ChromaTonnetz’s primary feature is its system of triangular noteheads. There are four different orientations and three different “fill patterns” for the triangles, yielding a unique appearance for each of the twelve pitches of the chromatic scale. (The fill patterns are solid, i.e., black, open, i.e., white, and a pattern that approximates gray by placing a smaller triangle inside the triangular notehead.) The four orientations cycle as one ascends the chromatic scale, as do the three fill patterns, and their cycling is simultaneous rather than nested. As a result, noteheads that share the same orientation belong to the same augmented triad (which consists of stacked major thirds), and noteheads that share the same fill pattern belong to the same diminished seventh chord (stacked minor thirds). This emphasis on intervals of a major or minor third is intended to highlight traditional tonality, whose chords are typically constructed by stacking thirds. The design was inspired by Leonhard Euler’s Tonnetz and by the three-color scheme that Roy Pertchik uses on his 6-6 vibraphone.
Because each of the 12 pitches has a unique appearance, the system can be considered a shape-note system for the chromatic scale. The picture above shows the chromatic scale starting on C, but Austin says the system can also be used in movable-do fashion, in which case the series of shapes would be transposed to start on the tonic of the current key.
The 12 different notehead appearances also mean that the system can in principle be used with any staff, or even no staff. Austin uses it with the 7-5 staff shown above, and presumes some sort of chromatic staff will be used, although he has also demonstrated it with the traditional staff. The above staff is similar to Mirck but it is usually vertically oriented as in Klavar. Whereas Mirck uses gray lines for C# and D#, the above staff uses dashed lines.
Similarly, Austin says that most any rhythmic notation can be used that does not depend on notehead shape or fill pattern. This includes traditional rhythmic notation modified slightly, e.g., with double-stemmed half notes. Austin also sometimes uses proportional spacing, in which noteheads have no stems and are placed proportionally to their onset times. In this case, the convention is that a note continues to sound until that voice’s next note appears, or until a “rest” symbol (%) appears. A “continue” symbol (“) is used: (1) when another note is added at the same time instant but the original note continues; and (2) when a note continues after a line or page break.
To address Criterion 17 of the Music Notation Project’s desirable criteria for notation systems, Austin says that in handwriting ChromaTonnetz, one could make do with a wedge (>, <, ^, or v) for the white noteheads, with the addition of a stroke to represent a “gray” notehead or a squiggle to represent a black one.
Source: Joe Austin. ChromaTonnetz introduced Sept. 20, 2010.
Website: http://drtechdaddy.com/2010/09/24/tonnetz-based-4×3-notation/
Similar Notations: Mirck
