Harry Partch's 43-tone scale: Difference between revisions
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[[File:Harry Partch Institute-3.jpg|thumb|right|250px|The [[Quadrangularis Reversum]], one of Partch's instruments featuring the 43-tone scale]] | [[File:Harry Partch Institute-3.jpg|thumb|right|250px|The [[Quadrangularis Reversum]], one of Partch's instruments featuring the 43-tone scale]] | ||
The '''43-tone scale''' is a [[just intonation]] scale with 43 pitches in each [[octave]]. It is based on an eleven-limit tonality diamond, similar to the seven-limit diamond previously devised by [[Max Friedrich Meyer]]<ref>[http://www.chrysalis-foundation.org/Meyer-s_Diamond.htm "Musical Mathematics: Meyer's Diamond"], ''Chrysalis-Foundation.org''.</ref> and refined by [[Harry Partch]].<ref>Kassel, R. (2001, January 20). Partch, Harry. [https://www.oxfordmusiconline.com/grovemusic/ ''Grove Music Online''].</ref> | The '''43-tone scale''' is a [[just intonation]] scale with 43 pitches in each [[octave]]. It is based on an eleven-limit [[tonality diamond]], similar to the seven-limit diamond previously devised by [[Max Friedrich Meyer]]<ref>[http://www.chrysalis-foundation.org/Meyer-s_Diamond.htm "Musical Mathematics: Meyer's Diamond"], ''Chrysalis-Foundation.org''.</ref> and refined by [[Harry Partch]].<ref>Kassel, R. (2001, January 20). Partch, Harry. [https://www.oxfordmusiconline.com/grovemusic/ ''Grove Music Online''].</ref> | ||
See [[Partch 43]] for the scale as a scala file. | See [[Partch 43]] for the scale as a scala file. | ||
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[[Erv Wilson]] who worked with Partch has pointed out that these added tones form a constant structure of 41 tones with two variables.<ref name="Anaphoria">"Letter to John from ERV Wilson, 19 October 1964 - SH 5 Chalmers" (PDF). Anaphoria.com. Retrieved 2016-10-28.page 11</ref> A constant structure giving one the property of anytime a ratio appears it will be subtended by the same number of steps. In this way Partch resolved his harmonic and melodic symmetry in one of the best ways possible.<ref name="Anaphoria" /> | [[Erv Wilson]] who worked with Partch has pointed out that these added tones form a constant structure of 41 tones with two variables.<ref name="Anaphoria">"Letter to John from ERV Wilson, 19 October 1964 - SH 5 Chalmers" (PDF). Anaphoria.com. Retrieved 2016-10-28.page 11</ref> A constant structure giving one the property of anytime a ratio appears it will be subtended by the same number of steps. In this way Partch resolved his harmonic and melodic symmetry in one of the best ways possible.<ref name="Anaphoria" /> | ||
==Comparison with 41edo== | |||
The 43-note scale is almost [[epimorphic]] under the [[41edo]] [[patent val]]. The only exceptions are the pair {11/10, 10/9} and its octave complement {9/5, 20/11}, which are tempered together in [[41edo]]. Other than those, 41edo does a decent job of representing everything, for an EDO (although of course Partch himself would scoff at such a claim). | The 43-note scale is almost [[epimorphic]] under the [[41edo]] [[patent val]]. The only exceptions are the pair {11/10, 10/9} and its octave complement {9/5, 20/11}, which are tempered together in [[41edo]]. Other than those, 41edo does a decent job of representing everything, for an EDO (although of course Partch himself would scoff at such a claim). | ||
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| 41 || 2/1 || 1200.00 || 1200.00 || 0.00 | | 41 || 2/1 || 1200.00 || 1200.00 || 0.00 | ||
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== Comparison with 72edo == | |||
Since [[72edo]] is [[distinctly consistent]] in the 11-limit and is a [[pepper ambiguity]] record in the 11-limit unsurpassed until 270, 72edo fits very well the Harry Partch's 43-tone scale. | |||
The mode is: 1 2 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 2 2 1 | |||
==References== | ==References== | ||