Harry Partch related scales: Difference between revisions
Wikispaces>genewardsmith **Imported revision 315926822 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 315933220 - 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>2012-03-29 15: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-29 15:23:54 UTC</tt>.<br> | ||
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By removing 11/10 and 20/11 from the Genesis scale, we obtain a 41 note scale which can be called Genesis Minus; this scale is close to being a [[Fokker blocks|Fokker block]], tempering to a MOS in cassandra, magic and rodan temperaments, for each of which the generators range from -20 to 20, leading to a symmetrical scale. [[Paul Erlich]] constructed [[cassmagoctrod|this]] Fokker block which is also a MOS in octacot temperament, with generator range -20 to 20. By chosing other linearly independent temperaments supported by the 11-limit patent val for 41edo to add to cassandra, magic and rodan and requiring the range of generators to be -20 to 20 for that temperament also, we can find other alternatives to Genesis Minus based on [[cassmagmonkrod|monkey]], [[cassmagsuprod|superkleismic]], or [[cassmagmirrod|miracle]], which do equally well measured by differences from Genesis Minus. | By removing 11/10 and 20/11 from the Genesis scale, we obtain a 41 note scale which can be called Genesis Minus; this scale is close to being a [[Fokker blocks|Fokker block]], tempering to a MOS in cassandra, magic and rodan temperaments, for each of which the generators range from -20 to 20, leading to a symmetrical scale. [[Paul Erlich]] constructed [[cassmagoctrod|this]] Fokker block which is also a MOS in octacot temperament, with generator range -20 to 20. By chosing other linearly independent temperaments supported by the 11-limit patent val for 41edo to add to cassandra, magic and rodan and requiring the range of generators to be -20 to 20 for that temperament also, we can find other alternatives to Genesis Minus based on [[cassmagmonkrod|monkey]], [[cassmagsuprod|superkleismic]], or [[cassmagmirrod|miracle]], which do equally well measured by differences from Genesis Minus. | ||
A 58 note scale is as small as is possible for an epimorphic scale containing Genesis, for example [[genesisplus|this one]]. By way of comparison, here is a Fokker block containing 35 of the 43 notes of Genesis: [[mynadiaechhemi]]. Mynadiaechhemi also contains a complete 11-limit tonality diamond, and 58 is the smallest size of | A 58 note scale is as small as is possible for an epimorphic scale containing Genesis, for example [[genesisplus|this one]]. By way of comparison, here is a Fokker block containing 35 of the 43 notes of Genesis: [[mynadiaechhemi]]. Mynadiaechhemi also contains a complete 11-limit tonality diamond, and 58 is the smallest size of epimorphic scale for which that is possible | ||
see also [[Harry Partch]]</pre></div> | see also [[Harry Partch]]</pre></div> | ||
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By removing 11/10 and 20/11 from the Genesis scale, we obtain a 41 note scale which can be called Genesis Minus; this scale is close to being a <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a>, tempering to a MOS in cassandra, magic and rodan temperaments, for each of which the generators range from -20 to 20, leading to a symmetrical scale. <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> constructed <a class="wiki_link" href="/cassmagoctrod">this</a> Fokker block which is also a MOS in octacot temperament, with generator range -20 to 20. By chosing other linearly independent temperaments supported by the 11-limit patent val for 41edo to add to cassandra, magic and rodan and requiring the range of generators to be -20 to 20 for that temperament also, we can find other alternatives to Genesis Minus based on <a class="wiki_link" href="/cassmagmonkrod">monkey</a>, <a class="wiki_link" href="/cassmagsuprod">superkleismic</a>, or <a class="wiki_link" href="/cassmagmirrod">miracle</a>, which do equally well measured by differences from Genesis Minus.<br /> | By removing 11/10 and 20/11 from the Genesis scale, we obtain a 41 note scale which can be called Genesis Minus; this scale is close to being a <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a>, tempering to a MOS in cassandra, magic and rodan temperaments, for each of which the generators range from -20 to 20, leading to a symmetrical scale. <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> constructed <a class="wiki_link" href="/cassmagoctrod">this</a> Fokker block which is also a MOS in octacot temperament, with generator range -20 to 20. By chosing other linearly independent temperaments supported by the 11-limit patent val for 41edo to add to cassandra, magic and rodan and requiring the range of generators to be -20 to 20 for that temperament also, we can find other alternatives to Genesis Minus based on <a class="wiki_link" href="/cassmagmonkrod">monkey</a>, <a class="wiki_link" href="/cassmagsuprod">superkleismic</a>, or <a class="wiki_link" href="/cassmagmirrod">miracle</a>, which do equally well measured by differences from Genesis Minus.<br /> | ||
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A 58 note scale is as small as is possible for an epimorphic scale containing Genesis, for example <a class="wiki_link" href="/genesisplus">this one</a>. By way of comparison, here is a Fokker block containing 35 of the 43 notes of Genesis: <a class="wiki_link" href="/mynadiaechhemi">mynadiaechhemi</a>. Mynadiaechhemi also contains a complete 11-limit tonality diamond, and 58 is the smallest size of | A 58 note scale is as small as is possible for an epimorphic scale containing Genesis, for example <a class="wiki_link" href="/genesisplus">this one</a>. By way of comparison, here is a Fokker block containing 35 of the 43 notes of Genesis: <a class="wiki_link" href="/mynadiaechhemi">mynadiaechhemi</a>. Mynadiaechhemi also contains a complete 11-limit tonality diamond, and 58 is the smallest size of epimorphic scale for which that is possible<br /> | ||
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see also <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a></body></html></pre></div> | see also <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a></body></html></pre></div> | ||