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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-12 16:15:55 UTC</tt>.<br>
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| : The original revision id was <tt>591725512</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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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">The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third [[@The Riemann Zeta Function and Tuning#Removing%20primes|no-twos zeta peak edt]].
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| Following [[@4edt]], this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to [[@7edo]] in diatonic music. | | Following [[4edt|4edt]], this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to [[7edo|7edo]] in diatonic music. |
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| This scale is also related to [[@17edo]] by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1. | | This scale is also related to [[17edo|17edo]] by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1. |
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| 0: 1/1 | | 0: 1/1 |
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| 1: 211.328 cents 9/8 | | 1: 211.328 cents 9/8 |
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| 2: 422.657 cents 9/7 | | 2: 422.657 cents 9/7 |
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| 3: 633.985 cents 13/9 | | 3: 633.985 cents 13/9 |
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| 4: 845.313 cents 5/3 | | 4: 845.313 cents 5/3 |
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| 5: 1056.642 cents 9/5 | | 5: 1056.642 cents 9/5 |
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| 6: 1267.970 cents 27/13 | | 6: 1267.970 cents 27/13 |
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| 7: 1479.298 cents 7/3 | | 7: 1479.298 cents 7/3 |
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| 8: 1690.627 cents 8/3 | | 8: 1690.627 cents 8/3 |
| 9: 3/1</pre></div>
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| <h4>Original HTML content:</h4>
| | 9: 3/1 |
| <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>9edt</title></head><body>The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes" target="_blank">no-twos zeta peak edt</a>.<br />
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| <br />
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| Following <a class="wiki_link" href="/4edt" target="_blank">4edt</a>, this is the next &quot;Lambda&quot; (BP related) equal division of the tritave; in a certain sense analogous to <a class="wiki_link" href="/7edo" target="_blank">7edo</a> in diatonic music.<br />
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| <br />
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| This scale is also related to <a class="wiki_link" href="/17edo" target="_blank">17edo</a> by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1.<br />
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| <br />
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| 0: 1/1<br />
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| 1: 211.328 cents 9/8<br />
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| 2: 422.657 cents 9/7<br />
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| 3: 633.985 cents 13/9<br />
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| 4: 845.313 cents 5/3<br />
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| 5: 1056.642 cents 9/5<br />
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| 6: 1267.970 cents 27/13<br />
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| 7: 1479.298 cents 7/3<br />
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| 8: 1690.627 cents 8/3<br />
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| 9: 3/1</body></html></pre></div> | |
The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third no-twos zeta peak edt.
Following 4edt, this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to 7edo in diatonic music.
This scale is also related to 17edo by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1.
0: 1/1
1: 211.328 cents 9/8
2: 422.657 cents 9/7
3: 633.985 cents 13/9
4: 845.313 cents 5/3
5: 1056.642 cents 9/5
6: 1267.970 cents 27/13
7: 1479.298 cents 7/3
8: 1690.627 cents 8/3
9: 3/1