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.
General
Intuitive Instruments for Improvisers (Paul Hirsh) – http://improvise.free.fr/ A website about isomorphic instruments, isomorphic panpipes, Janko keyboards, and more…
Keyboards, Accordions, Button Instruments
General
The DIY Keyboard Project (Drew Wagner) – http://diykeyboard.org 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) – http://www.AltKeyboards.com
Musix for iPad – http://www.shiverware.com/musix.html One of the layouts is the Wicki-Hayden.
Single Row of Keys (Chromatic Scale)
Robbins Keyboard – https://www.google.com/patents/US2627777
Dodeka Keyboard – http://www.dodeka.info/DodekaEnglish/Instruments.html
Multiple Rows of Keys (Chromatic Scales, Offset by a Perfect Fourth)
LinnStrument (chromatic scales a perfect fourth apart, reminiscent of a fretted string instrument) – http://www.rogerlinndesign.com/linnstrument.html
Two Rows of Keys (Whole-Tone Scales, Offset by a Semitone)
Symmetrical Keyboard (Dominique Waller) – http://www.le-nouveau-clavier.fr/english/
The Balanced Keyboard (Bart Willemse) – http://balanced-keyboard.com/
Multiple Rows of Keys (Duplicated Rows of Whole-Tone Scales, Offset by a Semitone)
Daskin brand Janko Keyboards (Paul Vandervoort) – http://daskin.com/
Lippens keyboard derived from Janko’s design
Chromatone brand Janko-style keyboards (Japanese company) – http://chromatone.jp/
Chromatone Lite for iPad – http://itunes.apple.com/us/app/chromatone-lite-for-ipad/id382628130?mt=8#
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 – http://www.thearraymbira.com/beyond-the-mbira.html
Multiple Rows of Keys (Series of Minor Thirds, Offset by a Semitone or Whole Step)
Chromatic Button Accordions – http://en.wikipedia.org/wiki/Chromatic_button_accordion
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 – http://www.c-thru-music.com/
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) – http://en.wikipedia.org/wiki/Generalized_keyboard , http://improvise.free.fr/bosanquet/bosanquet.html
Microtonal keyboards, including isomorphic keyboards – http://xenharmonic.wikispaces.com/Microtonal+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.)
Woodwinds
Isomorphic Saxophones and Flutes (Jim Schmidt) – http://www.jsengineering.net/
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. – http://www.marcodi.com/ – Wiki Page
Chromatic harp (strings arranged in whole-tone scales) – http://www.chromatiker.de/Harfenbauer.html (Page in German)
The Array Guitar, Psaltery, and Vina (Bill Wesley) – http://www.thearraymbira.com/beyond-the-mbira.html
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) – https://www.arraymbira.com/