Harry: Difference between revisions

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'''Harry''' is the rank-2 [[~~Regular~~ temperament|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993|made]] a third of [[4/3]]) and three of which [[1001/1000|made]] equal to [[15/13]] (which is [[676/675|made]] a half of 4/3). This means that harry splits 4/3 into 6 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].

{{Infobox regtemp

| Title = Harry

| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13

| Comma basis = [[2401/2400]], [[19683/19600]] (7-limit); <br>[[243/242]], [[441/440]], [[4000/3993]] (11-limit); <br>[[243/242]], [[351/350]], [[364/363]], [[441/440]]<br>(13-limit)

| Edo join 1 = 58 | Edo join 2 = 72

| Mapping = 2; -6 -17 -10 -15 -26

| Generators = 21/20 | Generators tuning = 83.1 | Optimization method = CWE

| MOS scales = [[2L 12s]], [[14L 2s]], [[14L 16s]], [[14L 30s]]

| Odd limit 1 = 9 | Mistuning 1 = 1.81 | Complexity 1 = 44

| Odd limit 2 = 13-limit 21 | Mistuning 2 = 3.30 | Complexity 2 = 58

}}

'''Harry''' is the rank-2 [[regular temperament|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993|made]] a third of [[4/3]]) and three of which [[1001/1000|made]] equal to [[15/13]] (which is [[676/675|made]] a half of 4/3). This means that harry splits 4/3 into 6 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].

Harry was named after [[Harry Partch]], which is ironic given that Harry Partch was adamantly opposed to the very idea of tempering. This is perhaps not so insulting to Harry when you consider that these mathematical structures can also be used to arrange JI intervals into patterns ([[constant structure]]s) and create JI [[detempering]]s of the temperament.

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== Chords ==

=== As a detemperament of 14et ===

Harry is naturally considered a detemperament of [[14edo|14 equal temperament]], thus containing both diatonic and interordinal interval catgories. The small step at 1/2 octave minus seven ~21/20 generators serves as a spacer between intervals in the same category, representing 81/80~91/90~99/98~100/99~105/104~121/120.

== Chords and harmony ==

== Scales ==

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-'''Harry''' is the rank-2 [[Regular temperament|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993|made]] a third of [[4/3]]) and three of which [[1001/1000|made]] equal to [[15/13]] (which is [[676/675|made]] a half of 4/3). This means that harry splits 4/3 into 6 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].
+{{Infobox regtemp
+| Title = Harry
+| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
+| Comma basis = [[2401/2400]], [[19683/19600]] (7-limit); <br>[[243/242]], [[441/440]], [[4000/3993]] (11-limit); <br>[[243/242]], [[351/350]], [[364/363]], [[441/440]]<br>(13-limit)
+| Edo join 1 = 58 | Edo join 2 = 72
+| Mapping = 2; -6 -17 -10 -15 -26
+| Generators = 21/20 | Generators tuning = 83.1 | Optimization method = CWE
+| MOS scales = [[2L 12s]], [[14L 2s]], [[14L 16s]], [[14L 30s]]
+| Odd limit 1 = 9 | Mistuning 1 = 1.81 | Complexity 1 = 44
+| Odd limit 2 = 13-limit 21 | Mistuning 2 = 3.30 | Complexity 2 = 58
+}}
+'''Harry''' is the rank-2 [[regular temperament|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993|made]] a third of [[4/3]]) and three of which [[1001/1000|made]] equal to [[15/13]] (which is [[676/675|made]] a half of 4/3). This means that harry splits 4/3 into 6 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].
 Harry was named after [[Harry Partch]], which is ironic given that Harry Partch was adamantly opposed to the very idea of tempering. This is perhaps not so insulting to Harry when you consider that these mathematical structures can also be used to arrange JI intervals into patterns ([[constant structure]]s) and create JI [[detempering]]s of the temperament.
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 |}
-== Chords ==
+=== As a detemperament of 14et ===
-{{Main| Chords of harry }}
+Harry is naturally considered a detemperament of [[14edo|14 equal temperament]], thus containing both diatonic and interordinal interval catgories. The small step at 1/2 octave minus seven ~21/20 generators serves as a spacer between intervals in the same category, representing 81/80~91/90~99/98~100/99~105/104~121/120.
+{{Todo|complete section}}
+== Chords and harmony ==
+{{See also| Chords of harry }}
 == Scales ==