Collective Reply once more

Salam'un aleykum brother Yahya,

This was the message that I prepared 12 days ago:

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

I’m finally back from Izmir. I have just this day for a collective response
to all the messages centering on Turkish Tanburs and Maqam Music Tuning
before I leave for Moscow.

First, let me post the revised 79 MOS out of 159tET that I have chosen to
implement on my Qanun:

|
0: 1/1 C
1: 15.092 cents C/| D\Y/
2: 30.185 cents C|) DY/
3: 45.277 cents C/|\ DY)
4: 60.369 cents C||) D\!!!/
5: 75.461 cents C||\ D!!!)
6: 90.554 cents C/||\ D\!!!
7: 105.646 cents C/||| D\!!/
8: 120.738 cents C|||) D!!/
9: 135.830 cents C/|||\ D!!)
10: 150.923 cents CX) D\!/
11: 166.015 cents CX\ D!)
12: 181.107 cents C/X\ D\!
13: 196.200 cents D
14: 211.292 cents D/| E\Y/
15: 226.384 cents D|) EY/
16: 241.476 cents D/|\ EY)
17: 256.569 cents D||) E\!!!/
18: 271.661 cents D||\ E!!!)
19: 286.753 cents D/||\ E\!!!
20: 301.845 cents D/||| E\!!/
21: 316.938 cents D|||) E!!/
22: 332.030 cents D/|||\ E!!)
23: 347.122 cents DX) E\!/
24: 362.215 cents DX\ E!)
25: 377.307 cents D/X\ E\!
26: 392.399 cents E
27: 407.491 cents E/| F\!!/
28: 422.584 cents E|) F!!/
29: 437.676 cents E/|\ F!!)
30: 452.768 cents E||) F\!/
31: 467.860 cents E||\ F!)
32: 482.953 cents E/||\ F\!
33: 498.045 cents F
34: 513.137 cents F/| G\Y/
35: 528.230 cents F|) GY/
36: 543.322 cents F/|\ GY)
37: 558.414 cents F||) G\!!!/
38: 573.506 cents F||\ G!!!)
39: 588.599 cents F/||\ G\!!!
40: 603.691 cents F/||| G\!!/
41: 618.783 cents F|||) G!!/
42: 633.875 cents F/|||\ G!!)
43: 648.968 cents FX) G\!/
44: 664.060 cents FX\ G!)
45: 679.152 cents F/X\ G\!
46: 701.955 cents G
47: 717.047 cents G/| A\Y/
48: 732.140 cents G|) AY/
49: 747.232 cents G/|\ AY)
50: 762.324 cents G||) A\!!!/
51: 777.416 cents G||\ A!!!)
52: 792.509 cents G/||\ A\!!!
53: 807.601 cents G/||| A\!!/
54: 822.693 cents G|||) A!!/
55: 837.785 cents G/|||\ A!!)
56: 852.878 cents GX) A\!/
57: 867.970 cents GX\ A!)
58: 883.062 cents G/X\ A\!
59: 898.155 cents A
60: 913.247 cents A/| B\Y/
61: 928.339 cents A|) BY/
62: 943.431 cents A/|\ BY)
63: 958.524 cents A||) B\!!!/
64: 973.616 cents A||\ B!!!)
65: 988.708 cents A/||\ B\!!!
66: 1003.800 cents A/||| B\!!/
67: 1018.893 cents A|||) B!!/
68: 1033.985 cents A/|||\ B!!)
69: 1049.077 cents AX) B\!/
70: 1064.170 cents AX\ B!)
71: 1079.262 cents A/X\ B\!
72: 1094.354 cents B
73: 1109.446 cents B/| C\!!/
74: 1124.539 cents B|) C!!/
75: 1139.631 cents B/|\ C!!)
76: 1154.723 cents B||) C\!/
77: 1169.815 cents B||\ C!)
78: 1184.908 cents B/||\ C\!
79: 1200.000 cents C

(All the decimals are actually rounded off, since no higher resolution can
be ascertained by the instrument maker.)

Here is my response to George:

I see that the sa79 notation is not displayed correctly on the SCALA
keyboard. Instead of the apotome sharp and flat, I get to see their
enharmonical respellings. Shouldn’t the apotome accidentals have the
priority with keyboard mapping?

The compatibility of basic 79MOS notation with 72tET is all the more
encouraging. Probably this means that the AFMM orchestra can interpret and
perform 79MOS when reading 72tET notation.

I like the way F# can be made enharmonically equivalent to Gb this way:

C-(702)-G-(694)-D-(702)-A-(694)-E-(702)-B-(694)-F#

C-(702)-F-(709)-Bb-(702)-Eb-(694)-Ab-(702)-Db-(702)-Gb

Such flexibility in notation is crucial to the correct representation of
Maqams.

I experimented with the 159, 19, 38 and 57n notations, but am most
comfortable when starting out with E79. I can then re-interpret all the
notes depending on the fifth I may use in the cycle. Thus, E can be the
26th, 27th or even the 28th step depending on my preferance. Hence the
distinction between Rast and Suz-i Dilara is only a matter of theoretical
nuance, not notational jargon.

While I understand that notating 159 requires 7 symbols per half-tone, you
should realize that I allow myself to use only 3 up to the apotome. The
first should be the Tartini quarter-tone sharp/flat, the second should be
the slashed flat in Maqam Music and its sharp equivalent, and the third
should be the regular sharp and flat. All the pitches of 79 MOS should be
represented by this arrangement.

True, 41 won’t work anymore, but 123 might. I found this to be the smallest
ET (41*3) that suits the kind of notational twizzle I have in mind.

For theory on paper, I have revised the 55 MOS out of 277tET:

0: 1/1 C unison, perfect prime
1: 21.654 cents C)
2: 43.308 cents C))
3: 64.962 cents C#(
4: 86.617 cents C# Db(
5: 108.271 cents C#) Db
6: 129.925 cents Db)
7: 151.579 cents D((
8: 173.233 cents D(
9: 194.887 cents D
10: 216.541 cents D)
11: 238.195 cents D))
12: 259.850 cents D#(
13: 281.504 cents D# Eb(
14: 303.158 cents D#) Eb
15: 324.812 cents Eb)
16: 346.466 cents E((
17: 368.120 cents E(
18: 389.774 cents E
19: 411.428 cents E) Fb
20: 433.083 cents E)) Fb)
21: 454.737 cents E#( F((
22: 476.391 cents E# F(
23: 498.045 cents F
24: 519.699 cents F)
25: 541.353 cents F))
26: 563.007 cents F#(
27: 584.662 cents F# Gb(
28: 606.316 cents F#) Gb
29: 627.970 cents Gb)
30: 649.624 cents G((
31: 671.278 cents G(
32: 701.955 cents G
33: 723.609 cents G)
34: 745.263 cents G))
35: 766.917 cents G#(
36: 788.572 cents G# Ab(
37: 810.226 cents G#) Ab
38: 831.880 cents Ab)
39: 853.534 cents A((
40: 875.188 cents A(
41: 896.842 cents A
42: 918.496 cents A)
43: 940.150 cents A))
44: 961.805 cents A#(
45: 983.459 cents A# Bb(
46: 1005.113 cents A#) Bb
47: 1026.767 cents Bb)
48: 1048.421 cents B((
49: 1070.075 cents B(
50: 1091.729 cents B
51: 1113.383 cents B) Cb
52: 1135.038 cents B)) Cb)
53: 1156.692 cents B#( C((
54: 1178.346 cents B# C(
55: 1200.000 cents C

However, the transition from one notation to another will be pretty rough
due to these fifths that border perceptual insanity:

692.932 cents
701.955 cents
714.586 cents

Still, one may think of 55 MOS as 55tET and thus calibrate the pitches and
carry the leftover 30.677 cent comma to any degree for correct scale
transpositions.

Of course I realize that 55 and 79 MOS are well-temperaments where scale
transpositions won’t be exact at certain degrees given their static
irregular nature, and in notation these will accumulate to become a
nuisance. But no equal temperament less than 120 would do and those are
simply too voluminous for practical usage. What I have in mind is a dynamic,
flexible MOS.

When I spoke of my desire to modulate freely, I did not mean an exact
transposition, but a fairly accurate transposition. 7.5 cents error is
thus acceptable for my tastes.

As for transposing through all of 159 tones, it was Gene’s idea of
dismissing 79 in favor of the monster. By no means do I desire to think of
79 as a MOS out of 159 tET, but a distinct temperament in its own right.

I require to transpose the Maqamat through 17 traditional pitches that are
more or less defined within 19tET. Trust me, 79 barely suffices and I am
pushing the limit in Qanun construction with my selection.

31 tones are just too many starting points for the Maqamat, the same goes
for 38. The reason I need as many tones as 79 arises from the fusion of
Usshaq, Saba, Huzzam, Segah and Suz-I Dilara over 17 traditional pitch
clusters. I need a 43tET kind of notation, and I would love to hear how you
would employ diacritical marks to indicate the step numbers in such a case.

I like your revision of 53tET to mean 53 pitch clusters, which in effect is
159tET yet again, and the standart mapping would lead to Suz-i Dilara, not
Rast. For Rast, you would need F C G D A< E<< B<<, which is not acceptable
at all. But I assume you would use all-naturals for those pitches even
though we are sticking to the 53 comma per octave argument that is
inevitably Pythagorean in nature. If the concern is the preservation of the
9-comma dichotomy, why not 55 MOS then?

Yes, I have observed myself that a chain of meantone fifths (92deg159) in
159 completes a cycle, and I observe with satisfaction that you have
proposed a shrewd notational scheme that only requires the Tartini symbols.
However, the usage of Tartini symbols in 38 is all wrong. Please consider a
43 notation like this:

C C+ C++ C# Db Db/ Dd D

Yes, I concur that ease of transposition is highly important to consider,
but it cannot usurp the throne of Rast, which MUST be notated as a natural C
Major scale without any accidentals whatsoever.

If we are searching for an equal temperament without making any regrettable
sacrifices as Gene also pointed out, then the correct choice is obviously
E165A (55*3). Now only if we could notate this as 55tET, all our problems
will be solved.

Your excellent contribution to Maqam Music is very much appreciated dear
George. I for one have benefitted immensely from our discourse and look
forward to the next sequel.

Cordially,
Ozan

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

Here is my long-awaited response to Yahya:

I am very glad to see your enthusiasm in Maqam Music Theory dear brother.
Indeed, the haven of Maqams is vast and I am pleased you shared your
research with the tuning list community in my absence. I am also glad to
have entertained you with that little quatrain of mine and hope that the
humor eased the pain of your sprained hand a little. :)

So, let me see what you have done here…

*
Rast:
C 0 197 Meantone
D 197 197 Meantone
E 394 94 Minor semitone
F 498 197 Meantone
G 695 197 Meantone
A 892 197 Meantone
B 1089 111 Minor semitone (111.731 minor diatonic semitone)
C' 1200
*

According to the revised 79 MOS, the Rast Scale is this:

0: 1/1 C +196
1: 196.200 cents D +196
2: 392.399 cents E +106
3: 498.045 cents F +204
4: 701.955 cents G +196
5: 898.155 cents A +196
6: 1094.354 cents B +106
7: 1200.000 cents C

It is a habit of this maqam to lower the third and seventh degrees of the
diatonical major scale by a step of 79 MOS when descending.

*
Altered Rast:
C 0 197 Meantone
D 197 212 Large Meantone
E 409 89 Sub-Minor semitone (90.225 limma, Pythagorean minor second)
F 498 197 Meantone
G 695 212 Large Meantone
A 907 89 Sub-Minor semitone (90.225 limma, Pythagorean minor second)
Bb 996 204 Major whole tone (203.910 major whole tone)
C' 1200
*

No need to alter Rast anymore with revised 79MOS, since 27/16 A is optimally
represented by 898 cents. For 5/3, one only needs to use 883 cents. The
cycle of fifths does not allow for a bearable leap to 5/3 in Rast however.
This pitch is reserved for the Segah Maqam and is reached from E to A by a
slightly wide fifth.

*
Suz-i Dilara:
C 0 212 Large Meantone
D 212 212 Large Meantone
E 424 74 Triquitone
F 498 212 Large Meantone
G 710 212 Large Meantone
A 922 212 Large Meantone
B 1134 66 Tristone (66.765 Pythagorean double diminished third)
C' 1200

Altered Suz-i Dilara:
C 0 212 Large Meantone
D 212 207 Large Major tone
E 409 89 Sub-Minor semitone (90.225 limma, Pythagorean minor second)
F 498 212 Large Meantone
G 710 197 Meantone
A 907 212 Large Meantone
B 1119 81 Small Sub-Minor semitone
C' 1200
*

According to revised 79 MOS, the Susie triplets are these:

0: 1/1 C unison, perfect prime
1: 196.200 cents D
2: 407.491 cents E
4: 498.045 cents F
5: 701.955 cents G
5: 898.155 cents A
7: 1109.446 cents B
9: 1200.000 cents C

(which is so close to Rast that little Susie can be ignored)

0: 1/1 C unison, perfect prime
1: 211.292 cents D
2: 407.491 cents E
4: 498.045 cents F
5: 701.955 cents G
6: 913.247 cents A
7: 1109.446 cents B
9: 1200.000 cents C

(which is strictly a Pythagorean Major, or Susie with braids.)

0: 1/1 C unison, perfect prime
1: 211.292 cents D
2: 422.583 cents E
4: 498.045 cents F
5: 701.955 cents G
6: 913.247 cents A
7: 1124.538 cents B
9: 1200.000 cents C

(which is the good-looking blonde girl that attracts the eye)

While I agree with you that the step sizes are plentiful and the object of
temperament is generally accepted as optimizing the number of meaningful
intervals, I am nevertheless bound to 79 MOS as a means of modestly
expressing Maqams transposed to all of the 17 traditional pitch-clusters.
The fact that I am consigning to a 7.5 cent error should tell you that 79 is
a really constricted solution for Qanuns, and I would not think anyone can
come up with something better to serve my purposes.

The step-sizes seen in Rast and Suz-i Dilara correspond to these intervals:

196: Meantone (9/8 and 10/9)
204: Untempered Wholetone (9/8)
211: Super-Pythagorean Wholetone (9/8)

106: Apotome (16/15 and 2187/2048)
90: Limma (20/19 and 256/243)
75: Classical Chromatic Semitone (25/24)

I hope I am not missing out any significant intervals in the analysis. SCALA
gives me these intervals per size between 68-212 cents:

4: 4 68.080 cents
5: 74 75.461 cents
5: 5 83.172 cents
6: 73 90.554 cents
6: 6 98.264 cents
7: 72 105.646 cents
7: 7 113.356 cents
8: 71 120.738 cents
8: 8 128.449 cents
9: 70 135.830 cents
9: 9 143.541 cents
10: 69 150.923 cents
10: 10 158.633 cents
11: 68 166.015 cents
11: 11 173.725 cents
12: 67 181.107 cents
12: 12 188.818 cents
13: 66 196.200 cents
13: 13 203.910 cents
14: 65 211.292 cents

I have already sacrificed a lot before deciding on 79 MOS. However, I find
7.5 cents error (variation) to be tolerable. I surmise that the timbre of
the Qanun shall incline favorably towards this temperament solution.

I would like to be able to think in terms of 55tET via E165A though. Now
that would lead to a historically sound proposition. However, you cannot use
55ET for the Qanuns, Tanburs, and other fretted Maqam Music instruments
unless you have the ability to move the frets. The Qanuns, due to their
static construction, are out of the league, and require either the 79 MOS
suggested, or its siblings 55 and 67 to be implemented.

I don’t know why some members react unfavorably towards 79, when obviously
it is the upper limit to optimally conflated practical temperaments compared
to such monsters as 159. The fact that most think the idea of making the
Tanbur frets immovable ought to be the last thing that should be done shows
the impossibility of expressing centenary tunings on the neck of string
instruments. The Qanun is the clear exception to this case and I have
every intention of exploiting this provision.

Cordially,
Ozan

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

Here is my response to Gene and co:

I think I answered most of your questions in my replies to George and Yahya.
I am displeased that you disregard 79MOS because of a maximum of 7.5 cents
error. You also forget that this is only meant for the Qanuns. What would
you propose then?

For a complete catalog of Maqam scales in JI terms, you should wait for my
doctorate thesis. There, I will attempt to show that the old `phenomenal`
theorists (despite their respectable contributions) did not always propose
or concern themselves with the correct solutions to Maqam Music Theory, and
their purpose was more of glorifying a timeless past and a biased
pre-disposition than actually measuring the pitches used. The notation issue
is equally messed up. Utilizing these sources as a means to justify the
Arel-Ezgi theory falls short of actual practice. It was afterall Farabi’s
dictum that:

`If the proposals made by theorists contradict the actual practice of
performers, the mistaken party are the theorists, not the practitioners.`

Sadly, some members choose to follow the lead of the mistaken theorists
rather than renown practitioners. Really, people who have never in their
life measured the frequencies of a musical genre they analyze are entitled
to total oblivion. Now, that and copy-pasting those like Signell who made
little or no contribution to actual pitch measurements in Maqam Music is
truly uninspiring. Even worse is the case where, the screeching desire by
performers to abandon the established `thousand-year old theory` known to us
all in favor of `haphazard fretting`, is interpreted as a gesture of
`musical expression`.

My senior colleague *Jon* Akkoc’s research cannot be dismissed blatently, or
brushed aside in wanton burlesque. He is right in saying that the works of
such great masters as Farabi, Safiyuddin and co were probably based on “ad
hoc meditations.” Hoping that he won’t be upset with me for quoting him,
here is what he says:

"I can never forget a comment made by a Western musicologist (forgot his
name though ) trying to solve the *mystery* of sounds and tuning systems
used in Indian music. After watching the pitches used by master musicians on
a computer screen during a live performance, he says something to the
effect, *they were not even using the pitches they said they were using*.

Tanbur might be a very difficult instrument for Turkish music because of its
frets, moveable or not. I would not go to the bank with what has been placed
in books, the internet, and otherwise in the way of *standard* tuning,
regardless of the signature underneath."

Here is what Carl says regarding this matter, which I hope is not intrusive
on my part to post here:

`A working intonation theory for non-fixed-pitch instruments simply
doesn't exist, and would have been virtually impossible to create it
before the advent of digital measurement tools.

Even for fixed pitch instruments limited (mainly) to the Western
tradition, only in the last 10 years, on the tuning and tuning-math
lists, has a satisfactory explanation of intonation come to light.`

Which brings me to Kraig’s words:

` While i think that Ozan is probably correct in in stating that 53
cannot accommodate a description of this music , i find the idea of a 79
subset of 159 really out in left field and lacks a real continuity with its
own history.one option is that one is dealing with a movable 53 tone system
which is almost impossible to measure, due to variation being due to the
context in which certain things are played.the concept is not so different
that 12 ET where the intonation varies in much the same degree as the charts
your painstaking analysis shows with this music.

I believe one of the best methods would be to have an instrument where the
players could pick out the intervals one at a time and adjust them to what
they hear, as what someone plays is not always what one would play given
enough time to play it without the limitations of the instruments. I think
that boomlitter and creel have a method that would apply well to examining
this music.`

My response to this would be that we have already done such measurements.
Even without them, I could tell which pitches the seyir of a particular
maqam demands. My ongoing experiments with the midi equipment at my disposal
clearly tells me that the `thousand year old theory` is wrong, terribly
wrong, both in pitch measurement, and in notation. This is why Maqam Music
is stuck in historical platitudes and thus, cannot progress.

Kraig also says:

`There also appears to be that there is much concern within your
group of Turkish musician to preserve a particular school or tradition.
It is quite hard to get a sense of the limits and range of interest as
to what it differentiates itself from and for what reasons, which might
be useful in understanding all the dynamics that are going on.
There are always rival schools and it it is important to understand how they
manifest and interact with each other. While there are names here we
associate with turkish music, these people seem to be possibly unknown to
Ozan for example, and i for one would like to understand, how such things
happen.`

The reference was to Talip Ozkan, who is known around here as a folk artist,
with possible interest in Maqam Music. More prominent examples include
Tanburi Djemil, Erjumend Batanay and Nedjdet Yashar, who should obviously be
taken as basis when investigating authentic Maqam Music performance. In
fact, it is said that the current Tanbur style of playing is owing to
Tanburi Djemil himself, since all other styles are practically lost to us.

It is a wonder, how a Fasil music incorporating Violins, Kemenchas, Ouds and
Tanburs can handle different tuning systems when they are performing in
unison! Equally baffling is how 5/4 and 8192/6561 can be considered to be
identical when even Rauf Yekta complains that 5/4 is used instead of the
3-limit pythagorean diminished fourth by the practitioners of his era.

The pitches given in this address
http://www.turkmusikisi.com/calgilar/tanbur/tanbur.htm clearly contradict
the fret system of the tanbur picture seen on the same page. Apparently
someone is not doing his work.

As for http://www.uam.es/personal_pdi/filoyletras/jsango/MapaTone/Tanbur.htm

3. 34th descending 3/2 is
18014398509481984/16677181699666569 = 133.53 ¢
or approx. 13/12 = 138.57 ¢.

4. 22nd descending 3/2 is
34359738368/31381059609 = 156.99 ¢
or approx. 12/11 = 150.64 ¢.

Just as I said, Maqam Music uses 13/12 and 12/11, not the ridiculously
complex 3-limit ratios given.

Cordially,
Ozan Yarman

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

Finally, here is my response to Michael Zapf:

Dear Michael, your interest and knowledge in Maqam Music is very inspiring.
It seems you have already amassed the critical resources for understanding
this genre. I’m afraid a dissertation matching your request does not exist
as yet, and may be available if I can ever get to write my doctorate thesis
on Maqam Music Theory in English. For starters, let me tell you that you
have selected the right instrument by studying the Ney. All the pitches
found in almost every corner of the Middle-East can be produced by this
crude reed-flute. Surprisingly enough, so little study is made on it, and
its construction is still largely a mystery. Apparently, tradition overrides
research and development when Ney is in question.

There are 9 basic Ney Ahengs in Maqam Music Theory:

Bolahenk {Nisfiye} (means half, the octave of tanbur tuning), Rast=D4
Sip-Bol Mabeyn (means middle, half-tone)
Sipurde, Rast=C4
Mustahzen, Rast=B3
Kiz-Mus Mabeyn
Kiz, Rast=A3
Man-Kiz Mabeyn
Mansur, Rast=G3
Shah-Man Mabeyn
Shah, Rast=F3
Davud, Rast=E3

Anything beyond Davud is impossible to play due to enormous sizes. Even Shah
is challenging for most people.

For construction details, you may want to obtain Suleyman Ergunet’s book
titled “Ney-Metod”. Let me know if you can’t find it.

Dervish is my cousin, not nephew as I wrongly referred the first time. As I
said, that would make me look old! ;) If it will interest you, I tend to
play the Ney a little and can give you some tips later on. For starters, you
should know that Maqam Music pitches are relative frequency clusters, not
absolute frequencies as wrongly expressed by most. Think of them as
diatonical degrees for building Maqam scales.

Cordially,
Ozan

----- Original Message -----
From: Yahya Abdal-Aziz
To: tuning@yahoogroups.com
Sent: 14 Temmuz 2005 Perşembe 7:04
Subject: [tuning] Re: Dave Keenan's scales

Ozan,

You wrote:
> Brother Yahya, I'm wondering if you ever received my lenghty response on
Maqam Music tuning prior to my Moscow journey > from which I returned
recently.
>
> Cordially,
> Ozan

Yes, I'm sure I did, an I appreciated it, but having searched
thru the digests for the past month, still can't find it. :-(

Would you mind terribly telling me the approximate date, or
even posting a link to the message on Yahoo?

Wa `alaikum salam,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.323 / Virus Database: 267.8.14/48 - Release Date: 13/7/05

Hi Ozan,

I see by adopting 79MOS you have sorted out some of the
difficulties - and also corrected my arithmetic. :-)

Still, we have far too many interval sizes remaining for
the resulting system to be very regular, don't we?

I wonder why you would not instead stick to exact JI ratios ...

You wrote: " I am nevertheless bound to 79 MOS as a means
of modestly expressing Maqams transposed to all of the 17
traditional pitch-clusters." Is this the requirement? Can you
not effect those transpositions at all with exact JI intervals?

It sounds that you regard 79MOS as the best available
compromise solution for Qanuns, but as not suitable for
tanbur. Can you effectively make music using both
instruments at once, if they are tuned to different pitch
standards? I can't see it ...

Regards,
Yahya

Original message:

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

Here is my long-awaited response to Yahya:
I am very glad to see your enthusiasm in Maqam Music Theory dear brother.
Indeed, the haven of Maqams is vast and I am pleased you shared your
research with the tuning list community in my absence. I am also glad to
have entertained you with that little quatrain of mine and hope that the
humor eased the pain of your sprained hand a little. :)
So, let me see what you have done here�
*
Rast:
C 0 197 Meantone
D 197 197 Meantone
E 394 94 Minor semitone
F 498 197 Meantone
G 695 197 Meantone
A 892 197 Meantone
B 1089 111 Minor semitone (111.731 minor diatonic semitone)
C' 1200
*
According to the revised 79 MOS, the Rast Scale is this:
0: 1/1 C +196
1: 196.200 cents D +196
2: 392.399 cents E +106
3: 498.045 cents F +204
4: 701.955 cents G +196
5: 898.155 cents A +196
6: 1094.354 cents B +106
7: 1200.000 cents C
It is a habit of this maqam to lower the third and seventh degrees of the
diatonical major scale by a step of 79 MOS when descending.

*
Altered Rast:
C 0 197 Meantone
D 197 212 Large Meantone
E 409 89 Sub-Minor semitone (90.225 limma, Pythagorean minor second)
F 498 197 Meantone
G 695 212 Large Meantone
A 907 89 Sub-Minor semitone (90.225 limma, Pythagorean minor second)
Bb 996 204 Major whole tone (203.910 major whole tone)
C' 1200
*

No need to alter Rast anymore with revised 79MOS, since 27/16 A is optimally
represented by 898 cents. For 5/3, one only needs to use 883 cents. The
cycle of fifths does not allow for a bearable leap to 5/3 in Rast however.
This pitch is reserved for the Segah Maqam and is reached from E to A by a
slightly wide fifth.

*
Suz-i Dilara:
C 0 212 Large Meantone
D 212 212 Large Meantone
E 424 74 Triquitone
F 498 212 Large Meantone
G 710 212 Large Meantone
A 922 212 Large Meantone
B 1134 66 Tristone (66.765 Pythagorean double diminished third)
C' 1200

Altered Suz-i Dilara:
C 0 212 Large Meantone
D 212 207 Large Major tone
E 409 89 Sub-Minor semitone (90.225 limma, Pythagorean minor second)
F 498 212 Large Meantone
G 710 197 Meantone
A 907 212 Large Meantone
B 1119 81 Small Sub-Minor semitone
C' 1200
*

According to revised 79 MOS, the Susie triplets are these:
0: 1/1 C unison, perfect prime
1: 196.200 cents D
2: 407.491 cents E
4: 498.045 cents F
5: 701.955 cents G
5: 898.155 cents A
7: 1109.446 cents B
9: 1200.000 cents C
(which is so close to Rast that little Susie can be ignored)
0: 1/1 C unison, perfect prime
1: 211.292 cents D
2: 407.491 cents E
4: 498.045 cents F
5: 701.955 cents G
6: 913.247 cents A
7: 1109.446 cents B
9: 1200.000 cents C
(which is strictly a Pythagorean Major, or Susie with braids.)

0: 1/1 C unison, perfect prime
1: 211.292 cents D
2: 422.583 cents E
4: 498.045 cents F
5: 701.955 cents G
6: 913.247 cents A
7: 1124.538 cents B
9: 1200.000 cents C
(which is the good-looking blonde girl that attracts the eye)

While I agree with you that the step sizes are plentiful and the object of
temperament is generally accepted as optimizing the number of meaningful
intervals, I am nevertheless bound to 79 MOS as a means of modestly
expressing Maqams transposed to all of the 17 traditional pitch-clusters.
The fact that I am consigning to a 7.5 cent error should tell you that 79 is
a really constricted solution for Qanuns, and I would not think anyone can
come up with something better to serve my purposes.
The step-sizes seen in Rast and Suz-i Dilara correspond to these intervals:
196: Meantone (9/8 and 10/9)
204: Untempered Wholetone (9/8)
211: Super-Pythagorean Wholetone (9/8)
106: Apotome (16/15 and 2187/2048)
90: Limma (20/19 and 256/243)
75: Classical Chromatic Semitone (25/24)
I hope I am not missing out any significant intervals in the analysis. SCALA
gives me these intervals per size between 68-212 cents:
4: 4 68.080 cents
5: 74 75.461 cents
5: 5 83.172 cents
6: 73 90.554 cents
6: 6 98.264 cents
7: 72 105.646 cents
7: 7 113.356 cents
8: 71 120.738 cents
8: 8 128.449 cents
9: 70 135.830 cents
9: 9 143.541 cents
10: 69 150.923 cents
10: 10 158.633 cents
11: 68 166.015 cents
11: 11 173.725 cents
12: 67 181.107 cents
12: 12 188.818 cents
13: 66 196.200 cents
13: 13 203.910 cents
14: 65 211.292 cents

I have already sacrificed a lot before deciding on 79 MOS. However, I find
7.5 cents error (variation) to be tolerable. I surmise that the timbre of
the Qanun shall incline favorably towards this temperament solution.
I would like to be able to think in terms of 55tET via E165A though. Now
that would lead to a historically sound proposition. However, you cannot use
55ET for the Qanuns, Tanburs, and other fretted Maqam Music instruments
unless you have the ability to move the frets. The Qanuns, due to their
static construction, are out of the league, and require either the 79 MOS
suggested, or its siblings 55 and 67 to be implemented.
I don�t know why some members react unfavorably towards 79, when obviously
it is the upper limit to optimally conflated practical temperaments compared
to such monsters as 159. The fact that most think the idea of making the
Tanbur frets immovable ought to be the last thing that should be done shows
the impossibility of expressing centenary tunings on the neck of string
instruments. The Qanun is the clear exception to this case and I have
every intention of exploiting this provision.
Cordially,
Ozan
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Dear Yahya,

Far be it for me to correct your arithmetic, I merely pointed out the way to obtain better results with the revised 79 MOS.

If it is a matter of regularity, here are the SCALA facts about 79 MOS 159tET:

-- Interval properties --
Smallest one step interval : 15.092 cents
Average step (divided formal octave) : 15.190 cents
Average / Smallest step : 1.006467
Largest one step interval : 22.803 cents
Largest / Average step : 1.501179
Largest / Smallest step : 1.510887
Linear approximation average step : 15.1901 cents
Number of one step interval sizes : 2
Median interval of one step : 15.092 cents
Most common interval of one step : 15.092 cents, amount: 78

Scale is strictly proper
Scale has Myhill's property
generators: 1 of 15.0923 cents and 78 of 1184.9077 cents
Scale is maximally even for L / S <= 2
Scale is distributional even
Scale contains two identical "tetrachords" of 34 notes
Scale is a Constant Structure, by a margin of 7.382 cents

Number of different intervals : 156 = 2.00000 / class
Smallest interval difference : 7.382 cents
Most common intervals : 15.092 cents & inv., amount: 78
Scale is a chain of 39 triads 0.0 588.599 1184.908 cents
Number of recognisable fifths : 203, average 702.014 cents
Number of appreciable fifths : 111, average 701.791 cents
Rothenberg stability : 1.000000 = 1
Lumma stability : 0.498821
Rothenberg efficiency : 0.675105 redundancy : 0.324895
Efficiency x scale size : 53.333333
Inversional symmetry on degrees :
6
Inversional symmetry on intervals :
45-46

Formal octave complements present : 67 = 84.8101%
-- Statistical properties --
Standard deviation of one step : 0.8620 cents
Skew of one step intervals : 0.0000 cents
Average distance from equal tempered : 1.9971 cents, 0.131473 steps
Standard deviation from equal tempered : 2.3161 cents, 0.152476 steps
Maximum distance from equal tempered : 4.3920 cents, 0.289141 steps
Geometric average of pitches 0..n : 599.422 cents
Arithmetic average of pitches 0..n : 635.026 cents
Harmonic average of pitches 0..n : 563.817 cents
Geometric average of pitches 1..n-1 : 599.407 cents
Arithmetic average of pitches 1..n-1 : 633.276 cents
Harmonic average of pitches 1..n-1 : 565.538 cents
Geometric average of pitches 1..n : 607.009 cents
Arithmetic average of pitches 1..n : 641.742 cents
Harmonic average of pitches 1..n : 572.276 cents

Seems to me that 79 MOS is pretty regular for a MOS. How else would you have me map Rast and Suz-i Dilara both unto the white keys then?

As an alternative, here is 67 MOS 135tET:

|
0: 1/1 C unison, perfect prime
1: 17.771 cents C)
2: 35.542 cents C7
3: 53.313 cents C7) DbL(
4: 71.084 cents C#( DbL
5: 88.855 cents C# Db(
6: 106.626 cents C#) Db
7: 124.397 cents C#7 Db)
8: 142.168 cents C#7) DL(
9: 159.939 cents DL
10: 177.710 cents D(
11: 195.481 cents D
12: 213.252 cents D)
13: 231.023 cents D7
14: 248.794 cents D7) EbL(
15: 266.565 cents D#( EbL
16: 284.336 cents D# Eb(
17: 302.107 cents D#) Eb
18: 319.878 cents D#7 Eb)
19: 337.649 cents D#7) EL(
20: 355.420 cents EL
21: 373.191 cents E(
22: 390.962 cents E
23: 408.733 cents E) Fb
24: 426.504 cents E7 Fb)
25: 444.275 cents E7) FL(
26: 462.046 cents E#( FL
27: 479.817 cents E# F(
28: 497.588 cents F
29: 515.359 cents F)
30: 533.130 cents F7
31: 550.901 cents F7) GbL(
32: 568.672 cents F#( GbL
33: 586.443 cents F# Gb(
34: 604.214 cents F#) Gb
35: 621.985 cents F#7 Gb)
36: 639.756 cents F#7) GL(
37: 657.527 cents GL
38: 675.298 cents G(
39: 702.412 cents G
40: 720.183 cents G)
41: 737.954 cents G7
42: 755.725 cents G7) AbL(
43: 773.496 cents G#( AbL
44: 791.267 cents G# Ab(
45: 809.038 cents G#) Ab
46: 826.809 cents G#7 Ab)
47: 844.580 cents G#7) AL(
48: 862.351 cents AL
49: 880.122 cents A(
50: 897.893 cents A
51: 915.664 cents A)
52: 933.435 cents A7
53: 951.206 cents A7) BbL(
54: 968.977 cents A#( BbL
55: 986.748 cents A# Bb(
56: 1004.519 cents A#) Bb
57: 1022.290 cents A#7 Bb)
58: 1040.061 cents A#7) BL(
59: 1057.832 cents BL
60: 1075.603 cents B(
61: 1093.374 cents B
62: 1111.145 cents B) Cb
63: 1128.916 cents B7 Cb)
64: 1146.687 cents B7) CL(
65: 1164.458 cents B#( CL
66: 1182.229 cents B# C(
67: 1200.000 cents C

And here is a neat 12-tone well temperament from it:

0: 1/1 C Dbb unison, perfect prime
1: 88.855 cents C# Db
2: 195.481 cents D Ebb
3: 284.336 cents D# Eb
4: 390.962 cents E Fb
5: 497.588 cents F Gbb
6: 586.443 cents F# Gb
7: 702.412 cents G Abb
8: 791.267 cents G# Ab
9: 897.893 cents A Bbb
10: 986.748 cents A# Bb
11: 1093.374 cents B Cb
12: 1200.000 cents C Dbb

JI ratios? They do not bode well with transpositions over a wide selection of pitches. Surely you do not claim to be able to execute a Chopin etude on a JI keyboard? The same is true for Maqam Music. That is why 53-tET has been chosen by many when performing this genre. Still, 53 is not a correct represenation of Maqam pitches, not by a long shot (unless you consign your thinking to the Yekta-Arel-Ezgi perde-ratios), however 106 may do (due to the marginal 690 cent fifth):

C
702
G
702
D
690
A
690
E
702
B
702
F#/Gb
702
C#/Db
702
G#/Ab
702
D#/Eb
702
A#/Bb
702
F
702
C

0: 1/1 C Dbb unison, perfect prime
1: 90.566 cents C# Db
2: 203.774 cents D Ebb
3: 294.340 cents D# Eb
4: 384.906 cents E Fb
5: 498.113 cents F Gbb
6: 588.679 cents F# Gb
7: 701.887 cents G Abb
8: 792.453 cents G# Ab
9: 894.340 cents A Bbb
10: 996.226 cents A# Bb
11: 1086.792 cents B Cb
12: 2/1 C Dbb octave

If you can transpose all maqam scales over 17-traditional pitch clusters in JI terms, by all means do so, for I have failed myself due to great variances observed.

I did not say 79MOS was not suitable for Tanburs. I am merely considering it solely for Qanuns at the moment. For all I know, the neck of tanburs can accomodate 79 frets quite easily.

As to your question:

Can you effectively make music using both
instruments at once, if they are tuned to different pitch
standards? I can't see it ...

If you can't see it, listen to a Maqam Music ensemble perform, with Qanuns at 72tET, tanburs at 53tET, Kemenchas with JI and Neys with Adaptive Tuning. You will see what I mean.

Hopefully, the mess will be cleared by an optimal solution like the one I came up with.

Cordially,
Ozan
----- Original Message -----
From: Yahya Abdal-Aziz
To: Tuning group at yahoo
Sent: 18 Temmuz 2005 Pazartesi 5:32
Subject: [tuning] Re: Collective Reply once more

Hi Ozan,

I see by adopting 79MOS you have sorted out some of the
difficulties - and also corrected my arithmetic. :-)

Still, we have far too many interval sizes remaining for
the resulting system to be very regular, don't we?

I wonder why you would not instead stick to exact JI ratios ...

You wrote: " I am nevertheless bound to 79 MOS as a means
of modestly expressing Maqams transposed to all of the 17
traditional pitch-clusters." Is this the requirement? Can you
not effect those transpositions at all with exact JI intervals?

It sounds that you regard 79MOS as the best available
compromise solution for Qanuns, but as not suitable for
tanbur. Can you effectively make music using both
instruments at once, if they are tuned to different pitch
standards? I can't see it ...

Regards,
Yahya