Re: Organ Study #1 in 26 EDO

Dear Daniel,

What a nice piece in 26-EDO: I'd call the colors rather consonant and
at the same time profound, reminding me a bit an arrangement I once
heard of a Russian song called _Meadowlands_. The fifths and fourths
are very pleasing in the timbre you chose, and I would not have
guessed that they were actually almost 10 cents respectively narrow
and wide of 4:3 and 3:2.

The modal flavor sounds Dorian or Aeolian to me, and your setting fits
it nicely. Those beautiful minor thirds of around 277 cents are what I
term _Monzian thirds_ (or in Latin _tertiae Monzianae_) after Joe
Monzo, who for one of his pieces sought the ideal tuning for a certain
third and selected 279 cents by ear, then deciding on a just ratio of
75:64 or around 275 cents. Thus I use the term for a third somewhere
around 274-280 cents, with 26-EDO right in the middle of the range.

A scale in 26-EDO with some neutral intervals occurs to me which could
actually be seen as a tempered version of a beautiful JI tuning by the
Persian theorist Ibn Sina with steps of 14:13-13:12-8:7 in each
tetrachord (or 128-139-231 cents). Here the two neutral seconds are
equal (3 tuning steps), and the 8:7 is virtually just, a notable
interval as Herman Miller has described here.

0 138 277 508 692 831 969 1200
0 3 6 11 15 18 21 26
138 138 231 184 138 138 231
3 3 5 4 3 3 5

! 26EDO-IbnSina.scl
!
Tempering of Ibn Sina's 1/1-14/13-7/6-4/3-3/2-21/13-7/4-2/1
7
!
138.46154
276.92308
507.69231
692.30769
830.76923
969.23077
2/1

This includes the small neutral third of 18 steps at 831 cents, very
close to a just 21:13, and a 3-step neutral second very close to
13:12. Ibn Sina's 7:4 minor seventh is also virtually just.

However, the main point is your beautiful piece, whose charming and
deep consonance reminds me a bit, curiously, of Hudson Lacerda's piece
a bit back in George Secor's 17-tone well-temperament -- a piece in
quite a different tuning system, yet with a certain resemblance.

Congratulations, with peace and love,

Margo

Margo Schulter wrote:

> A scale in 26-EDO with some neutral intervals occurs to me which could
> actually be seen as a tempered version of a beautiful JI tuning by the
> Persian theorist Ibn Sina with steps of 14:13-13:12-8:7 in each
> tetrachord (or 128-139-231 cents). Here the two neutral seconds are
> equal (3 tuning steps), and the 8:7 is virtually just, a notable
> interval as Herman Miller has described here.
> > 0 138 277 508 692 831 969 1200
> 0 3 6 11 15 18 21 26
> 138 138 231 184 138 138 231
> 3 3 5 4 3 3 5
> > ! 26EDO-IbnSina.scl
> !
> Tempering of Ibn Sina's 1/1-14/13-7/6-4/3-3/2-21/13-7/4-2/1
> 7
> !
> 138.46154
> 276.92308
> 507.69231
> 692.30769
> 830.76923
> 969.23077
> 2/1

That's a nice sounding scale (I like scales with lots of neutral seconds). It could be interesting to start with a scale like this and fill in the other notes of a 12-note per octave keyboard to have a range of different scales to pick from. Here's one possibility I came up with, having a diatonic scale on the white keys; I'm sure there are many other ways of filling in the extra notes that would make sense.

! 12of26-IbnSina-plus.scl
!
Tempering of Ibn Sina's 1/1-14/13-7/6-4/3-3/2-21/13-7/4-2/1
12
!
138.46154
184.61538
276.92308
369.23077
507.69231
553.84615
692.30769
830.76923
876.92308
969.23077
1061.53846
2/1