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>[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]] | |||