79MOS 159edo: Difference between revisions
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:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.</tt>'' | :''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.</tt>'' | ||
My tuning scheme involves 33 equal divisions of the pure fourth. | My tuning scheme involves [[33ed4/3|33 equal divisions of the pure fourth]]. | ||
1. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 cents. | 1. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 [[cents]]. | ||
2. Carry the comma to the 79th step and you reach 1192.2895433828604241874408519317 cents. | 2. Carry the [[comma]] to the 79th step and you reach 1192.2895433828604241874408519317 cents. | ||
3. Complete the octave to 1200 cents and move the 22.802729318188441941514095561079 cent comma between steps 45-46. You do this by key transposing the tuning to the -46th step. | 3. Complete the octave to 1200 cents and move the 22.802729318188441941514095561079 cent comma between steps 45-46. You do this by key transposing the tuning to the -46th step. | ||
Voila! You now have a circulating temperament which is practically a subset of 159-tET. There are three sizes of fifths by which one can formulate diatonical scales: | Voila! You now have a [[circulating temperament]] which is practically a subset of [[159edo|159-tET]]. There are three sizes of fifths by which one can formulate [[diatonic|diatonical]] scales: | ||
0: 1/1 C RAST | 0: 1/1 C RAST | ||
| Line 15: | Line 15: | ||
1: 15.092 cents C/ | 1: 15.092 cents C/ | ||
2: 30.185 cents C | 2: 30.185 cents C// | ||
3: 45.277 cents C^ Db( | 3: 45.277 cents C^ Db( | ||
| Line 27: | Line 27: | ||
7: 105.646 cents C#/ Db | 7: 105.646 cents C#/ Db | ||
8: 120.738 cents C# | 8: 120.738 cents C#// Db/ | ||
9: 135.830 cents C#^ D( | 9: 135.830 cents C#^ D( | ||
| Line 53: | Line 53: | ||
20: 301.845 cents D#/ Eb | 20: 301.845 cents D#/ Eb | ||
21: 316.938 cents D# | 21: 316.938 cents D#// Eb/ | ||
22: 332.030 cents D#^ E( | 22: 332.030 cents D#^ E( | ||
| Line 81: | Line 81: | ||
34: 513.137 cents F/ | 34: 513.137 cents F/ | ||
35: 528.230 cents F | 35: 528.230 cents F// | ||
36: 543.322 cents F^ Gb( | 36: 543.322 cents F^ Gb( | ||
| Line 93: | Line 93: | ||
40: 603.691 cents F#/ Gb | 40: 603.691 cents F#/ Gb | ||
41: 618.783 cents F# | 41: 618.783 cents F#// Gb/ | ||
42: 633.875 cents F#^ G( | 42: 633.875 cents F#^ G( | ||
| Line 107: | Line 107: | ||
47: 717.047 cents G/ | 47: 717.047 cents G/ | ||
48: 732.140 cents G | 48: 732.140 cents G// | ||
49: 747.232 cents G^ Ab( | 49: 747.232 cents G^ Ab( | ||
| Line 119: | Line 119: | ||
53: 807.601 cents G#/ Ab | 53: 807.601 cents G#/ Ab | ||
54: 822.693 cents G# | 54: 822.693 cents G#// Ab/ | ||
55: 837.785 cents G#^ A( | 55: 837.785 cents G#^ A( | ||
| Line 133: | Line 133: | ||
60: 913.247 cents A/ Huseyni again | 60: 913.247 cents A/ Huseyni again | ||
61: 928.339 cents A | 61: 928.339 cents A// | ||
62: 943.431 cents A^ Bb( | 62: 943.431 cents A^ Bb( | ||
| Line 145: | Line 145: | ||
66: 1003.800 cents A#/ Bb | 66: 1003.800 cents A#/ Bb | ||
67: 1018.893 cents A# | 67: 1018.893 cents A#// Bb/ | ||
68: 1033.985 cents A#^ B( | 68: 1033.985 cents A#^ B( | ||
| Line 159: | Line 159: | ||
73: 1109.446 cents B/ Cb Mahur | 73: 1109.446 cents B/ Cb Mahur | ||
74: 1124.539 cents B | 74: 1124.539 cents B// Cb/ Mahurek (my proposal) | ||
75: 1139.631 cents B^ C( | 75: 1139.631 cents B^ C( | ||
| Line 171: | Line 171: | ||
79: 1200.000 cents C GERDANIYE | 79: 1200.000 cents C GERDANIYE | ||
Some degrees yield excellent 11 limit results, while others produce adorable 5 limit and sufficiently close 7 limit intervals. I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me. | Some degrees yield excellent [[11 limit]] results, while others produce adorable [[5-limit|5 limit]] and sufficiently close [[7-limit|7 limit]] intervals. | ||
I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me. | |||
[[Category:159edo]] | |||
Latest revision as of 03:57, 9 January 2024
- Original article by Ozan Yarman, on the Yahoo tuning forum, is quoted here.
My tuning scheme involves 33 equal divisions of the pure fourth.
1. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 cents.
2. Carry the comma to the 79th step and you reach 1192.2895433828604241874408519317 cents.
3. Complete the octave to 1200 cents and move the 22.802729318188441941514095561079 cent comma between steps 45-46. You do this by key transposing the tuning to the -46th step.
Voila! You now have a circulating temperament which is practically a subset of 159-tET. There are three sizes of fifths by which one can formulate diatonical scales:
0: 1/1 C RAST
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 DUGAH
14: 211.292 cents D/ Dugah again
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\ lower segah
26: 392.399 cents E SEGAH
27: 407.491 cents E/ Fb Buselik
28: 422.584 cents E Fb/ Nishabur
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 CHARGAH
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: 701.955 cents G NEVA
47: 717.047 cents G/
48: 732.140 cents G//
49: 747.232 cents G^ Ab(
50: 762.324 cents G) Abv
51: 777.416 cents G#\ Ab\\
52: 792.509 cents G# Ab\
53: 807.601 cents G#/ Ab
54: 822.693 cents G#// Ab/
55: 837.785 cents G#^ A(
56: 852.878 cents G#) Av
57: 867.970 cents A\\
58: 883.062 cents A\ Hisar
59: 898.155 cents A HUSEYNI/Hisarek
60: 913.247 cents A/ Huseyni again
61: 928.339 cents A//
62: 943.431 cents A^ Bb(
63: 958.524 cents A) Bbv
64: 973.616 cents A#\ Bb\\
65: 988.708 cents A# Bb\
66: 1003.800 cents A#/ Bb
67: 1018.893 cents A#// Bb/
68: 1033.985 cents A#^ B(
69: 1049.077 cents A#) Bv
70: 1064.170 cents B\\
71: 1079.262 cents B\
72: 1094.354 cents B EVDJ
73: 1109.446 cents B/ Cb Mahur
74: 1124.539 cents B// Cb/ Mahurek (my proposal)
75: 1139.631 cents B^ C(
76: 1154.723 cents B) Cv
77: 1169.815 cents B#\ C\\
78: 1184.908 cents B# C\
79: 1200.000 cents C GERDANIYE
Some degrees yield excellent 11 limit results, while others produce adorable 5 limit and sufficiently close 7 limit intervals.
I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me.