11/9: Difference between revisions
Wikispaces>Chartrekhan **Imported revision 593234932 - Original comment: ** |
Wikispaces>Chartrekhan **Imported revision 593234990 - 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:Chartrekhan|Chartrekhan]] and made on <tt>2016-09-25 08: | : This revision was by author [[User:Chartrekhan|Chartrekhan]] and made on <tt>2016-09-25 08:49:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>593234990</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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In the 11-limit theyxad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Persony temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle|miracle]], [[Breedsmic temperaments#Harry|harry]], and [[Schismatic family#Sesquiquartififths|sesquart]], conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family#Jove,%20aka%20Wonder|jove]]. | In the 11-limit theyxad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Persony temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle|miracle]], [[Breedsmic temperaments#Harry|harry]], and [[Schismatic family#Sesquiquartififths|sesquart]], conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family#Jove,%20aka%20Wonder|jove]]. | ||
By coincidence, the ratio between the common tuning frequency 440hz and the most common AC power frequency of 60hz is exactly | By coincidence, the ratio between the common tuning frequency 440hz and the most common AC power frequency of 60hz is exactly 11/9 (but 6 octaves up) | ||
See: [[Gallery of Just Intervals]]</pre></div> | See: [[Gallery of Just Intervals]]</pre></div> | ||
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In the 11-limit theyxad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Persony temperaments, including <a class="wiki_link" href="/17edo">17edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/130edo">130edo</a>, <a class="wiki_link" href="/202edo">202edo</a>, <a class="wiki_link" href="/Gamelismic%20clan#Miracle">miracle</a>, <a class="wiki_link" href="/Breedsmic%20temperaments#Harry">harry</a>, and <a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths">sesquart</a>, conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament <a class="wiki_link" href="/Breed%20family#Jove,%20aka%20Wonder">jove</a>.<br /> | In the 11-limit theyxad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Persony temperaments, including <a class="wiki_link" href="/17edo">17edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/130edo">130edo</a>, <a class="wiki_link" href="/202edo">202edo</a>, <a class="wiki_link" href="/Gamelismic%20clan#Miracle">miracle</a>, <a class="wiki_link" href="/Breedsmic%20temperaments#Harry">harry</a>, and <a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths">sesquart</a>, conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament <a class="wiki_link" href="/Breed%20family#Jove,%20aka%20Wonder">jove</a>.<br /> | ||
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By coincidence, the ratio between the common tuning frequency 440hz and the most common AC power frequency of 60hz is exactly | By coincidence, the ratio between the common tuning frequency 440hz and the most common AC power frequency of 60hz is exactly 11/9 (but 6 octaves up)<br /> | ||
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See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | ||