Harry

See also Gravity family #Harry or Breedsmic temperaments #Harry.

Harry temperament has 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 cents. 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 structures) and create JI detemperings 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 the unique 11-limit rank-2 temperament tempering those out is harry.)

Interval chain

#	Period 0		Period 1
	Cents	Approx. Ratios	Cents	Approx. Ratios
0	0.00	1/1	600.00	99/70, 140/99
1	83.12	21/20, 22/21	683.12	40/27
2	166.23	11/10	766.23	14/9
3	249.35	15/13	849.35	18/11, 44/27
4	332.46	40/33	932.46	12/7
5	415.58	14/11	1015.58	9/5
6	498.70	4/3	1098.70	66/35
7	581.81	7/5	1181.81	160/81
8	664.92	22/15	64.92	26/25, 27/26, 28/27
9	748.04	54/35	148.04	12/11
10	831.16	21/13	231.16	8/7
11	914.28	22/13	314.28	6/5
12	997.39	16/9	397.39	44/35, 63/50
13	1080.51	28/15	480.51	33/25
14	1163.62	49/25, 88/45, 108/55	563.62	18/13
15	46.74	36/35	646.74	16/11

Chords

Main article: Chords of harry

Scales

• Harry58

Tuning spectrum

eigenmonzo (unchanged interval)	generator (¢)	comments
9/7	82.458
11/10	82.502
15/13	82.580
13/11	82.799
13/10	82.865
15/11	82.881
4/3	83.007
14/13	83.019
16/13	83.057
13/12	83.071
18/13	83.099	13- and 15-odd-limit minimax
8/7	83.117
16/15	83.119
15/14	83.120
5/4	83.158	5-, 7- and 9-odd-limit minimax
7/5	83.216
6/5	83.240
11/8	83.245	11-odd-limit minimax
7/6	83.282
12/11	83.404
14/11	83.502
10/9	83.519
11/9	84.197

See also

• Lumatone mapping for harry