Pseudo-pythagorean???

Hi

Is "384edo-pseudo-pythagrean" a good term for scales like :
0
90.625
203.125
293.75
406.25
496.875
609.375
700.
790.625
903.125
993.75
1106.25
1196.875

With these pythagorean pattern ABABABAABABA and these 2 different divisions as limma and appotome:
A=90.625
B=112.5 and comma as 21.875 cent
It has these deviations from fifth chain of 3^(-6…..5):
1: -0.400
2: 0.785
3: 0.385
4: 1.570
5: 1.170
6: 2.355
7: 1.955
8: 1.555
9: 2.740
10: 2.340
11: 3.525
12: 3.125

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web siteوب سايت شاهين مهاجري <http://240edo.googlepages.com/>

My farsi page in Harmonytalk صفحه اختصاصي در هارموني تاك <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia شاهين مهاجري دردائره المعارف ويكي پديا <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
>
> Hi
>
> Is "384edo-pseudo-pythagrean" a good term for scales like :

The 384edo part makes sense, but I wouldn't call it any kind of
Pythagorean. It has six 12-et fifths of 700 cents in interval class
seven, and seven of size 703.125, 1 1/6 cent sharp, in class eight. It
also has a few well-in-tune major and minor thirds, so that you end up
with three each of nearly pure major and minor triads.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@> wrote:

> > Is "384edo-pseudo-pythagrean" a good term for scales like :
>
> The 384edo part makes sense, but I wouldn't call it any kind of
> Pythagorean.

Why 384, by the way? It's popped up on my radar screen as a tuning for
3136/3125-planar, and for misty temperament, but I doubt that has
anything to do with your choice of it. It's 12*32, which might be nice
for something.

Pseudo-pythagorean???You could probably call it that, but there is probably a better word for what you and I came up with. I just pulled the term "pseudo-Pythagorean" out of my head. The idea is a tuning that's similar to Pythagorean (and the diminished fourth corresponds to a just major third, etc.). 41- and 53-TET could be called "pseudo-Pythagorean" but there are better things to call them. Both are called "schismic", for example.

As Gene said, 384-EDO divides the 12-ET semitone by 32 equal parts, and a some microtunable synths tune in increments of a 64th of a semitone, or 768-EDO, so it could be used there, though I'd go ahead and use Pythagorean rounded to the nearest step in 768.

The JI scale I came up with was a rough approximation of Pythagorean using ratios where the denoninator was no more than 16 as much as possible. For the minor second, approximating 256/243, I had to go outside the square; you can use 21/20 or 22/21.

I extended the tuning to a 53-tone scale, up and down 26 fifths, and the worst fifth I got was 640/429 (~ 692.5131 cents), which occurs between the fifths 13/10-64/33 and 33/32-20/13.

~D.

----- Original Message ----- From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: Wednesday, February 07, 2007 9:05 AM
Subject: [tuning] Pseudo-pythagorean???

Hi

Is "384edo-pseudo-pythagrean" a good term for scales like :
0
90.625
203.125
293.75
406.25
496.875
609.375
700.
790.625
903.125
993.75
1106.25
1196.875
With these pythagorean pattern ABABABAABABA and these 2 different divisions as limma and appotome:
A=90.625
B=112.5 and comma as 21.875 cent

Hi

Now ,I resulted that the scale is a comperessed 5/74-schismatic temperament.Scala stretched it so we have:
0.
90.885
203.646
294.531
407.292
498.177
610.938
701.823
792.708
905.469
996.354
1109.115
1200.000
so if considering 701.955 and schisma as 1.953720788 and 5/74 schisma as we see that 701.823 is a 5/74-schisma tempered "5th".

i found that :

1) 1.823 * 12 = 21.876 which is very near to 7th degree of 383-EDO(21.932)
2) Best approximtion of it is 383-EDO.
3) By stretching it with -3.125 cent we have the main scale which is based on 384-EDO.
4) Comma of this scale is 21.876 cent
5) Mercator comma <http://tonalsoft.com/enc/m/mercator-comma.aspx> is -53 degree of tempered Pythagorean chain based on 701.823 which is 3.381 cents
6) wolf fifth is about 679.947 cent.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web siteوب سايت شاهين مهاجري <http://240edo.googlepages.com/>

My farsi page in Harmonytalk صفحه اختصاصي در هارموني تاك <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia شاهين مهاجري دردائره المعارف ويكي پديا <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Danny Wier
Sent: Thursday, February 08, 2007 1:13 AM
To: tuning@yahoogroups.com
Subject: Re: [tuning] Pseudo-pythagorean???

Pseudo-pythagorean???You could probably call it that, but there is probably
a better word for what you and I came up with. I just pulled the term
"pseudo-Pythagorean" out of my head. The idea is a tuning that's similar to
Pythagorean (and the diminished fourth corresponds to a just major third,
etc.). 41- and 53-TET could be called "pseudo-Pythagorean" but there are
better things to call them. Both are called "schismic", for example.

As Gene said, 384-EDO divides the 12-ET semitone by 32 equal parts, and a
some microtunable synths tune in increments of a 64th of a semitone, or
768-EDO, so it could be used there, though I'd go ahead and use Pythagorean
rounded to the nearest step in 768.

The JI scale I came up with was a rough approximation of Pythagorean using
ratios where the denoninator was no more than 16 as much as possible. For
the minor second, approximating 256/243, I had to go outside the square; you
can use 21/20 or 22/21.

I extended the tuning to a 53-tone scale, up and down 26 fifths, and the
worst fifth I got was 640/429 (~ 692.5131 cents), which occurs between the
fifths 13/10-64/33 and 33/32-20/13.

~D.

----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>
Sent: Wednesday, February 07, 2007 9:05 AM
Subject: [tuning] Pseudo-pythagorean???

Hi

Is "384edo-pseudo-pythagrean" a good term for scales like :
0
90.625
203.125
293.75
406.25
496.875
609.375
700.
790.625
903.125
993.75
1106.25
1196.875
With these pythagorean pattern ABABABAABABA and these 2 different divisions
as limma and appotome:
A=90.625
B=112.5 and comma as 21.875 cent