Leapday

Leapday is a temperament for the 7, 11, 13, 17, and 19 prime limits. It is a member of trisayo family, sengic temperaments and hemifamity temperaments. It has a fifth generator of ~3/2 = 704.2¢, eight of them makes ~13/8, eleven of them makes ~11/8, fifteen of them makes ~7/4, twenty-one of them makes ~5/4 and twenty-four of them makes ~17/16. Equivalently, the fifth of leapday in size is ~2.3 cents sharp of 3/2, 13/8 is represented by an augmented fifth, 11/8 is represented by an augmented third, 7/4 is represented by a double-augmented fifth, 5/4 is represented by a triple-augmented unison, and 17/16 is represented by a negative triple-diminished third.

See Hemifamity temperaments for more technical data.

Tuning spectrum

Gencom: [2 3/2; 91/90 121/120 133/132 136/135 154/153 169/168]

Gencom mapping: [⟨1 1 -10 -6 -3 -1 -10 6], ⟨0 1 21 15 11 8 24 -3]]

ET generator	eigenmonzo (unchanged interval)	fifth (¢)	comments
	19/16	700.829
	24/19	701.110
	19/18	701.279
	4/3	701.955
24\41		702.439
	15/14	702.778
	7/5	702.915
	21/20	703.107
	15/11	703.359
	15/13	703.410
17\29		703.448
	11/10	703.500
	13/10	703.522
	13/11	703.597
	19/15	703.630
	20/19	703.700
	26/21	703.782
	22/19	703.843
	21/19	703.856
	22/21	703.893
	26/19	703.910
	19/14	703.962
	19/17	703.979	19 and 21-odd-limit minimax
44\75		704.000
	16/15	704.012
	17/14	704.014
	17/13	704.027
	14/13	704.043
	5/4	704.110	5-odd-limit minimax
	22/17	704.126
71\121		704.132
	6/5	704.218	7, 15 and 17-odd-limit minimax
	21/17	704.272
	10/9	704.337	9, 11 and 13-odd-limit minimax
27\46		704.348
	17/16	704.373
	14/11	704.377
	21/16	704.424
	24/17	704.478
	8/7	704.588
	18/17	704.593
	11/8	704.665
37\63		704.762
	7/6	704.776
	12/11	704.936
	9/7	704.994
	16/13	705.066
	11/9	705.268
	13/12	705.510
10\17		705.882
	18/13	706.103
	20/17	706.214
	17/15	708.343