On 8 Nov 2013, at 01:47, Keith OHara <k-ohara5...@oco.net> wrote: > On Thu, 07 Nov 2013 13:26:04 -0800, Hans Aberg <haber...@telia.com> wrote: >> >> On 7 Nov 2013, at 21:47, Keith OHara <k-ohara5...@oco.net> wrote: >>> >>> Hans, I am late, but can I persuade you to try this with sharp and flat >>> representing 4 tone-steps rather than 5 ? >> >> No, since in regular E53, the minor second m = 4, and the major second M = >> 9, so sharps and flats alter with M - m = 5 E53 tonesteps. > > But you also have arrow alterations, so you can distinguish more than two > types of second. > > You have the diatonic scale of the bare note-names > C -9- D -9- E -4- F -9- G -9- A -9- B -4- C > but the major scale build on the major triads is closer to > C -9- D -8- E, -5- F -9- G -8- A, -9- B, -5- C > (with , lowering one step) > > You might choose seconds from the set m=4 n=5 N=8 M=9 and have alterations > M - n = N - m = 4 close to a traditional sharp > M - N = n - m = 1 close to an 81/80 comma > then the D major scale, for example, looks more simple > D -9- E -8- F# -5- G -9- A -8- B, -9- C# -5- D > > M-m = 5 steps is another choice for an alteration, but if I write that with a > sharp I find it harder to understand because I have learned that a sharp is a > tiny bit less than half a whole tone.
It is not possible to do that with current LilyPond; Graham Breed retuned the fifth in his regular.ly, so there is still only two generators. What I wrote here [1] will do it, though. When describing Just intonation, I think most will depart from Pythagorean tuning and reach Just intonation via syntonic commas 81/80, or in E53, a tonestep. In JI C major, the D minor triad is out of tune. If trying to pivot sequence of triads C F Dm G C the pitch will slip with a syntonic comma. So the pitch must be adapted somehow. 1. https://lists.gnu.org/archive/html/lilypond-devel/2013-11/msg00062.html _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-devel
