Re: [tuning] Meantone Maqams

Dear Gene,
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 07 Haziran 2005 Salı 5:37
Subject: [tuning] Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:

> It is with great excitement that I wish to proclaim that I
determined (after several days of trial and error) 43tET to be an
excellent basic choice in both the JI approximation and the proper
notation of Maqam Music in general.

This is extemely interesting; it suggests you can notate Maquam music
very nicely using Western-style sharps and flats. 43-et is a good
compromise between the advocates of 55 and 31, and since it is almost
precisely the same as 1/5-comma, has excellent historical credentials
also.

I'm so glad that you are in alignment with me. But you also need the quarter-tone accidentals for the rest of the pitches adjacent to the natural/sharped/flattened ones, as I will demonstrate below.

``It appears that nothing other than dense meantone ETs with a
generator of ~698 cents suffice for the job.''

So what's a dense meantone et?

Dense, as in, meantones with high pitch resolution above and including 43tET.

``This means that East and West may musically converge without
perceptual barriers at long last. For a better representation, 67tET
(which I notice is not claimed or used by anyone yet according to
`Monzopedia`) is even better with a 43tET mapping.''

Now it gets confusing. That is a good enough 5-limit meantone, but in
the 7-limit one might want to use a different version of septimal
meantone, with an otonal tetrad given by C:E:G:G### rather than
C:E:G:A#. Is this the mapping you'd use? You also skipped over 55; how
does that work for Maquam music?

Why, on second thought, I think 55 is much better than 67. I shall use then 55tET on my Qanun, since it is also very good in 29-limit. Considering its advantages, its closeness to 53, its historical foundations, and ease of adaptability to the 9-comma per whole-tone way of thinking, I find strong arguments in favor of 55. Then, the mapping would be close to that of 31tET, a perfect representation of Maqam Music perdes:

0: 1/1 C unison, perfect prime (Rast)
1: 21.818 cents C+ Dbb
2: 43.636 cents C+ Dbb
3: 65.455 cents C# Ddb
4: 87.273 cents C# Ddb
5: 109.091 cents C#+ Db
6: 130.909 cents C#+ Db
7: 152.727 cents Cx Dd
8: 174.545 cents Cx Dd
9: 196.364 cents D (Dugah)
10: 218.182 cents D+ Ebb
11: 240.000 cents D+ Ebb
12: 261.818 cents D# Edb
13: 283.636 cents D# Edb
14: 305.455 cents D#+ Eb
15: 327.273 cents D#+ Eb
16: 349.091 cents Dx Ed
17: 370.909 cents Dx Ed (Segah)
18: 392.727 cents E (Segah)
19: 414.545 cents E+ Fb
20: 436.364 cents E+ Fb
21: 458.182 cents E# Fd
22: 480.000 cents E# Fd
23: 501.818 cents F (Chargah)
24: 523.636 cents F+ Gbb
25: 545.455 cents F+ Gbb
26: 567.273 cents F# Gdb
27: 589.091 cents F# Gdb
28: 610.909 cents F#+ Gb (Saba)
29: 632.727 cents F#+ Gb (Saba)
30: 654.545 cents Fx Gd
31: 676.364 cents Fx Gd
32: 698.182 cents G (Neva)
33: 720.000 cents G+ Abb
34: 741.818 cents G+ Abb
35: 763.636 cents G# Adb
36: 785.455 cents G# Adb
37: 807.273 cents G#+ Ab
38: 829.091 cents G#+ Ab
39: 850.909 cents Gx Ad (Hisar)
40: 872.727 cents Gx Ad (Hisar)
41: 894.545 cents A (Huseini)
42: 916.364 cents A+ Bbb
43: 938.182 cents A+ Bbb
44: 960.000 cents A# Bdb
45: 981.818 cents A# Bdb
46: 1003.636 cents A#+ Bb
47: 1025.455 cents A#+ Bb
48: 1047.273 cents Ax Bd
49: 1069.091 cents Ax Bd (Evdj)
50: 1090.909 cents B (Evdj)
51: 1112.727 cents B+ Cb
52: 1134.545 cents B+ Cb
53: 1156.364 cents B# Cd
54: 1178.182 cents B# Cd
55: 2/1 C octave (Gerdaniye)

Then the otonal tetrad can be represented either way with just a single A#. Also, 43tET is still a perfect match.

``In fact, I believe I'm on the verge of solving the
intonational/notational problems caused by the Yekta-Arel-Ezgi school
by utilizing only the quarter-tone (Tartini) accidentals proposed by
George Secor.''

Evidently you don't need quarter-tone accidentals at all.

I do, in order to express the other pitches that are represented by double flats and sharps enharmonically.

By the way, you might take a look at 103-et; this tuning can be used
as a very mild meantone (very roughly 1/7 comma vs the 1/6 comma of
67) but is also a miracle system. If it worked for Maquam music, as it
seems it might, you'd get a common meantone-miracle relationship to
Maquam music, which could concievably be useful.

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

Oh no, that number is way too high to convince people to accept a meantone solution, which is indispensible for inverse sharp/flat notation that Maqam Music inevitably requires. Why miracle at all?

Cordially,
Ozan

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

Could you give some of the Maqams in 43 or 55-et, or in extended
meantone notation?

> By the way, you might take a look at 103-et; this tuning can be used
> as a very mild meantone (very roughly 1/7 comma vs the 1/6 comma of
> 67) but is also a miracle system. If it worked for Maquam music, as it
> seems it might, you'd get a common meantone-miracle relationship to
> Maquam music, which could concievably be useful.

> Oh no, that number is way too high to convince people to accept a
meantone solution, which is indispensible for inverse sharp/flat
notation that Maqam Music inevitably requires. Why miracle at all?

Your switching from 43 to 67 made me think you wanted a sharper fifth,
and moreover from Helmholtz, admittedly not the best source, I had the
idea that originally Maqam music was Pythagorean, and that
Schismatic[17] would be good for the older tunings at any rate. The
Turkish use of 53-et suggested their version works like that still.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 07 Haziran 2005 Salı 23:30
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

Could you give some of the Maqams in 43 or 55-et, or in extended
meantone notation?

Not yet! That would be telling. Be a little patient, as I am still formulating my doctorate thesis.

---------

Your switching from 43 to 67 made me think you wanted a sharper fifth,
and moreover from Helmholtz, admittedly not the best source, I had the
idea that originally Maqam music was Pythagorean, and that
Schismatic[17] would be good for the older tunings at any rate. The
Turkish use of 53-et suggested their version works like that still.

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

I was looking for a sharper fifth, but I also prioritized the least number of pitches sufficient to express Maqam Music on every tone. Oh yes, Maqam Music is described as Pythagorean, but only on paper! See, not many understand the JI nature of this genre of music, and 53tET is evidently so wrong a representation of perdes. People just don't know what they hear. For one thing, they do not play the commas at all! It's all a rough approximation to them. Haven't you seen Can Akkoc's paper on this matter?

Eureka. I think 62tET might work in the majority of cases.

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 9:01
Subject: [tuning] Re: Meantone Maquams

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

> hi Gene and Ozan,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > If you need both meantone and Pythagorean fifths in
> > a single equal temperament, and if 12-et won't do, you
> > have to go with something like 270, because you must
> > have two different fifths.
>
>
> By my calculations, 92-edo is the first cardinality which
> gives you two different 5ths, one resembling the pythagorean
> 3/2 ratio and the other a ~1/3-comma meantone 5th.

I clicked "send" too soon on that one. I meant to
add the ~cents values for the two 92-edo 5ths:
704.3478261 and 691.3043478.

Also, i see that there are lower cardinality EDOs
which do get somewhat close to the two targets.
73-edo has ~706.8493151 and ~690.4109589 cents,
so it looks like the lowest cardinality which
could possibly qualify.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Eureka. I think 62tET might work in the majority of cases.

I thought you were looking for an EDO that gave two 5ths,
one close to meantone and one close to pythagorean.
The notes of 62-edo which could qualify as a "5th" are:

62-edo
degree .. ~cents

.. 35 .. 677.4193548
.. 36 .. 696.7741935
.. 37 .. 716.1290323

36 degrees is the 31-edo meantone 5th, but there's nothing
here resembling pythagorean.

?

-monz
http://tonalsoft.com
Tonescape microtonal music software

I have found out that a 79tET system with two fifths, 700 cents and 696.970 cents respectively might solve the problem admirably:

0: 1/1 C unison, perfect prime
1: 15.152 cents C/
2: 30.303 cents C//
3: 45.455 cents C^ Db(
4: 60.606 cents C) Dbv
5: 75.758 cents C#\ Db\\
6: 90.909 cents C# Db\
7: 106.061 cents C#/ Db
8: 121.212 cents C#// Db/
9: 136.364 cents C#^ D(
10: 151.515 cents C#) Dv
11: 166.667 cents D\\
12: 181.818 cents D\
13: 196.970 cents D
14: 212.121 cents D/
15: 227.273 cents D//
16: 242.424 cents D^ Eb(
17: 257.576 cents D) Ebv
18: 272.727 cents D#\ Eb\\
19: 287.879 cents D# Eb\
20: 303.030 cents D#/ Eb
21: 318.182 cents D#// Eb/
22: 333.333 cents D#^ E(
23: 348.485 cents D#) Ev
24: 363.636 cents E\\
25: 378.788 cents E\
26: 393.939 cents E
27: 409.091 cents E/ Fb
28: 424.242 cents E// Fb/
29: 439.394 cents E^ F(
30: 454.545 cents E) Fv
31: 469.697 cents E#\ F\\
32: 484.848 cents E# F\
33: 500.000 cents F
34: 515.152 cents F/
35: 530.303 cents F//
36: 545.455 cents F^ Gb(
37: 560.606 cents F) Gbv
38: 575.758 cents F#\ Gb\\
39: 590.909 cents F# Gb\
40: 606.061 cents F#/ Gb
41: 621.212 cents F#// Gb/
42: 636.364 cents F#^ G(
43: 651.515 cents F#) Gv
44: 666.667 cents G\\
45: 681.818 cents G\
46: 696.970 cents G
47: 712.121 cents G/
48: 727.273 cents G//
49: 742.424 cents G^ Ab(
50: 757.576 cents G) Abv
51: 772.727 cents G#\ Ab\\
52: 787.879 cents G# Ab\
53: 803.030 cents G#/ Ab
54: 818.182 cents G#// Ab/
55: 833.333 cents G#^ A(
56: 848.485 cents G#) Av
57: 863.636 cents A\\
58: 878.788 cents A\
59: 893.939 cents A
60: 909.091 cents A/
61: 924.242 cents A//
62: 939.394 cents A^ Bb(
63: 954.545 cents A) Bbv
64: 969.697 cents A#\ Bb\\
65: 984.848 cents A# Bb\
66: 1000.000 cents A#/ Bb
67: 1015.152 cents A#// Bb/
68: 1030.303 cents A#^ B(
69: 1045.455 cents A#) Bv
70: 1060.606 cents B\\
71: 1075.758 cents B\
72: 1090.909 cents B
73: 1106.061 cents B/ Cb
74: 1121.212 cents B// Cb/
75: 1136.364 cents B^ C(
76: 1151.515 cents B) Cv
77: 1166.667 cents B#\ C\\
78: 1181.818 cents B# C\
79: 2/1 C octave

Notice the beautiful arrangement of the sharps/flats the size of a limma. This bodes extremely well for the Hijaz tetrachord: D Eb F# G.

Now, the issue remains as to how all these pitches can be expressed by the few symbols learned by maqam musicians today.

Also, how will it be possible to make the distinction between Rast (Zarlino major) and Suz-i Dilara (Pythagorean major)?

Cordially,
Ozan

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 6:54
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> For one thing, a Zarlino diatonical gamut with the 6th alterating by
a syntonic comma is the Rast scale, and MUST be notated as
C-D-E-F-G-A-B-C without any accidentals whatsoever.

This is just a diatonic gamut with the sixth not altered by anything.
If it is required that you have this in your system of scales, a
tuning system which can handle meantone does make sense, which makes
24-et rather marginal, and bodes ill for 53 or 65.

> If I do so, however, and choose any one of 41, 53 or 65 ETs with a
near-pure fifth, I must use your 5-comma flat for the 3rd and 7th
degrees, and for the 6th degree when the occasion demands it.

It's not really the same scale when you use the commas, but that might
not matter if you are not going to use harmony.

HOWEVER, I must avoid this at all costs. Rast scale for all
instruments must be notated as I delineated above.

But you must avoid it at all costs--then, back to 43 or 55!

> The only way without sacrificing transposition over every key and
without requiring hundreds of ratios is by meantone temperaments above
43tET. However, then I am troubled by being unable to make the
distinction between Rast and Suz-i Dilara, 5-limit major and 3-limit
major.

If you need both meantone and Pythagorean fifths in a single equal
temperament, and if 12-et won't do, you have to go with something like
270, because you must have two different fifths.

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Sorry about that, it was a false alarm. No, I'm not looking for an EDO that gives two types of fifths if I can squeeze both Rast and Suz-i Dilara into the same pot. I was thinking, maybe a quick re-tuning will fix that problem with my Qanun. I think you should take a look at the last mail where I came up with a version of 79tET.

Ozan
----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 19:44
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Eureka. I think 62tET might work in the majority of cases.

I thought you were looking for an EDO that gave two 5ths,
one close to meantone and one close to pythagorean.
The notes of 62-edo which could qualify as a "5th" are:

62-edo
degree .. ~cents

.. 35 .. 677.4193548
.. 36 .. 696.7741935
.. 37 .. 716.1290323

36 degrees is the 31-edo meantone 5th, but there's nothing
here resembling pythagorean.

?

-monz
http://tonalsoft.com
Tonescape microtonal music software

Come to think of it, 79 tones with two fifths 694.245 cents and 701.955 cents seem much better:

0: 1/1 C unison, perfect prime
1: 15.092 cents C/
2: 30.185 cents C//
3: 45.277 cents C^ Db(
4: 60.369 cents C) Dbv
5: 75.461 cents C#\ Db\\
6: 90.554 cents C# Db\
7: 105.646 cents C#/ Db
8: 120.738 cents C#// Db/
9: 135.830 cents C#^ D(
10: 150.923 cents C#) Dv
11: 166.015 cents D\\
12: 181.107 cents D\
13: 196.200 cents D
14: 211.292 cents D/
15: 226.384 cents D//
16: 241.476 cents D^ Eb(
17: 256.569 cents D) Ebv
18: 271.661 cents D#\ Eb\\
19: 286.753 cents D# Eb\
20: 301.845 cents D#/ Eb
21: 316.938 cents D#// Eb/
22: 332.030 cents D#^ E(
23: 347.122 cents D#) Ev
24: 362.215 cents E\\
25: 377.307 cents E\
26: 392.399 cents E
27: 407.491 cents E/ Fb
28: 422.584 cents E// Fb/
29: 437.676 cents E^ F(
30: 452.768 cents E) Fv
31: 467.860 cents E#\ F\\
32: 482.953 cents E# F\
33: 498.045 cents F
34: 513.137 cents F/
35: 528.230 cents F//
36: 543.322 cents F^ Gb(
37: 558.414 cents F) Gbv
38: 573.506 cents F#\ Gb\\
39: 588.599 cents F# Gb\
40: 603.691 cents F#/ Gb
41: 618.783 cents F#// Gb/
42: 633.875 cents F#^ G(
43: 648.968 cents F#) Gv
44: 664.060 cents G\\
45: 679.152 cents G\
46: 694.245 cents G
47: 709.337 cents G/
48: 724.429 cents G//
49: 739.521 cents G^ Ab(
50: 754.614 cents G) Abv
51: 769.706 cents G#\ Ab\\
52: 784.798 cents G# Ab\
53: 799.890 cents G#/ Ab
54: 814.983 cents G#// Ab/
55: 830.075 cents G#^ A(
56: 845.167 cents G#) Av
57: 860.260 cents A\\
58: 875.352 cents A\
59: 890.444 cents A
60: 905.536 cents A/
61: 920.629 cents A//
62: 935.721 cents A^ Bb(
63: 950.813 cents A) Bbv
64: 965.905 cents A#\ Bb\\
65: 980.998 cents A# Bb\
66: 996.090 cents A#/ Bb
67: 1011.182 cents A#// Bb/
68: 1026.275 cents A#^ B(
69: 1041.367 cents A#) Bv
70: 1056.459 cents B\\
71: 1071.551 cents B\
72: 1086.644 cents B
73: 1101.736 cents B/ Cb
74: 1116.828 cents B// Cb/
75: 1131.920 cents B^ C(
76: 1147.013 cents B) Cv
77: 1162.105 cents B#\ C\\
78: 1177.197 cents B#\ C\\
79: 2/1 C octave

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 19:44
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Eureka. I think 62tET might work in the majority of cases.

I thought you were looking for an EDO that gave two 5ths,
one close to meantone and one close to pythagorean.
The notes of 62-edo which could qualify as a "5th" are:

62-edo
degree .. ~cents

.. 35 .. 677.4193548
.. 36 .. 696.7741935
.. 37 .. 716.1290323

36 degrees is the 31-edo meantone 5th, but there's nothing
here resembling pythagorean.

?

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I have found out that a 79tET system with two fifths, 700 cents and
696.970 cents respectively might solve the problem admirably:

I don't think you can notate things using a fixed scale as neatly as
with a regular temperament, but if you do not want or need to
transpose, it should work. But in that case, why not simply take all
of the notes used in all of the maqams as nearly as you can determine,
and call that your scale? Why do this at all?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Sorry about that, it was a false alarm. No, I'm not looking for an
EDO that gives two types of fifths if I can squeeze both Rast and
Suz-i Dilara into the same pot. I was thinking, maybe a quick
re-tuning will fix that problem with my Qanun. I think you should take
a look at the last mail where I came up with a version of 79tET.

What you came up with was a scale or gamut; it's not really a version
of 79-et or even close to being that. I'll take a look at it in Scala,
which you might try also.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Come to think of it, 79 tones with two fifths 694.245 cents and
701.955 cents seem much better:

This scale is so close (within 1/6 cent) to something in 159-et that I
think you may as well identify it as a 159-et scale. It has 58 steps
of size 2, and one of size 3. This makes it a MOS, with a generator of
2 steps of 159 equal.

159 actually turns up as a strong system in higher limits, 23-29
particularly.

One of the first things to note about 159 is that 159 = 3*53, and
159 represents the 5-limit in a "contorted" manner. This shouldn't be
a problem; 24 does the same thing and has been used to represent maqam
music for some time. 159, therefore, has the excellent fifth and good
major third of 53, but as I remarked it is really a high-limit system
considered as a way of approximating ratios.

Here is the 13-limit TM comma basis for 159:

{325/324, 364/363, 385/384, 625/624, 10976/10935}

There are all sorts of temperaments supported, but this is probably
not very relevant to maqam music.

I desire and need to transpose. Why not this 79 tone well-temperament with two consecutive generator fifths? The notation would be none other than that of 79tET, and that is why I have been constantly referring to it that way. Besides the values are so negligible in my sight that one can easily think in terms of 79ET.

But specifying all the ratios singly? Why, that would amount to hundreds of pitches that no one would know what to do with at a glance. Besides, the notation should be feasible, compact, comprehensible.

I will, of course, indicate all Maqams one by one with their specific ratios, but require a high-cardinality ET or near-ET notation to express them all. Thus, 79tET is the mapping I proposed for Qanuns. I would much rather notate these pitches with 31tET symbols though.

Cordially,
Ozan
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 22:44
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I have found out that a 79tET system with two fifths, 700 cents and
696.970 cents respectively might solve the problem admirably:

I don't think you can notate things using a fixed scale as neatly as
with a regular temperament, but if you do not want or need to
transpose, it should work. But in that case, why not simply take all
of the notes used in all of the maqams as nearly as you can determine,
and call that your scale? Why do this at all?

And what do you think I've been doing for the last week? I've over-worked Scala so much that the poor thing crashed two dozen times by now. Apparently, there are some `minor` bugs that need to be taken care of.

Cordially,
Ozan
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 22:47
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Sorry about that, it was a false alarm. No, I'm not looking for an
EDO that gives two types of fifths if I can squeeze both Rast and
Suz-i Dilara into the same pot. I was thinking, maybe a quick
re-tuning will fix that problem with my Qanun. I think you should take
a look at the last mail where I came up with a version of 79tET.

What you came up with was a scale or gamut; it's not really a version
of 79-et or even close to being that. I'll take a look at it in Scala,
which you might try also.

What about its notation? Can I have a 79, 55, 43 EDO meantone notation then?
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 23:18
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Come to think of it, 79 tones with two fifths 694.245 cents and
701.955 cents seem much better:

This scale is so close (within 1/6 cent) to something in 159-et that I
think you may as well identify it as a 159-et scale. It has 58 steps
of size 2, and one of size 3. This makes it a MOS, with a generator of
2 steps of 159 equal.

159 actually turns up as a strong system in higher limits, 23-29
particularly.

And what do you think of 110?
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 23:45
Subject: [tuning] 159 et

One of the first things to note about 159 is that 159 = 3*53, and
159 represents the 5-limit in a "contorted" manner. This shouldn't be
a problem; 24 does the same thing and has been used to represent maqam
music for some time. 159, therefore, has the excellent fifth and good
major third of 53, but as I remarked it is really a high-limit system
considered as a way of approximating ratios.

Here is the 13-limit TM comma basis for 159:

{325/324, 364/363, 385/384, 625/624, 10976/10935}

There are all sorts of temperaments supported, but this is probably
not very relevant to maqam music.

I made sure that the meantone fifth and the super-pythagorean fifth were equally apart, and indeed, this 79 tone system seems to be a sub-set of 159tET:

0: 1/1 C unison, perfect prime
1: 15.097 cents C/
2: 30.194 cents C//
3: 45.290 cents C^ Db(
4: 60.387 cents C) Dbv
5: 75.484 cents C#\ Db\\
6: 90.581 cents C# Db\
7: 105.678 cents C#/ Db
8: 120.774 cents C#// Db/
9: 135.871 cents C#^ D(
10: 150.968 cents C#) Dv
11: 166.065 cents D\\
12: 181.162 cents D\
13: 196.258 cents D
14: 211.355 cents D/
15: 226.452 cents D//
16: 241.549 cents D^ Eb(
17: 256.646 cents D) Ebv
18: 271.743 cents D#\ Eb\\
19: 286.839 cents D# Eb\
20: 301.936 cents D#/ Eb
21: 317.033 cents D#// Eb/
22: 332.130 cents D#^ E(
23: 347.227 cents D#) Ev
24: 362.323 cents E\\
25: 377.420 cents E\
26: 392.517 cents E
27: 407.614 cents E/ Fb
28: 422.711 cents E// Fb/
29: 437.807 cents E^ F(
30: 452.904 cents E) Fv
31: 468.001 cents E#\ F\\
32: 483.098 cents E# F\
33: 498.195 cents F
34: 513.291 cents F/
35: 528.388 cents F//
36: 543.485 cents F^ Gb(
37: 558.582 cents F) Gbv
38: 573.679 cents F#\ Gb\\
39: 588.775 cents F# Gb\
40: 603.872 cents F#/ Gb
41: 618.969 cents F#// Gb/
42: 634.066 cents F#^ G(
43: 649.163 cents F#) Gv
44: 664.260 cents G\\
45: 679.356 cents G\
46: 694.453 cents G
47: 709.550 cents G/
48: 724.647 cents G//
49: 739.744 cents G^ Ab(
50: 754.840 cents G) Abv
51: 769.937 cents G#\ Ab\\
52: 785.034 cents G# Ab\
53: 800.131 cents G#/ Ab
54: 815.228 cents G#// Ab/
55: 830.324 cents G#^ A(
56: 845.421 cents G#) Av
57: 860.518 cents A\\
58: 875.615 cents A\
59: 890.712 cents A
60: 905.808 cents A/
61: 920.905 cents A//
62: 936.002 cents A^ Bb(
63: 951.099 cents A) Bbv
64: 966.196 cents A#\ Bb\\
65: 981.292 cents A# Bb\
66: 996.389 cents A#/ Bb
67: 1011.486 cents A#// Bb/
68: 1026.583 cents A#^ B(
69: 1041.680 cents A#) Bv
70: 1056.777 cents B\\
71: 1071.873 cents B\
72: 1086.970 cents B
73: 1102.067 cents B/ Cb
74: 1117.164 cents B// Cb/
75: 1132.261 cents B^ C(
76: 1147.357 cents B) Cv
77: 1162.454 cents B#\ C\\
78: 1177.551 cents B# C\
79: 2/1 C octave
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Haziran 2005 Cuma 23:18
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Come to think of it, 79 tones with two fifths 694.245 cents and
701.955 cents seem much better:

This scale is so close (within 1/6 cent) to something in 159-et that I
think you may as well identify it as a 159-et scale. It has 58 steps
of size 2, and one of size 3. This makes it a MOS, with a generator of
2 steps of 159 equal.

159 actually turns up as a strong system in higher limits, 23-29
particularly.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I desire and need to transpose. Why not this 79 tone
well-temperament with two consecutive generator fifths?

I think calling it a MOS makes more sense; it seems to me that is what
it is.

The notation would be none other than that of 79tET, and that is why I
have been constantly referring to it that way. Besides the values are
so negligible in my sight that one can easily think in terms of 79ET.

You can't call it 79-et with any accuracy. It is not any such thing.

> I will, of course, indicate all Maqams one by one with their
specific ratios, but require a high-cardinality ET or near-ET notation
to express them all. Thus, 79tET is the mapping I proposed for Qanuns.
I would much rather notate these pitches with 31tET symbols though.

I'd suggest if you want the pitches of 159edo, which it seems you do,
then by all means use them. The 79 notes are a scale, not an equal
temperament. If you don't want to use all the notes of 159, then you'd
better make clear that you are *not* proposing 79-et. You don't want
to get the two confused, and it doesn't mean anyone has to rush out
and build an instrument with either 79 or 159 notes in an octave.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> What about its notation? Can I have a 79, 55, 43 EDO meantone
notation then?

Its pure fifths come in three chains of 53, so you can't notate just
with those. Certainly, you can notate it as a meantone EDO if you
like. The number of sharps and flats gets pretty ugly, and I'd suggest
more than that. It would be interesting to hear from George and Dave
on the subject of how they would go about notating 159 equal.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> And what do you think of 110?

As a meantone system, it's a contorted 55, and you would not notate it
pure in terms of sharps and flats, certainly. I don't see much point
in it; what's your idea for how it would be used?

As you say, I will call it a 79-note MOS scale out of 159tET. Is that pleasing enough?
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 7:11
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I desire and need to transpose. Why not this 79 tone
well-temperament with two consecutive generator fifths?

I think calling it a MOS makes more sense; it seems to me that is what
it is.

The notation would be none other than that of 79tET, and that is why I
have been constantly referring to it that way. Besides the values are
so negligible in my sight that one can easily think in terms of 79ET.

You can't call it 79-et with any accuracy. It is not any such thing.

> I will, of course, indicate all Maqams one by one with their
specific ratios, but require a high-cardinality ET or near-ET notation
to express them all. Thus, 79tET is the mapping I proposed for Qanuns.
I would much rather notate these pitches with 31tET symbols though.

I'd suggest if you want the pitches of 159edo, which it seems you do,
then by all means use them. The 79 notes are a scale, not an equal
temperament. If you don't want to use all the notes of 159, then you'd
better make clear that you are *not* proposing 79-et. You don't want
to get the two confused, and it doesn't mean anyone has to rush out
and build an instrument with either 79 or 159 notes in an octave.

I was trying to draw a parallel to 55tET, where 9 commas per whole tone understanding prevails, and is compatible with 53tET way of thinking to a great extent.
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 7:15
Subject: [tuning] Re: 159 et

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> And what do you think of 110?

As a meantone system, it's a contorted 55, and you would not notate it
pure in terms of sharps and flats, certainly. I don't see much point
in it; what's your idea for how it would be used?

So, can I or can I not use the notation of 79tET with the 79-tone MOS scale out of 159tET?
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 7:14
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> What about its notation? Can I have a 79, 55, 43 EDO meantone
notation then?

Its pure fifths come in three chains of 53, so you can't notate just
with those. Certainly, you can notate it as a meantone EDO if you
like. The number of sharps and flats gets pretty ugly, and I'd suggest
more than that. It would be interesting to hear from George and Dave
on the subject of how they would go about notating 159 equal.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> As you say, I will call it a 79-note MOS scale out of 159tET. Is
that pleasing enough?

It works for me. You can probably find a good enough definition in the
Monzopedia.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I was trying to draw a parallel to 55tET, where 9 commas per whole
tone understanding prevails, and is compatible with 53tET way of
thinking to a great extent.

I don't think that is a very big deal at all, but I'm afraid if you
want a multiple of 55 which has a fifth within a cent of pure, the
first example is 275-edo. That's five more notes to the octave than 270!.

Multiples of 19 are more interesting--152 and 171.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> So, can I or can I not use the notation of 79tET with the 79-tone
MOS scale out of 159tET?

I don't know what you mean by "the notation of 79et", but you can use
meantone notation; it would get a little ridiculous to use only that
for such a large scale with such a flat fifth, though. Your MOS
suggests a certain linear temperament, but not one I'd recommend
using. Again, Dave and George might have some notation suggestions.

How do you come up with all this stuff? I've been tiring myself out simply by the endless trials and errors. Pray tell.

BTW, 9-comma stuff is a big deal for me, because I want people here to make a smooth transition from the old way of thinking to the new.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 13:03
Subject: [tuning] Re: 159 et

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I was trying to draw a parallel to 55tET, where 9 commas per whole
tone understanding prevails, and is compatible with 53tET way of
thinking to a great extent.

I don't think that is a very big deal at all, but I'm afraid if you
want a multiple of 55 which has a fifth within a cent of pure, the
first example is 275-edo. That's five more notes to the octave than 270!.

Multiples of 19 are more interesting--152 and 171.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> How do you come up with all this stuff? I've been tiring myself out
simply by the endless trials and errors. Pray tell.

I've got a big collection of Maple routines which allows me to do all
kinds of things with tunings, temperaments and scales.

> BTW, 9-comma stuff is a big deal for me, because I want people here
to make a smooth transition from the old way of thinking to the new.

But that 9-comma business is only a footnote in Western tuning history.
Very few people would know about it and even fewer would care. Is
there some other 9-comma business I don't know about? If you want
something close to the old way of thinking as it is now in the West,
that would mean a multiple of 12, I suppose. Which, of course, has
already been tried.

I prefer the 5-diesis business to the 9-comma business myself.

Huh? Can you explain further what Maple routines are?

Everyone educated in Maqam Music in Turkey knows the 9-comma business. You cannot ignore this fact when proposing an alternative to the Yekta-Arel-Ezgi school. And I cannot care less for 12-tones per octave approach when Maqam Music is in question unless we are talking about transposing the entire mesh of intervals through half-tones.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 13:28
Subject: [tuning] Re: 159 et

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> How do you come up with all this stuff? I've been tiring myself out
simply by the endless trials and errors. Pray tell.

I've got a big collection of Maple routines which allows me to do all
kinds of things with tunings, temperaments and scales.

> BTW, 9-comma stuff is a big deal for me, because I want people here
to make a smooth transition from the old way of thinking to the new.

But that 9-comma business is only a footnote in Western tuning history.
Very few people would know about it and even fewer would care. Is
there some other 9-comma business I don't know about? If you want
something close to the old way of thinking as it is now in the West,
that would mean a multiple of 12, I suppose. Which, of course, has
already been tried.

I prefer the 5-diesis business to the 9-comma business myself.

How about alternating meantone and super-pythagorean notations then? Is that permissable? And what does George and Dave think of this?
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 13:18
Subject: [tuning] Re: Meantone Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> So, can I or can I not use the notation of 79tET with the 79-tone
MOS scale out of 159tET?

I don't know what you mean by "the notation of 79et", but you can use
meantone notation; it would get a little ridiculous to use only that
for such a large scale with such a flat fifth, though. Your MOS
suggests a certain linear temperament, but not one I'd recommend
using. Again, Dave and George might have some notation suggestions.

In a message dated 6/11/2005 10:22:27 AM Eastern Standard Time,
ozanyarman@superonline.com writes:
Everyone educated in Maqam Music in Turkey knows the 9-comma business.
This is also what Juilliard students are taught in New York City. French
pedagogue Rene Longy instituted this theory among her NYC and Boston students,
including Aaron Copland, Leonard Bernstein, George Gershwin.

I studied with her on the last year of her teaching at The Juilliard, when
she was stone deaf. This was my only class, as it was between degree studies.
I was working in the cafeteria making sandwiches at the same time.

It took me years to make the connection between "Pythagorean" tuning
principles and how the 5th part of the comma and the 4th part of the comma would
invert their spellings.

all best, Johnny Reinhard

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Huh? Can you explain further what Maple routines are?

Programs written in the language of the computer algebra system Maple.

> Everyone educated in Maqam Music in Turkey knows the 9-comma
business. You cannot ignore this fact when proposing an alternative to
the Yekta-Arel-Ezgi school. And I cannot care less for 12-tones per
octave approach when Maqam Music is in question unless we are talking
about transposing the entire mesh of intervals through half-tones.

159 certainly fits into the Turkish school excellently; it strikes me
as one reason to use it. I thought the 9-comma business you were
talking about was the division of a meantone tone into 9 parts by 55,
the division of the major whole tone by 53 into 9 parts is really a
different animal.

hi Gene,

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

> Ozan wrote:
>
> > BTW, 9-comma stuff is a big deal for me, because I
> > want people here to make a smooth transition from the
> > old way of thinking to the new.
>
> But that 9-comma business is only a footnote in Western
> tuning history.
> Very few people would know about it and even fewer would
> care. Is there some other 9-comma business I don't know
> about? If you want something close to the old way of
> thinking as it is now in the West, that would mean a
> multiple of 12, I suppose. Which, of course, has
> already been tried.

ah ... but Ozan isn't concerning himself with *Western*
tuning history, but rather with *Turkish*, which does
indeed have a long history of a 53-edo basis, at least
in theory.

-monz
http://tonalsoft.com
Tonescape microtonal music software

You mean the recently sprouted Turkish school based on 53tET. Turkish Qanuns are lately prepared according to 60tET, with 100 cent semi-tones. I find it quite appalling that some people here don't even have the faintest idea as to what would sound right for Maqams.

159 sounds appealing to me only because it is triple 53, and it would be a convincing argument in defense of my 79 MOS gamut.

The majority of Turkish musicians don't even know what size of a major whole tone they are dividing into 9 parts. Some even think, nay assert, that the pythagorean comma is the smallest audible interval. They really need to get their facts straight, or else, someone ought to show them the way to the moon.

I am personally against such macaronic attempts as `9-commas per whole tone` to justify biased theories that have no practical use in explaining musical genres.

Cordially,
Ozan

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Haziran 2005 Cumartesi 20:35
Subject: [tuning] Re: 159 et

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Huh? Can you explain further what Maple routines are?

Programs written in the language of the computer algebra system Maple.

> Everyone educated in Maqam Music in Turkey knows the 9-comma
business. You cannot ignore this fact when proposing an alternative to
the Yekta-Arel-Ezgi school. And I cannot care less for 12-tones per
octave approach when Maqam Music is in question unless we are talking
about transposing the entire mesh of intervals through half-tones.

159 certainly fits into the Turkish school excellently; it strikes me
as one reason to use it. I thought the 9-comma business you were
talking about was the division of a meantone tone into 9 parts by 55,
the division of the major whole tone by 53 into 9 parts is really a
different animal.

Indeed so Monz. But the Meantone Temperament out of that 79 MOS of mine is also extremely suitable for Western Tonal Music, and that is a welcome bonus:

12-note meantone out of 79 MOS from 159tET
|
0: 1/1 C unison, perfect prime
1: 90.575 cents
2: 196.245 cents D
3: 301.916 cents D# Eb
4: 392.491 cents
5: 498.162 cents F
6: 588.736 cents
7: 694.407 cents G
8: 784.982 cents G#\ Ab\
9: 890.653 cents
10: 996.323 cents A# Bb
11: 1086.898 cents
12: 2/1 C octave

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 12 Haziran 2005 Pazar 0:01
Subject: [tuning] Re: 159 et

hi Gene,

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

> Ozan wrote:
>
> > BTW, 9-comma stuff is a big deal for me, because I
> > want people here to make a smooth transition from the
> > old way of thinking to the new.
>
> But that 9-comma business is only a footnote in Western
> tuning history.
> Very few people would know about it and even fewer would
> care. Is there some other 9-comma business I don't know
> about? If you want something close to the old way of
> thinking as it is now in the West, that would mean a
> multiple of 12, I suppose. Which, of course, has
> already been tried.

ah ... but Ozan isn't concerning himself with *Western*
tuning history, but rather with *Turkish*, which does
indeed have a long history of a 53-edo basis, at least
in theory.

-monz
http://tonalsoft.com
Tonescape microtonal music software