Re: [tuning] 79-tone Qanun

Hello,

Here are two pictures I took of my Qanun not very long ago:

http://www.ozanyarman.com/anonymous/Qanun1.JPG
http://www.ozanyarman.com/anonymous/Qanun2.JPG

Here is a not-so-recent recording I made with it:

http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3

There are 26 tricordi (3 strings tuned each to the unison) covering a range
of 3 and 1/2 octaves from A2 to E6, where the frequency of A4 is
specifically 440hz.

All the mandals (little metallic levers that alter the vibration lenghts)
from A2 to E5 are exactly 7-up for diatonical *harmonious* major scale
naturals (hence, this denotes the 0th position) and 8 more for sharps. The
rest of the levers decrease in number as the pitches rise. This is due to
the contraction of physical space as we move up the frequency ladder.
Therefore, we preserve the 0th and max-sharp positions while the spaces in
between are divided equally. This does not pose a serious problem, however,
as the pitches upward from E5 are much less sensitive to mistuning of
consonant interval relationships... that is to say, octave, fifths, fourths
and thirds on several keys in this register are more than tolerable.

Regarding sharp keys, it is perhaps desirable to go for +10 mandals (for
lower registers) to be on the safe side when transpositions involve double
sharp accidentals and where enharmonical equivalance of flat and sharp keys
are preserved in all cases.

As the mandals for all tricordi are raised or lowered to the 0th position,
the diatonical gamut becomes:

0: 1/1 A2--------54.8930 Hertz
1: 196.642 cents B 61.4960 Hertz
2: 302.526 cents C 65.3745 Hertz
3: 499.168 cents D 73.2382 Hertz
4: 701.955 cents E3--------82.3396 Hertz
5: 807.839 cents F 87.5327 Hertz
6: 1004.481 cents G 98.0618 Hertz
7: 1201.123 cents A3-------109.8573 Hertz
8: 1397.765 cents B 123.0718 Hertz
9: 1503.650 cents C 130.8339 Hertz
10: 1700.292 cents D 146.5715 Hertz
11: 1903.078 cents E4-------164.7860 Hertz
12: 2008.962 cents F 175.1791 Hertz
13: 2205.605 cents G 196.2509 Hertz
14: 2402.247 cents A4-------219.8573 Hertz
15: 2598.889 cents B 246.3033 Hertz
16: 2704.773 cents C 261.8377 Hertz
17: 2901.415 cents D 293.3333 Hertz
18: 3104.202 cents E---------329.7860 Hertz
19: 3210.086 cents F 350.5856 Hertz
20: 3406.728 cents G 392.7565 Hertz
21: 3603.370 cents A---------440.0000 Hertz
22: 3800.012 cents B 492.9263 Hertz
23: 3905.896 cents C 524.0152 Hertz
24: 4102.538 cents D 587.0474 Hertz
25: 4299.180 cents E---------657.6616 Hertz
26: 4405.064 cents F 699.1404 Hertz
27: 4601.706 cents G 783.2380 Hertz
28: 4798.349 cents A---------877.4513 Hertz
29: 5001.135 cents B 986.4924 Hertz
30: 5107.019 cents C 1048.7107 Hertz
31: 5303.661 cents D 1174.8569 Hertz
32: 5500.304 cents E---------1316.1770 Hertz

This tuning scheme equates to the traditional Sipurde Ahenk, where 440 hz
correlates to perde Huseyni (27/16... tempered or not) or its octave
derivatives. I advise against any other kind of setting whilst using Staff
Notation, as one should not treat the Qanun as if it was Key Transposable.
The current practice is another story altogether of course. Thus, mine is a
`Sipurde Qanun` flaunting 79 discrete pitches per octave by default.

The most prominent tradition hereabouts is that of Arel-Ezgi, based on the
24-tone Pythagorean system proposed first by Rauf Yekta. One can extract a
similar 24-tone tuning from my 79-tone thingamajig with maximum absolute
error of about 8 cents:

0: 1/1 C Dbb unison, perfect prime
1: 90.758 cents C# Db
2: 121.010 cents C#| Db-
3: 181.516 cents C## Dd
4: 211.768 cents D Ebb
5: 287.400 cents D# Eb
6: 317.653 cents D#| Eb-
7: 378.158 cents D## Ed
8: 408.410 cents E Dx
9: 499.168 cents F Gbb
10: 529.421 cents F| Gb=
11: 589.926 cents F# Gb
12: 620.179 cents F#| Gb-
13: 680.684 cents F## Gd
14: 701.955 cents G Abb
15: 792.713 cents G# Ab
16: 822.965 cents G#| Ab-
17: 883.471 cents G## Ad
18: 913.723 cents A Bbb
19: 989.355 cents A# Bb
20: 1019.608 cents A#| Bb-
21: 1080.113 cents A## Bd
22: 1110.365 cents B Ax
23: 1170.871 cents Cd
24: 1201.123 cents C Dbb

Moreover, one can close a cycle of 12-tones to have a neat well-temperament
when accompanying keyboards:

0: 1/1 C Dbb unison, perfect prime
1: 90.758 cents C# Db
2: 196.642 cents D Ebb
3: 302.526 cents D# Eb
4: 393.284 cents E Fb
5: 499.168 cents F Gbb
6: 589.926 cents F# Gb
7: 701.955 cents G Abb
8: 792.713 cents G# Ab
9: 898.597 cents A Bbb
10: 1004.481 cents A# Bb
11: 1095.239 cents B Cb
12: 1201.123 cents C Dbb
|
0: 0.000 cents 0.000 0 0 commas C
7: 701.955 cents -0.000 0 0 commas G
2: 695.810 cents -6.145 -189 -2/7 synt. commas D
9: 701.955 cents -6.145 -189 -2/7 synt. commas A
4: 695.810 cents -12.289 -377 -4/7 synt. commas E
11: 701.955 cents -12.289 -377 -4/7 synt. commas B
6: 695.810 cents -18.434 -566 -6/7 synt. commas F#
1: 701.955 cents -18.434 -566 -6/7 synt. commas C#
8: 701.955 cents -18.434 -566 -6/7 synt. commas G#
3: 710.937 cents -9.452 -290 Eb
10: 701.955 cents -9.452 -290 Bb
5: 695.810 cents -15.597 -479 F
12: 701.955 cents -15.597 -479 C
Average absolute difference: 11.8557 cents
Root mean square difference: 13.6922 cents
Maximum absolute difference: 18.4340 cents
Maximum formal fifth difference: 8.9817 cents

Other suggestions are the 41-tone out of 106-tET by Tore-Karadeniz, 53-tET
by such as Zeren and Sayan, an unpronounced 72-tET by Qanun makers, a 60-tET
study by Yavuzoglu, undetailed 17-tET by Akkoc and Karaosmanoglu, various JI
sketches and several whatnots by many others etc...

Earlier sources of Maqam Music expound a 17-tone system that is rather
arbitrary, if not Pythagorean. That is to say, certain pitches are treated
ultra-flexibly, whereas others are determinate. Arabs seem to have revived
the Farabian quarter-tones after Mushaqa and settled with 24-tET. Armenian
Qanuns sacrifice all but 12-tET. Persians could be using 22 `pitch-clusters`
per octave much like Indians and their sruti-system.

If you like hearing my amateurish opinion, the new and improved 79-tone MOS
out of practically 159-tET (not anymore I hope!) is the only sure means
serving both traditions and xenharmony in Maqam Music at the same time. It
is the ONLY system where high prime limit consonances are approximated
decently over all keys. I dare say this model will not only interest Turks,
but Arabs and Persians as well.

Cordially,
Oz.

----- Original Message -----
From: "J.Smith" <jsmith9624@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 08 Nisan 2006 Cumartesi 21:40
Subject: [tuning] 79-tone Qanun

>
> Oz,
>
> Do you mean 79 strings, or 79 discrete pitches, for that qanun? I
> would also like to ask you sometime, about what you would consider to
> be accurate and traditional tunings for various widely-used maqamat,
> if you are willing.
>
> Peace,
> jl
>

Uh... I made some mistakes with that table. Here it is again:

0: 1/1 A2--------109.8574 Hertz
1: 196.642 cents B 123.0718 Hertz
2: 302.526 cents C 130.8339 Hertz
3: 499.168 cents D 146.5716 Hertz
4: 695.810 cents E3--------164.2022 Hertz
5: 801.695 cents F 174.5585 Hertz
6: 1004.481 cents G 196.2509 Hertz
7: 1201.123 cents A3--------219.8573 Hertz
8: 1397.765 cents B 246.3033 Hertz
9: 1503.650 cents C 261.8377 Hertz
10: 1700.292 cents D 293.3334 Hertz
11: 1896.934 cents E4--------328.6167 Hertz
12: 2002.818 cents F 349.3435 Hertz
13: 2205.605 cents G 392.7565 Hertz
14: 2402.247 cents A4--------440.0000 Hertz
15: 2598.889 cents B 492.9263 Hertz
16: 2704.773 cents C 524.0153 Hertz
17: 2901.415 cents D 587.0475 Hertz
18: 3098.057 cents E5---------657.6617 Hertz
19: 3203.941 cents F 699.1405 Hertz
20: 3406.728 cents G 786.0229 Hertz
21: 3603.370 cents A5---------880.5713 Hertz
22: 3800.012 cents B 986.4925 Hertz
23: 3905.896 cents C 1048.7108 Hertz
24: 4102.538 cents D 1174.8571 Hertz
25: 4299.180 cents E6--------1316.1771 Hertz

----- Original Message -----
From: "J.Smith" <jsmith9624@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 08 Nisan 2006 Cumartesi 21:40
Subject: [tuning] 79-tone Qanun

>
> Oz,
>
> Do you mean 79 strings, or 79 discrete pitches, for that qanun? I
> would also like to ask you sometime, about what you would consider to
> be accurate and traditional tunings for various widely-used maqamat,
> if you are willing.
>
> Peace,
> jl
>