Comments on The Keyboard Section
The most important paper here is the Gral Keyboard Guide. It concludes Wilson search on how to map any Moment of Symmetry to a generalized keyboard. The most detailed guide and analysis of this has been done by Terumi Narushima in her PhD thesis "Mapping the Microtonal Spectrum using Erv Wilson's Generalized Keyboard" now being prepared for publication.
This section is in many ways the most complex. Wilson's ideas evolved for sometime before he arrived at the Gral keyboard guide and the related designs. There is thus some inconsistancy with the labeling of keyboards which will have to be dealt with later. Most often it will involve a renaming in terms of the numerator and the renaming involves using the recipcal number in terms of the numerator to the denomiator. For instance something he originally calls a 3/7 keyboard he later calls a 4/7 keyboard or a 2/5 keyboard became a 3/5 keyboard or vice versa.
It is not possible to go into all the details of this renaming, but it stems from Wilson originally thinking of all keyboards being based on the half octave or half period with the largers being inversions. This would have been consistant with this straight line drawings. In the end due to mapping strategy of the Gral guide he changed this to convey the mapping in that regard. To be dealt in detail later.
A word can be said about the notation Wilson used that incorporated 5 Greek letters. This was his borrowing from Yasser who did this to represent flat/sharps so one could use 12 symbols that did not require any accidentals. Yasser was one of the most prominent persons working in microtonality at the time and Wilson began by springboarding off his work. Later as in the case of 31ET he suggested a sequence like C, C+, C#, Db, D-, D as an alternative. The generalized keyboard though always remains the basis of his approach to notation forit is the generalized keyboard he foresaw the future of microtonality.
~Comments and Questions Welcome~