Harry: Difference between revisions

'''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.

This particular rank-2 temperament might be called "harry" because the lowest [[edo]] in which [[Harry Partch's 43-tone scale]] is represented distinctly is [[58edo]], and harry is one of the best temperaments supported by 58edo (it is 58 & 72). Alternatively, if you look at the tempered image of the 43-tone JI scale in this temperament, it is relatively compact and never "backtracks" from one of the 14 clusters to the previous one. In fact, the entire temperament can be derived from knowing that the fragment [12/11, 11/10, 10/9, 9/8] is supposed to be equidistant, and [14/11, 9/7] also has that same separation. The steps of those scale fragments are 121/120, 100/99, 81/80, and 99/98. Tempering these together means that 4000/3993, 243/242, and 9801/9800 are all tempered out, and harry is the unique 11-limit rank-2 temperament tempering those out.

See [[Gravity family #Harry]] for more technical data.

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{{Main| Chords of harry }}

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! [[eigenmonzo|eigenmonzo<br>(unchanged interval)]]