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Wikispaces>Osmiorisbendi **Imported revision 255963504 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 257653838 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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>2011-09- | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-09-23 19:09:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>257653838</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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">=<span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span>= | <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">=<span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span>= | ||
**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 | **39-EDO, 39-ED2** or **39-tET** divides the Octave (Duple 2/1) 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 that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, implemented in [[16edo|16-ED2]], and, allied systems ([[25edo|25-ED2]] [1/3-tone]; [[41edo|41-ED2]] [1/5-tone]; [[55edo|55]] and [[57edo|57]] ED2s [1/7-tones]; [[71edo|71]] and [[73edo|73]] ED2s [1/9-tones]; [[87edo|87]] and [[89edo|89]] ED2s [1/11-tones] & [[101edo|101]] and [[103edo|103]] ED2s [1/13-tones]). **Hornbostel Temperaments** is included too on the list: [[23edo|23-ED2]] [1/3-tone]; 39-ED2 [1/5-tone]; [[62edo|62-ED2]] [1/8-tone]; [[85edo|85-ED2]] [1/11-tone] and larger: [[131edo|131-ED2]] [1/17-tone]; [[177edo|177-ED2]] [1/23-tone]; [[200edo|200-ED2]] [1/26-tone] & [[223edo|223-ED2]] [1/29-tone]. Note that 101, 131, 177 & 200 ED2s are tempered systems that Alexei Ogolevets was proposing in his List of Temperaments. | ||
However, its 23\39 fifth, 5.737 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**__== | ==__**39-EDO Intervals**__== | ||
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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><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span></h1> | <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><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
<strong>39-EDO, 39-ED2</strong> or <strong>39-tET</strong> 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 | <strong>39-EDO, 39-ED2</strong> or <strong>39-tET</strong> divides the Octave (Duple 2/1) 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 that use the scheme of <a class="wiki_link" href="/7L%202s">Superdiatonic</a> LLLsLLLLs like a basical scale for notation and theory, implemented in <a class="wiki_link" href="/16edo">16-ED2</a>, and, allied systems (<a class="wiki_link" href="/25edo">25-ED2</a> [1/3-tone]; <a class="wiki_link" href="/41edo">41-ED2</a> [1/5-tone]; <a class="wiki_link" href="/55edo">55</a> and <a class="wiki_link" href="/57edo">57</a> ED2s [1/7-tones]; <a class="wiki_link" href="/71edo">71</a> and <a class="wiki_link" href="/73edo">73</a> ED2s [1/9-tones]; <a class="wiki_link" href="/87edo">87</a> and <a class="wiki_link" href="/89edo">89</a> ED2s [1/11-tones] &amp; <a class="wiki_link" href="/101edo">101</a> and <a class="wiki_link" href="/103edo">103</a> ED2s [1/13-tones]). <strong>Hornbostel Temperaments</strong> is included too on the list: <a class="wiki_link" href="/23edo">23-ED2</a> [1/3-tone]; 39-ED2 [1/5-tone]; <a class="wiki_link" href="/62edo">62-ED2</a> [1/8-tone]; <a class="wiki_link" href="/85edo">85-ED2</a> [1/11-tone] and larger: <a class="wiki_link" href="/131edo">131-ED2</a> [1/17-tone]; <a class="wiki_link" href="/177edo">177-ED2</a> [1/23-tone]; <a class="wiki_link" href="/200edo">200-ED2</a> [1/26-tone] &amp; <a class="wiki_link" href="/223edo">223-ED2</a> [1/29-tone]. Note that 101, 131, 177 &amp; 200 ED2s are tempered systems that Alexei Ogolevets was proposing in his List of Temperaments.<br /> | ||
However, its 23\39 fifth, 5.737 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|.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x39 tone equal temperament-39-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>39-EDO Intervals</strong></u></h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x39 tone equal temperament-39-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>39-EDO Intervals</strong></u></h2> | ||
Revision as of 19:09, 23 September 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Osmiorisbendi and made on 2011-09-23 19:09:24 UTC.
- The original revision id was 257653838.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=<span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span>= **39-EDO, 39-ED2** or **39-tET** divides the Octave (Duple 2/1) 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 that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, implemented in [[16edo|16-ED2]], and, allied systems ([[25edo|25-ED2]] [1/3-tone]; [[41edo|41-ED2]] [1/5-tone]; [[55edo|55]] and [[57edo|57]] ED2s [1/7-tones]; [[71edo|71]] and [[73edo|73]] ED2s [1/9-tones]; [[87edo|87]] and [[89edo|89]] ED2s [1/11-tones] & [[101edo|101]] and [[103edo|103]] ED2s [1/13-tones]). **Hornbostel Temperaments** is included too on the list: [[23edo|23-ED2]] [1/3-tone]; 39-ED2 [1/5-tone]; [[62edo|62-ED2]] [1/8-tone]; [[85edo|85-ED2]] [1/11-tone] and larger: [[131edo|131-ED2]] [1/17-tone]; [[177edo|177-ED2]] [1/23-tone]; [[200edo|200-ED2]] [1/26-tone] & [[223edo|223-ED2]] [1/29-tone]. Note that 101, 131, 177 & 200 ED2s are tempered systems that Alexei Ogolevets was proposing in his List of Temperaments. However, its 23\39 fifth, 5.737 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 (1/5-tone up) * **b** = Flat (3/5-tone down) * **#** = Sharp (3/5-tone up) * **v** = Semiflat (1/5-tone down) || || **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 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 || || 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·** || **3b** || **215.3846** || **17/15** || **216.6867** || **-1.3021** || || 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·** || **4b** || **369.2308** || **26/21** || **369.7468** || **-0.516** || || 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 || || 16 || 4t (5v) || 492.3077 || 85/64 || 491.2691 || +1.0386 || || **17·** || **5** || **523.0769** || **23/17** || **523.3189** || **-0.242** || || 18 || 5t || 553.8462 || 11/8 || 551.3179 || +2.5283 || || 19 || 6b || 584.6154 || 7/5 || 582.5122 || +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 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 || || 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 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 || || 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 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 || || 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 || || 38 || 9t (1v) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 || || **39··(or 0)** || **1** || **1200** || **2/1** || **1200** || **None** || ==__Instruments (prototypes):__== [[image:TECLADO_39-EDO.PNG width="743" height="431" caption="Armodue-Hornbostel 1/5-tone keyboard prototype"]] [[image:Custom_700mm_5-str_Tricesanonaphonic_Guitar.png width="992" height="278" caption="Visualization of a 39-EDO Fretboard, by Tútim Deft"]] ==**__39 tone equal [[modes]]__:**== 15 15 9 - [[MOSScales|MOS]] of type [[2L 1s]] 14 14 11 - [[MOSScales|MOS]] of type [[2L 1s]] 13 13 13 = [[3edo]] 11 11 11 6 - [[MOSScales|MOS]] of type [[3L 1s]] 10 10 10 9 - [[MOSScales|MOS]] of type [[3L 1s]] 11 3 11 11 3 - [[MOSScales|MOS]] of type [[3L 2s|3L 2s (father)]] 11 3 11 3 11 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[3L 2s|3L 2s (father)]]</span> 9 6 9 9 6 - [[MOSScales|MOS]] of type [[3L 2s|3L 2s (father)]] 9 6 9 6 9 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[3L 2s|3L 2s (father)]]</span> 9 9 9 9 3 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] 9 3 9 9 9 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[4L 1s|4L 1s (bug)]]</span> 8 8 8 8 7 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] 10 3 10 3 10 3 - [[MOSScales|MOS]] of type [[3L 3s|3L 3s (augmented)]] 9 4 9 4 9 4 - [[MOSScales|MOS]] of type [[3L 3s|3L 3s (augmented)]] 8 5 8 5 8 5 - [[MOSScales|MOS]] of type [[3L 3s|3L 3s (augmented)]] 7 7 7 7 7 4 - [[MOSScales|MOS]] of type [[5L 1s|5L 1s (Grumpy hexatonic)]] 7 4 7 7 7 7 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="cursor: pointer;">[[5L 1s|5L 1s (Grumpy hexatonic)]]</span> 3 9 3 9 3 9 3 - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] 5 5 7 5 5 5 7 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] 5 5 5 7 5 5 7 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] 5 7 5 5 7 5 5 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] 6 3 6 6 3 6 6 3 - [[MOSScales|MOS]] of type [[5L 3s|5L 3s (unfair father)]] 5 5 5 5 5 5 5 4 - [[MOSScales|MOS]] of type [[7L 1s|7L 1s (Grumpy octatonic)]] 5 4 5 5 5 5 5 5 - [[MOSScales|MOS]] of type [[7L 1s|7L 1s (Grumpy octatonic)]] **5 5 5 2 5 5 5 5 2** - [[MOSScales|MOS]] of type [[7L 2s|7L 2s (mavila superdiatonic)]] 5 5 2 5 5 5 2 5 5 - [[MOSScales|MOS]] of type [[7L 2s|7L 2s (mavila superdiatonic)]] 5 5 3 5 5 3 5 5 3 - [[MOSScales|MOS]] of type [[6L 3s|6L 3s (unfair augmented)]] 5 4 4 5 4 4 5 4 4 - [[MOSScales|MOS]] of type [[3L 6s|3L 6s (fair augmented)]] 4 4 4 4 4 4 4 4 4 3 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] 4 4 3 4 4 4 4 4 4 4 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] **3 3 5 3 3 3 5 3 3 3 5** - [[MOSScales|MOS]] of type [[3L 8s|3L 8s (undecimal anti-triatonic)]] 3 3 3 3 3 3 3 3 3 3 3 3 3 = [[13edo]] **3 3 3 2 3 3 3 3 2 3 3 3 3 2** - [[MOSScales|MOS]] of type [[11L 3s|11L 3s (tetradecimal triatonic)]] 3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - [[MOSScales|MOS]] of type [[9L 6s]] 3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - [[MOSScales|MOS]] of type [[7L 9s]] **2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3** - [[MOSScales|MOS]] of type [[5L 12s]] 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - [[MOSScales|MOS]] of type [[3L 15s]] **3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3** - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type [[10L 9s]] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - [[MOSScales|MOS]] of type [[19L 1s]] 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of type [[17L 5s]] **2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1** - [[MOSScales|MOS]] of type [[16L 7s]] 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - [[MOSScales|MOS]] of type [[13L 13s]] **2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** - [[MOSScales|MOS]] of type [[10L 19s]] 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[8L 23s]] 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[6L 27s]]
Original HTML content:
<html><head><title>39edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #007a23; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span></h1>
<br />
<strong>39-EDO, 39-ED2</strong> or <strong>39-tET</strong> divides the Octave (Duple 2/1) 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 that use the scheme of <a class="wiki_link" href="/7L%202s">Superdiatonic</a> LLLsLLLLs like a basical scale for notation and theory, implemented in <a class="wiki_link" href="/16edo">16-ED2</a>, and, allied systems (<a class="wiki_link" href="/25edo">25-ED2</a> [1/3-tone]; <a class="wiki_link" href="/41edo">41-ED2</a> [1/5-tone]; <a class="wiki_link" href="/55edo">55</a> and <a class="wiki_link" href="/57edo">57</a> ED2s [1/7-tones]; <a class="wiki_link" href="/71edo">71</a> and <a class="wiki_link" href="/73edo">73</a> ED2s [1/9-tones]; <a class="wiki_link" href="/87edo">87</a> and <a class="wiki_link" href="/89edo">89</a> ED2s [1/11-tones] & <a class="wiki_link" href="/101edo">101</a> and <a class="wiki_link" href="/103edo">103</a> ED2s [1/13-tones]). <strong>Hornbostel Temperaments</strong> is included too on the list: <a class="wiki_link" href="/23edo">23-ED2</a> [1/3-tone]; 39-ED2 [1/5-tone]; <a class="wiki_link" href="/62edo">62-ED2</a> [1/8-tone]; <a class="wiki_link" href="/85edo">85-ED2</a> [1/11-tone] and larger: <a class="wiki_link" href="/131edo">131-ED2</a> [1/17-tone]; <a class="wiki_link" href="/177edo">177-ED2</a> [1/23-tone]; <a class="wiki_link" href="/200edo">200-ED2</a> [1/26-tone] & <a class="wiki_link" href="/223edo">223-ED2</a> [1/29-tone]. Note that 101, 131, 177 & 200 ED2s are tempered systems that Alexei Ogolevets was proposing in his List of Temperaments.<br />
However, its 23\39 fifth, 5.737 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|.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x39 tone equal temperament-39-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>39-EDO Intervals</strong></u></h2>
<table class="wiki_table">
<tr>
<td><strong>NOMENCLATURE</strong><br />
</td>
</tr>
<tr>
<td><ul><li><strong>t</strong> = Semisharp (1/5-tone up)</li><li><strong>b</strong> = Flat (3/5-tone down)</li><li><strong>#</strong> = Sharp (3/5-tone up)</li><li><strong>v</strong> = Semiflat (1/5-tone down)</li></ul></td>
</tr>
</table>
<br />
<table class="wiki_table">
<tr>
<td><strong>Degrees</strong><br />
</td>
<td><strong>Armodue note</strong><br />
</td>
<td><strong>Cents size</strong><br />
</td>
<td><strong><a class="wiki_link" href="/Nearest%20just%20interval">Nearest Just I</a>nterval</strong><br />
</td>
<td><strong>Cents value</strong><br />
</td>
<td><strong>Error</strong><br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td><strong>1</strong><br />
</td>
<td>0<br />
</td>
<td><strong>1/1</strong><br />
</td>
<td>0<br />
</td>
<td><strong>None</strong><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>1t<br />
</td>
<td>30.7692<br />
</td>
<td>57/56<br />
</td>
<td>30.6421<br />
</td>
<td>+0.1271<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>2b<br />
</td>
<td>61.5385<br />
</td>
<td>29/28<br />
</td>
<td>60.7513<br />
</td>
<td>+0.7872<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>1#<br />
</td>
<td>92.3077<br />
</td>
<td>39/37<br />
</td>
<td>91.1386<br />
</td>
<td>+1.1691<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>2v<br />
</td>
<td>123.0769<br />
</td>
<td>44/41<br />
</td>
<td>122.2555<br />
</td>
<td>+0.8214<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>2<br />
</td>
<td>153.8462<br />
</td>
<td>35/32<br />
</td>
<td>155.1396<br />
</td>
<td>-1.2934<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>2t<br />
</td>
<td>184.6154<br />
</td>
<td>10/9<br />
</td>
<td>182.4037<br />
</td>
<td>+2.2117<br />
</td>
</tr>
<tr>
<td><strong>7·</strong><br />
</td>
<td><strong>3b</strong><br />
</td>
<td><strong>215.3846</strong><br />
</td>
<td><strong>17/15</strong><br />
</td>
<td><strong>216.6867</strong><br />
</td>
<td><strong>-1.3021</strong><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>2#<br />
</td>
<td>246.1538<br />
</td>
<td>15/13<br />
</td>
<td>247.7411<br />
</td>
<td>-1.5873<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>3v<br />
</td>
<td>276.9231<br />
</td>
<td>27/23<br />
</td>
<td>277.5907<br />
</td>
<td>-0.6676<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>3<br />
</td>
<td>307.6923<br />
</td>
<td>43/36<br />
</td>
<td>307.6077<br />
</td>
<td>+0.0846<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>3t<br />
</td>
<td>338.4615<br />
</td>
<td>17/14<br />
</td>
<td>336.1295<br />
</td>
<td>+2.332<br />
</td>
</tr>
<tr>
<td><strong>12·</strong><br />
</td>
<td><strong>4b</strong><br />
</td>
<td><strong>369.2308</strong><br />
</td>
<td><strong>26/21</strong><br />
</td>
<td><strong>369.7468</strong><br />
</td>
<td><strong>-0.516</strong><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>3#<br />
</td>
<td>400<br />
</td>
<td>34/27<br />
</td>
<td>399.0904<br />
</td>
<td>+0.9096<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>4v<br />
</td>
<td>430.7692<br />
</td>
<td>41/32<br />
</td>
<td>429.0624<br />
</td>
<td>+1.7068<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>4<br />
</td>
<td>461.5385<br />
</td>
<td>30/23<br />
</td>
<td>459.9944<br />
</td>
<td>+1.5441<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>4t (5v)<br />
</td>
<td>492.3077<br />
</td>
<td>85/64<br />
</td>
<td>491.2691<br />
</td>
<td>+1.0386<br />
</td>
</tr>
<tr>
<td><strong>17·</strong><br />
</td>
<td><strong>5</strong><br />
</td>
<td><strong>523.0769</strong><br />
</td>
<td><strong>23/17</strong><br />
</td>
<td><strong>523.3189</strong><br />
</td>
<td><strong>-0.242</strong><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>5t<br />
</td>
<td>553.8462<br />
</td>
<td>11/8<br />
</td>
<td>551.3179<br />
</td>
<td>+2.5283<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>6b<br />
</td>
<td>584.6154<br />
</td>
<td>7/5<br />
</td>
<td>582.5122<br />
</td>
<td>+2.1032<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>5#<br />
</td>
<td>615.3846<br />
</td>
<td>10/7<br />
</td>
<td>617.4878<br />
</td>
<td>-2.1032<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>6v<br />
</td>
<td>646.1538<br />
</td>
<td>16/11<br />
</td>
<td>648.6821<br />
</td>
<td>-2.5283<br />
</td>
</tr>
<tr>
<td><strong>22·</strong><br />
</td>
<td><strong>6</strong><br />
</td>
<td><strong>676.9231</strong><br />
</td>
<td><strong>34/23</strong><br />
</td>
<td><strong>676.6811</strong><br />
</td>
<td><strong>+0.242</strong><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>6t<br />
</td>
<td>707.6923<br />
</td>
<td>128/85<br />
</td>
<td>708.7309<br />
</td>
<td>-1.0386<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>7b<br />
</td>
<td>738.4615<br />
</td>
<td>23/15<br />
</td>
<td>740.0056<br />
</td>
<td>-1.5441<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>6#<br />
</td>
<td>769.2308<br />
</td>
<td>64/41<br />
</td>
<td>770.9376<br />
</td>
<td>-1.7068<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>7v<br />
</td>
<td>800<br />
</td>
<td>27/17<br />
</td>
<td>800.9096<br />
</td>
<td>-0.9096<br />
</td>
</tr>
<tr>
<td><strong>27·</strong><br />
</td>
<td><strong>7</strong><br />
</td>
<td><strong>830.7692</strong><br />
</td>
<td><strong>21/13</strong><br />
</td>
<td><strong>830.2532</strong><br />
</td>
<td><strong>+0.516</strong><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>7t<br />
</td>
<td>861.5385<br />
</td>
<td>28/17<br />
</td>
<td>863.8705<br />
</td>
<td>-2.332<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>8b<br />
</td>
<td>892.3077<br />
</td>
<td>72/43<br />
</td>
<td>892.3923<br />
</td>
<td>-0.0846<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>7#<br />
</td>
<td>923.0769<br />
</td>
<td>46/27<br />
</td>
<td>922.4093<br />
</td>
<td>+0.6676<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>8v<br />
</td>
<td>953.8462<br />
</td>
<td>26/15<br />
</td>
<td>952.2589<br />
</td>
<td>+1.5873<br />
</td>
</tr>
<tr>
<td><strong>32·</strong><br />
</td>
<td><strong>8</strong><br />
</td>
<td><strong>984.6154</strong><br />
</td>
<td><strong>30/17</strong><br />
</td>
<td><strong>983.3133</strong><br />
</td>
<td><strong>+1.3021</strong><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>8t<br />
</td>
<td>1015.3846<br />
</td>
<td>9/5<br />
</td>
<td>1017.5963<br />
</td>
<td>-2.2117<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>9b<br />
</td>
<td>1046.1538<br />
</td>
<td>64/35<br />
</td>
<td>1044.8604<br />
</td>
<td>+1.2934<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>8#<br />
</td>
<td>1076.9231<br />
</td>
<td>41/22<br />
</td>
<td>1077.7445<br />
</td>
<td>-0.8214<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>9v<br />
</td>
<td>1107.6923<br />
</td>
<td>74/39<br />
</td>
<td>1108.8614<br />
</td>
<td>-1.1691<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>9<br />
</td>
<td>1138.4615<br />
</td>
<td>56/29<br />
</td>
<td>1139.2487<br />
</td>
<td>-0.7872<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>9t (1v)<br />
</td>
<td>1169.2308<br />
</td>
<td>112/57<br />
</td>
<td>1169.3579<br />
</td>
<td>-0.1271<br />
</td>
</tr>
<tr>
<td><strong>39··(or 0)</strong><br />
</td>
<td><strong>1</strong><br />
</td>
<td><strong>1200</strong><br />
</td>
<td><strong>2/1</strong><br />
</td>
<td><strong>1200</strong><br />
</td>
<td><strong>None</strong><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x39 tone equal temperament-Instruments (prototypes):"></a><!-- ws:end:WikiTextHeadingRule:4 --><u>Instruments (prototypes):</u></h2>
<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:604:<img src="/file/view/TECLADO_39-EDO.PNG/258413072/743x431/TECLADO_39-EDO.PNG" alt="Armodue-Hornbostel 1/5-tone keyboard prototype" title="Armodue-Hornbostel 1/5-tone keyboard prototype" style="height: 431px; width: 743px;" /> --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/TECLADO_39-EDO.PNG/258413072/743x431/TECLADO_39-EDO.PNG" alt="TECLADO_39-EDO.PNG" title="TECLADO_39-EDO.PNG" style="height: 431px; width: 743px;" /></td></tr><tr><td class="imageCaption">Armodue-Hornbostel 1/5-tone keyboard prototype</td></tr></table><!-- ws:end:WikiTextLocalImageRule:604 --><br />
<br />
<!-- ws:start:WikiTextLocalImageRule:605:<img src="/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/992x278/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Visualization of a 39-EDO Fretboard, by Tútim Deft" title="Visualization of a 39-EDO Fretboard, by Tútim Deft" style="height: 278px; width: 992px;" /> --><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><!-- ws:end:WikiTextLocalImageRule:605 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x39 tone equal temperament-39 tone equal modes:"></a><!-- ws:end:WikiTextHeadingRule:6 --><strong><u>39 tone equal <a class="wiki_link" href="/modes">modes</a></u>:</strong></h2>
<br />
15 15 9 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%201s">2L 1s</a><br />
14 14 11 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%201s">2L 1s</a><br />
13 13 13 = <a class="wiki_link" href="/3edo">3edo</a><br />
11 11 11 6 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%201s">3L 1s</a><br />
10 10 10 9 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%201s">3L 1s</a><br />
11 3 11 11 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s (father)</a><br />
11 3 11 3 11 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/3L%202s">3L 2s (father)</a></span><br />
9 6 9 9 6 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s (father)</a><br />
9 6 9 6 9 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/3L%202s">3L 2s (father)</a></span><br />
9 9 9 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br />
9 3 9 9 9 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/4L%201s">4L 1s (bug)</a></span><br />
8 8 8 8 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br />
10 3 10 3 10 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s (augmented)</a><br />
9 4 9 4 9 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s (augmented)</a><br />
8 5 8 5 8 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s (augmented)</a><br />
7 7 7 7 7 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%201s">5L 1s (Grumpy hexatonic)</a><br />
7 4 7 7 7 7 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="cursor: pointer;"><a class="wiki_link" href="/5L%201s">5L 1s (Grumpy hexatonic)</a></span><br />
3 9 3 9 3 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
5 5 7 5 5 5 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br />
5 5 5 7 5 5 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br />
5 7 5 5 7 5 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br />
6 3 6 6 3 6 6 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%203s">5L 3s (unfair father)</a><br />
5 5 5 5 5 5 5 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%201s">7L 1s (Grumpy octatonic)</a><br />
5 4 5 5 5 5 5 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%201s">7L 1s (Grumpy octatonic)</a><br />
<strong>5 5 5 2 5 5 5 5 2</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%202s">7L 2s (mavila superdiatonic)</a><br />
5 5 2 5 5 5 2 5 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%202s">7L 2s (mavila superdiatonic)</a><br />
5 5 3 5 5 3 5 5 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/6L%203s">6L 3s (unfair augmented)</a><br />
5 4 4 5 4 4 5 4 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%206s">3L 6s (fair augmented)</a><br />
4 4 4 4 4 4 4 4 4 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br />
4 4 3 4 4 4 4 4 4 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br />
<strong>3 3 5 3 3 3 5 3 3 3 5</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%208s">3L 8s (undecimal anti-triatonic)</a><br />
3 3 3 3 3 3 3 3 3 3 3 3 3 = <a class="wiki_link" href="/13edo">13edo</a><br />
<strong>3 3 3 2 3 3 3 3 2 3 3 3 3 2</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/11L%203s">11L 3s (tetradecimal triatonic)</a><br />
3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%206s">9L 6s</a><br />
3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%209s">7L 9s</a><br />
<strong>2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%2012s">5L 12s</a><br />
2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%2015s">3L 15s</a><br />
<strong>3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <a class="wiki_link" href="/10L%209s">10L 9s</a><br />
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/19L%201s">19L 1s</a><br />
2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/17L%205s">17L 5s</a><br />
<strong>2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/16L%207s">16L 7s</a><br />
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/13L%2013s">13L 13s</a><br />
<strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/10L%2019s">10L 19s</a><br />
2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/8L%2023s">8L 23s</a><br />
2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/6L%2027s">6L 27s</a></body></html>