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79MOS 159edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
[http://launch.groups.yahoo.com/group/tuning/message/64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.
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 33 equal divisions of the pure fourth.
Line 19: Line 12:


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 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.
<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;
&lt;br /&gt;
My tuning scheme involves 33 equal divisions of the pure fourth.&lt;br /&gt;
&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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