26EDO-IbnSina

From: Margo Schulter (2007-02-12)
Subject: 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

From: Margo Schulter (2007-02-12)
Subject: 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

From: Herman Miller (2007-02-13)
Subject: Re: [MMM] Re: Organ Study #1 in 26 EDO

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