39edo: Difference between revisions

Revision as of 20:09, 2 March 2011

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Original Wikitext content:

=<span style="color: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span>= 


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 ways allied to 12EDO 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 39et tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|.

[[image:Teclado_Tricésimononafónico.PNG width="504" height="297"]]

**39-EDO Intervals:**
|| **NOMENCLATURE** ||
|| **|** = Semisharp
**t** = Semiflat ||

|| **DEGREE** || **NOTE** || **CENTS** || **[[Nearest just interval|Nearest Just I]]nterval** || **Cents** || **Error** ||
|| 0 || **1** || 0 || **1/1** || 0 || **None** ||
|| 1 || 1| || 30.7692 || 57/56 || 30.6421 || +0.1271 ||
|| 2 || 1# || 61.5385 || 29/28 || 60.7513 || +0.7872 ||
|| 3 || 2b || 92.3077 || 39/37 || 91.1386 || +1.1691 ||
|| 4 || 2t || 123.0769 || 44/41 || 122.2555 || +0.8214 ||
|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 ||
|| 6 || 2| || 184.6154 || 10/9 || 182.4037 || +2.2117 ||
|| **7·** || **2#** || **215.3846** || **17/15** || **216.6867** || **-1.3021** ||
|| 8 || 3b || 246.1538 || 15/13 || 247.7411 || -1.5873 ||
|| 9 || 3t || 276.9231 || 27/23 || 277.5907 || -0.6676 ||
|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 ||
|| 11 || 3| || 338.4615 || 17/14 || 336.1295 || +2.332 ||
|| **12·** || **3#** || **369.2308** || **26/21** || **369.7468** || **-0.516** ||
|| 13 || 4b || 400 || 34/27 || 399.0904 || +0.9096 ||
|| 14 || 4t || 430.7692 || 41/32 || 429.0624 || +1.7068 ||
|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||
|| 16 || 4| (5t) || 492.3077 || 85/64 || 491.2691 || +1.0386 ||
|| **17·** || **5** || **523.0769** || **23/17** || **523.3189** || **-0.242** ||
|| 18 || 5| || 553.8462 || 11/8 || 551.3179 || +2.5283 ||
|| 19 || 5# || 584.6154 || 7/5 || 582.5122 || +2.1032 ||
|| 20 || 6b || 615.3846 || 10/7 || 617.4878 || -2.1032 ||
|| 21 || 6t || 646.1538 || 16/11 || 648.6821 || -2.5283 ||
|| **22·** || **6** || **676.9231** || **34/23** || **676.6811** || **+0.242** ||
|| 23 || 6| || 707.6923 || 128/85 || 708.7309 || -1.0386 ||
|| 24 || 6# || 738.4615 || 23/15 || 740.0056 || -1.5441 ||
|| 25 || 7b || 769.2308 || 64/41 || 770.9376 || -1.7068 ||
|| 26 || 7t || 800 || 27/17 || 800.9096 || -0.9096 ||
|| **27·** || **7** || **830.7692** || **21/13** || **830.2532** || **+0.516** ||
|| 28 || 7| || 861.5385 || 28/17 || 863.8705 || -2.332 ||
|| 29 || 7# (A) || 892.3077 || 72/43 || 892.3923 || -0.0846 ||
|| 30 || 8b || 923.0769 || 46/27 || 922.4093 || +0.6676 ||
|| 31 || 8t || 953.8462 || 26/15 || 952.2589 || +1.5873 ||
|| **32·** || **8** || **984.6154** || **30/17** || **983.3133** || **+1.3021** ||
|| 33 || 8| || 1015.3846 || 9/5 || 1017.5963 || -2.2117 ||
|| 34 || 8# || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||
|| 35 || 9b || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||
|| 36 || 9t || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||
|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||
|| 38 || 9| (1t) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 ||
|| **39··(or 0)** || **1** || **1200** || **2/1** || **1200** || **None** ||


**39 tone equal [[modes]]:**

15 15 9
14 14 11
13 13 13
11 11 11 6
10 10 10 9
9 9 9 9 3 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]]
8 8 8 8 7 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]]
7 7 7 7 7 4 - [[MOSScales|MOS]] of type [[5L 1s|5L 1s (Grumpy hexatonic)]]
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 5 5 7 5 7 5 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]]
5 5 5 5 5 5 5 4 - [[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 (unfair mavila)]]
5 5 2 5 5 5 2 5 5 - [[MOSScales|MOS]] of type [[7L 2s|7L 2s (unfair mavila)]]
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)]]
3 3 3 3 3 3 3 3 3 3 3 3 3
**3 3 3 2 3 3 3 3 2 3 3 3 3 2** - [[MOSScales|MOS]] of type [[11L 3s]]
2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2 - [[MOSScales|MOS]] of type [[5L 12s]]
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 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]]

Original HTML content:

<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: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span></h1>
 <br />
<br />
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 <strong>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]).</strong> 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 ways allied to 12EDO 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 39et tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:588:&lt;img src=&quot;/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/504x297/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 297px; width: 504px;&quot; /&gt; --><img src="/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/504x297/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG" alt="Teclado_Tricésimononafónico.PNG" title="Teclado_Tricésimononafónico.PNG" style="height: 297px; width: 504px;" /><!-- ws:end:WikiTextLocalImageRule:588 --><br />
<br />
<strong>39-EDO Intervals:</strong><br />


<table class="wiki_table">
    <tr>
        <td><strong>NOMENCLATURE</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>|</strong> = Semisharp<br />
<strong>t</strong> = Semiflat<br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td><strong>DEGREE</strong><br />
</td>
        <td><strong>NOTE</strong><br />
</td>
        <td><strong>CENTS</strong><br />
</td>
        <td><strong><a class="wiki_link" href="/Nearest%20just%20interval">Nearest Just I</a>nterval</strong><br />
</td>
        <td><strong>Cents</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>1|<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>1#<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>2b<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>2t<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>2|<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>2#</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>3b<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>3t<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>3|<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>3#</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>4b<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>4t<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>4| (5t)<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>5|<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>5#<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>6b<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>6t<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>6|<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>6#<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>7b<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>7t<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>7|<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>7# (A)<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>8b<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>8t<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>8|<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>8#<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>9b<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>9t<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>9| (1t)<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 />
<br />
<strong>39 tone equal <a class="wiki_link" href="/modes">modes</a>:</strong><br />
<br />
15 15 9<br />
14 14 11<br />
13 13 13<br />
11 11 11 6<br />
10 10 10 9<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 />
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 />
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 />
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 5 5 7 5 7 5 - <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 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 />
<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 (unfair mavila)</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 (unfair mavila)</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 />
3 3 3 3 3 3 3 3 3 3 3 3 3<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</a><br />
2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2 - <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 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 />
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 />
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 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/10L%2019s">10L 19s</a></body></html>

@@ 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>2010-09-19 00:15:56 UTC</tt>.<br>
+: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-03-02 20:09:27 UTC</tt>.<br>
-: The original revision id was <tt>163682373</tt>.<br>
+: The original revision id was <tt>206747286</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 9: / Line 9: @@
-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 (23EDO) and allied systems. 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 ways allied to 12EDO 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 39et tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.
+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 ways allied to 12EDO 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 39et tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.
 [[image:Teclado_Tricésimononafónico.PNG width="504" height="297"]]
@@ Line 19: / Line 19: @@
 || **DEGREE** || **NOTE** || **CENTS** || **[[Nearest just interval|Nearest Just I]]nterval** || **Cents** || **Error** ||
-|| **0** || **1** || **0** || **1/1** || **0** || **None** ||
+|| 0 || **1** || 0 || **1/1** || 0 || **None** ||
-|| 1 || 1| || 30.7692 || 58/57 || 30.1092 || +0.66 ||
+|| 1 || 1| || 30.7692 || 57/56 || 30.6421 || +0.1271 ||
-|| 2 || 1# || 61.5385 || 28/27 || 62.9609 || - 1.4224 ||
+|| 2 || 1# || 61.5385 || 29/28 || 60.7513 || +0.7872 ||
-|| 3 || 2b || 92.3077 || 58/55 || 91.9455 || +0.3622 ||
+|| 3 || 2b || 92.3077 || 39/37 || 91.1386 || +1.1691 ||
-|| 4 || 2t || 123.0769 || 29/27 || 123.7122 || -0.6353 ||
+|| 4 || 2t || 123.0769 || 44/41 || 122.2555 || +0.8214 ||
-|| 5 || 2 || 153.8462 || 82/75 || 154.48 || -0.6338 ||
+|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 ||
 || 6 || 2| || 184.6154 || 10/9 || 182.4037 || +2.2117 ||
 || **7·** || **2#** || **215.3846** || **17/15** || **216.6867** || **-1.3021** ||
 || 8 || 3b || 246.1538 || 15/13 || 247.7411 || -1.5873 ||
 || 9 || 3t || 276.9231 || 27/23 || 277.5907 || -0.6676 ||
-|| 10 || 3 || 307.6923 || 49/41 || 308.5894 || -0.8971 ||
+|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 ||
-|| 11 || 3| || 338.4615 || 62/51 || 338.1252 || +0.3363 ||
+|| 11 || 3| || 338.4615 || 17/14 || 336.1295 || +2.332 ||
 || **12·** || **3#** || **369.2308** || **26/21** || **369.7468** || **-0.516** ||
 || 13 || 4b || 400 || 34/27 || 399.0904 || +0.9096 ||
 || 14 || 4t || 430.7692 || 41/32 || 429.0624 || +1.7068 ||
-|| 15 || 4 || 461.5385 || 43/33 || 458.2448 || +3.2937 ||
+|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||
 || 16 || 4| (5t) || 492.3077 || 85/64 || 491.2691 || +1.0386 ||
 || **17·** || **5** || **523.0769** || **23/17** || **523.3189** || **-0.242** ||
@@ Line 43: / Line 43: @@
 || **22·** || **6** || **676.9231** || **34/23** || **676.6811** || **+0.242** ||
 || 23 || 6| || 707.6923 || 128/85 || 708.7309 || -1.0386 ||
-|| 24 || 6# || 738.4615 || 66/43 || 741.7552 || -3.2937 ||
+|| 24 || 6# || 738.4615 || 23/15 || 740.0056 || -1.5441 ||
 || 25 || 7b || 769.2308 || 64/41 || 770.9376 || -1.7068 ||
 || 26 || 7t || 800 || 27/17 || 800.9096 || -0.9096 ||
 || **27·** || **7** || **830.7692** || **21/13** || **830.2532** || **+0.516** ||
-|| 28 || 7| || 861.5385 || 51/31 || 861.8748 || -0.3363 ||
+|| 28 || 7| || 861.5385 || 28/17 || 863.8705 || -2.332 ||
-|| 29 || 7# (A) || 892.3077 || 82/49 || 891.4106 || +0.8971 ||
+|| 29 || 7# (A) || 892.3077 || 72/43 || 892.3923 || -0.0846 ||
 || 30 || 8b || 923.0769 || 46/27 || 922.4093 || +0.6676 ||
 || 31 || 8t || 953.8462 || 26/15 || 952.2589 || +1.5873 ||
 || **32·** || **8** || **984.6154** || **30/17** || **983.3133** || **+1.3021** ||
 || 33 || 8| || 1015.3846 || 9/5 || 1017.5963 || -2.2117 ||
-|| 34 || 8# || 1046.1538 || 75/41 || 1045.52 || +0.6338 ||
+|| 34 || 8# || 1046.1538 || 64/35 || 1044.8604 || +1.2934 ||
-|| 35 || 9b || 1076.9231 || 54/29 || 1076.2878 || +0.6353 ||
+|| 35 || 9b || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||
-|| 36 || 9t || 1107.6923 || 55/29 || 1108.0545 || -0.3622 ||
+|| 36 || 9t || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||
-|| 37 || 9 || 1138.4615 || 27/14 || 1137.0391 || +1.4224 ||
+|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||
-|| 38 || 9| (1t) || 1169.2308 || 57/29 || 1169.8908 || -0.66 ||
+|| 38 || 9| (1t) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 ||
 || **39··(or 0)** || **1** || **1200** || **2/1** || **1200** || **None** ||
@@ Line 91: / Line 91: @@
   &lt;br /&gt;
 &lt;br /&gt;
-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 (23EDO) and allied systems. 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 ways allied to 12EDO 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 39et tempers out 99/98 and 121/120 also. This better choice for 39et is &amp;lt;39 62 91 110 135|.&lt;br /&gt;
+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 &lt;strong&gt;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]).&lt;/strong&gt; 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 ways allied to 12EDO 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 39et 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:WikiTextLocalImageRule:588:&amp;lt;img src=&amp;quot;/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/504x297/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 297px; width: 504px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/504x297/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG" alt="Teclado_Tricésimononafónico.PNG" title="Teclado_Tricésimononafónico.PNG" style="height: 297px; width: 504px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:588 --&gt;&lt;br /&gt;
@@ Line 149: / Line 149: @@
          &lt;td&gt;30.7692&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;58/57&lt;br /&gt;
+         &lt;td&gt;57/56&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;30.1092&lt;br /&gt;
+         &lt;td&gt;30.6421&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.66&lt;br /&gt;
+         &lt;td&gt;+0.1271&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 163: / Line 163: @@
          &lt;td&gt;61.5385&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;28/27&lt;br /&gt;
+         &lt;td&gt;29/28&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;62.9609&lt;br /&gt;
+         &lt;td&gt;60.7513&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;- 1.4224&lt;br /&gt;
+         &lt;td&gt;+0.7872&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 177: / Line 177: @@
          &lt;td&gt;92.3077&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;58/55&lt;br /&gt;
+         &lt;td&gt;39/37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;91.9455&lt;br /&gt;
+         &lt;td&gt;91.1386&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.3622&lt;br /&gt;
+         &lt;td&gt;+1.1691&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 191: / Line 191: @@
          &lt;td&gt;123.0769&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;29/27&lt;br /&gt;
+         &lt;td&gt;44/41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;123.7122&lt;br /&gt;
+         &lt;td&gt;122.2555&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.6353&lt;br /&gt;
+         &lt;td&gt;+0.8214&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 205: / Line 205: @@
          &lt;td&gt;153.8462&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;82/75&lt;br /&gt;
+         &lt;td&gt;35/32&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;154.48&lt;br /&gt;
+         &lt;td&gt;155.1396&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.6338&lt;br /&gt;
+         &lt;td&gt;-1.2934&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 275: / Line 275: @@
          &lt;td&gt;307.6923&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;49/41&lt;br /&gt;
+         &lt;td&gt;43/36&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;308.5894&lt;br /&gt;
+         &lt;td&gt;307.6077&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.8971&lt;br /&gt;
+         &lt;td&gt;+0.0846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 289: / Line 289: @@
          &lt;td&gt;338.4615&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;62/51&lt;br /&gt;
+         &lt;td&gt;17/14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;338.1252&lt;br /&gt;
+         &lt;td&gt;336.1295&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.3363&lt;br /&gt;
+         &lt;td&gt;+2.332&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 345: / Line 345: @@
          &lt;td&gt;461.5385&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;43/33&lt;br /&gt;
+         &lt;td&gt;30/23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;458.2448&lt;br /&gt;
+         &lt;td&gt;459.9944&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+3.2937&lt;br /&gt;
+         &lt;td&gt;+1.5441&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 471: / Line 471: @@
          &lt;td&gt;738.4615&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;66/43&lt;br /&gt;
+         &lt;td&gt;23/15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;741.7552&lt;br /&gt;
+         &lt;td&gt;740.0056&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-3.2937&lt;br /&gt;
+         &lt;td&gt;-1.5441&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 527: / Line 527: @@
          &lt;td&gt;861.5385&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;51/31&lt;br /&gt;
+         &lt;td&gt;28/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;861.8748&lt;br /&gt;
+         &lt;td&gt;863.8705&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.3363&lt;br /&gt;
+         &lt;td&gt;-2.332&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 541: / Line 541: @@
          &lt;td&gt;892.3077&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;82/49&lt;br /&gt;
+         &lt;td&gt;72/43&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;891.4106&lt;br /&gt;
+         &lt;td&gt;892.3923&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.8971&lt;br /&gt;
+         &lt;td&gt;-0.0846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 611: / Line 611: @@
          &lt;td&gt;1046.1538&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;75/41&lt;br /&gt;
+         &lt;td&gt;64/35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1045.52&lt;br /&gt;
+         &lt;td&gt;1044.8604&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.6338&lt;br /&gt;
+         &lt;td&gt;+1.2934&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 625: / Line 625: @@
          &lt;td&gt;1076.9231&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;54/29&lt;br /&gt;
+         &lt;td&gt;41/22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1076.2878&lt;br /&gt;
+         &lt;td&gt;1077.7445&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.6353&lt;br /&gt;
+         &lt;td&gt;-0.8214&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 639: / Line 639: @@
          &lt;td&gt;1107.6923&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;55/29&lt;br /&gt;
+         &lt;td&gt;74/39&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1108.0545&lt;br /&gt;
+         &lt;td&gt;1108.8614&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.3622&lt;br /&gt;
+         &lt;td&gt;-1.1691&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 653: / Line 653: @@
          &lt;td&gt;1138.4615&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;27/14&lt;br /&gt;
+         &lt;td&gt;56/29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1137.0391&lt;br /&gt;
+         &lt;td&gt;1139.2487&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+1.4224&lt;br /&gt;
+         &lt;td&gt;-0.7872&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 667: / Line 667: @@
          &lt;td&gt;1169.2308&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;57/29&lt;br /&gt;
+         &lt;td&gt;112/57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1169.8908&lt;br /&gt;
+         &lt;td&gt;1169.3579&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-0.66&lt;br /&gt;
+         &lt;td&gt;-0.1271&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

39edo: Difference between revisions

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