39edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 01:34:07 UTC</tt>.

: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-09-20 01:45:37 UTC</tt>.

: The original revision id was <tt>~~240943889~~</tt>.

: The original revision id was <tt>255961080</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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<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">=39 tone equal temperament=

**39-EDO** or **39-tET** divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, **Hornbostel Temperament** and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] & 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|.

**39-EDO, 39-ED2** or **39-tET** divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, **Hornbostel Temperament** and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] & 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|.

==__**39-EDO Intervals**__==

|| **NOMENCLATURE** ||

|| **t** = Semisharp

|| **t** = Semisharp (1/5-tone up)

**v** = Semiflat ||

**b** = Flat (3/5-tone down)

**#** = Sharp (3/5-tone up)

**v** = Semiflat (1/5-tone down) ||

|| **~~DEGREE~~** || **~~NOTE~~** || **~~CENTS~~** || **[[Nearest just interval|Nearest Just I]]nterval** || **Cents** || **Error** ||

|| **Degrees** || **Armodue note** || **Cents size** || **[[Nearest just interval|Nearest Just I]]nterval** || **Cents value** || **Error** ||

|| 0 || **1** || 0 || **1/1** || 0 || **None** ||

|| 1 || 1t || 30.7692 || 57/56 || 30.6421 || +0.1271 ||

|| 2 || 1# || 61.5385 || 29/28 || 60.7513 || +0.7872 ||

|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||

|| 3 || 2b || 92.3077 || 39/37 || 91.1386 || +1.1691 ||

|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||

|| 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 ||

|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 ||

|| 6 || 2t || 184.6154 || 10/9 || 182.4037 || +2.2117 ||

|| **7·** || **2#** || **215.3846** || **17/15** || **216.6867** || **-1.3021** ||

|| **7·** || **3b** || **215.3846** || **17/15** || **216.6867** || **-1.3021** ||

|| 8 || 3b || 246.1538 || 15/13 || 247.7411 || -1.5873 ||

|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 ||

|| 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 ||

|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 ||

|| 11 || 3t || 338.4615 || 17/14 || 336.1295 || +2.332 ||

|| **12·** || **3#** || **369.2308** || **26/21** || **369.7468** || **-0.516** ||

|| **12·** || **4b** || **369.2308** || **26/21** || **369.7468** || **-0.516** ||

|| 13 || 4b || 400 || 34/27 || 399.0904 || +0.9096 ||

|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 ||

|| 14 || 4v || 430.7692 || 41/32 || 429.0624 || +1.7068 ||

|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||

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|| **17·** || **5** || **523.0769** || **23/17** || **523.3189** || **-0.242** ||

|| 18 || 5t || 553.8462 || 11/8 || 551.3179 || +2.5283 ||

|| 19 || 5# || 584.6154 || 7/5 || 582.5122 || +2.1032 ||

|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 ||

|| 20 || 6b || 615.3846 || 10/7 || 617.4878 || -2.1032 ||

|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 ||

|| 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 ||

|| **22·** || **6** || **676.9231** || **34/23** || **676.6811** || **+0.242** ||

|| 23 || 6t || 707.6923 || 128/85 || 708.7309 || -1.0386 ||

|| 24 || 6# || 738.4615 || 23/15 || 740.0056 || -1.5441 ||

|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 ||

|| 25 || 7b || 769.2308 || 64/41 || 770.9376 || -1.7068 ||

|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 ||

|| 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 ||

|| **27·** || **7** || **830.7692** || **21/13** || **830.2532** || **+0.516** ||

|| 28 || 7t || 861.5385 || 28/17 || 863.8705 || -2.332 ||

|| 29 || ~~7# (A)~~ || 892.3077 || 72/43 || 892.3923 || -0.0846 ||

|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 ||

|| 30 || 8b || 923.0769 || 46/27 || 922.4093 || +0.6676 ||

|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 ||

|| 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 ||

|| **32·** || **8** || **984.6154** || **30/17** || **983.3133** || **+1.3021** ||

|| 33 || 8t || 1015.3846 || 9/5 || 1017.5963 || -2.2117 ||

|| 34 || 8# || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||

|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||

|| 35 || 9b || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||

|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||

|| 36 || 9v || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||

|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||

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<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"><html><head><title>39edo</title></head><body><h1 id="toc0"><a name="x39 tone equal temperament"></a>39 tone equal temperament</h1>

39-EDO or 39-tET divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, Hornbostel Temperament and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.

39-EDO, 39-ED2 or 39-tET divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, Hornbostel Temperament and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.

<h2 id="toc1"><a name="x39 tone equal temperament-39-EDO Intervals"></a>39-EDO Intervals</h2>

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</tr>

<tr>

<td>t = Semisharp

<td>t = Semisharp (1/5-tone up)

v = Semiflat

b = Flat (3/5-tone down)

<ul><ul><ul><ul><ul><li>= Sharp (3/5-tone up)</li></ul></ul></ul></ul></ul>v = Semiflat (1/5-tone down)

</td>

</tr>

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<tr>

<td>~~DEGREE~~

<td>Degrees

</td>

<td>~~NOTE~~

<td>Armodue note

</td>

<td>~~CENTS~~

<td>Cents size

</td>

<td><a class="wiki_link" href="/Nearest%20just%20interval">Nearest Just I</a>nterval

</td>

<td>Cents

<td>Cents value

</td>

<td>Error

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<td>2

</td>

<td>1#

<td>2b

</td>

<td>61.5385

Line 193:

Line 196:

<td>3

</td>

<td>2b

<td>1#

</td>

<td>92.3077

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Line 252:

<td>7·

</td>

<td>2#

<td>3b

</td>

<td>215.3846

Line 263:

Line 266:

<td>8

</td>

<td>3b

<td>2#

</td>

<td>246.1538

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Line 322:

<td>12·

</td>

<td>3#

<td>4b

</td>

<td>369.2308

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Line 336:

<td>13

</td>

<td>4b

<td>3#

</td>

<td>400

Line 417:

Line 420:

<td>19

</td>

<td>5#

<td>6b

</td>

<td>584.6154

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Line 434:

<td>20

</td>

<td>6b

<td>5#

</td>

<td>615.3846

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Line 490:

<td>24

</td>

<td>6#

<td>7b

</td>

<td>738.4615

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Line 504:

<td>25

</td>

<td>7b

<td>6#

</td>

<td>769.2308

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Line 560:

<td>29

</td>

<td>~~7# (A)~~

<td>8b

</td>

<td>892.3077

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<td>30

</td>

<td>8b

<td>7#

</td>

<td>923.0769

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Line 630:

<td>34

</td>

<td>8#

<td>9b

</td>

<td>1046.1538

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Line 644:

<td>35

</td>

<td>9b

<td>8#

</td>

<td>1076.9231

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<h2 id="toc2"><a name="x39 tone equal temperament-Instruments (prototypes):"></a>Instruments (prototypes):</h2>

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/TECLADO_39-EDO.PNG/258413072/TECLADO_39-EDO.PNG" alt="TECLADO_39-EDO.PNG" title="TECLADO_39-EDO.PNG" /></td></tr><tr><td class="imageCaption">39-EDO Keyboard Classic Prototype.</td></tr></table>

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/TECLADO_39-EDO.PNG/258413072/TECLADO_39-EDO.PNG" alt="TECLADO_39-EDO.PNG" title="TECLADO_39-EDO.PNG" /></td></tr><tr><td class="imageCaption">39-EDO Keyboard Classic Prototype.</td></tr></table>

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/992x278/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 278px; width: 992px;" /></td></tr><tr><td class="imageCaption">Visualization of a 39-EDO Fretboard, by Tútim Deft</td></tr></table>

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/992x278/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 278px; width: 992px;" /></td></tr><tr><td class="imageCaption">Visualization of a 39-EDO Fretboard, by Tútim Deft</td></tr></table>

<h2 id="toc3"><a name="x39 tone equal temperament-39 tone equal modes:"></a>39 tone equal <a class="wiki_link" href="/modes">modes</a>:</h2>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 01:34:07 UTC</tt>.<br>
+: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-09-20 01:45:37 UTC</tt>.<br>
-: The original revision id was <tt>240943889</tt>.<br>
+: The original revision id was <tt>255961080</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>
@@ Line 8: / Line 8: @@
 <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">=&lt;span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;39 tone equal temperament&lt;/span&gt;=
-**39-EDO** or **39-tET** divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, **Hornbostel Temperament** and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.
+**39-EDO, 39-ED2** or **39-tET** divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, **Hornbostel Temperament** and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.
 ==__**39-EDO Intervals**__==
 || **NOMENCLATURE** ||
-|| **t** = Semisharp
+|| **t** = Semisharp (1/5-tone up)
-**v** = Semiflat ||
+**b** = Flat (3/5-tone down)
+**#** = Sharp (3/5-tone up)
+**v** = Semiflat (1/5-tone down) ||
-|| **DEGREE** || **NOTE** || **CENTS** || **[[Nearest just interval|Nearest Just I]]nterval** || **Cents** || **Error** ||
+|| **Degrees** || **Armodue note** || **Cents size** || **[[Nearest just interval|Nearest Just I]]nterval** || **Cents value** || **Error** ||
 || 0 || **1** || 0 || **1/1** || 0 || **None** ||
 || 1 || 1t || 30.7692 || 57/56 || 30.6421 || +0.1271 ||
-|| 2 || 1# || 61.5385 || 29/28 || 60.7513 || +0.7872 ||
+|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||
-|| 3 || 2b || 92.3077 || 39/37 || 91.1386 || +1.1691 ||
+|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||
 || 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 ||
 || 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 ||
 || 6 || 2t || 184.6154 || 10/9 || 182.4037 || +2.2117 ||
-|| **7·** || **2#** || **215.3846** || **17/15** || **216.6867** || **-1.3021** ||
+|| **7·** || **3b** || **215.3846** || **17/15** || **216.6867** || **-1.3021** ||
-|| 8 || 3b || 246.1538 || 15/13 || 247.7411 || -1.5873 ||
+|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 ||
 || 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 ||
 || 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 ||
 || 11 || 3t || 338.4615 || 17/14 || 336.1295 || +2.332 ||
-|| **12·** || **3#** || **369.2308** || **26/21** || **369.7468** || **-0.516** ||
+|| **12·** || **4b** || **369.2308** || **26/21** || **369.7468** || **-0.516** ||
-|| 13 || 4b || 400 || 34/27 || 399.0904 || +0.9096 ||
+|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 ||
 || 14 || 4v || 430.7692 || 41/32 || 429.0624 || +1.7068 ||
 || 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||
@@ Line 35: / Line 37: @@
 || **17·** || **5** || **523.0769** || **23/17** || **523.3189** || **-0.242** ||
 || 18 || 5t || 553.8462 || 11/8 || 551.3179 || +2.5283 ||
-|| 19 || 5# || 584.6154 || 7/5 || 582.5122 || +2.1032 ||
+|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 ||
-|| 20 || 6b || 615.3846 || 10/7 || 617.4878 || -2.1032 ||
+|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 ||
 || 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 ||
 || **22·** || **6** || **676.9231** || **34/23** || **676.6811** || **+0.242** ||
 || 23 || 6t || 707.6923 || 128/85 || 708.7309 || -1.0386 ||
-|| 24 || 6# || 738.4615 || 23/15 || 740.0056 || -1.5441 ||
+|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 ||
-|| 25 || 7b || 769.2308 || 64/41 || 770.9376 || -1.7068 ||
+|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 ||
 || 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 ||
 || **27·** || **7** || **830.7692** || **21/13** || **830.2532** || **+0.516** ||
 || 28 || 7t || 861.5385 || 28/17 || 863.8705 || -2.332 ||
-|| 29 || 7# (A) || 892.3077 || 72/43 || 892.3923 || -0.0846 ||
+|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 ||
-|| 30 || 8b || 923.0769 || 46/27 || 922.4093 || +0.6676 ||
+|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 ||
 || 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 ||
 || **32·** || **8** || **984.6154** || **30/17** || **983.3133** || **+1.3021** ||
 || 33 || 8t || 1015.3846 || 9/5 || 1017.5963 || -2.2117 ||
-|| 34 || 8# || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||
+|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||
-|| 35 || 9b || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||
+|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||
 || 36 || 9v || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||
 || 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||
@@ Line 113: / Line 115: @@
 <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;39edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x39 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;39 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;strong&gt;39-EDO&lt;/strong&gt; or &lt;strong&gt;39-tET&lt;/strong&gt; divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, &lt;strong&gt;Hornbostel Temperament&lt;/strong&gt; and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp;amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &amp;lt;39 62 91 110 135|.&lt;br /&gt;
+&lt;strong&gt;39-EDO, 39-ED2&lt;/strong&gt; or &lt;strong&gt;39-tET&lt;/strong&gt; divides the Octave in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, &lt;strong&gt;Hornbostel Temperament&lt;/strong&gt; and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp;amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &amp;lt;39 62 91 110 135|.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x39 tone equal temperament-39-EDO Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;u&gt;&lt;strong&gt;39-EDO Intervals&lt;/strong&gt;&lt;/u&gt;&lt;/h2&gt;
@@ Line 124: / Line 126: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;t&lt;/strong&gt; = Semisharp&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;t&lt;/strong&gt; = Semisharp (1/5-tone up)&lt;br /&gt;
-&lt;strong&gt;v&lt;/strong&gt; = Semiflat&lt;br /&gt;
+&lt;strong&gt;b&lt;/strong&gt; = Flat (3/5-tone down)&lt;br /&gt;
+&lt;ul&gt;&lt;ul&gt;&lt;ul&gt;&lt;ul&gt;&lt;ul&gt;&lt;li&gt;= Sharp (3/5-tone up)&lt;/li&gt;&lt;/ul&gt;&lt;/ul&gt;&lt;/ul&gt;&lt;/ul&gt;&lt;/ul&gt;&lt;strong&gt;v&lt;/strong&gt; = Semiflat (1/5-tone down)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 135: / Line 138: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;DEGREE&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;Degrees&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;NOTE&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;Armodue note&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;CENTS&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;Cents size&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/Nearest%20just%20interval"&gt;Nearest Just I&lt;/a&gt;nterval&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;Cents value&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;Error&lt;/strong&gt;&lt;br /&gt;
@@ Line 179: / Line 182: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1#&lt;br /&gt;
+         &lt;td&gt;2b&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;61.5385&lt;br /&gt;
@@ Line 193: / Line 196: @@
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2b&lt;br /&gt;
+         &lt;td&gt;1#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;92.3077&lt;br /&gt;
@@ Line 249: / Line 252: @@
          &lt;td&gt;&lt;strong&gt;7·&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;2#&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;3b&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;215.3846&lt;/strong&gt;&lt;br /&gt;
@@ Line 263: / Line 266: @@
          &lt;td&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3b&lt;br /&gt;
+         &lt;td&gt;2#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;246.1538&lt;br /&gt;
@@ Line 319: / Line 322: @@
          &lt;td&gt;&lt;strong&gt;12·&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;3#&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;4b&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;369.2308&lt;/strong&gt;&lt;br /&gt;
@@ Line 333: / Line 336: @@
          &lt;td&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4b&lt;br /&gt;
+         &lt;td&gt;3#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;400&lt;br /&gt;
@@ Line 417: / Line 420: @@
          &lt;td&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5#&lt;br /&gt;
+         &lt;td&gt;6b&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;584.6154&lt;br /&gt;
@@ Line 431: / Line 434: @@
          &lt;td&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6b&lt;br /&gt;
+         &lt;td&gt;5#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;615.3846&lt;br /&gt;
@@ Line 487: / Line 490: @@
          &lt;td&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6#&lt;br /&gt;
+         &lt;td&gt;7b&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;738.4615&lt;br /&gt;
@@ Line 501: / Line 504: @@
          &lt;td&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7b&lt;br /&gt;
+         &lt;td&gt;6#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;769.2308&lt;br /&gt;
@@ Line 557: / Line 560: @@
          &lt;td&gt;29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7# (A)&lt;br /&gt;
+         &lt;td&gt;8b&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;892.3077&lt;br /&gt;
@@ Line 571: / Line 574: @@
          &lt;td&gt;30&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8b&lt;br /&gt;
+         &lt;td&gt;7#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;923.0769&lt;br /&gt;
@@ Line 627: / Line 630: @@
          &lt;td&gt;34&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8#&lt;br /&gt;
+         &lt;td&gt;9b&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1046.1538&lt;br /&gt;
@@ Line 641: / Line 644: @@
          &lt;td&gt;35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9b&lt;br /&gt;
+         &lt;td&gt;8#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1076.9231&lt;br /&gt;
@@ Line 713: / Line 716: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x39 tone equal temperament-Instruments (prototypes):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;u&gt;Instruments (prototypes):&lt;/u&gt;&lt;/h2&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:594:&amp;lt;img src=&amp;quot;/file/view/TECLADO_39-EDO.PNG/258413072/TECLADO_39-EDO.PNG&amp;quot; alt=&amp;quot;39-EDO Keyboard Classic Prototype.&amp;quot; title=&amp;quot;39-EDO Keyboard Classic Prototype.&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/TECLADO_39-EDO.PNG/258413072/TECLADO_39-EDO.PNG" alt="TECLADO_39-EDO.PNG" title="TECLADO_39-EDO.PNG" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDO Keyboard Classic Prototype.&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:594 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:606:&amp;lt;img src=&amp;quot;/file/view/TECLADO_39-EDO.PNG/258413072/TECLADO_39-EDO.PNG&amp;quot; alt=&amp;quot;39-EDO Keyboard Classic Prototype.&amp;quot; title=&amp;quot;39-EDO Keyboard Classic Prototype.&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/TECLADO_39-EDO.PNG/258413072/TECLADO_39-EDO.PNG" alt="TECLADO_39-EDO.PNG" title="TECLADO_39-EDO.PNG" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDO Keyboard Classic Prototype.&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:606 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:595:&amp;lt;img src=&amp;quot;/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/992x278/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;Visualization of a 39-EDO Fretboard, by Tútim Deft&amp;quot; title=&amp;quot;Visualization of a 39-EDO Fretboard, by Tútim Deft&amp;quot; style=&amp;quot;height: 278px; width: 992px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/992x278/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 278px; width: 992px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Visualization of a 39-EDO Fretboard, by Tútim Deft&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:595 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:607:&amp;lt;img src=&amp;quot;/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/992x278/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;Visualization of a 39-EDO Fretboard, by Tútim Deft&amp;quot; title=&amp;quot;Visualization of a 39-EDO Fretboard, by Tútim Deft&amp;quot; style=&amp;quot;height: 278px; width: 992px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/992x278/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 278px; width: 992px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Visualization of a 39-EDO Fretboard, by Tútim Deft&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:607 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x39 tone equal temperament-39 tone equal modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;strong&gt;&lt;u&gt;39 tone equal &lt;a class="wiki_link" href="/modes"&gt;modes&lt;/a&gt;&lt;/u&gt;:&lt;/strong&gt;&lt;/h2&gt;