Harry Partch related scales
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The famous Partch scale is his 43 note Genesis or "pure" scale. The Wikipedia article on it is [[http://en.wikipedia.org/wiki/Harry_Partch%27s_43-tone_scale|here]], and the scale itself [[partch_43|here]]. Other Partch scales are his 29-note [[partch_29-av|adapted viola scale]], his 37-note [[partch_37|draft exposition scale]], his 41 note [[partch_41a|exposition scale]] and his 43-note [[partch_43a|exposition scale]]. 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]], [[cassmagmirrod|miracle]] or [[cassmagrodkara|karadeniz]]. 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 epimprphoic scale for which that is possible see also [[Harry Partch]]
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<html><head><title>Harry Partch related scales</title></head><body>The famous Partch scale is his 43 note Genesis or "pure" scale. The Wikipedia article on it is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch%27s_43-tone_scale" rel="nofollow">here</a>, and the scale itself <a class="wiki_link" href="/partch_43">here</a>. Other Partch scales are his 29-note <a class="wiki_link" href="/partch_29-av">adapted viola scale</a>, his 37-note <a class="wiki_link" href="/partch_37">draft exposition scale</a>, his 41 note <a class="wiki_link" href="/partch_41a">exposition scale</a> and his 43-note <a class="wiki_link" href="/partch_43a">exposition scale</a>.<br /> <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>, <a class="wiki_link" href="/cassmagmirrod">miracle</a> or <a class="wiki_link" href="/cassmagrodkara">karadeniz</a>.<br /> <br /> 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 epimprphoic scale for which that is possible<br /> <br /> see also <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a></body></html>