New Brian Hayden Web Article

[JackWoehr]

Hayden Duet Concertina inventor Brian Hayden examines similar types of fingering systems for accordion and concertina: read Brian Hayden on the Reuther Uniform System and other self-transposing systems

Edited December 21, 2005 by JackWoehr

[Plamondon]

A more general discussion of "self-transposing" note-layouts can be found at www.thummer.com/thummusic12.asp (an earlier version of which I shared with Brian over a year ago).

 

The characteristic of "self-transposition" -- having the same fingering in all keys -- is just the tip of the iceberg. The fundamental characteristic of such note-layouts is that each given interval has the "same shape" everywhere. "Isomorph" being Greek for "same shape," these note-layouts are more generally called "isomorphic," and the general property "isomorphism."

 

The even deeper property is “periodic isomorphism,” in which the periodic structure of M-dimensional data is exposed in an N-dimensional display, where (a) 0 < M < N and ( each of the N axes are scaled using a sub-period of M. Periodic isomorphism is imperfectly displayed in the Periodic Table of the Elements (displaying linear atomic weight data in 2D and 3D) and in calendars (displaying linear Julian Day Number data in 2D). Periodic isomorphism may have particularly good application to fractal data, which is self-similar at every scale.

 

Pitch data (linear in frequency) is kinda-sorta self-similar, due to the periodic structure of the Harmonic Series. A 2D isomorphic note-layout uses different scales along each axis of button-adjacency, providing an excellent example of periodic isomorphism. This geometry tempers out the syntonic comma and tempers the major second to the mean of the major third, providing a geometric manifestation of meantone tuning (as Andy Milne pointed out to me).

 

A meantone tuning is one in which (a) the syntonic comma is tempered to unison, and ( the major second is exactly half -- the "mean" of the major third. 12-tone equal temperament (12-tet) is one possible meantone tuning; many others have been used by composers of the Renaissance and Baroque periods. Other meantone tunings are used today by non-Western cultures.

 

If the musical intervals between adjacent buttons are defined more generally in terms of diatonic intervals -- such as perfect fifth, major second, octave, etc. -- then it can be seen that they retain this property of isomorphism not just in 12-tet, but in all meantone tunings (some of which are equally-tempered, some of which are not). That is, the fingering is the same not just in all keys of 12-tet, but in all meantone tunings as well.

 

The Wicki/Hayden note-layout -- if implemented using electronic rather than mechanical buttons -- can pack 19 buttons under the span of a single hand's fingers, making it especially appropriate for use with meantone tunings, in which the pitch of (say) G# and Ab can differ. (Check an unaltered early Wheatstone English concertina, which provided different buttons for these two notes specifically to support 1/4-comma meantone tuning, and you'll hear the difference.) A 19-button-per-octave Wicki/Hayden layout provides not just separate buttons for each "enharmonic pair" in 12-tet (such as G#/Ab), but also for B/Cb and E#/F, which are different notes in many meantone tunings (which is why they have different names in traditional music notation, which is based on meantone tuning).

 

The combination of an isomorphic note-layout and electronic music synthesis opens up many new creative possibilities. First, it makes such an instrument the natural meeting-ground for the music of many cultures -- Thai, Indonesian, African, Arabic, etc. -- which use different meantone tunings. Second, it provides a convenient means of exploring historically-important Western meantone tunings, in their extended form (in which no "wolf" intervals occur, since those are artefacts of shoe-horning those tunings into a 12-key-per-octave piano keyboard). Third, it offers the opportunity to explore finer divisions of the octave, such as 19-tet and 31-tet (especially when combined with electronic transposition). Because all of these tunings have exactly the same fingering on an isomorphic keyboard, they can be explored at the flip of a switch, without having to learn anything new. The pentatonic scale (for example) is played exactly the same way in 5-tet, 7-tet, 12-tet, 19-tet, 31-tet, and in 1/3-comma, 1/4-comma, 1/6-comma, etc., all of which are meantone tunings. This is only possible with an electronic isomorphic instrument.

 

It is entirely possible that on such an instrument, composers will find ways to use “tuning progressions” the way one currently used “chord progressions," changing tunings on the fly.

 

Please let me thank Brian Hayden once again for his independent re-invention of the Wicki/Hayden note-layout, and also thank concertina.net on which I learned about it, without which I would never have begun my own explorations of isomorphism, on which the fortunes of my company are based.

 

Jim Plamondon

CEO, Thumtronics Ltd

The New Shape of Music™

www.thummer.com

Edited December 22, 2005 by Plamondon

[JackWoehr]

A more general discussion of "self-transposing" note-layouts can be found at www.thummer.com/thummusic12.asp (an earlier version of which I shared with Brian over a year ago).

 

Interesting discussion. But everything I've tried to find out about your "Thummer", e.g., a picture here on c'.net, seems to be disappeared!?