Ozan Yarman's proposed 79-tone tuning is a novel system for Maqam Music applied to a Turkish qanun, which has been presented to and acclaimed by an audience of professional qanun performers and enthusiasts in an academical establishment in Istanbul. (Yarman, O., Invited Speaker, "A Revolutionary and Comprehensive 79-tone Tuning for the Kanun", Kanun Circle 4, Yıldız Technical University Auditorium, May 28 2006.)


The tuning is,


(Step 1.) derived from 33 logarithmically equal divisions of the pure fourth (represented as 4:3),


<math>log10 (4:3) * 1200 / log10 (2:1) = 498.045 cents </math>

<math>498.045 / 33 = 15.0923 cents </math>


(Step 2.) whereafter the resultant comma is stacked 79 times,


<math>15.0923 * 79 = 1192.29 cents </math>


(Step 3.) and the 79th degree is completed to the octave, yielding a larger comma,


<math>1200 - 1192.29 = 7.710457 cents </math>

<math>15.0923 7.710457 = 22.80273 cents </math>


(Step 4.) which is carried between degrees 45-46 to produce the following scale:



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

otherwise equivalent to 79-tone moment of symmetry out of 159-tone equal temperament. For this reason, the tuning is referred to as 79 MOS 159-tET for short.

----

The frequency table is modified thusly to acquire proportional beat ratios in common chords:

0: 261.9046 Hertz 262
1: 264.1978 Hertz 264.25
2: 266.5110 Hertz 266.75
3: 268.8445 Hertz 269
4: 271.1985 Hertz 271.5
5: 273.5730 Hertz 273.75
6: 275.9683 Hertz 276.25
7: 278.3846 Hertz 278.5
8: 280.8221 Hertz 281
9: 283.2809 Hertz 283.5
10: 285.7613 Hertz 286
11: 288.2633 Hertz 288.5
12: 290.7873 Hertz 291
13: 293.3333 Hertz 293.5
14: 295.9017 Hertz 296
15: 298.4925 Hertz 298.75
16: 301.1061 Hertz 301.25
17: 303.7425 Hertz 304
18: 306.4020 Hertz 306.5
19: 309.0847 Hertz 309.25
20: 311.7910 Hertz 312
21: 314.5210 Hertz 314.75
22: 317.2748 Hertz 317.5
23: 320.0528 Hertz 320.25
24: 322.8551 Hertz 323
25: 325.6819 Hertz 326
26: 328.5335 Hertz 328.75
27: 331.4101 Hertz 331.75
28: 334.3118 Hertz 334.5
29: 337.2390 Hertz 337.5
30: 340.1918 Hertz 340.5
31: 343.1704 Hertz 343.5
32: 346.1751 Hertz 346.5
33: 349.2061 Hertz 349.5
34: 352.2637 Hertz 352.5
35: 355.3480 Hertz 355.5
36: 358.4594 Hertz 358.75
37: 361.5979 Hertz 361.75
38: 364.7640 Hertz 365
39: 367.9578 Hertz 368.25
40: 371.1795 Hertz 371.5
41: 374.4295 Hertz 374.75
42: 377.7079 Hertz 378
43: 381.0150 Hertz 381.25
44: 384.3511 Hertz 384.5
45: 387.7164 Hertz 388
46: 392.8569 Hertz 393
47: 396.2967 Hertz 396.5
48: 399.7665 Hertz 400
49: 403.2668 Hertz 403.5
50: 406.7977 Hertz 407
51: 410.3595 Hertz 410.5
52: 413.9525 Hertz 414
53: 417.5770 Hertz 417.75
54: 421.2332 Hertz 421.25
55: 424.9214 Hertz 425
56: 428.6419 Hertz 428.75
57: 432.3950 Hertz 432.5
58: 436.1809 Hertz 436.25
59: 440.0000 Hertz 440
60: 443.8525 Hertz 443.75
61: 447.7388 Hertz 447.75
62: 451.6591 Hertz 452
63: 455.6137 Hertz 456
64: 459.6029 Hertz 459.75
65: 463.6271 Hertz 463.75
66: 467.6865 Hertz 468
67: 471.7814 Hertz 472
68: 475.9122 Hertz 476
69: 480.0792 Hertz 480.25
70: 484.2827 Hertz 484.5
71: 488.5229 Hertz 488.75
72: 492.8003 Hertz 493
73: 497.1151 Hertz 497.25
74: 501.4678 Hertz 501.5
75: 505.8585 Hertz 506
76: 510.2876 Hertz 510.25
77: 514.7556 Hertz 514.75
78: 519.2627 Hertz 519.25
79: 523.8092 Hertz 524

The scale contains 33 meantone fifths (~695 cents), 46 just fifths (~702 cents) and 32 super-pythagorean fifths (~710 cents). The cycle can be closed either with the first two types in 79 tones, or the latter two types in 80-tones if the 46th degree of the tuning is considered to accomodate both the meantone fifth and the just fifth.

Also, a closed 12-tone scale can be extracted from the tuning, which works well as a 12-tone temperament with proportional beat frequencies.

Most importantly, the microtonal subtleties of the Maqamat can be sounded over all tones.

For details of the tuning, see http://www.ozanyarman.com\misc\79tone.xls