Re: Microtonal accidentals

[Keith OHara]

Hans Aberg <haberg-1 <at> telia.com> writes:

> I have just defined pitch names for E53 note c with accidentals, using 
Graham’s file regular.ly:
>       cff cffu cffuu cfdd | cfd cf cfu cfuu | cdd cd c cu |
>       cuu csdd csd cs | csu csuu cssdd cssd | css r2. |
> Here, d (resp. u) is down (resp. up) one E53 comma (tonestep). I just 
checked with midicomp that the output is
> correct. 
> 

Hans, I am late, but can I persuade you to try this with sharp and flat
representing 4 tone-steps rather than 5 ?

Then a sharp is 91 cents, near the 92-cent alteration corresponding to
the ratio 5.3.3.3/128 that is often represented by a sharp -- the shift
from F that is the IV of C-major to the F-sharp in a D-major chord that
we see when we modulate to G-major.

By comparison the Helmholtz notation uses sharp to mean 114 cents,
taking F to the F-sharp from a sequence of 7 perfect fifths as in 
Pythagorean tuning, but in music this sharp is most often seen
lowered by a 22-cent comma.

Ben Johnston's notation uses flat to mean -70 cents (a ratio 24/25)
but this is most often seen on notes B E and A that Johnston has lowered
already from the cycle of fifths by a 22-cent comma.

The notation looks simpler and more familiar if we define sharp and flat
such that C-sharp is below D-flat <http://k-ohara.oco.net/Lilypond/>