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.

Leapday is not to be confused with temperaments derived from calendar leap year cycles, such as Gregorian leap day in 400edo.

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