80tET MOS

From the 13-limit ratios you have given here:

13/12, 9/8, 13/11, 14/11, 4/3, 13/9, 3/2, 11/7, 22/13, 16/9, 21/11, 2

I can tell that it contains many fundamental intervals used in Maqam Music. What do we get if we expand the scale to 17 tones?

--------------

It looks great for neo-Gothic music; I don't know enough to tell you if it is a grand idea for Turkish music but I suppose it might be. I think 17 notes of it instead of 12 would be nice.

--- In tuning-math@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> From the 13-limit ratios you have given here:
>
> 13/12, 9/8, 13/11, 14/11, 4/3, 13/9, 3/2, 11/7, 22/13, 16/9, 21/11, 2
>
> I can tell that it contains many fundamental intervals used in Maqam
Music. What do we get if we expand the scale to 17 tones?

We get something which looks downright interesting to me:

[1 22/21 13/12 9/8 13/11 16/13 14/11 4/3 18/13 13/9 3/2 11/7
13/8 22/13 16/9 13/7 21/11]

This 80-et detempered chain of fifths is actually a circle of fifths,
with the fifths going from one flat fifth of 691.681 cents, through
eight pure fifths, and then sharp fifths up to the single sharpest at
718.945 cents. The scale is epimorphic and constant structure as well
as strictly proper. It's 13-limit no-fives, and may be tempered using
80-equal, but could be a good basis for a well-tempering preserving
the circle of fifths.

! oz17.scl
80-et commas 13-limit detempering of a chain of 16 fifths
17
!
22/21
13/12
9/8
13/11
16/13
14/11
4/3
18/13
13/9
3/2
11/7
13/8
22/13
16/9
13/7
21/11
2

This 17-tone scale surprisingly contains all the maqams that I can come up with. Here are a few examples:

Rast degrees:

0, 3, 5, 7, 10, 13, 15, 17 rising
17, 14, 13, 10, 7, 5, 3, 0 falling

Usshaq degrees:

3, 5, 7, 10, 13, 14, 13, 10, 7, 5, 3, 0, 3
(15, 17, 20 instead for Huseyni)

Hijaz degrees:

3, 5, 8, 10, 13, 15, 17, 20, 17, 14, 13, 10, 8, 5, 3

Huzzam degrees:

5, 7, 10, 12, 15, 17, 15, 12, 10, 7, 5, 4, 5
(13 instead for Segah)

Karjighar degrees:

3, 5, 7, 10, 12, 15, 17, 20, 17, 15, 12, 10, 7, 5, 3

Nihavend degrees:

0, 3, 4, 7, 10, 11, 14, 17, 14, 11, 10, 7, 4, 3, 0
(1 instead for Kurdi)

----- Original Message -----
From: Gene Ward Smith
To: tuning-math@yahoogroups.com
Sent: 14 Mart 2005 Pazartesi 3:28
Subject: [tuning-math] Re: 80tET MOS

We get something which looks downright interesting to me:

[1 22/21 13/12 9/8 13/11 16/13 14/11 4/3 18/13 13/9 3/2 11/7
13/8 22/13 16/9 13/7 21/11]

This 80-et detempered chain of fifths is actually a circle of fifths,
with the fifths going from one flat fifth of 691.681 cents, through
eight pure fifths, and then sharp fifths up to the single sharpest at
718.945 cents. The scale is epimorphic and constant structure as well
as strictly proper. It's 13-limit no-fives, and may be tempered using
80-equal, but could be a good basis for a well-tempering preserving
the circle of fifths.

! oz17.scl
80-et commas 13-limit detempering of a chain of 16 fifths
17
!
22/21
13/12
9/8
13/11
16/13
14/11
4/3
18/13
13/9
3/2
11/7
13/8
22/13
16/9
13/7
21/11
2