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Re: Microtonal accidentals
From: |
Hans Aberg |
Subject: |
Re: Microtonal accidentals |
Date: |
Thu, 7 Nov 2013 22:26:04 +0100 |
On 7 Nov 2013, at 21:47, Keith OHara <address@hidden> wrote:
> 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 ?
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. So the minor second in
E53 is 4*1200/53 = 90.566 cents, which is very close to the Pythagorean m =
256/243 which 1200*log_2(256/243) = 90.225 cents. The sharp alter with
5*1200/53 = 113.208 cents.
> 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.
The normal is to depart from the Pythagorean tuning, and adding approximations
for JI.
> 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/>
So you need to choose your m and M first, but for regular ETs that is done by
merely seeking the best approximation of the perfect fifth 3/2.
Quarter-comma meantone, which sets the major third exact, is approximated by
E31, which has m = 3, M = 5, and 1/3 comma meantone, which sets the minor third
to 6/5, is approximated by E19. These would give narrower sharps alterations.
- Re: Microtonal accidentals, (continued)
- Re: Microtonal accidentals, Hans Aberg, 2013/11/03
- Re: Microtonal accidentals, Hans Aberg, 2013/11/03
- Re: Microtonal accidentals, Joseph Rushton Wakeling, 2013/11/03
- Re: Microtonal accidentals, Hans Aberg, 2013/11/03
- Re: Microtonal accidentals, Keith OHara, 2013/11/07
- Re: Microtonal accidentals,
Hans Aberg <=
- Re: Microtonal accidentals, Keith OHara, 2013/11/07
- Re: Microtonal accidentals, Hans Aberg, 2013/11/08
- Re: Microtonal accidentals, Keith OHara, 2013/11/08
- Re: Microtonal accidentals, Hans Aberg, 2013/11/08
- Re: Microtonal accidentals, Hans Aberg, 2013/11/03
- Re: Microtonal accidentals, Hans Aberg, 2013/11/03
- Re: Microtonal accidentals, Hans Aberg, 2013/11/04
- Re: Microtonal accidentals, Graham Breed, 2013/11/03
- Re: Microtonal accidentals, Hans Aberg, 2013/11/03
Re: Microtonal accidentals, Keith OHara, 2013/11/07