Yahoo Tuning Groups Ultimate Backup tuning A 7-limit version of the Idris Raghib Bey scale

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> In an attempt to figure out this scale, I had Scala fit it
> to equal temperaments, on which list nothing stood out, but
> I noticed 171 was on it. I used Scala's fitting to this, and
> then detempered the result to the 7-limit, obtaining a 7-limit
> version of the scale which I give below.
>
> <7-limit Scala file snipped>

thanks for doing this ... but i suggest that the primes
we're really looking for in this scale are most likely
3 and 11.

i do not claim to be any kind of expert on
Arab/Persian/Turkish music, but i do know that many of
the theorists from that part of the world have advocated
scales rife with ratios having those prime-factors.

having written that, it suddenly occurs to me why
24-edo would seem so attractive as a Westernized temperament
for "middle-eastern" music: prime-factors 3 and 11 are
exactly the two which are approximated very well by 24-edo.
this can be seen clearly on this two pages of mine:

http://tonalsoft.com/enc/edo-prime-error.htm

http://tonalsoft.com/enc/edo-11-odd-limit-error.htm

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> thanks for doing this ... but i suggest that the primes
> we're really looking for in this scale are most likely
> 3 and 11.
>
> i do not claim to be any kind of expert on
> Arab/Persian/Turkish music, but i do know that many of
> the theorists from that part of the world have advocated
> scales rife with ratios having those prime-factors.

This suggests the {2,3,11} rank 2 temperament with 243/242 as its
comma might be interesting. This has a half-fifth as a generator, the
mapping being given by

[<1 1 2|, <0 2 5|]

The 24 et, with a generator of 7 steps, is excellent for this scale,
and the 10 or 17 note MOS might be of interest. Another equal
temperament for it would be 65-et, with a generator of 19 steps; of
course this has the 10 and 17 MOS, and also a 24 note MOS. Of course
with 24-et in particular, it would be easy to interpret it in terms of
hemififths, a meantone-related temperament with two generators making
a meantone fifth, tempering out 81/80; this could be used as a
{2,3,5,11} system reasonably enough also.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> This suggests the {2,3,11} rank 2 temperament with 243/242 as its
> comma might be interesting.

If we take a chain of 16 11/9 generators for this and detemper, we get

1, 33/32, 12/11, 9/8, 32/27, 11/9, 81/64, 4/3, 11/8, 16/11, 3/2,
128/81, 18/11, 27/16, 16/9, 11/6, 64/33

This might be interesting, but people who don't follow tuning-math
might want to know about another scale which forms a very rough circle
of fifths and seems very well suited to Maqam music. Ozan's post
pointing this out is here:

/tuning-math/message/11798

My original post here:

/tuning-math/message/11788

🔗Ozan Yarman <ozanyarman@superonline.com>

Here is a list of 17-limit just intervals whose ratios do not exceed number eighteen. I found this when I tried to mix the scales Gene mentioned. It contains all the series involving the pattern 17/9 17/10 17/11 etc... Very palatable to my ears:

0: 1/1 0.000 unison, perfect prime
1: 18/17 98.955 Arabic lute index finger
2: 17/16 104.955 17th harmonic
3: 16/15 111.731 minor diatonic semitone
4: 15/14 119.443 major diatonic semitone
5: 14/13 128.298 2/3-tone
6: 13/12 138.573 tridecimal 2/3-tone
7: 12/11 150.637 3/4-tone, undecimal neutral second
8: 11/10 165.004 4/5-tone, Ptolemy's second
9: 10/9 182.404 minor whole tone
10: 9/8 203.910 major whole tone
11: 17/15 216.687
12: 8/7 231.174 septimal whole tone
13: 15/13 247.741
14: 7/6 266.871 septimal minor third
15: 13/11 289.210 tridecimal minor third
16: 6/5 315.641 minor third
17: 17/14 336.130 supraminor third
18: 11/9 347.408 undecimal neutral third
19: 16/13 359.472 tridecimal neutral third
20: 5/4 386.314 major third
21: 14/11 417.508 undecimal diminished fourth or major third
22: 9/7 435.084 septimal major third, BP third
23: 13/10 454.214 tridecimal diminished fourth
24: 17/13 464.428
25: 4/3 498.045 perfect fourth
26: 15/11 536.951 undecimal augmented fourth
27: 11/8 551.318 undecimal semi-augmented fourth
28: 18/13 563.382 tridecimal augmented fourth
29: 7/5 582.512 septimal or Huygens' tritone, BP fourth
30: 17/12 603.000 2nd septendecimal tritone
31: 10/7 617.488 Euler's tritone
32: 13/9 636.618 tridecimal diminished fifth
33: 16/11 648.682 undecimal semi-diminished fifth
34: 3/2 701.955 perfect fifth
35: 17/11 753.637
36: 14/9 764.916 septimal minor sixth
37: 11/7 782.492 undecimal augmented fifth
38: 8/5 813.686 minor sixth
39: 13/8 840.528 tridecimal neutral sixth
40: 18/11 852.592 undecimal neutral sixth
41: 5/3 884.359 major sixth, BP sixth
42: 17/10 918.642 septendecimal diminished seventh
43: 12/7 933.129 septimal major sixth
44: 7/4 968.826 harmonic seventh
45: 16/9 996.090 Pythagorean minor seventh
46: 9/5 1017.596 just minor seventh, BP seventh
47: 11/6 1049.363 21/4-tone, undecimal neutral seventh
48: 13/7 1071.702 16/3-tone
49: 15/8 1088.269 classic major seventh
50: 17/9 1101.045 septendecimal major seventh
51: 2/1 1200.000 octave

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 14 Mart 2005 Pazartesi 21:51
Subject: [tuning] Re: 243/242 and Arabic inspired music?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> This suggests the {2,3,11} rank 2 temperament with 243/242 as its
> comma might be interesting.

If we take a chain of 16 11/9 generators for this and detemper, we get

1, 33/32, 12/11, 9/8, 32/27, 11/9, 81/64, 4/3, 11/8, 16/11, 3/2,
128/81, 18/11, 27/16, 16/9, 11/6, 64/33

/tuning-math/message/11798

My original post here:

/tuning-math/message/11788

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

From: "Gene Ward Smith"

> If we take a chain of 16 11/9 generators for this and detemper, we get
>
> 1, 33/32, 12/11, 9/8, 32/27, 11/9, 81/64, 4/3, 11/8, 16/11, 3/2,
> 128/81, 18/11, 27/16, 16/9, 11/6, 64/33

In the Scala archive, that's "pipedum_17f.scl", with vertices 243/242 and 8192/8019.

> This might be interesting, but people who don't follow tuning-math
> might want to know about another scale which forms a very rough circle
> of fifths and seems very well suited to Maqam music. Ozan's post
> pointing this out is here:
>
> /tuning-math/message/11798

This should work well as an alternative to 17-TET. I don't really do much of anything with 13-limit, but 13/11 as a minor third and 16/13 as a neutral third are good ideas.

I said earlier about Idris Raghib's scale that the major third was wide, but I like that kind of tension you have in a 9/7-type major third (especially in a 7:9:11 "train whistle augmented" triad), or at least 81/64. Ozan's major third (14/11) lies between those notes.

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

From: "monz":

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
>> In an attempt to figure out this scale, I had Scala fit it
>> to equal temperaments, on which list nothing stood out, but
>> I noticed 171 was on it. I used Scala's fitting to this, and
>> then detempered the result to the 7-limit, obtaining a 7-limit
>> version of the scale which I give below.
>>
>> <7-limit Scala file snipped>
>
> thanks for doing this ... but i suggest that the primes
> we're really looking for in this scale are most likely
> 3 and 11.

It still includes Zalzal's 54/49 neutral second, again derived from the midpoint on the string between 1/1 and 27/22, which just happens to be 7-limit.

Al-Farabi listed ten divisions of the tetrachord, and four of them are linear averages; the three main notes are a succession of 9/8's. (Safi ad-Din al-Urmawi simply added more Pythagorean ratios.)

I think we solved the puzzle, however.

> i do not claim to be any kind of expert on
> Arab/Persian/Turkish music, but i do know that many of
> the theorists from that part of the world have advocated
> scales rife with ratios having those prime-factors.

I thought Persian and Turkish music made use of 5-limit a lot more, since it approximates extended Pythagorean so well.

Reminds me, I need to review Karadeniz's 41-tone. He seems to take 53-tone and average some of the pitches.

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Daniel A. Wier" <dawiertx@s...> wrote:
> From: "Gene Ward Smith"
>
> > If we take a chain of 16 11/9 generators for this and detemper, we get
> >
> > 1, 33/32, 12/11, 9/8, 32/27, 11/9, 81/64, 4/3, 11/8, 16/11, 3/2,
> > 128/81, 18/11, 27/16, 16/9, 11/6, 64/33
>
> In the Scala archive, that's "pipedum_17f.scl", with vertices
243/242 and
> 8192/8019.

Thanks; apparently Manuel has been adding more scales, as I don't have
it. That means it is a block scale, and 243/242 with 4096/3993 would
be another possibility.

> I like that kind of tension you have in a 9/7-type major third
(especially
> in a 7:9:11 "train whistle augmented" triad), or at least 81/64. Ozan's
> major third (14/11) lies between those notes.

What a useful name--"train whistle augmented". I'll have to keep it in
mind.

🔗monz <monz@tonalsoft.com>

hi Danny and Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Daniel A. Wier" <dawiertx@s...>
wrote:
> >
> > I like that kind of tension you have in a 9/7-type
> > major third (especially in a 7:9:11 "train whistle augmented"
> > triad), or at least 81/64. Ozan's major third (14/11) lies
> > between those notes.
>
> What a useful name--"train whistle augmented". I'll have
> to keep it in mind.

i like it too.

my interested was piqued by taking note of how close
11:7 is to 25:16, the typical 5-limit augmented-5th.

i've had 31-edo on my mind a lot lately, and just took
a look at how it does this ... turns out that 31-edo gives
decent approximations to both the "classic" 5-limit augmented
triad, and the train-whistle augmented. here's a comparison
of the JI, 31-edo, and 72-edo versions of these two chords:

triad and ~cents

JI 16:20:25, 0 - 386.3 - 772.6 (classic 5-limit augmented)
31-edo 0-11-20, 0 - 387.1 - 774.2
72-edo 0-23-47, 0 - 383.3 - 783.3

JI 7:9:11, 0 - 435 - 782.5 (train-whistle augmented)
31-edo 0-11-20, 0 - 425.8 - 774.2
72-edo 0-26-47, 0 - 433.3 - 783.3

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> JI 16:20:25, 0 - 386.3 - 772.6 (classic 5-limit augmented)
> 31-edo 0-11-20, 0 - 387.1 - 774.2

This should be 0-10-20

> 72-edo 0-23-47, 0 - 383.3 - 783.3

And this 0-23-46, 0 - 383.3 - 766.7

The classic 5-limit augmented triad in 1/4-kleismic marvel becomes

0 - 384.4 - 768.8

The 1 - 11/9 - 11/7 augmented triad in one version of 11-limit marvel is

0 - 347.4 - 780.2

🔗monz <monz@tonalsoft.com>

oops, my bad ... thanks, Gene.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > JI 16:20:25, 0 - 386.3 - 772.6 (classic 5-limit augmented)
> > 31-edo 0-11-20, 0 - 387.1 - 774.2
>
> This should be 0-10-20
>
> > 72-edo 0-23-47, 0 - 383.3 - 783.3
>
> And this 0-23-46, 0 - 383.3 - 766.7

however, 2^(47/72) is a possible alternate for
the augmented-5th ... but 2^(46/72) *is* the "standard"
one which follows the "rules" for how 72-edo approximates JI.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

From: "monz":

> hi Danny and Gene,

>> What a useful name--"train whistle augmented". I'll have
>> to keep it in mind.
>
> i like it too.

I'm not really sure it's a true train-whistle tuning (I'm sure they vary quite a lot), but when I plugged 7:9:11 into Scala and used a saxophone patch, it sure sounded like a locomotive engine horn I heard almost every day when I lived near the tracks in Nacogdoches, Texas. Back then I knew nothing about anything outside of 12-equal, but I could easily recognize it as an augmented chord in C or D-flat (not regarding any change in pitch by Doppler effect).

To me, the chord has an effect of tension and even terror, comparable to being stuck on the tracks with a train coming, blaring a C augmented triad. I find augmented chords more disturbing than diminished, which sound merely angry and aggressive to me.

> my interested was piqued by taking note of how close
> 11:7 is to 25:16, the typical 5-limit augmented-5th.
>
> i've had 31-edo on my mind a lot lately, and just took
> a look at how it does this ... turns out that 31-edo gives
> decent approximations to both the "classic" 5-limit augmented
> triad, and the train-whistle augmented. here's a comparison
> of the JI, 31-edo, and 72-edo versions of these two chords:

I've been playing with 41-tone scales, reinterpreting Karadeniz and Partch among other things. I just came up with a type of well-temperament involving the 18th root of 3^65/2^41, and I'm working on an extension of Yekta Bey's 24-tone Pythagorean, adding intermediary steps of the cube root of 256/243 and the square root of 134217728/129140163 (20480/19683 or 25/24 if you apply schismic alterations).

Which leads me to this: http://www.turkmuzigi.net/arastirmalar/ekoller_sistemler/. We need a translation.

Erv Wilson also came up with a 41-tone just scale, "wilson_41.scl" in the Scala archive.

> triad and ~cents
>
> JI 16:20:25, 0 - 386.3 - 772.6 (classic 5-limit augmented)
> 31-edo 0-11-20, 0 - 387.1 - 774.2
> 72-edo 0-23-47, 0 - 383.3 - 783.3

(As Gene stated earlier, 31-EDO should be 0-10-20, but you got the cents right.)

In 41-equal, that would be 0-13-26. 53-equal is a better approximation: 0-17-34.

> JI 7:9:11, 0 - 435 - 782.5 (train-whistle augmented)
> 31-edo 0-11-20, 0 - 425.8 - 774.2
> 72-edo 0-26-47, 0 - 433.3 - 783.3

41-tone: 0-15-27. 53 doesn't work so well, coming out as 0-19-34.5. The half-comma makes me think of Karadeniz again.