72edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 264023367 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 264024823 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-10-12 11: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-12 11:47:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>264024823</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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72-tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, and is the ninth [[The Riemann Zeta Function and Tuning#Zeta EDO lists|Zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33. | 72-tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, and is the ninth [[The Riemann Zeta Function and Tuning#Zeta EDO lists|Zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33. | ||
72 is an excellent tuning for [[Gamelismic clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament prodigy, and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic. | 72 is an excellent tuning for [[Gamelismic clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament [[Marvel family#Prodigy|prodigy]], and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic. | ||
=Harmonic Scale= | =Harmonic Scale= | ||
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72-tone equal temperament approximates <a class="wiki_link" href="/11-limit">11-limit just intonation</a> exceptionally well, and is the ninth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">Zeta integral tuning</a>. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33.<br /> | 72-tone equal temperament approximates <a class="wiki_link" href="/11-limit">11-limit just intonation</a> exceptionally well, and is the ninth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">Zeta integral tuning</a>. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33.<br /> | ||
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72 is an excellent tuning for <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>, especially the 11-limit version, and the related rank three temperament prodigy, and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic.<br /> | 72 is an excellent tuning for <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>, especially the 11-limit version, and the related rank three temperament <a class="wiki_link" href="/Marvel%20family#Prodigy">prodigy</a>, and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Harmonic Scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Harmonic Scale</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Harmonic Scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Harmonic Scale</h1> | ||