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79MOS 159edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.</tt>''
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-08-08 06:59:44 UTC</tt>.<br>
: The original revision id was <tt>6654877</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[http://launch.groups.yahoo.com/group/tuning/message/64171|Original article]] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.


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
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(
4: 60.369 cents C) Dbv
4: 60.369 cents C) Dbv
5: 75.461 cents C#\ Db\\
5: 75.461 cents C#\ Db\\
6: 90.554 cents C# Db\
6: 90.554 cents C# Db\
7: 105.646 cents C#/ Db
7: 105.646 cents C#/ Db
8: 120.738 cents C#// Db/
8: 120.738 cents C#// Db/
9: 135.830 cents C#^ D(
9: 135.830 cents C#^ D(
10: 150.923 cents C#) Dv
10: 150.923 cents C#) Dv
11: 166.015 cents D\\
11: 166.015 cents D\\
12: 181.107 cents D\
12: 181.107 cents D\
13: 196.200 cents D DUGAH
13: 196.200 cents D DUGAH
14: 211.292 cents D/ Dugah again
14: 211.292 cents D/ Dugah again
15: 226.384 cents D//
 
15: 226.384 cents D
 
16: 241.476 cents D^ Eb(
16: 241.476 cents D^ Eb(
17: 256.569 cents D) Ebv
17: 256.569 cents D) Ebv
18: 271.661 cents D#\ Eb\\
18: 271.661 cents D#\ Eb\\
19: 286.753 cents D# Eb\
19: 286.753 cents D# Eb\
20: 301.845 cents D#/ Eb
20: 301.845 cents D#/ Eb
21: 316.938 cents D#// Eb/
21: 316.938 cents D#// Eb/
22: 332.030 cents D#^ E(
22: 332.030 cents D#^ E(
23: 347.122 cents D#) Ev
23: 347.122 cents D#) Ev
24: 362.215 cents E\\
24: 362.215 cents E\\
25: 377.307 cents E\ lower segah
25: 377.307 cents E\ lower segah
26: 392.399 cents E SEGAH
26: 392.399 cents E SEGAH
27: 407.491 cents E/ Fb Buselik
27: 407.491 cents E/ Fb Buselik
28: 422.584 cents E// Fb/ Nishabur
 
28: 422.584 cents E'' Fb/ Nishabur''
 
29: 437.676 cents E^ F(
29: 437.676 cents E^ F(
30: 452.768 cents E) Fv
30: 452.768 cents E) Fv
31: 467.860 cents E#\ F\\
31: 467.860 cents E#\ F\\
32: 482.953 cents E# F\
32: 482.953 cents E# F\
33: 498.045 cents F CHARGAH
33: 498.045 cents F CHARGAH
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(
37: 558.414 cents F) Gbv
37: 558.414 cents F) Gbv
38: 573.506 cents F#\ Gb\\
38: 573.506 cents F#\ Gb\\
39: 588.599 cents F# Gb\
39: 588.599 cents F# Gb\
40: 603.691 cents F#/ Gb
40: 603.691 cents F#/ Gb
41: 618.783 cents F#// Gb/
41: 618.783 cents F#// Gb/
42: 633.875 cents F#^ G(
42: 633.875 cents F#^ G(
43: 648.968 cents F#) Gv
43: 648.968 cents F#) Gv
44: 664.060 cents G\\
44: 664.060 cents G\\
45: 679.152 cents G\
45: 679.152 cents G\
46: 701.955 cents G NEVA
46: 701.955 cents G NEVA
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(
50: 762.324 cents G) Abv
50: 762.324 cents G) Abv
51: 777.416 cents G#\ Ab\\
51: 777.416 cents G#\ Ab\\
52: 792.509 cents G# Ab\
52: 792.509 cents G# Ab\
53: 807.601 cents G#/ Ab
53: 807.601 cents G#/ Ab
54: 822.693 cents G#// Ab/
54: 822.693 cents G#// Ab/
55: 837.785 cents G#^ A(
55: 837.785 cents G#^ A(
56: 852.878 cents G#) Av
56: 852.878 cents G#) Av
57: 867.970 cents A\\
57: 867.970 cents A\\
58: 883.062 cents A\ Hisar
58: 883.062 cents A\ Hisar
59: 898.155 cents A HUSEYNI/Hisarek
59: 898.155 cents A HUSEYNI/Hisarek
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(
63: 958.524 cents A) Bbv
63: 958.524 cents A) Bbv
64: 973.616 cents A#\ Bb\\
64: 973.616 cents A#\ Bb\\
65: 988.708 cents A# Bb\
65: 988.708 cents A# Bb\
66: 1003.800 cents A#/ Bb
66: 1003.800 cents A#/ Bb
67: 1018.893 cents A#// Bb/
67: 1018.893 cents A#// Bb/
68: 1033.985 cents A#^ B(
68: 1033.985 cents A#^ B(
69: 1049.077 cents A#) Bv
69: 1049.077 cents A#) Bv
70: 1064.170 cents B\\
70: 1064.170 cents B\\
71: 1079.262 cents B\
71: 1079.262 cents B\
72: 1094.354 cents B EVDJ
72: 1094.354 cents B EVDJ
73: 1109.446 cents B/ Cb Mahur
73: 1109.446 cents B/ Cb Mahur
74: 1124.539 cents B// Cb/ Mahurek (my proposal)
74: 1124.539 cents B// Cb/ Mahurek (my proposal)
75: 1139.631 cents B^ C(
75: 1139.631 cents B^ C(
76: 1154.723 cents B) Cv
76: 1154.723 cents B) Cv
77: 1169.815 cents B#\ C\\
77: 1169.815 cents B#\ C\\
78: 1184.908 cents B# C\
78: 1184.908 cents B# C\
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.</pre></div>
Some degrees yield excellent [[11 limit]] results, while others produce adorable [[5-limit|5 limit]] and sufficiently close [[7-limit|7 limit]] intervals.  
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;79MOS 159edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/64171" rel="nofollow"&gt;Original article&lt;/a&gt; by Ozan Yarman, on the Yahoo tuning forum, is quoted here.&lt;br /&gt;
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.
&lt;br /&gt;
 
My tuning scheme involves 33 equal divisions of the pure fourth.&lt;br /&gt;
[[Category:159edo]]
&lt;br /&gt;
1. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 cents.&lt;br /&gt;
&lt;br /&gt;
2. Carry the comma to the 79th step and you reach 1192.2895433828604241874408519317 cents.&lt;br /&gt;
&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
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:&lt;br /&gt;
&lt;br /&gt;
0: 1/1 C RAST&lt;br /&gt;
1: 15.092 cents C/&lt;br /&gt;
2: 30.185 cents C&lt;em&gt;&lt;br /&gt;
3: 45.277 cents C^ Db(&lt;br /&gt;
4: 60.369 cents C) Dbv&lt;br /&gt;
5: 75.461 cents C#\ Db\\&lt;br /&gt;
6: 90.554 cents C# Db\&lt;br /&gt;
7: 105.646 cents C#/ Db&lt;br /&gt;
8: 120.738 cents C#&lt;/em&gt; Db/&lt;br /&gt;
9: 135.830 cents C#^ D(&lt;br /&gt;
10: 150.923 cents C#) Dv&lt;br /&gt;
11: 166.015 cents D\\&lt;br /&gt;
12: 181.107 cents D\&lt;br /&gt;
13: 196.200 cents D DUGAH&lt;br /&gt;
14: 211.292 cents D/ Dugah again&lt;br /&gt;
15: 226.384 cents D&lt;em&gt;&lt;br /&gt;
16: 241.476 cents D^ Eb(&lt;br /&gt;
17: 256.569 cents D) Ebv&lt;br /&gt;
18: 271.661 cents D#\ Eb\\&lt;br /&gt;
19: 286.753 cents D# Eb\&lt;br /&gt;
20: 301.845 cents D#/ Eb&lt;br /&gt;
21: 316.938 cents D#&lt;/em&gt; Eb/&lt;br /&gt;
22: 332.030 cents D#^ E(&lt;br /&gt;
23: 347.122 cents D#) Ev&lt;br /&gt;
24: 362.215 cents E\\&lt;br /&gt;
25: 377.307 cents E\ lower segah&lt;br /&gt;
26: 392.399 cents E SEGAH&lt;br /&gt;
27: 407.491 cents E/ Fb Buselik&lt;br /&gt;
28: 422.584 cents E&lt;em&gt; Fb/ Nishabur&lt;br /&gt;
29: 437.676 cents E^ F(&lt;br /&gt;
30: 452.768 cents E) Fv&lt;br /&gt;
31: 467.860 cents E#\ F\\&lt;br /&gt;
32: 482.953 cents E# F\&lt;br /&gt;
33: 498.045 cents F CHARGAH&lt;br /&gt;
34: 513.137 cents F/&lt;br /&gt;
35: 528.230 cents F&lt;/em&gt;&lt;br /&gt;
36: 543.322 cents F^ Gb(&lt;br /&gt;
37: 558.414 cents F) Gbv&lt;br /&gt;
38: 573.506 cents F#\ Gb\\&lt;br /&gt;
39: 588.599 cents F# Gb\&lt;br /&gt;
40: 603.691 cents F#/ Gb&lt;br /&gt;
41: 618.783 cents F#&lt;em&gt; Gb/&lt;br /&gt;
42: 633.875 cents F#^ G(&lt;br /&gt;
43: 648.968 cents F#) Gv&lt;br /&gt;
44: 664.060 cents G\\&lt;br /&gt;
45: 679.152 cents G\&lt;br /&gt;
46: 701.955 cents G NEVA&lt;br /&gt;
47: 717.047 cents G/&lt;br /&gt;
48: 732.140 cents G&lt;/em&gt;&lt;br /&gt;
49: 747.232 cents G^ Ab(&lt;br /&gt;
50: 762.324 cents G) Abv&lt;br /&gt;
51: 777.416 cents G#\ Ab\\&lt;br /&gt;
52: 792.509 cents G# Ab\&lt;br /&gt;
53: 807.601 cents G#/ Ab&lt;br /&gt;
54: 822.693 cents G#&lt;em&gt; Ab/&lt;br /&gt;
55: 837.785 cents G#^ A(&lt;br /&gt;
56: 852.878 cents G#) Av&lt;br /&gt;
57: 867.970 cents A\\&lt;br /&gt;
58: 883.062 cents A\ Hisar&lt;br /&gt;
59: 898.155 cents A HUSEYNI/Hisarek&lt;br /&gt;
60: 913.247 cents A/ Huseyni again&lt;br /&gt;
61: 928.339 cents A&lt;/em&gt;&lt;br /&gt;
62: 943.431 cents A^ Bb(&lt;br /&gt;
63: 958.524 cents A) Bbv&lt;br /&gt;
64: 973.616 cents A#\ Bb\\&lt;br /&gt;
65: 988.708 cents A# Bb\&lt;br /&gt;
66: 1003.800 cents A#/ Bb&lt;br /&gt;
67: 1018.893 cents A#&lt;em&gt; Bb/&lt;br /&gt;
68: 1033.985 cents A#^ B(&lt;br /&gt;
69: 1049.077 cents A#) Bv&lt;br /&gt;
70: 1064.170 cents B\\&lt;br /&gt;
71: 1079.262 cents B\&lt;br /&gt;
72: 1094.354 cents B EVDJ&lt;br /&gt;
73: 1109.446 cents B/ Cb Mahur&lt;br /&gt;
74: 1124.539 cents B&lt;/em&gt; Cb/ Mahurek (my proposal)&lt;br /&gt;
75: 1139.631 cents B^ C(&lt;br /&gt;
76: 1154.723 cents B) Cv&lt;br /&gt;
77: 1169.815 cents B#\ C\\&lt;br /&gt;
78: 1184.908 cents B# C\&lt;br /&gt;
79: 1200.000 cents C GERDANIYE&lt;br /&gt;
&lt;br /&gt;
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 &amp;quot;unfortunate&amp;quot; enough to have met me.&lt;/body&gt;&lt;/html&gt;</pre></div>
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