V distances), while the spaces between the lines are for the rest of the notes.

4. This is to emphasize the importance of these notes, melodically and harmonically. Melodically the set of notes representing I, III and V give (relative) “stability”, rest or cadence. These notes are the one “pulling” the other neighboring notes, which are known to be “tensed” notes, looking for a “line” to rest on. Therefore, this scheme is probably beneficial for the consciousness of musical tensions, and therefore, of special importance for music students and external people trying to learn it.

5. The 3 lines are not spaced equally. The distance between each two reflect the distance between the chord notes concerned.

6. Therefore, the staff of the minor scale is different than that of major, reflecting the difference between the two kinds of scales. The distance between the two lower lines are greater than that between the middle and upper line in the major scale staff, reflecting the difference between the distance between the root note and the third, being a major third, (2 full notes), and that between the 3rd and the 5th (being a minor 3rd). For the minor scale staff, the distance differences between the lines are inverted, as it is in music.

7. The notes of the scale are represented differently from those of those outside the scale (like accidental sharped notes in C major or A minor). Here scale notes are shown as full ellipses and the rest as half ellipses. This makes it easy to distinguish any accidental without using additional signs or having to remember ones printed earlier in the staff.

8. The fact that (only) I chord notes fall on the lines, makes it very easy to recognize such chords, whether in arpeggio form or other. This is true even for other forms of I chord, such as inverted chords (see figures).

9. Being instantly able to distinguish the I chord, other chords would also be easier to recognize. A (I) chord with extra note, for example, will be easier to distinguish too. The combination will be more easily related to the original chord, and thus “understood”. The special effect of the extra note will be stressed in the mind of the music reader.

10. The system doesn’t make use of notehead “color” to represent pitch, so the traditional use of it to represent duration is possible as in traditional notation, but if half ovals were found not so easily distinguishable, especially with hand writing, then they can be replaced by a hollow triangle, with the advantages and disadvantages as shown by previous experience.

11. While it has a unique place for each pitch just like chromatic staff, it doesn’t have its drawback of too many lines.

12. The asymmetry of the staff lines gives “special position”, not only for I chord notes, but the other notes too. The system would repeat the positions of the same notes in the next and previous octaves. Thus a “C” note will have similar position in different octaves, thus making it easier to recognize, unlike traditional notation system.


Plain Music Notation system by Pashkuli

For a fancy visual presentations of the Plain Music Notation (PMN) system, please, visit this page: Plain Music Notation (PMN) system

The idea is plain and simple. In 12-TET there are 12 tones that have their names as follows:

Bo, Da, Le, Gu, Ro, Ma, Ne, Pu, Fo, Sa, Te, Vu

The tones are designated according to the first consonant letter of their corresponding names:

B, D, L, G, R, M, N, P, F, S, T, V

The vowels: O, A, E, U have been used as they are the most common and easy to get sung in vocal exercises.

The intervals in the Plain Notation System are also straightforward as follows:

  • zero interval means – unison
  • the smallest interval – first (prime)
  • second
  • third
  • fourth
  • fifth
  • sixth
  • seventh
  • octave (eight)
  • ninth
  • tenth
  • eleventh
  • renova (anew, again)
  • refirst
  • resecond
  • rethird
  • … and so on

The inversions of the intervals obey the formula: Ia + a = 12 (Ia is the inversion of a)
An interval and its inversion sum up to 12, because 12 is the number of the notes we have in 12-TET (so called European and Western music).

Mapping of the noteletters and noteheads on a “standard” layout of a piano keyboard:
PMN Noteheads Map

A small comparison between the conventional notation system and PMN:
*notice the amount of saved space and the improved clarity of PMN in contrast to the standard music notation

PMN-basic chords

For videos about Pashkuli products, please see also: Pashkuli Keyboard Instruments (YouTube channel)

Express Stave Nomenclature

It is useful to sometimes have unique names for the black keys on the piano, instead of always having to refer to them as either sharps or flats.

John Keller’s proposal simply uses the next five letters of the alphabet.Wide and Back Keys Page 1.jpg

The THREE-BLACK-KEY group is KLH. The middle note, L can be thought of as the “link” between one set of 7 white keys ABCDEFG and the next.

H is on the high side of the three-black-key group. K is on the left (<-) side |<

The TWO BLACK KEYS are I and J, the two dotted letters of the alphabet. They look like two eyes, so the first is named I, and J is its “twin”.

A further mnemonic is that in German terminology, B and H are swapped.

In traditional notation and terminology, the black keys are called sharps or flats, and related to the letter-name of the white key they replace. Thus if the black key K is used in place of the white key F, then the K is called F sharp. We can write this as K = F#. One rule of traditional terminology is that every diatonic scale must use the seven letters A to G in order.

One reason for proposing unique letter-names for the black keys, is that sometimes we may NOT want to imply which white key is being replaced.

Slantnote by David Zethmayr

Slantnote-bis Intro for Students

Teapot rails-sq-clef-C.png

The Squiggle–that diagram between the two phrases above, with the footprints–will leap-frog you over the worst beginning difficulties of music reading and music theory. There are many-plenty examples of Slantnote-bis at for practice on familiar songs. Watchit! the examples link has some files that do NOT use either slantnote or slantmarkup. You have to read the short KEY TO FILE TYPES at the top to decide which ones to download.

Slantnote-bis Intro for Educators

ThreeBlindMice rails&sq.png

Slantnote notations and markups are based on the squiggle, a vertical alternative to the keyboard for visualizing melodic and harmonic structures. The squiggle and its notations are motivated by weaknesses in conventional notation in the areas of fast sight-singing and of amateur self-education for accurate reading a cappella.

Slantnote-bis on Rails

Slantnote on rails uses a staff of rails: tonic rails and dominant rails only. Rails are key-free moveable in the same sense that “moveable-do” solfeggio is not locked to a specific pitch. Usually they are used in threes, in either authentic or plagal lie. When tonic rails are at bottom and top the arrangement is in authentic lie, with a dominant rail intermediate—4/7 the tonic octave separation above the lower tonic.

Rails in authentic lie

The reverse arrangement is plagal lie: dominant rails outermost, with tonic intermediate at 3/7 the octave distance.

Leger lines are likewise dominant or tonic only.

Rails in plagal lie

Slantnote-bis on Clefs

Slantnote on clefs uses the well-known 5-line staff with clef sign and key signature, much as on rails. In addition to slanting the noteheads, the 3-2-1 footprint follows immediately after the key signature.

The slant of notes, and the small marks on né-slant notes, can be easily ignored by those who don’t want to use them because they already know how to read in 5-line clefs. On the other hand, bright beginners can note their import and use them to settle the Final Semitone Uncertainty, without tutelage.

Generations of amateur choir members have taught themselves to “almost-read” in clefs, relying on Fickle Dame Memory and someone pounding out the FSU on a piano. This, unfortunately, also teaches that a keyboardist is necessary for rehearsals and that diatonic theory is beyond the reach of those not having studied some instrument.

Further, the practice habituates both choir and accompanist to too-loud performance, destroying the possibility of solid intonation, since that depends on hearing oneself and the ensemble at once.


The third squiggle-informed notation, slantmarkup, is the most conservative in respect of usual notation. It is a markup schema that can be retrofitted to existing conventional scores as redundant information in aid to sight-reading precision.

Slantmarkup HappyTrails.png

In slantmarkup, first a squiggle footprint outlining the 1-2-3 degrees locates (foots) the diatonic reference on the staff. The squiggle footprint serves as a “key signature decode”. (On “rails”, the footprint tells the mode.)

Once the diatonic pattern is thus footed, a small slant is drawn next to the printed notehead of notes referable to the side (footprint side) of the squiggle (the opposite side is the side; notes are left unmarked). Vowel accents over and reflect the slant orientation. Squiggle side and squiggle side are right-left reversible. The side where 3-2-1 diatonic degrees happen to reside is always the side.


Squiggle Solfege—”né-nà”

Solfege Squiggle.png

The two squiggle cis-trans syllables make up squiggle solfeggio, or né-nà-feggio. The diatonic-7 pattern 1-2-3-4-5-6-7, solmized do-re-mi-fa-so-la-ti US style, is rendered né-né-né-nà-nà-nà-nà in squiggle solfege, because -side squiggle is where the “/Three Blind Mice/” hang out. Also “/Mary” and her “Little Lamb/” and “/Yankee Doodle Went to Town/”.

Rhyming Major Thirds Solfege

Solfege rM3.png

A solfeggio minimally changed from Sound of Music “Doe, a Deer” style is RM3, where major thirds rhyme throughout and minor thirds reliably fail to rhyme (sopranos take especial note!). Using the vowel sequence o-à-é-i (ascending semitones) in cyclic fashion, the major scale is rendered do-re-mo-fa-si-la-ti-do. Names of accidentals are, of course, adjusted with regard to the same semitone cycle.

MS Paper

For your convenience, this MS file can be printed off to serve for either authentic or plagal transcription. Turn it upside down to reverse the lie.

The rails manuscript paper is for both Slantnote-bis and Slantnote-tris transcription.

Early Simplification: For beginning students who will not have to deal with the classical staff very soon, just two rails are enough: tonic low, dominant high. Lines of pre-college lined notebook paper are at suitable distance. When a tune goes to the low dominant or the high tonic, a leger line 3/4 that distance to the next printed line is drawn, both for notes “beaded” thereon and notes tangent thereto.


— “Slantnote” (David Zethmayr), 3 February 2012

Modulation, Dominant, Subdominant

Modulation is a shifting of key-center (the tonic), or “the key.” A semitone alteration upward at diatonic degree 4 (whether by sharping or by removing a flat) makes the diatonic pattern reappear with a different tonic–a new key, the dominant of the old key. For example, this changes the key of C major to G major, or B-flat major to F major.

Altering degree 7 downward by a semitone (by removing a sharp or by flatting) re-forms the diatonic pattern with a different new tonic, the subdominant of the old key. For example, this changes the key of A major to D major, or B-flat major to E-flat major.

Circle of Fifths

On the Squiggle page a pattern-generalized explanation (without key name examples) shows how the same diatonic pattern re-forms on first-degree modulation. The Circle of Fifths (Clock of Dominants) is a practical way of schematizing progress through the keys by first-degree modulation, in either direction: clockwise through successive dominant keys, counter-clockwise through subdominant keys.

— “Slantnote” (David Zethmayr) 2 December 2011 (MST)

The Squiggle Method of Pitch Visualization

An Alternative Model for Seeing Note Combinations

The Squiggle is a vertical alternative to the traditional keyboard for visualizing combinations of notes, by David Zethmayr. The Squiggle is the organizing principle of Zethmayr’s Slantnote notation.

Squig keyboard.png

The Squiggle is all about pattern, diatonic and otherwise. It’s a communication medium between ear and eye that is easy to cultivate. Ear-first musicians such as singers and multi-instrumentalists will find it convenient for converting improv and intuition skills to music reading, transposing and arranging skills.

Squiggle Theory is A Key-free Pattern Language

Squig namings four.png

All the basics of music theory are quicker to teach and to self-teach with squiggle theory. Squiggle, like movable solfege, is not tied to a fixed, absolute naming schema for notes. It is “key-agnostic,” letting you focus on pattern rather than prematurely plunging into note name calculations: “E/F is a semitone, and B/C is a semitone, and all the rest … so the C/E third is major because no semitone intervenes.”

Cis-Trans Diatonic Pattern

Notice how the squiggle preserves the cyclic diatonic visual …-3-4-… pattern through all the naming conventions schematized on it above. This is the cis-trans principle at work.

Squig triad types four.png

Since there are but two banks to Squiggle River, notes residing on either side participate in intervals and patterns of intervals according to whether their semitone distances are even or odd. Squiggle terminology expresses even-odd in terms of same side or opposite sides, shortened to cis and trans respectively.

The terminology of squiggle theory hinges on the cis-trans distinction, crucial to characterizing intervals, triads and chords. Notes on opposite sides (banks) of the squiggle are trans to each other. Notes on the same side are cis (pronounce as in “cistern”).

It may not be obvious to a beginner that left-right mirroring is not important in squiggle. Only cis-trans matters. The diatonic …-3-4-… pattern (or any other cis-trans pattern) is independent of the left-right distinction. Saying so explicitly is preliminary to a discussion of modulation.

How Keys Happen: Dominant, Subdominant


Being key-agnostic does not mean the concept of keys is too advanced for squiggle theory. To the contrary, squiggle clarifies how keys happen. Modulation is a pattern concept requiring either a ready familiarity with the diatonic implications of C-D-EF-G-A-BC as notes are flatted or sharped, or a visual such as the squiggle or some Category Eight-compliant notation staff. Independent of any staff reference, the squiggle offers its clear cis-trans binary distinction, the distinction that is implicated in most of the theoretic difficulties in front of the beginning musician.

When a slanted note shifts sides, it might be the degree 4 note (slanted right-end-down) sharping (raised a semitone) to become the 7th degree of a new key, the dominant of the old key. The diatonic “34” pattern resumes but with the cis groupings on reversed squiggle banks.

Similarly, flatting the 7th degree (lowering it a semitone) makes it become degree 4 of a new key, the subdominant of the old key, preserving the diatonic “34” pattern as in the opposite modulation.

— “Slantnote” (David Zethmayr) 3 December 2011 (MST)

Wicki-Hayden Note Layout

The hexagonal Wicki-Hayden note layout has been used for concertinas, button accordions, and more recently for electronic midi instruments. An isomorphic layout, it follows the same principle of isomorphism that is found in many alternative music notation systems.

Wicki-Hayden note layout diagram



Wicki-Hayden Layout on an Axis-49 Midi Instrument

The image below illustrates a remapping of the Axis-49 (a midi instrument from C-Thru Music) to the Wicki-Hayden layout. The Axis-49 has been rotated ninety degrees from its usual “wide” orientation to a “tall” orientation. This is necessary in order to realign the hexagonal button pattern. Ideally, the horizontal rows of buttons would then include nine or ten buttons (as shown in the image above), rather than just seven. This restricts the number of keys in which you can play while using the same fingering patterns (and without transposing the instrument).


The remapping above is “centered” in terms of the circle of fifths, making it easiest to play in the simplest, most common keys. Without changing the basic fingering patterns you can play in keys that have as many as three flats, or three sharps. In keys with more than three flats or sharps the fingering patterns get ‘wrapped’ from one side to the other as you run out of notes on either side. (If you restrict yourself to the bottom or the top half of the layout, you can also play in keys that have 4 flats or 4 sharps, respectively, without wrapping fingering patterns.)

The color scheme helps to highlight the enharmonically equivalent notes on either side of the button-field, by making the A-flats and G-sharps blue. Those that sound the same are the same shade of blue, either dark or light. This helps with orientation if you have to ‘wrap’ a fingering pattern to the opposite side.

See Music Science Guy’s Website for more on remapping the Axis-49 to the Wicki-Hayden and other note layouts.


More Color Schemes

Here are some more possibilities for color schemes. (The Axis-49 comes with 4 colors of buttons, but not in the right numbers to be able to recreate these color schemes.)

Strong 7-5 and Weak 6-6 Color Scheme


Strong 6-6 and Weak 7-5 Color Scheme


Major Thirds (3-3-3-3) Color Scheme


Minor Thirds (4-4-4) Color Scheme


6-6 Colored Traditional (7-5) Keyboard

It can be useful to re-color the keys on a traditional keyboard according to a 6-6 pitch pattern, coloring one wholetone scale black (C D E F# G# A#) and the other white (F G A B C# D#). This helps clarify the interval relationships between the keys.

Illustration of a 6-6 colored traditional (7-5) keyboard

Playing on a keyboard with this 6-6 color scheme helps the musician to see the interval patterns between the keys as she plays. The consistent interval patterns of scales and chords are made readily apparent by the regularity of the 6-6 color pattern. For example:

  • Adjacent keys that are different colors are always half-steps.
  • Adjacent keys of the same color are always whole-steps.
  • Any major scale can be played as three notes of one color followed by four notes of the other color.
  • Any minor scale can be played as two notes of one color, followed by three of the other color, and then two of the first color.
  • Major thirds are always two notes of the same color with one note of that color between them.
  • Minor thirds are always two notes of a different color with one note of each color between them.
  • Of course, major and minor triads are combinations of major and minor thirds.

(These patterns are easier to see and hear than to describe with words…)

The image below shows a MIDI keyboard that has been re-colored using black and white electric tape.

6-6 colored traditional (7-5) electronic keyboard

The regularly alternating 6-6 pattern is analogous to the distinction between odd and even numbers, and how they help reveal patterns in mathematics. It also correlates very well with chromatic notation systems that exhibit this alternating pattern in their staff line pattern or in the shapes or colors of their noteheads. For example, see the 6-6 notation systems in this tutorial. The 6-6 pattern and its usefulness are mutually reinforced by having it present in both one’s notation system and instrument.

Given that the color scheme has changed, it may be useful to refer to the traditional sets of black and white keys as “back keys” and “wide keys”. This is nice because, as well as being an accurate description, the words are close to the original “black keys” and “white keys”. (This was Doug Keislar’s proposal for a new way to refer to these groups of notes.)

This color scheme provides a great improvement over the traditional keyboard, which (like traditional notation) obscures the interval relationships between notes, and the consistent interval patterns of scales and chords.

Of course, taking this principle a step further, one could change the physical arrangement of the keys so that they are isomorphic in their physical layout, rather than in their color scheme, as on a Janko keyboard.


The Harpejji is an isomorphic string instrument. It is like a cross between an electric guitar and a Janko Keyboard. The pitch layout is similar to a Janko keyboard except that there are no duplicated rows; each row is a half-step higher.


24 strings are tuned a whole step apart, for a four-octave range of open strings, plus 15 frets a half-step apart, for a total range of over 5 octaves (A0, by which they probably mean the lowest A on the piano, to A5). There is also a smaller model with 16 strings and 19 frets for a four-octave total range.

For more about the pitch layout and the instrument, see the Harpejji website, particularly here and here.

The Harpejji was preceded by the StarrBoard, which was invented years ago by John Starrett. The patent on the StarrBoard has now expired. According to the Harpejji website, the StarrBoard had strings tuned a semitone apart rather than a whole tone. So the Harpejji layout is closer to the Janko keyboard layout.

Janko Keyboard

The Jankó keyboard with its “6-6” layout was designed by Paul von Jankó in 1882. Because it has an isomorphic layout, each chord, scale, and interval has a consistent shape and can be played with the same fingering, regardless of its pitch or what the current key is. If you know a piece of music in one key you can transpose it simply by starting at a different pitch because the fingering is the same in every key.

This provides much more consistency than the traditional keyboard layout where each chord, scale, and interval has multiple shapes and requires learning multiple fingering patterns. On the Jankó layout there are twelve times fewer chord shapes and scale patterns to learn. This greater consistency also improves awareness of interval patterns and harmony, and makes it easier to improvise and play by ear.

Here is an image of the layout:

Janko keyboard.png

The span of notes that can be reached with the stretch of one hand is greater than on the traditional layout. Larger intervals such as an octave are about 14% smaller on a Jankó layout.

The multiple rows offer greater freedom and flexibility with fingering patterns. The higher rows are typically played with the fingers, while the lower rows are played by the thumbs. This basically eliminates the need to learn fingering patterns that require specific placement of a thumb-undertuck that are necessary on a traditional layout.

Follow this link to a Janko-style, isomorphic keyboard that you can play online at the Intuitive Instruments for Improvisers site. It is a nice resource with information about various isomorphic instruments and related topics.

Daskin Manufacturing has announced electronic MIDI Janko keyboards.

Janko Keyboard Article on Wikipedia

Here are two images of pianos built with the Janko key layout (courtesy of the Wikimedia Commons).

MIM Janko Piano 2.jpg

Janko piano.JPG

4-4-4 Pitch Pattern

As discussed on the Isomorphism page, there are various isomorphic patterns, ways of dividing up the twelve notes of the chromatic scale. One of these is the 4-4-4 pattern, found for example in chromatic notation systems with lines spaced three semitones apart (a minor third apart), such as Numbered Notes by Jason MacCoy.

This pattern is also found on the Chromatic Button Accordion, where the buttons are arranged chromatically in rows of three. It is also present in the three-color pattern of Roy Pertchick’s Isomorphic Vibraphone (YouTube video), where it overlays a 6-6 pattern physical layout of the instrument.

The tutorial on Intervals in 6-6 Music Notation Systems explores how notation systems with a 6-6 pitch pattern improves upon the appearance of intervals in traditional notation. The following image expands on that discussion by showing how intervals appear in a 4-4-4 notation system. With the 4-4-4 pitch pattern each interval has three distinct appearances (whereas with a 6-6 pitch pattern each interval has two appearances).



The term “isomorphic” is defined as “being of identical or similar form, shape, or structure.”

The idea of “isomorphism” as applied to music notation is that any given musical pattern (like a scale, chord, interval, or particular melody) should always have the same basic appearance regardless of which pitch it starts on. There should be consistency in the relationship between what you see and what you hear.

Each aspect of music — notation, nomenclature, and instruments — can be simplified through isomorphism. Using an isomorphic notation system with an isomorphic nomenclature and/or an isomorphic instrument so that these different aspects match each other, would likely result in added benefits.

There are several basic isomorphic patterns, different ways of distinguishing the twelve notes of the chromatic scale. (Numbers are used in the table below just to illustrate the different patterns in a formal, abstract way.)


Basic Isomorphic Patterns A A#
B C C#
D D#
E F F#
G G#
6-6 pattern (binary), cycles every 2 semitones (major second). 1 2 1 2 1 2 1 2 1 2 1 2
4-4-4 pattern (tertiary), cycles every 3 semitones (minor third). 1 2 3 1 2 3 1 2 3 1 2 3
3-3-3-3 pattern (quaternary), cycles every 4 semitones (major third). 1 2 3 4 1 2 3 4 1 2 3 4
2-2-2-2-2-2 pattern (senary), cycles every 6 semitones (tritone). 1 2 3 4 5 6 1 2 3 4 5 6

See also: 6-6 and 7-5 Pitch Patterns Tutorial and 4-4-4 Pitch Pattern.


Notation Systems

Isomorphic notation systems are pitch-proportional and have regularly repeating patterns. This typically takes the form of a regular line pattern with a consistent interval distance between each line. For example, notations with lines a major second apart have a 6-6 line pattern, notations with lines a minor third apart have a 4-4-4 line pattern, and notations with lines a major third apart have a 3-3-3-3 line pattern. Isomorphism can also be achieved through the use of alternating hollow and solid notes (a 6-6 pattern) or different patterns of notehead shapes.



The traditional musical nomenclature (note names, interval names, etc) is tied to the same complicated framework as traditional notation (sharps and flats, enharmonic equivalents, etc). So there is good reason to consider new nomenclatures that do not have these complications. There are also benefits to using a nomenclature that correlates well with a given alternative, isomorphic notation system.

(Of course, there are also benefits to having a standard nomenclature for easy communication between musicians. For that reason is probably easier for an individual to adopt an alternative notation system or instrument, than it would be to adopt an alternative nomenclature.)



Instruments are isomorphic when the same musical pattern can be played in the same basic way regardless of the starting pitch. Common examples of isomorphic instruments are stringed instruments like the violin, viola, cello, string bass, bass guitar, and mandolin. (The guitar is mostly isomorphic, but in its usual tuning it has a slightly irregular pattern, because the interval between the G and B strings is a major third while other neighboring strings are all separated by a perfect fourth. Some advocate tuning the guitar completely in either perfect fourths or major thirds for this reason.)  The traditional piano keyboard is not isomorphic (it has a 7-5 pattern), so it is necessary to learn many different fingerings to play the same scale or chord when starting on different pitches. A number of new keyboard layouts and instrument designs have been introduced to provide the benefits of isomorphism. See Isomorphic Instruments.

There are benefits to using instruments that correlate well with a given notation and nomenclature. This is why tablature is popular: the notation matches the instrument. It is also why isomorphic instruments are a logical companion to isomorphic notation systems. That is why many people interested in isomorphic notation systems are also interested in isomorphic instruments.

Hass Music Notation (original version) by Peter Hass


This is the original version of Hass notation. It uses a five-line, pitch-proportional chromatic staff whose lines are spaced three semitones (a minor third) apart. Three noteheads shapes are used: an oval on lines, and downward and upward triangles in the spaces. This regularly alternating pattern of three noteheads corresponds directly to the three rows of a chromatic button accordion, which has an isomorphic layout. The staff does not cycle at the octave (MNP criterion 9). Hass later created a version that does.

The traditional treble and bass clefs are replaced by an E and an O clef, respectively. As in traditional notation, each of these clefs gives a different set of note names to the staff lines. A note on the lower staff is an octave and a major sixth lower than the note at the same position on the upper staff.

An unusual property of the system is that the majority of the positions on each staff are the same as in traditional notation (as long as one applies the necessary sharps and flats in traditional notation). The stem is horizontally centered on the notehead, rather than placed at the left or right as in traditional notation. Rhythmic notation is traditional.

Pitch nomenclature uses traditional German pitch names for the naturals (with B for the pitch a whole step below C, and H for a half-step below C), and the new names O, S, V, and I for the traditional C#, D#, F#, and G#.

Hass, who died in September 2015, stated in 2009 that he was not sure exactly when he invented this notation system but believed it was 1974.

See also the Hass Notation Website (Denmark), and the three-line version of Hass Notation on our site.

Howe-Way Music Notation by Hilbert Howe

This is an illustration of the Howe-Way music notation system from the cover of Book Two of the Howe-Way Music Method, by Hilbert A. Howe (year: 1964).


On the Howe-Way staff there are six vertical staff positions per octave: three lines and three spaces. Each line or space represents two of the twelve pitches of the chromatic scale. The two pitches appearing on a given line or space are distinguished by their noteheads. The lower pitch has a white/hollow notehead and the pitch a half-step higher has a black/solid notehead. (This pattern corresponds to the keys of a 6-6 piano keyboard, see below.)

In practice the music is apparently always written on a six-line staff, covering two octaves. The third line from the top is a heavier line (this is not so obvious in the image above). This line and the bottom line of the six-line staff are both C. For piano music, each hand has its own six-line staff.

6-6 Piano

The Howe-Way music method is designed for learning to play an isomorphic, 6-6 piano that has two rows of keys (like this, but with different coloring). The keys in the upper row are shaped like the black keys of a regular piano, grouped in two groups of three per octave: three black keys alternating with three red keys. All the keys in the lower row are white keys, shaped like the D key on a standard keyboard. C is in the lower row, as on a standard keyboard. C#, D#, and F are black keys in the back row; G, A, and B are red keys in the back row. This piano keyboard was built by Orville Wood of the piano company Pratt & Read and is mentioned here:

The references to “black” and “red” in the image above do not refer to colors in the notation, but to the colors of the keys in the back row of the keyboard. The notation is black and white.

Note Names

Pitches are named with numbers. Unlike most numerical nomenclatures, successive numbers refer to whole steps. One whole-tone scale (corresponding to the white keys of the piano) has regular numerals, and the other whole-tone scale has numerals with underlines. 1 is C, 1 with an underline is C#, 2 is D, etc. C# is referred to as “one and a half,” D# as “two and a half,” etc., but for speed they can be pronounced 1u, 2u, etc.

Octave Registers

Registers are indicated with Roman numerals. Middle C is the beginning of register IV (matching the Acoustical Society of America and later the ISO standard).

Rhythm Notation

Rhythmic notation is mostly traditional. The whole note has a stem, half of which rises from the notehead, and half of which descends from it. The half note has no stem. There is a note saying that the inventor hoped for a special typewriter key that would render a special notehead shape for a whole note, perhaps a diamond shape, in place of the aforementioned special stem on a regular round notehead.

Express Stave by John Keller

My preferred version of Express Stave, is the ‘reverse colour’ version, where the naturals (white keys on a piano) are represented with black note-heads, and the black keys (sharps and flats) have white note-heads. See the following PDF files for illustration:

Practice locating the 3 groups of 2s and 4 groups of 3s encompassed by the grand stave.
Remember, white note-heads mean you play black keys!
Page 2 shows 3 groups of naturals ABCDEFG.

The following ES guide shows some of its properties, terminology and coding:

Beginner piano method:

Here are the links to this website’s descriptions of the three versions of Express Stave:

Some YouTube tutorials:

Free PDF files of piano music in Express Stave notation (reverse color):

Original Compositions:

Sheet Music

Note: This is a heading/parent page, and any text written here will not be shown on the site.  It is set up so that this page will just contain a list of its child pages.

Related Websites and Publications


See the various publications and conference proceedings published by the MNMA.

Source Book of Proposed Music Notation Reforms – by Gardner Read (1987)

“A New Twelve-Tone Notation” Part VII, #18 of Style and Idea: Selected Writings – by Arnold Schoenberg (1924)


See our More Notation Systems page for links to the websites of particular alternative music notation systems.

See the Isomorphic Instruments page for links to instrument websites.

See the Software page for links to online digital sheet music libraries, and the bottom of  Open-Source Strategy for music notation software and file format links.

The links below are to other sites of general interest:

Music Notation Reference Guide Basic info on different elements of traditional notation.

Music Notation from the 2nd/3rd century CE

Notational Engineering Laboratory, (broken link) a research project dedicated to studying and engineering a wide variety of notation systems in general.

Isomorphic Instruments

The instruments listed here and on the websites linked below follow the principle of isomorphism, the identical or similar appearance of intervals in all transpositions. This means they are key-neutral and scale-neutral. Isomorphism is also found in many alternative notation systems.


Intuitive Instruments for Improvisers (Paul Hirsh) –  A website about isomorphic instruments, isomorphic panpipes, Janko keyboards, and more…

Keyboards, Accordions, Button Instruments


The DIY Keyboard Project (Drew Wagner) –  Focuses on building alternative, isomorphic keyboards. It is an open-source hardware development project with the goal of making all of the CAD files, microcontroller code, etc. necessary for a hobbyist to build a digital keyboard freely available.

AltKeyboards website on isomorphic keyboards, focusing on the Wicki-Hayden note layout (Ken Rushton) –

Musix for iPad – One of the layouts is the Wicki-Hayden.

Single Row of Keys (Chromatic Scale)

Robbins Keyboard –

Dodeka Keyboard –

Multiple Rows of Keys (Chromatic Scales, Offset by a Perfect Fourth)

LinnStrument (chromatic scales a perfect fourth apart, reminiscent of a fretted string instrument) –

Two Rows of Keys (Whole-Tone Scales, Offset by a Semitone)

Symmetrical Keyboard (Dominique Waller) –

The Balanced Keyboard (Bart Willemse) –

Multiple Rows of Keys (Duplicated Rows of Whole-Tone Scales, Offset by a Semitone)

Janko Keyboard Layout

Daskin brand Janko Keyboards (Paul Vandervoort) –

Lippens keyboard derived from Janko’s design

Chromatone brand Janko-style keyboards (Japanese company) –

Chromatone Lite for iPad –

Multiple Rows of Keys (Whole-Tone Scales, Offset by a Perfect Fourth or Fifth)

Wicki-Hayden is a hexagonal layout in which odd-numbered rows are not duplicated as in Janko but instead are separated by octaves, as are even-numbered rows.  MNP Wiki page on Wicki-Hayden Layout

The Array Musicboard (Bill Wesley) uses a layout closely related to Wicki-Hayden –

Multiple Rows of Keys (Series of Minor Thirds, Offset by a Semitone or Whole Step)

Chromatic Button Accordions –

Multiple Rows of Keys (Series of Perfect Fifths, Offset by a Minor or Major Third)

The Tonnetz is a hexagonal grid in which the three diagonals are intervals of a perfect fifth, major third, and minor third.  One example is C-thru music’s “Axis” instruments using the “harmonic table” note layout –

Microtonal Keyboards

Generalized keyboard, a predecessor of the Janko keyboard that accommodates microtonal tunings (invented by R. H. M. Bosanquet, extended by Erv Wilson and others) – ,

Microtonal keyboards, including isomorphic keyboards –

6-6 Colored Traditional (7-5) Keyboard (on this wiki)

(Strictly speaking, this is not an isomorphic instrument, because only the coloring, not the physical layout, is isomorphic.)


Isomorphic Saxophones and Flutes (Jim Schmidt) –

String Instruments

Many traditional string instruments are isomorphic in their usual tunings (violin, viola, cello, double bass, mandolin, bass guitar). The guitar is mostly isomorphic in its usual tuning, with the exception being the major third between the G and B strings. Some people tune the guitar with all neighboring strings a major third apart, or all a perfect fourth apart, making the tuning completely isomorphic. Wikipedia page on regular tunings for guitar

The Harpejji, a fretted string instrument whose strings are tuned a whole tone apart, making it like a combination of a Janko keyboard and an electric guitar. – Page

Chromatic harp (strings arranged in whole-tone scales) – (Page in German)

The Array Guitar,  Psaltery, and Vina (Bill Wesley) –

Percussion Instruments

Isomorphic Vibraphone whose bars are arranged in whole-tone scales and have a three-color pattern (Roy Pertchik) – see Tri-Chromatic Keyboard Pattern

The Array Mbira, Nail Violin, Rasp, etc. (Bill Wesley) –

Alternative Key Signatures

The following is a chronological list of proposals for alternative key signatures. Entries in this list are based on Source Book of Proposed Music Notation Reforms by Gardner Read (Greenwood Press, 1987).

As of June 20, 2012, the list includes items through page 203 of Read’s book, which is over 400 pages long. (The systems in the book are chronological within chapters, but not across chapters.) To come: An introductory overview and a categorization of the approaches (e.g., systems that depict the notes corresponding to traditional key signatures, systems that indicate the tonic and/or modality, systems that depict all the notes in the key, systems that depict a tonic triad, etc.)


1810. Charles Guillaume Riebesthal. Key signature is an oversized capital letter indicating the key note.

1838. Michel Eisenmenger. Piano tablature staff (horizontal). Key signatures: three solid noteheads on the notes of the tonic triad (whether major or minor), connected by a stem.

1844. Arthur Wallbridge. Key signature: a number indicating the tonic: 1 (indicating C) through 12 (indicating B). (Read’s two examples imply that the numbers instead go from 0 to 11. This is incorrect, as shown by the inventor’s illustration in Example 4-17, where the key of Ab has a 9.) Below the number is a semicircle distinguishing major from minor: the top half of a circle for major, and the bottom half for minor.

1846. Joseph Raymondi. Key signature: a note whose notehead is the tonic and which has a downward stem with straight flags extending downward to the left or upward to the right. The number of flats or sharps is indicated by the number of flats on the stem. (Read’s description here is unclear, but my interpretation is based on the inventor’s figure.) Sharps are indicated by upward flags to the right; flats by downward to the left.

1855. Juan-Nepomuceno Adorno. Melographie. Piano-tablature staff, vertical. Idiosyncratic symbols on line or space of tonic, indicating modality (maj/min) plus distinguishing between enharmonic equivalents (sharp or flat) for the tonic.

1870. Gustave Decher. Chromatic staff. Like traditional key signatures, except with noteheads instead of sharps or flats. The noteheads are all in one column and share a stem.

1883. August Wilhelm Ambros. Like Decher’s key signatures, except no stem.

1888. Paul Austman. Novel key signature apparently indicated by a notehead on the tonic, but Read’s description is unclear.

1893. Levi Orcher. Staff: 2 lines plus 3 lines, but not with the piano tablature arrangement. Key signature: one of two symbols, apparently centered on the tonic line or space. Sharp keys are indicated by a right-pointing triangle; flat keys by a left-pointing heart symbol.

1896. K. M. Mayerhofers. Key signature indicated textually, e.g. “Eb maj.,” in between the time signatures of the upper and lower staves.

1897. Walter H. Thelwall. Chromatic staff. Key signature: a black triangle on the line or space corresponding to the tonic of the major key. (A minor key uses the key signature of its relative major.) The triangle points up if the key traditionally has sharps (e.g., A major), down if it traditionally has flats (e.g., Db major).

1900-1907. K. M. Baessler. 14 different proposed notation systems, most of which have unique staves and/or notehead shapes. Proposals 1-10 have key signatures in the form of a special sort of chord: noteheads (of the variety specified by the particular notation system) for each of the flats or sharps from the corresponding traditional key signature, placed at the position on the staff corresponding to that note. The noteheads are all attached to a single stem that extends both upwards and downwards (unlike a traditional stem, which points either up or down). At the top of the stem are two horizontal (but slightly diagonal) parallel lines, and a similar pair of lines is also placed at the bottom of the stem. Proposals 12 and 13 have each of the noteheads separated on the horizontal axis and attached to its own stem, instead of being grouped in a chord. Another proposal (Read, p. 53) represents key signatures by the letters of the first three notes of the scale (the third of which distinguishes major from minor).

1930. Otto Studer. Neno. Piano-tablature, horizontal. Key signature: noteheads on all seven degrees of the scale. Tonic notehead is full size, the other six are miniature. Enharmonics are distinguished by slashes attached to the notehead (rising to the left for sharps, descending to the left for flats).

1931. Cornelis Pot. Klavarskribo. Key signature: a single notehead on the tonic, enclosed in a circle for major or a diamond for minor.

1947. Ernest-Jean Chatillon, Notation musicale bilineare. Diatonic staff. Key signatures: Greek phi on line or space of tonic, preceded by a novel flat or sharp sign depending on whether the traditional key signature has sharps or flats.

1964. M. A. Marcelin. Key signatures like Eisenmenger’s (1838), except that the stem is vertically centered on the noteheads, and the noteheads are hollow.

1965. Nell Esslinger. Revised Notation. Piano tablature staff (horizontal). “Key signature” appears to be a single symbol: a flat sign for a key containing flats, or a sort of cursive S for a key containing sharps.

1968. Traugott Rohner. Musica. Key signatures are conventional, except that minor keys are distinguished from major by the addition of a solid notehead on the tonic, following the conventional key signature.

Nomenclatures Overview

This page gives a summary overview of proposals for new naming schemes for notes.

Alphabetical Nomenclatures

Some proposals maintain the traditional letter names for the notes A B C D E F G and introduce five new names for the “sharp or flat” notes (black keys on the piano).  Hass Notation retains the traditional German nomenclature in which B is called H and A#/Bb is called B.  VaWu follows traditional solfege names for the white key notes and adds five new names for the black key notes (when used as a fixed do system).

Some proposals rename all twelve notes of the chromatic scale, and some employ repeating patterns for consonants and/or vowels. NoteTrace uses two repeating patterns: B M T for the consonants and e i o a for the vowels. Bakedi (Chromatic Pairs) similarly uses B K D for the consonants and e i o a for the vowels, but it cycles through the vowels first (at a lower level), before cycling through the consonants, which is the opposite approach from NoteTrace’s. SaLaTa uses a 6-6 pattern of alternating “a” and “o” for the vowels, while retaining the initial consonants of the seven traditional solfege names and introducing new consonants for the other five. Plain Notation System uses the cycle o u e a i for the vowels while retaining the seven traditional consonants and introducing five new ones.

Alphabetical Nomenclatures A A#
B C C#
D D#
E F F#
G G#
Hass Notation
by Peter Hass:
Express Stave Nomenclature
by John Keller:
by Dan Lindgren:
La Bo Ta Do Pa Ro Na Mo Fa Wo Sa Go
Plain Notation System
by Ivaylo Naydenov:
by Robert Stuckey and Richard  Parncutt:
La Ze TSi Do=Ut Va Re Wu Mi Fa Xe Sol Yu
by Enrique Prieto:
Be Me Te Bi Mi Ti Bo Mo To Ba Ma Ta
Bakedi (Chromatic Pairs)
by Fernando Terra:
De Di Do Ba Be Bi Bo Ka Ke Ki Ko Da


Numerical Nomenclatures

Many proposals rename the notes using numbers, or even use numbers in visual music notation systems. See the MNP’s tutorial on Numerical Notation Systems for more thorough documentation.

Numerical Nomenclatures A A#
B C C#
D D#
E F F#
G G#
Base-12 symbols
by Dominique Waller:
9 0 1 2 3 4 5 6 7 8
Dozenal (Pitman digits)
by Joe Austin:
9 Ɛ 0 1 2 3 4 5 6 7 8
Nueva Escritura Musical
by Julián Carrillo:
9 10 11 0 1 2 3 4 5 6 7 8
Untitled Notation System
by Robert Stuckey:
9 X N 0 1 2 3 4 5 6 7 8
Hamburg Music Notation
by Robert Elisabeth Key:
A B 0 1 2 3 4 5 6 7 8 9
Numbered Notes
by Jason MacCoy:
10 11 12 1 2 3 4 5 6 7 8 9
FinKeys Notation System
by Victor Mataele
X Y Z 1 2 3 4 5 6 7 8 9


Single-Digit Symbols for Ten and Eleven (PDF) by Dominique Waller

Dominique Waller designed a numeric notation system, and wrote this article (PDF) about his search for single-digit symbols to substitute for the numbers 10 and 11. He writes: “To make it easier to write and read, a duodecimal music notation that goes from 0 to 11 needs two new single-digit symbols for 10 and 11. But how to choose them? I’ve been searching for ten years now and have often changed my mind, but I now have come to a conclusion. That’s what I’m going to explain here.”


Relative “Movable-Do-Style” Nomenclatures

In addition to the fixed-pitch nomenclatures described above, there are also relative  nomenclatures along the lines of moveble-do and the equivalent major scale numbering which goes by the various names of Jianpu/Galin-Paris-Cheve/Nashville.

Relative “Moveable-Do” Nomenclatures Do Di
Re Ri
Mi Fa Fi
Sol Si
La Li
Express Stave Sol-fa
by John Keller:
Doh Zaw Ray Naw Mee Fah Vee Soh Yaw Lah Paw Tee
by Robert Stuckey and Richard Parncutt:
do=ut va re wu mi fa xe so yu la ze tsi
Rhyming Major Thirds Solfege
by David Zethmayr:
Do Re Mo Fa Si La Ti
Squiggle Solfege—”né-nà”
by David Zethmayr:
Ne Ne Ne Na Na Na Na

Rhythm Notation Overview

There are various approaches to notating rhythm in alternative music notation systems. This page gives a brief overview of some of these approaches, and provides a place to collect additional information about them.

Traditional and Modified Traditional Rhythm Notation

Many alternative music notation systems use the established rhythmic symbols of traditional notation. Sometimes these are adopted with slight modifications, often introducing new ways to differentiate between quarter notes and half notes so that hollow and solid notes can be used to help indicate pitch (see this tutorial: Noteheads and Pitch ). This provides continuity with traditional notation, but does not really attempt to improve upon the traditional notation of rhythm.

Proportional Rhythm Notation

Some alternative music notation systems use proportional spacing on the time-axis of the staff (whether vertical or horizontal) to indicate rhythm. Klavar Music Notation is a well-established example of this approach. To help the reader see the intended rhythm, Klavar uses not only the usual solid bar lines but also dashed beat lines.

(Proportional spacing has also been used by many composers, starting in the 20th century, on a traditional staff with traditional pitch notation. Typically this is done when the composer doesn’t wish to imply a meter or a regular beat, and often the composer uses black noteheads without stems. This approach is referred to as “proportional notation,” “time notation,” or “spatial notation.”  The first of these terms is also used by music historians to refer to mensural notation, however.)

Alternative Symbol-Based Rhythm Notation

Other alternative music notation systems introduce more thoroughly re-designed rhythmic symbol systems. An example of this approach is Mark Gould’s rhythm notation system for Equiton, as described in these presentation slides (Gould_Equiton_Slides.pdf) that were originally posted on his website. Another example is Panot.

Kevin Dalley’s LilyPond Code

This page documents some earlier important work by Kevin Dalley.  See the main LilyPond wiki page for the most current information.

Kevin Dalley volunteered his time and skills to add features to LilyPond to support chromatic-staff notation systems.  He wrote a set of patches (initially for LilyPond version 2.11.0) that provided for basic chromatic staff functionality. Now most of these patches have been incorporated into Lilypond, as you can see here. (He submitted a patch for internal-ledger-lines but it was never finished. However, it has been superseded by a newer patch by another developer that adds this functionality to LilyPond.)

Mark Hanlon also contributed by updating and maintaining Kevin’s code so that it would continue to work with more recent versions of LilyPond (although it is no longer compatible with newer LilyPond releases). Andrew Wagner set up a git repository for the patches and additional files on to help organize and facilitate future work.

How to Use Dalley’s “” Approach

Most of the content on this page comes from Dalley’s website, and documents his approach to using LilyPond for alternative notation systems — using his “” and template files. There are some non-functioning features (see below).

It is also possible to use LilyPond for alternative notation systems without using Kevin’s “” and template files. See the main LilyPond wiki page for more about working more directly with LilyPond rather than using Dalley’s files. (Both of these approaches are possible because of the code that Dalley contributed to LilyPond.)


Using LilyPond to transnotate music into an alternative notation

Assuming you have already installed LilyPond, here is how you would use it to transnotate music into an alternative notation.

  1. You will need a LilyPond music file (.ly) in standard LilyPond format, in a form similar to The LilyPond website explains how to write such files from scratch. You can also download them from the Mutopia project or other online sources.
  2. You will need a copy of the file which contains the definitions of various alternative music notation systems.
  3. You will also need a template file like this one:
  4. Open the template in any basic text editor and change the following line to refer to your LilyPond music file:\include “”
  5. Next edit the following line near the top of the template so it refers to your desired notation. (See below for a list of notation system names that can be entered here. Each system is defined in the file.)#(define notation-style “6-6-tetragram”)
  6. In the template, change these lines to define how many octaves your music covers.#(define lower-octave -2)
    #(define upper-octave 1)
  7. In the template, the following should be edited so they are appropriate for your file. You can add another voice, or another staff, but should consult the LilyPond documentation for details on this.\VoiceOne
  8. Now open the template file with LilyPond. It should output your music file in the designated alternative notation, except for the following non-functioning features.

Non-Functioning Features

When used with the standard LilyPond application, Dalley’s “” and template files do not currently render ledger lines that are internal to the staff, or different note head shapes. Dalley created a modified version of LilyPond that provided these two features, but they were not incorporated into the official LilyPond application. (See below for more about his patches to LilyPond.)

LilyPond now has support for internal ledger lines, so at some point it would be worth updating Dalley’s files to use this feature (rather than the one he wrote in his custom version of LilyPond). Different note head shapes can also be achieved. (See the main LilyPond wiki page, for more about these features.)  So there is work to be done integrating Dalley’s and template files / code / method with the current version of LilyPond.


Notation Systems

Here is a list of notation names that can be entered in the template in step four above. Each name corresponds to a particular notation system (or “notation-style”). Note that many of these are not fully implemented and are only approximations or first steps towards full support of a given notation system. This list is defined in the file (see below).

6-6-tetragram (6-6 Tetragram by Richard Parncutt)
a-b (Albert Brennink’s Ailler-Brennink notation)
ailler (Johann Ailler’s 4-line notation)
5-line (a basic 5-line chromatic staff)
frix (Grace Frix’s 5-line chromatic staff)
avique (Anne & Bill Collins’ Avique notation)
mirck (Klavar, Mirck version by Jean de Buur)
twinline (Twinline, by Tom Reed)
twinline-2 (Kevin Dalley’s experimental version of Twinline)
beyreuther-untitled (Johannes Beyreuther’s Untitled notation)
isomorph (Isomorph notation by Tadeusz Wojcik)
kevin (an experimental notation by Kevin Dalley)
express (Express Stave notation by John Keller)


Note that your music file may need to be slightly edited beforehand to produce the desired result. For instance, when Dalley transnotated J. S. Bach’s Invention 9 into various notation systems, he had to make a few changes to the original file that he had downloaded from the Mutopia project. For the most part, the note section remained the same. However, the lower staff in the original switched between bass and treble clefs, which he had to modify before transnotating. Here is his slightly modified file for reference:

(Eventually it would be nice to create a simple front-end application with a graphical user interface to handle most of these steps. Then the user would not have to directly edit the template file at all. The user could be presented with a window where they could specify the music file, select the desired notation system, define a few parameters like the number of octaves required, and click a button to transnotate the file with LilyPond.)

Note that Dalley also created a script that allows one to easily generate sheet music in many different notation systems at the same time. This “batch processing” script is not currently documented here, but it can be found on his website.

For Developers

This section has detailed information for programmers and anyone who is interested in what is going on “under the hood” with Dalley’s approach.  Most of the information below originally came from Dalley’s website.

How different alternative notation systems are defined and supported

Supported notation systems are defined in a table that is contained in the file This table makes it possible to quickly transnotate a given music file into any supported notation system. To add support for additional notation systems one would modify the file in order to add more notation systems to the table.

The table contains the following information, which is sufficient to describe a wide range of systems. This information would be needed for any notation system that was to be added.

A numeric list of each staff line position in an octave.
A numeric list of each ledger line position in an octave.
A number stating the position of middle C. (This lets you shift all the pitches of the staff up or down by changing the center pitch to a higher or lower note.)
The numeric distance between C and G, which is where the G clef is positioned.
The number of distinct positions in an octave.
Describes how notes are positioned. Currently either “semitone” or “twinline”.
For notations which have changing noteheads, a list of each notehead for each of the 12 semitones, starting with C.


The notation systems that are currently supported (and included in the table) are listed above. More systems could be easily added, but some systems cannot yet be fully supported since certain features are not yet possible. For example, automatically using black and white note heads for pitch, bold or dotted staff lines, or automatically placing notes on a particular side of the stem.  (These things can be done with LilyPond.  They just have not been integrated with Dalley’s code.  See the main LilyPond wiki page.)

Note that the average user does not have to be able to read or modify the file and its table of notations. Once a notation system has been set up, any user can transnotate music into it by calling it from the template file, as described above.

Note that the file also allows the use of “lower-octave” and “upper-octave” in the template file, see above. This provides the octave number of the lowest octave and highest octave displayed for a continuous staff.


To Do List

This was Dalley’s to do list. They are listed in roughly the order he considered to be most important, with later items in the list less precisely ordered than the earlier items.

  1. Center time-signature-engraver and rests when staff is not at 0.
  2. Investigate non-standard note heads.
    (See, Shape note heads, Note head styles, and The Feta Font.)
  3. Add a LilyPond conversion file which makes clef and key commands do nothing, or at least be consistent with alternative notations.
  4. Add other notation systems with standard note heads.
  5. Allow a notehead to be either hollow or solid (white or black) according to the note’s pitch, for notations that require this.
  6. Add dotted staff lines.
  7. Allow multiple clefs.
  8. Allow for non-standard stems.
  9. Drop octaves which are unused for several measures.
  10. Make conversion between notations easier.

This is an incomplete list of just a few of the items that Dalley completed:

  1. Allow arbitrary center point for staves, which allows other notations similar to 6-6 Tetragram.
  2. Make creation of arbitrary size staves easier. (In progress).
  3. check for 8va and 15ma signs, or some type of register signs for alternative notations.

If you would like to help contribute to this effort, please contact us. See also: Participating in LilyPond development


Patches to LilyPond

Kevin Dalley’s patches for alternative notations that have been committed to LilyPond

An “internal-leger-lines” patch by Dalley was submitted to LilyPond, but was not committed because it still required additional work.  It has now been superseded by code contributed by Piers Titus that added more comprehensive support for customizing ledger lines, see LilyPond. (For the record: Issue 1193: (PATCH) Enhancement: internal leger lines, and here is a separate feature request concerning custom ledger lines: Issue 1292: Enhancement: twelve-notation support and a related email exchange.)

Dalley also worked on shapeLayoutFunction for custom note head shapes. A patch for it was never submitted to LilyPond. Here’s an email exchange about it on the lilypond-user listserv from April 2007.  It and his full modified version of LilyPond can be found here on GitHub.

Since most of Kevin’s patches are now part of LilyPond, his file and template file will work, except for:

  1. The missing “internal-leger-lines” patch (see above).  It should now be possible to revise Kevin’s files so they will work with LilyPond’s custom ledger lines feature.
  2. His shapeLayoutFunction for customizing note head shapes, for notations that require this.
  3. Additional note head symbols, for notations that require them, such as Twinline and TwinNote.

Of course, 2 and 3 are only relevant for systems that use custom note head shapes.

Hamburg Music Notation by Robert Elisabeth Key

The Application of Mathematical Principles in Music

 We decided to set this text bilingual, since our native language is German and we are not sure that the translation is correct in all aspects.

Wir haben beschlossen diesen Text zweisprachig einzustellen, da unsere Muttersprache deutsch ist und wir nicht sicher sind , dass die Übersetzung in allen Punkten korrekt ist.

The application of mathematical principles in music

 by Christian Pörksen and Harry Schreiber

The decimal system is not very helpful for the subdivision of circles. The Duodezimalsystem with its potential to divide by 2,3,4 and 6 on the other hand almost ideal. The duodecimal system has proven itself for the subdivision of time in 12 hour sections for the structure of the days. With a circular hand like at the clock, this can be mapped well. In the sequel we would like to show that the circle is not sufficient as a mathematical model for the subdivision of the tonal worlds of music.

If we start with the C as one, the octave tone c ‘of the higher octave would be the thirteenth tone, or if the duodecimal system is used, the duodecimal eleven. The 13 notes of the twelve pitch steps are given the following ciphers in the Hamburg Musicnotation Version 1705 (HMN1705). (HMN)

 1,2,3,4,5,6,7,8,9, A, B, ʘ, separation of the previous octave and beginning of the new octave 1. The letter expansion of our numeral system, which is also used with IBM’s hexadecimal system, is applied.

A for the tenth tone and B for the eleventh tone of decimal counting. For the duodecimal 10 and zero the cipher ʘ is used with a point in the middle. The H, which is designated by a large B in the Anglo-American musical literature, stands at the position of the ten (ʘ) in the duodecimal system. Usually, the sound planes arranged in “octaves” are designated or numbered in different ways. (Eg as by us in the figure 1 duodecimal from 00* to BB* of the Midi table). Midiwerte

 One can write each note as a duodecimal number with two digits, e.g. 51 * for the middle C on the piano. The following applies: If the right digit is increased by 1, the next semitone is obtained. If the left digit is increased by 1, the octave of the tone is equal to twice the frequency. The same applies to the subtraction.

We have decided to name the first note of the octave (= C), as usual, as 1. Then the ʘ is the separator for the next octave. The circle is unsuitable for the correct mathematical representation of the duodecimal system in music, since it does not take into account that the diatonic Western music consists of twelve sound steps, but 13 sounds are required for obtaining 12 steps, which are not identical. This means that after the circle round the same one appears, but actually the one of the next octave is meant.

If one applies the above sequence of numbers to a spiral on plane paper, which has two lines at the same distance, marked at the same intervals as a clock, and then cuts out the zero or tens line along a paper strip, this strip can be applied to a blunt cone And thus gives a very vivid representation of the different sound spaces as the figure 1 shows.

Also by means of a ladder (the piano keyboard offers a model for it) all the harmonies of all the scales can be represented upwards and downwards at a clear and correct distance.

A fifths (seven halftones) up from 1=C leads to eight equal to G, and the fifths downwards fom c’ leads to F equal to six. This fact should be given greater attention in the teaching of harmonics and shows the advantages of a mathematical approach. By means of the (ʘ) or (1ʘ) as plane separators, one can move in a circle in any direction by addition or subtraction, but it is necessary to have a plane separator like the ten.

If a fixed value is repeatedly added in a circular scheme, all the numbers in the scheme are obtained if the value of this number is coprime to all numbers in the circle. That means: in the case of 12 numbers, the values are 5,7,11, in this case all primes.

Each tone has its own circles and its own sound planes and this circumstance leads to the almost inexhaustible variety of musical expression.

If the (ʘ) or duodecimal ten (1ʘ) is introduced into the table, which we have already published in 2010 Link, we can move correctly in both directions. See the figure 2 for zero (ʘ) equal to H or B and C equal to one (1).This applies to all other numbers in the same way.

Looking more closely at the above principles, the introduction of a free space above number ten in the HMN 1705 seems to be the key point in simplifying the readability of notations.

A vivid model for the testing of new notations, that meet criterion 8 according to Tom Reed, whose merits and ideas for alternative notations are to be recalled here, can be produced with the table semitones and frequencies from Wikipedia commons.

If the table is supplemented by the separator level 10, you can create a cylindrical spiral on which the notes can be mapped ascending and descending as we recently did with the HMN1705. (HMN)


Figure 1 – Abbildung 1


Figure 2 – Abbildung 2


 Die Anwendung mathematischer Prinzipien in der Musik

 von Christian Pörksen und Harry Schreiber

Das Dezimalsystem ist für die Aufgliederung von Kreisen wenig hilfreich. Das Duodezimalsystem mit seiner Möglichkeit durch 2,3,4 und 6 zu teilen dagegen geradezu ideal. Das Duodezimalsystem hat sich für die Unterteilung der Zeit in 12 Stunden Abschnitte für die Gliederung der Tage bewährt. Mit einem kreisenden Zeiger wie bei der Uhr lässt sich dieses analog gut abbilden. In der Folge möchten wir darstellen dass der Kreis aber als mathematisches Modell zur Untergliederung der Tonwelten in der Musik nicht ausreicht. Falls wir mit dem C als eins beginnen wäre der Oktavton c’ der höheren Oktave der dreizehnte Ton oder bei Anwendung des Duodezimalsystems die duodezimale elf. Die 13 Töne der zwölf Tonschritte werden in der Hamburger Musiknotation Version 1705 (HMN1705) mit folgenden Ziffernbezeichnet. (HMN)

 1,2,3,4,5,6,7,8,9,A,B,ʘ, Trennung der vorigen Oktave und Beginn der neuen Oktave 1. Die Buchstabenerweiterung unseres Zahlensystems, die auch beim Hexadezimalsystem von IBM benutzt wird, kommt zur Anwendung. A für den zehnten Ton und B für den elften Ton dezimaler Zählweise. Als Ziffer für die duodezimale 10 und Null wird die ʘ mit einem Punkt in der Mitte benutzt. Das H, welches in der angloamerikanischen Musikliteratur mit einem großen B bezeichnet wird steht auf der Position der Zehn (ʘ) im Duodezimalsystem. Üblicherweise werden die in “Oktaven” gegliederten Klangebenen auf verschiedene Weise bezeichnet oder durchnummeriert. (z. B. Wie von uns in der Abb. 1 Duodezimal von 00* bis BB* der Midi Tabelle angeglichen). Midiwerte

 Man kann jede Note als duodezimale Zahl mit zwei Ziffern schreiben, z.B. 51* für das mittlere C auf dem Klavier. Es gilt: Erhöht man jeweils die rechte Ziffer um 1, erhält man den nächsten Halbton. Erhöht man jeweils die linke Ziffer um 1, erreicht man die Oktave des Tons, gleich doppelte Frequenz. Entsprechendes gilt für die Subtraktion.

Wir haben uns entschieden, die erste Note der Oktave (= C), wie meist üblich, mit 1 zu bezeichnen. Dann ist die ʘ der Trenner für die nächste Oktave. Der Kreis ist für die korrekte mathematische Darstellung des Duodezimalsystems in der Musik ungeeignet, da nicht berücksichtigt wird, dass die diatonisch aufgebaute westliche Musik zwar aus zwölf Tonschritten besteht aber für die Erlangung von 12 Schritten 13 Töne benötigt werden, die nicht identisch sind. Das bedeutet, dass nach der Kreisumrundung die gleiche Eins erscheint, aber eigentlich die Eins der nächsten Oktave gemeint ist.

Wenn man die obige Zahlenfolge auf eine in der Fläche dargestellte Spirale, die zwei Linien im gleichen Abstand hat, in gleichen Abständen wie bei einer Uhr aufbringt und anschließend der null bzw. Zehnerlinie entlang einen Papierstreifen ausschneidet, kann man diesen Streifen auf einen stumpfen Kegel aufbringen und erhält so eine sehr anschauliche Darstellung der verschiedenen Klangräume wie die Abbildung 1 zeigt.

Auch mittels einer Leiter (Die Pianotastatur bietet sich als Modell dafür an) kann man alle Harmonien aler Tonleitern hinauf und hinab übersichtlich und in korrekten Abständen darstellen. Eine Quinte aufwärts (sieben Halbtöne) trifft vom C gleich eins das G oder die acht und die Quinte abwärts trifft von c’ aus das F gleich 6. Diese Tatsache sollte in der Harmonielehre größere Beachtung finden und zeigt die Vorteile einer mathematischen Betrachtungsweise auf. Mittels der ( ʘ) bzw. ( 1ʘ) als Ebenentrenner kann man sich durch Addition oder Subtraction in korrekten Abständen in jeder Richtung im Kreis bewegen aber es bedarf eben eines Ebenentrenners wie die zehn. Bei wiederholter Addition eines festen Wertes in einem Kreischema, ereicht man genau dann alle Zahlen im Schema, wenn dieser Wert teilerfremd zu der Anzahl der Zahlen im Kreis ist. D.h. Bei 12 Zahlen sind es die Werte 5,7,11, in diesem Fall alles Primzahlen.

Jeder der Töne hat seine eigenen Zirkel und seine eigenen Klangebenen und dieser Umstand führt zu der schier unerschöpflichen Vielfalt musikalischer Ausdrucksmöglichkeiten.

Wenn in die Tabelle, die wir bereits 2010 ins Internet Link gestellt haben, die ( ʘ) beziehungsweise Duodezimale zehn( 1ʘ) eingeführt wird, können wir uns in beiden Richtungen korrekt bewegen. Siehe Abbildung für die null ( ʘ) gleich H oder B und C gleich eins (1). Dieses gilt für alle anderen Zahlen in gleicher Weise. Abbildung 2

 Wenn man die oben genannten Prinzipien genauer betrachtet, scheint die Einführung eines freien Zwischenraumes über der Nummer zehn in der HMN 1705 der Schlüssel zur Vereinfachung der Lesbarkeit von Notationen zu sein.

Ein anschauliches Modell für das ausprobieren von neuen Notationen, die das Kriterium 8 nach Tom Reed erfüllen , an dessen Verdienste und Ideen zu alternativen Notationen hier erinnert werden soll, lässt sich mit der Tabelle Halbtöne und Frequenzen aus Wikipedia commons herstellen.

Wenn die Tabelle durch die Trennebene 10 ergänzt wird, können Sie eine zylindrische Spirale erstellen, auf der die Noten aufsteigend und absteigend abgebildet werden können, wie wir es vor kurzem mit der HMN 1705 gemacht haben. (HMN)


In the meantime we established a partnership with Pizzicato by Arpege Music and developed together the addon Alternative Notation
that can handle Hamburg Music Notation and all cipher notations based on twelve 
symbols as well as Numbered Musical Notation (Jianpu). In addition there is a 
vertical pitch version for alternative notations that allows to identify each tone on a 
vertical scale. The software allows to swing back and forthbetween Standard and 
Alternative Notations and can be downloaded for a trial.

The very useful manual for Alternative Notation is found on 

On you can read on my homepage about theory 
and practice of my Alternative Music Notation System. 

A short ebook with more information is available from AMAZON 
Numbers are Music - Hamburg Music Notation - Jianpu - 
and other Alternative Cipher Notations 
by Robert Elisabeth Key   








Click to view this image at full size:







Table of Duodecimal Musical Intervals All Scales








W.C. MacFarlane: Spring Song (excerpt)

Michael Johnston suggested this excerpt from “Spring Song,” a work for the organ written by Will C. McFarlane in 1914. (It was the second in a pair of works that also included “Reverie”.) This piece was designed to be easily playable by organists with a minimal level of technique such as church organists and community performers. It spans a fairly wide pitch range, and shows how proportional-pitch, chromatic-staff notation systems represent such a wide pitch range from a fairly common instance of traditional notation.

In Traditional Notation


In Various Alternative Notation Systems

Click the links to see the PDF file for each alternative notation system.

Audio – Listen to the Excerpt

Franz Liszt: Hungarian Rhapsody 2 (excerpt)

An excerpt of a chromatic passage from Franz Liszt’s “Hungarian Rhapsody 2” is used to illustrate various alternative notation systems in this tutorial on the main Music Notation Project site. Written in a key signature of six sharps, and having to use numerous accidental signs, it illustrates some of the difficulties and complications inherent in traditional music notation that are overcome by alternative notation systems.

Here is an illustration of a short excerpt from it in Hamburg Music Notation:

Variation II


Variation III


About the Music Notation Project Wiki

The Music Notation Project fosters communication, cooperation, and the exchange of ideas and resources among those interested in alternative music notation systems and similar subjects. As a companion to our Forum (Google group) and main website, this wiki is part of that effort. (What is a wiki?)

The wiki’s content is generated by the members of our community — alternative music notation enthusiasts who support the project and share its goals. It provides a platform for our community’s knowledge, ideas, proposals, examples, images, and sheet music for alternative notation systems — material that has typically been shared through our Forum (Google group). Organizing this material in a wiki will help make it more accessible and useful.

While our main website contains carefully edited tutorials and focused presentations of notation systems, the wiki supplements it by providing a way for our community to contribute additional information and ideas on these same topics, and on a broader range of topics that are still relevant to alternative music notation. It also provides a place to begin to collect and share examples of sheet music in alternative notation systems.

Navigating the Wiki

To browse the wiki, use the menu of categories and pages on the right, or use the search form to search our site (the search feature currently searches the whole site, not just the wiki).

Contribute to the Wiki

If you are interested in contributing to the wiki by editing pages or adding new content, see Contributing to the Wiki.


Note that the content of this wiki may or may not reflect the views or goals of the Music Notation Project as an organization. Except where otherwise noted, content in this wiki is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. This wiki was established in October of 2009.

Equiton Music Notation by Rodney Fawcett


Equiton is a notation system designed by Rodney Fawcett and published by him in Zurich in 1958. It uses a six-degree staff rather than either a pitch-proportional twelve-degree chromatic staff, or a traditional diatonic staff. It uses its own rhythm notation system rather than using the traditional duration symbols. In 2004, Mark Gould designed a variant of Equiton that uses his own novel rhythmic notation.

There’s more info on Equiton on this page from the Encyclopaedia of Tuning site, in an incomplete translation. On that same page are depictions of:

  1. Walter Steffens’s notation in an example by Webern
  2. Schoenberg’s notation system applied to his composition Pierrot Lunaire
  3. Klavarskribo in a sonata by Chopin
  4. A comparative table of a piece by Boulez in horizontal Klavarskribo, standard notation, and Equiton

The images on that site appear to come from a book by Erhard Karkoschka on new music. The book has been translated from German to English.

Mark Gould’s website Equiton Press discusses Equiton and presents his own version of Equiton that features a novel rhythm notation system. (In particular see his Equiton presentation slides document available via his website.)

This master’s thesis by Kevin Lewis on graphic music notation depicts Equiton in passing.

Equiton is illustrated on the influences page of the TwinNote site.

There’s also a brief description of Equiton on the More Notation Systems Page.

Chromatic Pairs by Fernando Terra

Chromatic Pairs is an alternative music notation system by Fernando Terra introduced in October of 2011.


Chromatic Pairs is based on the basic five-line chromatic staff. Below is an image of the chromatic scale on a traditional diatonic staff and a basic five-line chromatic staff. (This is just one of many different versions of chromatic staff.)


Im 1 Chromatic scale on traditional.png


Im 2 Chromatic scale on Basic Chromatic.png


This basic chromatic staff has great advantages over current traditional notation, as described on the Music Notation Project’s home page. However, the octave spans the full staff (one octave occupies six lines and spaces on the staff), which may make it inadequate if the music has a wide range.

The basic objective of Chromatic Pairs, therefore, was to retain as much of the simplicity of this basic chromatic staff as possible, while allowing more notes to be represented in the same space.

Chromatic Pairs represents two notes on each line and two notes on each space of the staff, doubling the amount of notes represented in the basic chromatic.

A two octave chromatic progression in Chromatic Pairs notation is shown below:
Page11 CP bakedi CDE.jpg
Notice that, as with a basic chromatic staff, in Chromatic Pairs there is also no need for key signatures, clefs or accidentals.


Staff, Note Names, and Intervals

Before any further explanation on the notation I would like to suggest that in addition to using a different staff notation system you would consider using a different nomenclature for the notes and different interval naming and notation, because they all share the same characteristic which ultimately makes understanding music much more difficult. This characteristic is that they all have an implicit musical format.

In this sense, the traditional staff notation and note names are worse than the intervals, since they are bound to a very specific format, the C major/A minor key. In this case, even if the music is in a common major or minor key, if it is not in C major/A minor, the music will be poorly represented and unnecessarily difficult. The interval notation should not be as bad, because it is not bound to a specific key, but it is based on the diatonic format, therefore being a bad option if the music departs from that format. Additionally, the interval notation does not profit from using the half-step as a unit, which might be the worst problem of the interval notation (more on this below).

The traditional approach does not take full advantage of equal temperament. Twelve tone equal temperament is the most common tuning today. In this system, the octave is divided equally in twelve half-steps.(1) If you then take the half-step as a unit, you can apply the properties of numbers (like relative position and counting), which are logical and familiar, to notes. This, however, is not easily done using traditional musical tools (the traditional staff, note names and intervals).

That said, we can now come back to the Chromatic Pairs notation that is shown below:

Page11 CP bakedi CDE.jpg

In the picture you see a chromatic progression of pitches starting in ‘Ba’. ‘Ba’ is equal to C in the ‘Bakedi’ note naming system, which I suggest as a better alternative to the alphabetic naming (although one can use the Chromatic Pairs notation with traditional note naming).


Bakedi Nomenclature

Bakedi is a simple nomenclature. I believe most people would be able to memorize it in less than five minutes.

Here is how Bakedi equates to the alphabetical system.

Ba Be Bi Bo Ka Ke Ki Ko Da De Di Do
C C# D D# E F F# G G# A A# B

In addition to being simple, this nomenclature takes full advantage of equal temperament. The purpose of Bakedi is basically to allow FAST INTERVAL CALCULATION and NOTE POSITION establishment. This is possible by means of treating the half-step as a unit and, therefore, profiting from the characteristics of numbers.

In fact, the names were conceived to be NUMBERS.

If I may give an example, imagine a sequence of thirty numbers starting in zero

0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29

Now imagine that we don’t use the decimal system, which is based on groups of ten numbers, but a system based on groups of four numbers, as such

0 1 2 3
10 11 12 13
20 21 22 23

Bakedi uses the letters ‘aeio’ to be the names and symbols of the “numbers” ‘0123’

a e i o
0 1 2 3

and consonants ‘B K D’ to correspond respectively to 0, 1 and 2, as the “tens” of the numbers. This is illustrated in the table below;

0 1 2 3
a e i o
0 B Ba Be Bi Bo
1 K Ka Ke Ki Ko
2 D Da De Di Do

In this way I have 12 notes Ba Be Bi Bo Ka Ke Ki Ko Da De Di Do, which are divided equally in three sets of four notes.

The sequence of vowels (aeio) is popularly known, and known in that specific order (from a to o), since children are educated that way while learning to read. I believe this note naming gives a good idea to the musician of the notes positions in relation to each other, and that could allow for the musician not to depart as much from the notes in ABSOLUTE terms (the actual note names), when they need to think in RELATIVE terms (i.e. intervals).



Regarding intervals I just use the names of the numbers, i.e. if a note is four half-steps apart, then their interval is four. Here is how this system equates to the traditional system:

0 1 2 3 4 5 6 7 8 9 10 11
unison Minor 2nd Major 2nd Minor 3rd Major 3rd Perfect 4th Dim 5th Perfect 5th Minor 6th Major 6th Minor 7th Major 7th

Beyond the octave a possibility is to use the letter – o – for octave, and proceed as o+1, o+2, o+3, … or o1, o2, o3, …


Chromatic Pairs Features

I would now like to talk about some of the characteristics of the CHROMATIC PAIRS notation. Here is the Chromatic Pairs notation again:

Page11 CP bakedi CDE.jpg

In Chromatic Pairs a chromatic progression occurs as successive changes in color and upward jumps as shown above.

Although this is a bit more complex than the basic chromatic staff (shown below),

Im 2 Chromatic scale on Basic Chromatic.png

image source:

Chromatic Pairs is favored by some nice properties. It is organized in PAIRS of BLACK and WHITE and counting in pairs (0,2,4,6,8,10) is almost as easy as counting units. It is also organized in GROUPS OF FOUR HALF-STEPS from one line to the next, as explained below:

In every staff there are four types of notes:

  • Black notes on lines (notes ending in a, Ba Ka Da)
  • White notes on lines (notes ending in e, Be Ke De)
  • Black notes on spaces (notes ending in i, Bi Ki Di)
  • White notes on spaces (notes ending in o, Bo Ko Do)

(You can notice how these four types of notes relate conveniently to Bakedi.)

Therefore, the interval of four half-steps is very easily recognizable. To jump to a note four half-steps apart just go to the next note of the same kind. By doing that, you will also arrive in a note ending in the same vowel in Bakedi.

It is essential for a notation to be logical, so you can follow some simple steps to conclude what is the interval between two given notes, while learning the notation. However, the idea is that, with some practice, you could abandon those steps and just instantly recognize any interval.

Relating Chromatic Pairs to Bakedi

As said earlier for each type of note representation in the staff, there is a vowel.

  • Black notes on lines (notes ending in a, Ba Ka Da)
  • White notes on lines (notes ending in e, Be Ke De)
  • Black notes on spaces (notes ending in i, Bi Ki Di)
  • White notes on spaces (notes ending in o, Bo Ko Do)

You can also notice every BLACK NOTE ends either with ‘A’ or ‘I’, every WHITE NOTE ends either with ‘E’ or ‘O’.

Besides that, every consonant represents a line and a space (the space immediately above it) on each octave, as shown in the image below, and this also represents a PROGRESSION IN 4 HALF-STEP INTERVALS.

Page12 CP bakedi consonants.jpg


The Octaves Display

To the LEFT OF THE STAFF you can see numbers that show the OCTAVES which encompasses the notes shown at their right in the staff.

Page13 CP octave numbers.jpg

So, for instance ‘Ba4’ to ‘Do4’ have to their left the number four, above ‘Do4’ the next note is ‘Ba5’ and this is represented in the left as the beginning of the fifth octave.

In the ledger line region there are two octaves that use the same space (as in traditional notation). From bottom to top, in our example above, the fourth octave is represented by a 4 with an arrow upwards coming from the third octave. From top to bottom there is a similar indication of the third octave coming from the fourth.

These octaves numbers are assignable and should be determined according to the musician’s necessity.

Page14 CP different octave settings.jpg


Chromatic Pairs borrows the rhythm of the traditional notation almost entirely, but since there is a conflict with the half-note and quarter-note because of the use of color to determine pitch, the half-note is changed to the form shown in the image below:

Page15 CP half-note.jpg

An explanation on the rhythm of notations that use color to indicate pitch is given in this tutorial.



The traditional musical staff notation and traditional nomenclature, both of intervals and notes, is overly complex and do not represent the music well. This is due to the fact that they have an intrinsic musical format.

This problem seems worst for the note nomenclature and traditional staff, since they are bound to a very specific format, the C major/A minor key. This bond inflicts a lot of unnecessary effort on the musician, who has work around this format.

Additionally, the traditional system doesn’t benefit enough from the properties of numbers, which can be used when you consider the half-step to be a unit.

Chromatic Pairs combined with the Bakedi nomenclature and different names for intervals were proposed as alternatives to the traditional system. This new system has the objective to be as simple as possible and to allow for the use of the half-step as unit, therefore permitting fast note positioning establishing and interval calculation.

The ultimate purpose of the system is to make learning, reading, writing and understanding music easier.

Note on Equiton: Although Chromatic Pairs was conceived based on the basic chromatic notation alone and without previous knowledge of similar notations, there is a notation which is similar to Chromatic Pairs in regard to pitch, but that makes further modifications to the traditional notation. The name of this notation is Equiton, and it was designed by Rodney Fawcett in 1958. In this page you will find a description of Rodney Fawcett’s notation along with a link to a page that describes his work (although it is a very bad translation), and a pdf file of Mark Gould’s work, that further develops on Equiton.

(1) This is a crude definition of twelve tone equal temperament, but fits the purpose of a quick explanation. On the following link the term is better defined

Black-Oval Twinline by Paul Morris

This is a collection of images illustrating Black-Oval Twinline. Black-Oval Twinline was briefly named “TwinNote” between June and December of 2009, before Morris introduced the new version of TwinNote. The images below originally appeared on the TwinNote website during this period. They were moved to this wiki page when the TwinNote website was updated to the new version of TwinNote in January 2010.

Basic Scales

C Major Scale:

WTTL CMajorScale.png

A Major Scale:

WTTL AMajorScale.png

C Minor Scale:

WTTL CMinorScale.png

A Minor Scale:

WTTL AMinorScale.png

Whole Tone Scales:


Chromatic Scale:

WTTL ChromaticScale.png


Major Scales with Whole Steps (W) and Half Steps (H)

WTTL MajorScales.png

Minor Scales with Whole Steps (W) and Half Steps (H)

WTTL MinorScales.png



WTTL Wholetonescales.png

WTTL Minorseconds.png

WTTL Majorseconds.png

WTTL Minorthirds.png

WTTL Majorthirds.png

WTTL Perfectfourths.png

WTTL Tritones.png

WTTL Perfectfifths.png

WTTL Minorsixths.png

WTTL Majorsixths.png

WTTL Minorsevenths.png

WTTL Majorsevenths.png

WTTL Octaves.png


Lilypond is free, open-source music notation software that can be used to create sheet music in alternative notation systems. One of LilyPond’s strengths is its flexibility.  It is designed so that its output can be modified using the Scheme programming language.  This opens the door to a world of customization without having to alter LilyPond’s source code. This page documents how to use LilyPond with alternative music notation systems with a chromatic staff.


The following files can be used to produce music in a number of alternative music notation systems.  These files demonstrate the use of the specific “lower-level” techniques documented below.

  • — A LilyPond file containing LilyPond and Scheme code that supports alternative music notation systems.
  • — A LilyPond music file demonstrating the use of the file.
  • MNP-music-demo.pdf — LilyPond’s PDF output from the file.

There are basically just a few steps to use an existing traditional LilyPond music file to create a PDF of music in an alternative notation system:

  1. Download the file above and put it in the same directory as your music file.
  2. Include the file at the top of the music file. (See Including LilyPond Files.) The file and the music file must be in the same directory for the \include command to work.
  3. Change “Staff” in the music file to the name of any alternative staff that is defined at the bottom of the file. (Examples are “StaffFiveLineOne” or “StaffKlavarMirckTwo”. See the file for more.)
  4. If the alternative staff is larger than two octaves and is not a compressed staff (i.e. Twinline, TwinNote), then you may need to make the following adjustment for any bass clefs that appear in the music. Enter “\set Staff.middleCPosition = #18” just after any instances of “\clef bass” in the music file. Otherwise the notes may not appear in the expected places on the staff.
  5. Run LilyPond on your music file. Voilà! You now have a PDF of music in an alternative notation system.

Older Demo Files

These are some older demo files that are inferior to those shown above.

Customizing Note Positions

Semitone Spacing

staffLineLayoutFunction is used to customize the default vertical positions of notes on the staff. For a standard pitch-proportional chromatic staff with a semitone between each adjacent note position (line or space), set it to use the ly:pitch-semitones function:

staffLineLayoutFunction = #ly:pitch-semitones

Other Spacing Patterns

For notation systems like Equiton or TwinNote that have a staff based on a whole tone scale with a whole tone between each adjacent note position (line or space), use the following function. (Thanks to Graham Breed for this function.)

staffLineLayoutFunction = #(lambda (p) (floor (/ (+ (ly:pitch-semitones p) 0) 2)))

For staves based on other intervals simply change the number 2 in the function above to the number of semitones in the interval you want. Change the number 0 in the formula to 1 (or 2, etc.) to adjust which notes share a line or space (and which are on different lines or spaces).  See: Snippet: Staves based on a whole tone scale (or other interval)

For Twinline and similar chromatic staves with one note on a line and three in a space, use the following version of the function which uses “banker’s rounding” to get the desired 1-3-1-3-1-3… pattern.

staffLineLayoutFunction = #(lambda (p) (+ 1 (round (+ -1 (/ (ly:pitch-semitones p) 2)))))

(Note: Graham Breed has also shown how to use the ly:set-default-scale scheme function to reposition notes: Dodecaphonic staff snippet)


Customizing Staff Lines

In LilyPond the vertical position of notes and the vertical position of staff lines are independent of each other.  Notes are not placed on a line or space per se, but at a vertical position that may or may not coincide with the vertical position of a line or space.

A staff’s line pattern can be customized using Staff.StaffSymbol and the line-positions property. See Changing the staff line pattern (Staff Symbol Properties). The numbers ( 4 2 0 -2 -4 ) in the line of code below represent the five standard line positions.  A different list of numbers will produce a custom line pattern.

\override Staff.StaffSymbol #'line-positions = #'( 4 2 0 -2 -4 )

It is possible to simulate bold lines by adding extra lines close together with the line-positions property.  Go to Modifying a single staff and scroll down to “Making some staff lines thicker than the others” for more about this trick.

Dashed or dotted lines can be achieved using the Scheme function found in this post to the LilyPond user list.  This function is also included in the file linked at the top of this page.


Customizing Ledger Lines

In LilyPond version 2.15.13 or higher, ledger line positions can be customized, including ledger lines that appear above or below the staff and those that are internal to it. Similar to customizing staff lines, you use Staff.StaffSymbol with the ledger-positions property:

\override Staff.StaffSymbol #'ledger-positions = #'(-12 -10 -8 -6 -4 -2 (0 2) 4 6 8 10 12)

The numbers define positions for a series of ledger lines, this series is repeated in a cycle extending both up and down the pitch axis. The last number in the series is also the first ledger line in the next repetition of the cycle (i.e. the last number refers to the same ledger line as the first number, just in the next iteration of the series).

Internal ledger lines appear by default when custom staff line positions are set with a gap between them of 4 steps or more.

You can group multiple ledger lines together by placing them in parentheses, as shown above: (0 2). When one of the ledger lines in a group appears all of the others will appear as well. This can be used to achieve thicker, bold ledger lines by using the same trick described above for bold staff lines.

Thanks goes to Piers Titus for his work adding this feature to LilyPond. (This supersedes Kevin Dalley’s code for internal ledger lines that was never added to LilyPond.) More details…

An Older Deprecated Method

Before the method above was available, internal ledger lines could be achieved by creating a custom notehead stencil (glyph) that has the ledger line included in it, and then assigning that notehead stencil to the pitches that require a ledger line. This is how it is done in the TwinNote Demo file (linked above). With systems that do not already use custom note heads this would be more difficult since you would have to access to the default oval note head stencil and combine it with a ledger line stencil. You would also need to create different stencils for quarter notes, half notes, and whole notes, and then have a script to determine when to use which based on a note’s duration.


Customizing Noteheads

Noteheads can be colored: Coloring notes depending on their pitch

Notehead styles (shapes) can be customized using a modified version of the code for coloring note heads. See our for the modified code.  This offers more fine-grained control than LilyPond’s shapeNoteStyles property that is used for Shape Note notation. That property only allows you to set custom shapes for each step of the scale (as set by the key signature or the tonic property). It does not let you customize each chromatic scale degree. For example, whatever shape you designate for G will also be the shape for G# and Gb.)

Documentation for notehead styles (shapes):

Custom notehead shapes can be created with ly:make-stencil, see this snippet on Using PostScript to generate special note head shapes. This PostScript stencil method was used to create the triangle note shapes in these TwinNote demo files:

This TwinNote demo also has a different, more streamlined script for customizing noteheads based on pitch.


Customizing Stems

This override prevents LilyPond from extending stems to the middle of the staff. This is particularly helpful with multiple-octave chromatic staves, otherwise you can get stems that extend an octave or more. It is shown in this snippet: Preventing Stem Extension

\override Stem #'no-stem-extend = ##t

The following TwinNote demo LilyPond file (.ly) includes a script for adjusting the stems so that they “attach” to the note head correctly in TwinNote (not too short or too long). It also includes a script that gives half notes a double stem to differentiate them from quarter notes.


Removing Unneeded Symbols

Accidental signs, key signatures, and clefs can be removed as follows. Other unneeded symbols can be hidden: Making symbols invisible

\remove "Accidental_engraver"
\remove "Key_engraver"
\remove "Clef_engraver"

Desired Features List

Most desired features can now be achieved as described above. Any additional desired features can be listed here, should they come to light.