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15edo

• 52ed11
• 11lim WE (79.770)
• 50ed10
• 47zpi (79.715)
• 54ed12

15edo's primes 3, 5, 11 and 13 are all tuned sharp, so it can benefit from octave shrinking.

18edo

• 42ed5
• 47ed6
• 60ed10
• 65ed12
• 7lim WE (66.148)
• 13lim WE (66.291)
• 60zpi (67.090)
• 61zpi (66.228)

18edo's primes 3, 5, 7 and 13 are all tuned sharp, so it can benefit from octave shrinking.

Approximation of prime harmonics in 18edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+31.4	+13.7	+31.2	-18.0	+26.1	+28.4	-30.8	-28.3	-29.6	-11.7
	Relative (%)	+0.0	+47.1	+20.5	+46.8	-27.0	+39.2	+42.6	-46.3	-42.4	-44.4	-17.6
Steps (reduced)		18 (0)	29 (11)	42 (6)	51 (15)	62 (8)	67 (13)	74 (2)	76 (4)	81 (9)	87 (15)	89 (17)

Approximation of prime harmonics in 42ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.9	+21.9	+0.0	+14.6	+28.2	+4.3	+4.3	+10.7	+11.7	+8.4	+25.6
	Relative (%)	-8.8	+33.1	+0.0	+21.9	+42.4	+6.5	+6.4	+16.2	+17.6	+12.7	+38.6
Steps (reduced)		18 (18)	29 (29)	42 (0)	51 (9)	63 (21)	67 (25)	74 (32)	77 (35)	82 (40)	88 (4)	90 (6)

Approximation of prime harmonics in 47ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-12.0	+12.0	-14.4	-2.9	+6.6	-18.6	-21.0	-15.6	-16.4	-21.7	-5.1
	Relative (%)	-18.2	+18.2	-21.7	-4.4	+10.0	-28.2	-31.9	-23.6	-24.8	-32.8	-7.8
Steps (reduced)		18 (18)	29 (29)	42 (42)	51 (4)	63 (16)	67 (20)	74 (27)	77 (30)	82 (35)	88 (41)	90 (43)

Approximation of prime harmonics in 60ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.1	+24.8	+4.1	+19.5	-32.1	+10.9	+11.5	+18.3	+19.7	+17.0	-32.0
	Relative (%)	-6.2	+37.3	+6.2	+29.4	-48.4	+16.3	+17.3	+27.5	+29.6	+25.6	-48.2
Steps (reduced)		18 (18)	29 (29)	42 (42)	51 (51)	62 (2)	67 (7)	74 (14)	77 (17)	82 (22)	88 (28)	89 (29)

{{harmonics in equal | 65 | 12 | 1 | intervals=prime}

Approximation of prime harmonics in 1ed66.148c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-9.3	+16.3	-8.1	+4.7	+16.0	-8.6	-10.0	-4.1	-4.1	-8.6	+8.3
	Relative (%)	-14.1	+24.7	-12.2	+7.1	+24.2	-13.0	-15.1	-6.2	-6.3	-12.9	+12.5
Step		18	29	42	51	63	67	74	77	82	88	90

Approximation of prime harmonics in 1ed66.291c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-6.8	+20.5	-2.1	+12.0	+25.0	+1.0	+0.6	+6.9	+7.6	+4.0	+21.2
	Relative (%)	-10.2	+30.9	-3.2	+18.1	+37.7	+1.5	+0.9	+10.4	+11.4	+6.1	+31.9
Step		18	29	42	51	63	67	74	77	82	88	90

Approximation of prime harmonics in 1ed67.09c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+7.6	-23.4	+31.5	-14.3	+8.3	-12.6	-7.4	+1.3	+6.0	+7.3	+26.0
	Relative (%)	+11.4	-34.9	+46.9	-21.4	+12.3	-18.8	-11.0	+2.0	+9.0	+10.8	+38.7
Step		18	28	42	50	62	66	73	76	81	87	89

Approximation of prime harmonics in 1ed66.228c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-7.9	+18.7	-4.7	+8.8	+21.0	-3.3	-4.1	+2.0	+2.4	-1.5	+15.5
	Relative (%)	-11.9	+28.2	-7.2	+13.3	+31.8	-4.9	-6.2	+3.1	+3.7	-2.3	+23.4
Step		18	29	42	51	63	67	74	77	82	88	90

25edo

• 65ed6
• 90ed12
• 13lim WE (47.946)
• 95zpi (48.067)
• 96zpi (47.642)

25edo's prime 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from octave shrinking.

Approximation of prime harmonics in 25edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+18.0	-2.3	-8.8	-23.3	+23.5	-9.0	-9.5	-4.3	-21.6	+7.0
	Relative (%)	+0.0	+37.6	-4.8	-18.4	-48.6	+48.9	-18.7	-19.8	-8.9	-45.0	+14.5
Steps (reduced)		25 (0)	40 (15)	58 (8)	70 (20)	86 (11)	93 (18)	102 (2)	106 (6)	113 (13)	121 (21)	124 (24)

Approximation of prime harmonics in 65ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-6.9	+6.9	-18.4	+19.5	+0.5	-2.3	+10.5	+8.8	+12.1	-7.4	+20.3
	Relative (%)	-14.5	+14.5	-38.6	+40.8	+1.1	-4.9	+21.9	+18.4	+25.3	-15.6	+42.5
Steps (reduced)		25 (25)	40 (40)	58 (58)	71 (6)	87 (22)	93 (28)	103 (38)	107 (42)	114 (49)	122 (57)	125 (60)

{{harmonics in equal | 90 | 12 | 1 | intervals=prime}

Approximation of prime harmonics in 1ed47.946c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.4	+15.9	-5.4	-12.6	+20.0	+18.5	-14.5	-15.2	-10.4	+19.8	+0.3
	Relative (%)	-2.8	+33.1	-11.4	-26.3	+41.7	+38.5	-30.2	-31.8	-21.6	+41.4	+0.6
Step		25	40	58	70	87	93	102	106	113	122	124

Approximation of prime harmonics in 1ed48.067c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.7	+20.7	+1.6	-4.1	-17.6	-18.4	-2.1	-2.4	+3.3	-13.5	+15.3
	Relative (%)	+3.5	+43.1	+3.3	-8.6	-36.5	-38.2	-4.4	-5.0	+6.9	-28.0	+31.8
Step		25	40	58	70	86	92	102	106	113	121	124

Approximation of prime harmonics in 1ed47.642c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-8.9	+3.7	-23.1	+13.8	-6.5	-9.8	+2.2	+0.2	+2.9	-17.3	+10.2
	Relative (%)	-18.8	+7.8	-48.4	+28.9	-13.6	-20.6	+4.6	+0.4	+6.1	-36.2	+21.4
Step		25	40	58	71	87	93	103	107	114	122	125

26edo

• 41edt
• 67ed6
• 86ed10
• 93ed12
• 96ed14
• 13lim WE (46.249) (octave identical to 11lim within 1/20th of a cent)
• 100zpi (46.268)

26edo's simple primes with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from octave stretching.

Approximation of prime harmonics in 26edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	-9.6	-17.1	+0.4	+2.5	-9.8	-12.6	-20.6	+17.9	-14.2	+8.8
	Relative (%)	+0.0	-20.9	-37.0	+0.9	+5.5	-21.1	-27.4	-44.6	+38.7	-30.8	+19.1
Steps (reduced)		26 (0)	41 (15)	60 (8)	73 (21)	90 (12)	96 (18)	106 (2)	110 (6)	118 (14)	126 (22)	129 (25)

Approximation of prime harmonics in 41edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+6.1	+0.0	-3.0	+17.6	-22.7	+12.8	+12.3	+5.3	-0.7	+15.5	-7.2
	Relative (%)	+13.2	+0.0	-6.4	+37.9	-48.9	+27.7	+26.5	+11.4	-1.6	+33.3	-15.6
Steps (reduced)		26 (26)	41 (0)	60 (19)	73 (32)	89 (7)	96 (14)	106 (24)	110 (28)	117 (35)	126 (3)	128 (5)

Approximation of prime harmonics in 67ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.7	-3.7	-8.4	+10.9	+15.5	+4.1	+2.6	-4.8	-11.4	+4.0	-18.9
	Relative (%)	+8.1	-8.1	-18.2	+23.6	+33.5	+8.8	+5.6	-10.3	-24.7	+8.5	-40.8
Steps (reduced)		26 (26)	41 (41)	60 (60)	73 (6)	90 (23)	96 (29)	106 (39)	110 (43)	117 (50)	126 (59)	128 (61)

Approximation of prime harmonics in 86ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+5.2	-1.5	-5.2	+14.9	+20.4	+9.3	+8.4	+1.3	-5.0	+10.8	-11.9
	Relative (%)	+11.1	-3.2	-11.1	+32.2	+44.0	+20.1	+18.1	+2.7	-10.9	+23.4	-25.7
Steps (reduced)		26 (26)	41 (41)	60 (60)	73 (73)	90 (4)	96 (10)	106 (20)	110 (24)	117 (31)	126 (40)	128 (42)

Approximation of prime harmonics in 93ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+2.7	-5.4	-10.9	+8.0	+11.9	+0.2	-1.7	-9.2	-16.1	-1.1	+22.2
	Relative (%)	+5.8	-11.7	-23.5	+17.2	+25.6	+0.4	-3.6	-19.8	-34.9	-2.4	+48.0
Steps (reduced)		26 (26)	41 (41)	60 (60)	73 (73)	90 (90)	96 (3)	106 (13)	110 (17)	117 (24)	126 (33)	129 (36)

Approximation of prime harmonics in 96ed14

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-10.2	+1.7	+21.6	+10.2	-10.8	-14.5	-3.0	-5.2	-2.8	-23.4	+4.0
	Relative (%)	-21.4	+3.6	+45.4	+21.4	-22.7	-30.4	-6.3	-10.9	-5.9	-49.1	+8.3
Steps (reduced)		25 (25)	40 (40)	59 (59)	71 (71)	87 (87)	93 (93)	103 (7)	107 (11)	114 (18)	122 (26)	125 (29)

Approximation of prime harmonics in 1ed46.249c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+2.5	-5.7	-11.4	+7.4	+11.1	-0.6	-2.6	-10.1	-17.1	-2.2	+21.1
	Relative (%)	+5.3	-12.4	-24.6	+15.9	+24.0	-1.3	-5.5	-21.9	-37.1	-4.8	+45.6
Step		26	41	60	73	90	96	106	110	117	126	129

Approximation of prime harmonics in 1ed46.268c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.0	-5.0	-10.2	+8.7	+12.8	+1.2	-0.5	-8.0	-14.9	+0.2	-22.7
	Relative (%)	+6.4	-10.7	-22.1	+18.9	+27.7	+2.6	-1.2	-17.4	-32.2	+0.4	-49.1
Step		26	41	60	73	90	96	106	110	117	126	128

29edo

• 46edt
• 105ed12
• 96ed10
• 100ed11
• 107ed13
• 16edf
• 11lim WE (41.482)
• 13lim WE (41.484)
• 116zpi (41.465)

29edo's primes 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from octave stretching.

Approximation of prime harmonics in 29edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+1.5	-13.9	-17.1	-13.4	-12.9	+19.2	-7.9	-7.6	+4.9	+13.6
	Relative (%)	+0.0	+3.6	-33.6	-41.3	-32.4	-31.3	+46.4	-19.0	-18.3	+11.9	+32.8
Steps (reduced)		29 (0)	46 (17)	67 (9)	81 (23)	100 (13)	107 (20)	119 (3)	123 (7)	131 (15)	141 (25)	144 (28)

Approximation of prime harmonics in 46edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.9	+0.0	-16.1	-19.7	-16.6	-16.4	+15.3	-11.9	-11.8	+0.3	+8.9
	Relative (%)	-2.3	+0.0	-38.9	-47.7	-40.2	-39.7	+37.1	-28.7	-28.6	+0.8	+21.6
Steps (reduced)		29 (29)	46 (0)	67 (21)	81 (35)	100 (8)	107 (15)	119 (27)	123 (31)	131 (39)	141 (3)	144 (6)

Approximation of prime harmonics in 96ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+4.2	+8.2	-4.2	-5.4	+1.1	+2.6	-5.1	+10.0	+11.4	-16.2	-7.1
	Relative (%)	+10.1	+19.6	-10.1	-12.9	+2.6	+6.1	-12.3	+24.0	+27.4	-39.0	-17.1
Steps (reduced)		29 (29)	46 (46)	67 (67)	81 (81)	100 (4)	107 (11)	118 (22)	123 (27)	131 (35)	140 (44)	143 (47)

Approximation of prime harmonics in 100ed11

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.9	+7.7	-4.9	-6.3	+0.0	+1.4	-6.4	+8.6	+10.0	-17.7	-8.7
	Relative (%)	+9.4	+18.4	-11.9	-15.1	+0.0	+3.3	-15.4	+20.7	+24.0	-42.7	-20.8
Steps (reduced)		29 (29)	46 (46)	67 (67)	81 (81)	100 (0)	107 (7)	118 (18)	123 (23)	131 (31)	140 (40)	143 (43)

Approximation of prime harmonics in 105ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-11.8	-17.3	-0.3	-9.2	-13.2	-15.7	+11.6	-17.1	-20.1	-11.7	-4.2
	Relative (%)	-28.9	-42.2	-0.7	-22.5	-32.3	-38.2	+28.2	-41.8	-49.1	-28.5	-10.4
Steps (reduced)		29 (29)	46 (46)	68 (68)	82 (82)	101 (101)	108 (3)	120 (15)	124 (19)	132 (27)	142 (37)	145 (40)

Approximation of prime harmonics in 107ed13

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.5	+7.1	-5.8	-7.3	-1.3	+0.0	-7.9	+7.0	+8.3	-19.5	-10.5
	Relative (%)	+8.5	+17.0	-14.0	-17.6	-3.1	+0.0	-19.1	+16.9	+19.9	-47.1	-25.3
Steps (reduced)		29 (29)	46 (46)	67 (67)	81 (81)	100 (100)	107 (0)	118 (11)	123 (16)	131 (24)	140 (33)	143 (36)

Approximation of prime harmonics in 16edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-15.5	-15.5	+21.5	+9.3	+16.5	-9.4	+8.7	-8.3	+11.9	+5.4	+21.6
	Relative (%)	-35.2	-35.2	+49.0	+21.3	+37.7	-21.5	+19.9	-19.0	+27.1	+12.4	+49.2
Steps (reduced)		27 (11)	43 (11)	64 (0)	77 (13)	95 (15)	101 (5)	112 (0)	116 (4)	124 (12)	133 (5)	136 (8)

Approximation of prime harmonics in 1ed41.482c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.0	+6.2	-7.0	-8.8	-3.1	-2.0	-10.1	+4.8	+5.9	+19.4	-13.1
	Relative (%)	+7.2	+15.0	-16.9	-21.2	-7.5	-4.7	-24.3	+11.5	+14.1	+46.7	-31.6
Step		29	46	67	81	100	107	118	123	131	141	143

Approximation of prime harmonics in 1ed41.484c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.0	+6.3	-6.9	-8.6	-2.9	-1.7	-9.8	+5.0	+6.1	+19.7	-12.8
	Relative (%)	+7.3	+15.2	-16.6	-20.8	-7.0	-4.2	-23.7	+12.1	+14.8	+47.4	-30.9
Step		29	46	67	81	100	107	118	123	131	141	143

Approximation of prime harmonics in 1ed41.465c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+2.5	+5.4	-8.2	-10.2	-4.8	-3.8	-12.1	+2.7	+3.6	+17.0	-15.5
	Relative (%)	+6.0	+13.1	-19.7	-24.5	-11.6	-9.1	-29.1	+6.5	+8.8	+41.0	-37.5
Step		29	46	67	81	100	107	118	123	131	141	143

30edo

• 78ed6
• 100ed10
• 104ed11
• 108ed12
• 11lim WE (79.770)
• 13lim WE (39.904)
• 39.918zpi (39.918)

30edo's simple primes with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from octave shrinking.

Approximation of prime harmonics in 30edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+18.0	+13.7	-8.8	+8.7	-0.5	+15.0	-17.5	+11.7	+10.4	+15.0
	Relative (%)	+0.0	+45.1	+34.2	-22.1	+21.7	-1.3	+37.6	-43.8	+29.3	+26.1	+37.4
Steps (reduced)		30 (0)	48 (18)	70 (10)	84 (24)	104 (14)	111 (21)	123 (3)	127 (7)	136 (16)	146 (26)	149 (29)

Approximation of prime harmonics in 78ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-6.9	+6.9	-2.5	+11.5	-15.4	+13.6	-13.4	-7.1	-19.7	+16.4	-19.5
	Relative (%)	-17.5	+17.5	-6.3	+28.9	-38.7	+34.1	-33.7	-17.9	-49.6	+41.3	-49.0
Steps (reduced)		30 (30)	48 (48)	70 (70)	85 (7)	104 (26)	112 (34)	123 (45)	128 (50)	136 (58)	147 (69)	149 (71)

Approximation of prime harmonics in 100ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.1	+11.5	+4.1	+19.5	-5.6	-15.7	-1.8	+5.0	-6.9	-9.6	-5.4
	Relative (%)	-10.3	+28.8	+10.3	+49.0	-13.9	-39.4	-4.5	+12.5	-17.3	-24.0	-13.6
Steps (reduced)		30 (30)	48 (48)	70 (70)	85 (85)	104 (4)	111 (11)	123 (23)	128 (28)	136 (36)	146 (46)	149 (49)

Approximation of prime harmonics in 104ed11

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.5	+14.0	+7.8	-15.8	+0.0	-9.8	+4.8	+11.8	+0.4	-1.8	+2.5
	Relative (%)	-6.3	+35.2	+19.6	-39.7	+0.0	-24.5	+12.0	+29.6	+0.9	-4.4	+6.3
Steps (reduced)		30 (30)	48 (48)	70 (70)	84 (84)	104 (0)	111 (7)	123 (19)	128 (24)	136 (32)	146 (42)	149 (45)

Approximation of prime harmonics in 108ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.0	+10.0	+2.0	+17.0	-8.7	-19.1	-5.5	+1.1	-11.0	-14.0	-9.9
	Relative (%)	-12.6	+25.2	+5.0	+42.6	-21.8	-47.9	-13.8	+2.8	-27.6	-35.1	-24.9
Steps (reduced)		30 (30)	48 (48)	70 (70)	85 (85)	104 (104)	111 (3)	123 (15)	128 (20)	136 (28)	146 (38)	149 (41)

Approximation of prime harmonics in 1ed79.77c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-3.5	+12.5	+5.6	-18.5	-3.3	+26.6	-39.0	+7.8	-3.9	-6.4	+37.7
	Relative (%)	-4.3	+15.7	+7.1	-23.2	-4.1	+33.3	-48.9	+9.7	-4.9	-8.0	+47.3
Step		15	24	35	42	52	56	61	64	68	73	75

Approximation of prime harmonics in 1ed39.904c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.9	+13.4	+7.0	-16.9	-1.3	-11.2	+3.2	+10.2	-1.3	-3.6	+0.7
	Relative (%)	-7.2	+33.7	+17.5	-42.3	-3.3	-28.0	+8.1	+25.6	-3.3	-9.0	+1.7
Step		30	48	70	84	104	111	123	128	136	146	149

Approximation of prime harmonics in 1ed39.918c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.5	+14.1	+7.9	-15.7	+0.2	-9.6	+5.0	+12.0	+0.6	-1.5	+2.7
	Relative (%)	-6.2	+35.3	+19.9	-39.4	+0.4	-24.1	+12.4	+30.0	+1.4	-3.9	+6.9
Step		30	48	70	84	104	111	123	128	136	146	149

34edo

• 54edt
• 79ed5
• 88ed6
• 108ed9
• 113ed10
• 122ed12
• 126ed13
• 11lim WE (35.284)
• 13lim WE (35.276)
• 144zpi (35.248)

34edo's primes 3, 5, 11 and 13 are all tuned sharp, and it has two about equally bad mappings of 7, so 34edo can benefit from octave shrinking.

Approximation of prime harmonics in 34edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+3.9	+1.9	-15.9	+13.4	+6.5	+0.9	-15.2	+7.0	-6.0	-15.6
	Relative (%)	+0.0	+11.1	+5.4	-45.0	+37.9	+18.5	+2.6	-43.0	+19.9	-17.1	-44.3
Steps (reduced)		34 (0)	54 (20)	79 (11)	95 (27)	118 (16)	126 (24)	139 (3)	144 (8)	154 (18)	165 (29)	168 (32)

Approximation of prime harmonics in 54edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.5	+0.0	-3.8	+12.4	+4.8	-2.6	-9.2	+9.6	-4.2	+17.2	+7.4
	Relative (%)	-7.0	+0.0	-10.9	+35.3	+13.6	-7.5	-26.1	+27.2	-11.9	+48.8	+21.0
Steps (reduced)		34 (34)	54 (0)	79 (25)	96 (42)	118 (10)	126 (18)	139 (31)	145 (37)	154 (46)	166 (4)	169 (7)

Approximation of prime harmonics in 79ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.8	+2.6	+0.0	+17.1	+10.5	+3.5	-2.5	+16.6	+3.3	-10.1	+15.6
	Relative (%)	-2.3	+7.4	+0.0	+48.4	+29.8	+9.8	-7.0	+47.1	+9.3	-28.5	+44.1
Steps (reduced)		34 (34)	54 (54)	79 (0)	96 (17)	118 (39)	126 (47)	139 (60)	145 (66)	154 (75)	165 (7)	169 (11)

Approximation of prime harmonics in 88ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.5	+1.5	-1.6	+15.1	+8.1	+0.9	-5.3	+13.7	+0.1	-13.4	+12.1
	Relative (%)	-4.3	+4.3	-4.6	+42.9	+23.0	+2.6	-15.0	+38.8	+0.4	-38.0	+34.4
Steps (reduced)		34 (34)	54 (54)	79 (79)	96 (8)	118 (30)	126 (38)	139 (51)	145 (57)	154 (66)	165 (77)	169 (81)

{{harmonics in equal | 108 | 9 | 1 | intervals=prime} {{harmonics in equal | 113 | 10 | 1 | intervals=prime}

Approximation of prime harmonics in 122ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.1	+2.2	-0.6	+16.3	+9.6	+2.5	-3.5	+15.5	+2.1	-11.4	+14.2
	Relative (%)	-3.1	+6.2	-1.8	+46.3	+27.2	+7.0	-10.1	+43.9	+5.8	-32.2	+40.4
Steps (reduced)		34 (34)	54 (54)	79 (79)	96 (96)	118 (118)	126 (4)	139 (17)	145 (23)	154 (32)	165 (43)	169 (47)

Approximation of prime harmonics in 126ed13

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.8	+1.1	-2.2	+14.4	+7.3	+0.0	-6.3	+12.6	-1.0	-14.6	+10.9
	Relative (%)	-5.0	+3.2	-6.2	+41.0	+20.6	+0.0	-17.8	+35.8	-2.7	-41.4	+31.0
Steps (reduced)		34 (34)	54 (54)	79 (79)	96 (96)	118 (118)	126 (0)	139 (13)	145 (19)	154 (28)	165 (39)	169 (43)

Approximation of prime harmonics in 1ed35.284c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.3	+3.4	+1.1	-16.8	+12.2	+5.3	-0.5	-16.6	+5.5	-7.7	-17.3
	Relative (%)	-1.0	+9.6	+3.2	-47.7	+34.6	+14.9	-1.4	-47.1	+15.5	-21.9	-49.1
Step		34	54	79	95	118	126	139	144	154	165	168

Approximation of prime harmonics in 1ed35.276c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.6	+2.9	+0.5	-17.6	+11.3	+4.2	-1.6	+17.5	+4.2	-9.0	+16.6
	Relative (%)	-1.7	+8.4	+1.4	-49.9	+31.9	+12.0	-4.5	+49.6	+12.0	-25.6	+47.1
Step		34	54	79	95	118	126	139	145	154	165	169

Approximation of prime harmonics in 1ed35.248c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.6	+1.4	-1.7	+15.0	+7.9	+0.7	-5.5	+13.4	-0.1	-13.7	+11.9
	Relative (%)	-4.4	+4.1	-4.9	+42.5	+22.5	+2.0	-15.6	+38.1	-0.2	-38.7	+33.7
Step		34	54	79	96	118	126	139	145	154	165	169

35edo

• 81ed5
• 90ed6
• 98ed7
• 116ed10
• 121ed11
• 125ed12
• 11lim WE (35.284)
• 13lim WE (35.276)
• 149zpi (34.359)

35edo's primes 3, 5, 7 and 11 are all tuned flat, and it has two about equally bad mappings of 13, so 35edo can benefit from octave stretching. {{harmonics in equal | 35 | 2 | 1 | intervals=prime}

Approximation of prime harmonics in 81ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+4.0	-10.0	+0.0	+2.3	+11.0	-3.1	+14.1	-6.5	+6.8	-16.2	+6.0
	Relative (%)	+11.5	-29.1	+0.0	+6.6	+31.8	-8.9	+41.0	-18.8	+19.6	-47.0	+17.4
Steps (reduced)		35 (35)	55 (55)	81 (0)	98 (17)	121 (40)	129 (48)	143 (62)	148 (67)	158 (77)	169 (7)	173 (11)

Approximation of prime harmonics in 90ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+6.3	-6.3	+5.4	+8.9	-15.4	+5.6	-10.8	+3.5	-17.1	-4.8	-16.9
	Relative (%)	+18.3	-18.3	+15.8	+25.7	-44.6	+16.3	-31.2	+10.1	-49.6	-13.9	-48.9
Steps (reduced)		35 (35)	55 (55)	81 (81)	98 (8)	120 (30)	129 (39)	142 (52)	148 (58)	157 (67)	169 (79)	172 (82)

{{harmonics in equal | 98 | 7 | 1 | intervals=prime} {{harmonics in equal | 116 | 10 | 1 | intervals=prime}

Approximation of prime harmonics in 121ed11

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.8	-15.0	-7.3	-6.6	+0.0	-14.7	+1.1	+14.4	-7.5	+2.9	-9.7
	Relative (%)	+2.3	-43.7	-21.4	-19.2	+0.0	-43.0	+3.3	+42.1	-22.0	+8.3	-28.2
Steps (reduced)		35 (35)	55 (55)	81 (81)	98 (98)	121 (0)	129 (8)	143 (22)	149 (28)	158 (37)	170 (49)	173 (52)

Approximation of prime harmonics in 125ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+4.5	-9.1	+1.4	+3.9	+13.0	-0.9	+16.5	-4.0	+9.4	-13.3	+8.9
	Relative (%)	+13.2	-26.4	+3.9	+11.4	+37.7	-2.6	+47.9	-11.6	+27.3	-38.7	+25.8
Steps (reduced)		35 (35)	55 (55)	81 (81)	98 (98)	121 (121)	129 (4)	143 (18)	148 (23)	158 (33)	169 (44)	173 (48)

Approximation of prime harmonics in 1ed35.284c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.3	+3.4	+1.1	-16.8	+12.2	+5.3	-0.5	-16.6	+5.5	-7.7	-17.3
	Relative (%)	-1.0	+9.6	+3.2	-47.7	+34.6	+14.9	-1.4	-47.1	+15.5	-21.9	-49.1
Step		34	54	79	95	118	126	139	144	154	165	168

Approximation of prime harmonics in 1ed35.276c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.6	+2.9	+0.5	-17.6	+11.3	+4.2	-1.6	+17.5	+4.2	-9.0	+16.6
	Relative (%)	-1.7	+8.4	+1.4	-49.9	+31.9	+12.0	-4.5	+49.6	+12.0	-25.6	+47.1
Step		34	54	79	95	118	126	139	145	154	165	169

Approximation of prime harmonics in 1ed34.359c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+2.6	-12.2	-3.2	-1.6	+6.1	-8.2	+8.4	-12.4	+0.4	+11.5	-0.9
	Relative (%)	+7.5	-35.5	-9.4	-4.8	+17.8	-23.9	+24.4	-36.0	+1.3	+33.3	-2.7
Step		35	55	81	98	121	129	143	148	158	170	173

37edo

• 59edt
• 86ed5
• 96ed6
• 104ed7
• 123ed10
• 128ed11
• 133ed12
• 137ed13
• 11lim WE (32.377)
• 13lim WE (32.383)
• 161zpi (32.408)

37edo's primes 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from octave shrinking.

Approximation of prime harmonics in 37edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+11.6	+2.9	+4.1	+0.0	+2.7	-7.7	-5.6	-12.1	+8.3	-9.9
	Relative (%)	+0.0	+35.6	+8.9	+12.8	+0.1	+8.4	-23.6	-17.3	-37.2	+25.5	-30.5
Steps (reduced)		37 (0)	59 (22)	86 (12)	104 (30)	128 (17)	137 (26)	151 (3)	157 (9)	167 (19)	180 (32)	183 (35)

Approximation of prime harmonics in 59edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-7.2	+0.0	-14.0	+16.0	+7.2	+8.1	-5.0	-4.1	-12.5	+5.2	-13.5
	Relative (%)	-22.5	+0.0	-43.3	+49.7	+22.3	+25.2	-15.5	-12.8	-38.9	+16.2	-41.9
Steps (reduced)		37 (37)	59 (0)	86 (27)	105 (46)	129 (11)	138 (20)	152 (34)	158 (40)	168 (50)	181 (4)	184 (7)

Approximation of prime harmonics in 86ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.2	+9.6	+0.0	+0.7	-4.2	-1.9	-12.7	-10.9	+14.8	+2.2	-16.0
	Relative (%)	-3.8	+29.6	+0.0	+2.1	-13.1	-5.8	-39.2	-33.6	+45.5	+6.9	-49.4
Steps (reduced)		37 (37)	59 (59)	86 (0)	104 (18)	128 (42)	137 (51)	151 (65)	157 (71)	168 (82)	180 (8)	183 (11)

Approximation of prime harmonics in 96ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.5	+4.5	-7.5	-8.4	-15.4	-13.8	+6.5	+7.8	+0.1	-13.4	+0.4
	Relative (%)	-13.8	+13.8	-23.1	-25.9	-47.6	-42.6	+20.0	+24.1	+0.5	-41.5	+1.2
Steps (reduced)		37 (37)	59 (59)	86 (86)	104 (8)	128 (32)	137 (41)	152 (56)	158 (62)	168 (72)	180 (84)	184 (88)

{{harmonics in equal | 104 | 7 | 1 | intervals=prime}

Approximation of prime harmonics in 123ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.9	+10.2	+0.9	+1.7	-3.0	-0.5	-11.2	-9.3	-16.0	+4.1	-14.2
	Relative (%)	-2.7	+31.4	+2.7	+5.3	-9.1	-1.5	-34.5	-28.7	-49.3	+12.5	-43.7
Steps (reduced)		37 (37)	59 (59)	86 (86)	104 (104)	128 (5)	137 (14)	151 (28)	157 (34)	167 (44)	180 (57)	183 (60)

Approximation of prime harmonics in 128ed11

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.0	+11.5	+2.9	+4.1	+0.0	+2.7	-7.7	-5.7	-12.1	+8.2	-9.9
	Relative (%)	-0.0	+35.6	+8.8	+12.7	+0.0	+8.3	-23.7	-17.5	-37.3	+25.3	-30.7
Steps (reduced)		37 (37)	59 (59)	86 (86)	104 (104)	128 (0)	137 (9)	151 (23)	157 (29)	167 (39)	180 (52)	183 (55)

Approximation of prime harmonics in 133ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-3.2	+6.4	-4.6	-4.9	-11.1	-9.2	+11.6	+13.1	+5.8	-7.4	+6.5
	Relative (%)	-9.9	+19.9	-14.2	-15.1	-34.3	-28.4	+35.8	+40.4	+17.9	-22.8	+20.2
Steps (reduced)		37 (37)	59 (59)	86 (86)	104 (104)	128 (128)	137 (4)	152 (19)	158 (25)	168 (35)	180 (47)	184 (51)

Approximation of prime harmonics in 137ed13

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.7	+10.4	+1.2	+2.1	-2.5	+0.0	-10.7	-8.7	-15.4	+4.7	-13.5
	Relative (%)	-2.3	+32.1	+3.6	+6.4	-7.7	+0.0	-32.9	-26.9	-47.4	+14.5	-41.7
Steps (reduced)		37 (37)	59 (59)	86 (86)	104 (104)	128 (128)	137 (0)	151 (14)	157 (20)	167 (30)	180 (43)	183 (46)

Approximation of prime harmonics in 1ed32.377c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.1	+8.3	-1.9	-1.6	-7.1	-4.9	-16.0	-14.3	+11.1	-1.7	+12.3
	Relative (%)	-6.3	+25.6	-5.8	-5.0	-21.8	-15.1	-49.5	-44.2	+34.2	-5.3	+38.1
Step		37	59	86	104	128	137	151	157	168	180	184

Approximation of prime harmonics in 1ed32.383c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.8	+8.6	-1.4	-1.0	-6.3	-4.1	-15.1	-13.4	+12.1	-0.6	+13.4
	Relative (%)	-5.6	+26.7	-4.2	-3.1	-19.4	-12.5	-46.7	-41.3	+37.3	-2.0	+41.5
Step		37	59	86	104	128	137	151	157	168	180	184

Approximation of prime harmonics in 1ed32.408c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.9	+10.1	+0.8	+1.6	-3.1	-0.6	-11.3	-9.5	-16.1	+3.9	-14.4
	Relative (%)	-2.8	+31.2	+2.4	+5.0	-9.5	-1.9	-35.0	-29.2	-49.8	+11.9	-44.3
Step		37	59	86	104	128	137	151	157	167	180	183

48edo

• 76edt
• 124ed6
• 152ed9
• 159ed10
• 166ed11
• 172ed12
• 28edf
• 11lim WE (25.017)
• 13lim WE (25.005)
• 226zpi (25.006)

Most of 48edo's simple primes have low error, but its 5 is substantially flat, so 48edo can benefit from slight octave stretching.

Approximation of prime harmonics in 48edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	-2.0	-11.3	+6.2	-1.3	+9.5	-5.0	+2.5	-3.3	-4.6	+5.0
	Relative (%)	+0.0	-7.8	-45.3	+24.7	-5.3	+37.9	-19.8	+9.9	-13.1	-18.3	+19.9
Steps (reduced)		48 (0)	76 (28)	111 (15)	135 (39)	166 (22)	178 (34)	196 (4)	204 (12)	217 (25)	233 (41)	238 (46)

Approximation of prime harmonics in 76edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.2	+0.0	-8.5	+9.6	+3.0	-11.0	+0.1	+7.7	+2.3	+1.4	+11.1
	Relative (%)	+4.9	+0.0	-33.8	+38.5	+11.8	-43.9	+0.3	+30.9	+9.2	+5.7	+44.3
Steps (reduced)		48 (48)	76 (0)	111 (35)	135 (59)	166 (14)	177 (25)	196 (44)	204 (52)	217 (65)	233 (5)	238 (10)

{{harmonics in equal | 124 | 6 | 1 | intervals=prime} {{harmonics in equal | 152 | 9 | 1 | intervals=prime}

Approximation of prime harmonics in 159ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.4	+3.5	-3.4	-9.3	+10.5	-2.9	+9.0	-8.1	+12.2	+12.0	-3.2
	Relative (%)	+13.6	+13.8	-13.6	-37.1	+41.9	-11.7	+35.9	-32.2	+48.5	+47.9	-12.7
Steps (reduced)		48 (48)	76 (76)	111 (111)	134 (134)	166 (7)	177 (18)	196 (37)	203 (44)	217 (58)	233 (74)	237 (78)

Approximation of prime harmonics in 166ed11

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.4	-1.4	-10.4	+7.2	+0.0	+10.9	-3.4	+4.1	-1.6	-2.7	+6.9
	Relative (%)	+1.5	-5.4	-41.7	+29.0	+0.0	+43.5	-13.6	+16.4	-6.2	-10.9	+27.4
Steps (reduced)		48 (48)	76 (76)	111 (111)	135 (135)	166 (0)	178 (12)	196 (30)	204 (38)	217 (51)	233 (67)	238 (72)

Approximation of prime harmonics in 172ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.5	-1.1	-10.1	+7.7	+0.6	+11.5	-2.7	+4.8	-0.8	-1.9	+7.7
	Relative (%)	+2.2	-4.4	-40.2	+30.8	+2.3	+46.0	-10.9	+19.2	-3.2	-7.7	+30.7
Steps (reduced)		48 (48)	76 (76)	111 (111)	135 (135)	166 (166)	178 (6)	196 (24)	204 (32)	217 (45)	233 (61)	238 (66)

Approximation of prime harmonics in 28edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.4	+3.4	-3.6	-9.5	+10.3	-3.2	+8.7	-8.3	+11.9	+11.7	-3.5
	Relative (%)	+13.4	+13.4	-14.2	-37.8	+41.0	-12.6	+34.8	-33.3	+47.4	+46.6	-13.9
Steps (reduced)		48 (20)	76 (20)	111 (27)	134 (22)	166 (26)	177 (9)	196 (0)	203 (7)	217 (21)	233 (9)	237 (13)

Approximation of prime harmonics in 1ed25.017c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.8	-0.7	-9.4	+8.5	+1.5	+12.5	-1.6	+6.0	+0.4	-0.6	+9.0
	Relative (%)	+3.3	-2.7	-37.7	+33.9	+6.0	+50.0	-6.5	+23.8	+1.7	-2.5	+36.0
Step		48	76	111	135	166	178	196	204	217	233	238

Approximation of prime harmonics in 1ed25.005c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.2	-1.6	-10.8	+6.8	-0.5	+10.4	-4.0	+3.5	-2.2	-3.4	+6.2
	Relative (%)	+1.0	-6.3	-43.0	+27.4	-2.0	+41.4	-15.9	+14.0	-8.8	-13.6	+24.6
Step		48	76	111	135	166	178	196	204	217	233	238

Approximation of prime harmonics in 1ed25.006c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.3	-1.5	-10.6	+7.0	-0.3	+10.5	-3.8	+3.7	-2.0	-3.2	+6.4
	Relative (%)	+1.2	-6.0	-42.6	+27.9	-1.3	+42.2	-15.1	+14.8	-7.9	-12.7	+25.6
Step		48	76	111	135	166	178	196	204	217	233	238

Medium-low priority

10edo

• 16edt
• 23ed5
• 26ed6
• 28ed7
• 32ed8
• 33ed10
• 36ed12
• 37ed13
• 6edf
• 2.3.7.13 WE (119.785)
• 2.5.7.13 WE (120.358)
• 13lim WE (119.776)
• 26zpi (119.899)

If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from octave shrinking. If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from octave stretching.

Approximation of prime harmonics in 10edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+18.0	-26.3	-8.8	+48.7	-0.5	+15.0	-57.5	-28.3	+50.4	+55.0
	Relative (%)	+0.0	+15.0	-21.9	-7.4	+40.6	-0.4	+12.5	-47.9	-23.6	+42.0	+45.8
Steps (reduced)		10 (0)	16 (6)	23 (3)	28 (8)	35 (5)	37 (7)	41 (1)	42 (2)	45 (5)	49 (9)	50 (0)

Approximation of prime harmonics in 23ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+11.4	+36.4	+0.0	+23.2	-32.4	+41.8	-59.2	-9.5	+23.2	-14.7	-9.0
	Relative (%)	+9.4	+30.0	+0.0	+19.2	-26.8	+34.5	-48.9	-7.8	+19.2	-12.1	-7.4
Steps (reduced)		10 (10)	16 (16)	23 (0)	28 (5)	34 (11)	37 (14)	40 (17)	42 (19)	45 (22)	48 (2)	49 (3)

{{harmonics in equal | 26 | 6 | 1 | intervals=prime} {{harmonics in equal | 28 | 7 | 1 | intervals=prime}

Approximation of prime harmonics in 32ed8

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+37.5	+10.5	+26.2	+6.2	+11.2	-53.0	+45.0	-35.0	-28.3	+20.4	+17.5
	Relative (%)	+33.3	+9.4	+23.3	+5.5	+9.9	-47.1	+40.0	-31.1	-25.1	+18.2	+15.5
Steps (reduced)		11 (11)	17 (17)	25 (25)	30 (30)	37 (5)	39 (7)	44 (12)	45 (13)	48 (16)	52 (20)	53 (21)

Approximation of prime harmonics in 33ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+8.0	+30.8	-8.0	+13.5	-44.2	+29.0	+47.7	-24.0	+7.6	-31.3	-26.0
	Relative (%)	+6.6	+25.5	-6.6	+11.2	-36.6	+24.0	+39.5	-19.9	+6.3	-25.9	-21.5
Steps (reduced)		10 (10)	16 (16)	23 (23)	28 (28)	34 (1)	37 (4)	41 (8)	42 (9)	45 (12)	48 (15)	49 (16)

Approximation of prime harmonics in 36ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.0	+10.0	-37.8	-22.9	+31.1	-19.1	-5.5	+40.9	-50.8	+25.9	+29.9
	Relative (%)	-4.2	+8.4	-31.7	-19.1	+26.1	-16.0	-4.6	+34.3	-42.5	+21.6	+25.0
Steps (reduced)		10 (10)	16 (16)	23 (23)	28 (28)	35 (35)	37 (1)	41 (5)	43 (7)	45 (9)	49 (13)	50 (14)

Approximation of prime harmonics in 37ed13

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.1	+18.3	-26.0	-8.4	+49.2	+0.0	+15.6	-56.9	-27.6	+51.1	+55.7
	Relative (%)	+0.1	+15.2	-21.7	-7.0	+41.0	+0.0	+13.0	-47.4	-23.0	+42.6	+46.4
Steps (reduced)		10 (10)	16 (16)	23 (23)	28 (28)	35 (35)	37 (0)	41 (4)	42 (5)	45 (8)	49 (12)	50 (13)

Approximation of prime harmonics in 6edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-30.1	-30.1	+21.5	+24.0	-56.6	+5.2	+8.7	+50.2	-46.6	+20.0	+21.6
	Relative (%)	-25.7	-25.7	+18.4	+20.5	-48.4	+4.4	+7.5	+42.9	-39.8	+17.1	+18.4
Steps (reduced)		10 (4)	16 (4)	24 (0)	29 (5)	35 (5)	38 (2)	42 (0)	44 (2)	46 (4)	50 (2)	51 (3)

Approximation of prime harmonics in 1ed119.785c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.2	+14.6	-31.3	-14.8	+41.2	-8.5	+6.2	+53.2	-37.9	+39.9	+44.2
	Relative (%)	-1.8	+12.2	-26.1	-12.4	+34.4	-7.1	+5.2	+44.4	-31.7	+33.3	+36.9
Step		10	16	23	28	35	37	41	43	45	49	50

Approximation of prime harmonics in 1ed120.358c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.6	+23.8	-18.1	+1.2	-59.1	+12.7	+29.7	-42.5	-12.2	-52.4	-47.5
	Relative (%)	+3.0	+19.8	-15.0	+1.0	-49.1	+10.6	+24.7	-35.3	-10.1	-43.5	-39.5
Step		10	16	23	28	34	37	41	42	45	48	49

Approximation of prime harmonics in 1ed119.776c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.2	+14.5	-31.5	-15.1	+40.8	-8.8	+5.9	+52.9	-38.4	+39.4	+43.8
	Relative (%)	-1.9	+12.1	-26.3	-12.6	+34.1	-7.4	+4.9	+44.1	-32.0	+32.9	+36.5
Step		10	16	23	28	35	37	41	43	45	49	50

Approximation of prime harmonics in 1ed119.899c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.0	+16.4	-28.6	-11.7	+45.1	-4.3	+10.9	+58.1	-32.8	+45.5	+49.9
	Relative (%)	-0.8	+13.7	-23.9	-9.7	+37.7	-3.6	+9.1	+48.5	-27.4	+37.9	+41.6
Step		10	16	23	28	35	37	41	43	45	49	50

11edo

• 27ed6
• 28ed6
• 31ed7
• 35ed9
• 37ed10
• 38ed10
• 38ed12
• 39ed12
• 41ed13
• 2.7.11.13 WE (108.821)
• 30zpi (108.722)

11edo has about equally bad sharp and flat mappings of primes 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight octave shrinking is advisable. To use its primes 3 or 5, extreme octave shrinking or octave stretching can be used, at the cost of making the octaves sound significantly weaker.

Approximation of prime harmonics in 11edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	-47.4	+50.0	+13.0	-5.9	+32.2	+4.1	+29.8	+26.3	-47.8	-54.1
	Relative (%)	+0.0	-43.5	+45.9	+11.9	-5.4	+29.5	+3.8	+27.3	+24.1	-43.8	-49.6
Steps (reduced)		11 (0)	17 (6)	26 (4)	31 (9)	38 (5)	41 (8)	45 (1)	47 (3)	50 (6)	53 (9)	54 (10)

Approximation of prime harmonics in 27ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-51.1	+51.1	-29.0	-37.1	-15.4	+40.1	+35.2	-42.5	-28.6	+29.7	+29.1
	Relative (%)	-44.5	+44.5	-25.3	-32.3	-13.4	+34.9	+30.6	-37.0	-24.9	+25.8	+25.3
Steps (reduced)		10 (10)	17 (17)	24 (24)	29 (2)	36 (9)	39 (12)	43 (16)	44 (17)	47 (20)	51 (24)	52 (25)

Approximation of prime harmonics in 28ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+18.6	-18.6	-16.7	-45.3	-52.3	-9.2	-30.5	-1.4	+0.1	+42.0	+37.3
	Relative (%)	+16.8	-16.8	-15.1	-40.9	-47.2	-8.3	-27.5	-1.3	+0.1	+37.9	+33.7
Steps (reduced)		11 (11)	17 (17)	25 (25)	30 (2)	37 (9)	40 (12)	44 (16)	46 (18)	49 (21)	53 (25)	54 (26)

Approximation of prime harmonics in 31ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.6	+54.1	+39.2	+0.0	-21.8	+15.0	-14.7	+10.1	+5.3	+38.7	+31.9
	Relative (%)	-4.2	+49.8	+36.0	+0.0	-20.1	+13.8	-13.5	+9.3	+4.9	+35.6	+29.4
Steps (reduced)		11 (11)	18 (18)	26 (26)	31 (0)	38 (7)	41 (10)	45 (14)	47 (16)	50 (19)	54 (23)	55 (24)

{{harmonics in equal | 35 | 9 | 1 | intervals=prime}

Approximation of prime harmonics in 37ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-14.9	+37.3	+14.9	-28.9	+50.5	-23.3	+51.0	-33.8	-41.4	-11.7	-19.4
	Relative (%)	-13.8	+34.7	+13.8	-26.9	+46.8	-21.6	+47.3	-31.4	-38.4	-10.9	-18.0
Steps (reduced)		11 (11)	18 (18)	26 (26)	31 (31)	39 (2)	41 (4)	46 (9)	47 (10)	50 (13)	54 (17)	55 (18)

Approximation of prime harmonics in 38ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-46.1	-13.7	+46.1	-11.9	+44.8	-34.6	+25.5	+42.7	+26.7	+45.0	+34.4
	Relative (%)	-43.9	-13.1	+43.9	-11.4	+42.7	-33.0	+24.3	+40.7	+25.4	+42.9	+32.8
Steps (reduced)		11 (11)	18 (18)	27 (27)	32 (32)	40 (2)	42 (4)	47 (9)	49 (11)	52 (14)	56 (18)	57 (19)

Approximation of prime harmonics in 38ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+45.3	+22.6	+43.9	+27.5	+37.4	-25.4	-37.0	-3.1	+5.8	-55.9	+55.1
	Relative (%)	+40.0	+20.0	+38.8	+24.3	+33.1	-22.4	-32.6	-2.7	+5.1	-49.4	+48.6
Steps (reduced)		11 (11)	17 (17)	25 (25)	30 (30)	37 (37)	39 (1)	43 (5)	45 (7)	48 (10)	51 (13)	53 (15)

Approximation of prime harmonics in 39ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+13.4	-26.7	-28.7	+50.7	+40.3	-28.3	-51.5	-23.4	-23.3	+16.7	+11.5
	Relative (%)	+12.1	-24.2	-26.0	+45.9	+36.6	-25.6	-46.7	-21.2	-21.1	+15.1	+10.4
Steps (reduced)		11 (11)	17 (17)	25 (25)	31 (31)	38 (38)	40 (1)	44 (5)	46 (7)	49 (10)	53 (14)	54 (15)

Approximation of prime harmonics in 41ed13

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-8.6	+47.5	+29.6	-11.4	-35.7	+0.0	-31.2	-7.2	-13.0	+18.9	+11.8
	Relative (%)	-8.0	+43.9	+27.4	-10.5	-33.0	+0.0	-28.8	-6.6	-12.0	+17.5	+10.9
Steps (reduced)		11 (11)	18 (18)	26 (26)	31 (31)	38 (38)	41 (0)	45 (4)	47 (6)	50 (9)	54 (13)	55 (14)

Approximation of prime harmonics in 1ed108.821c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-3.0	-52.0	+43.0	+4.6	-16.1	+21.1	-8.0	+17.1	+12.8	+46.8	+40.1
	Relative (%)	-2.7	-47.8	+39.5	+4.3	-14.8	+19.4	-7.4	+15.7	+11.7	+43.0	+36.9
Step		11	17	26	31	38	41	45	47	50	54	55

Approximation of prime harmonics in 1ed108.722c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.1	-53.7	+40.5	+1.6	-19.9	+17.1	-12.5	+12.4	+7.8	+41.4	+34.7
	Relative (%)	-3.7	-49.4	+37.2	+1.4	-18.3	+15.7	-11.5	+11.4	+7.2	+38.1	+31.9
Step		11	17	26	31	38	41	45	47	50	54	55

24edo ((13lim WE's octave is only 1/10th of a cent different from 24edo))

• 38edt
• 56ed5
• 62ed6
• 67ed7
• 9ed7/6
• 80ed10
• 83ed11
• 86ed12
• 89ed13
• 14edf
• 2.3.5.11.13 WE (49.942)
• 11lim WE (50.017)
• 90zpi (49.988)

If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight octave stretching, mostly to improve its prime 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight octave shrinking, mostly to improve its primes 5 and 13.

Approximation of prime harmonics in 24edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	-2.0	+13.7	-18.8	-1.3	+9.5	-5.0	+2.5	+21.7	+20.4	+5.0
	Relative (%)	+0.0	-3.9	+27.4	-37.7	-2.6	+18.9	-9.9	+5.0	+43.5	+40.8	+9.9
Steps (reduced)		24 (0)	38 (14)	56 (8)	67 (19)	83 (11)	89 (17)	98 (2)	102 (6)	109 (13)	117 (21)	119 (23)

Approximation of prime harmonics in 38edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.2	+0.0	+16.6	-15.4	+3.0	+14.1	+0.1	+7.7	-22.7	-23.6	+11.1
	Relative (%)	+2.5	+0.0	+33.1	-30.7	+5.9	+28.1	+0.2	+15.5	-45.4	-47.2	+22.2
Steps (reduced)		24 (24)	38 (0)	56 (18)	67 (29)	83 (7)	89 (13)	98 (22)	102 (26)	108 (32)	116 (2)	119 (5)

Approximation of prime harmonics in 56ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.9	-11.2	+0.0	+14.6	-21.6	-12.3	+20.8	-22.4	-4.9	-8.2	-24.1
	Relative (%)	-11.8	-22.6	+0.0	+29.3	-43.4	-24.7	+41.9	-45.1	-9.9	-16.4	-48.5
Steps (reduced)		24 (24)	38 (38)	56 (0)	68 (12)	83 (27)	89 (33)	99 (43)	102 (46)	109 (53)	117 (5)	119 (7)

Approximation of prime harmonics in 62ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.8	-0.8	+15.5	-16.7	+1.3	+12.3	-1.9	+5.7	-24.9	+24.1	+8.7
	Relative (%)	+1.5	-1.5	+30.9	-33.4	+2.6	+24.5	-3.7	+11.4	-49.7	+48.2	+17.4
Steps (reduced)		24 (24)	38 (38)	56 (56)	67 (5)	83 (21)	89 (27)	98 (36)	102 (40)	108 (46)	117 (55)	119 (57)

Approximation of prime harmonics in 67ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+6.7	+8.7	-20.9	+0.0	+22.0	-15.8	+22.6	-19.1	+2.1	+3.0	-11.9
	Relative (%)	+13.4	+17.3	-41.5	+0.0	+43.8	-31.4	+44.9	-38.1	+4.1	+6.0	-23.6
Steps (reduced)		24 (24)	38 (38)	55 (55)	67 (0)	83 (16)	88 (21)	98 (31)	101 (34)	108 (41)	116 (49)	118 (51)

Approximation of prime harmonics in 9ed7/6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-13.9	-4.2	+1.0	+11.5	+0.0	+7.3	-12.3	+2.7	-1.9	+11.9	-14.6
	Relative (%)	-46.9	-14.2	+3.4	+38.9	+0.0	+24.7	-41.6	+9.1	-6.4	+40.2	-49.1
Steps (reduced)		40 (4)	64 (1)	94 (4)	114 (6)	140 (5)	150 (6)	165 (3)	172 (1)	183 (3)	197 (8)	200 (2)

Approximation of prime harmonics in 80ed10

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.1	-8.5	+4.1	+19.5	-15.5	-5.8	-21.7	-15.0	+3.1	+0.4	-15.4
	Relative (%)	-8.2	-17.0	+8.2	+39.2	-31.1	-11.5	-43.6	-30.0	+6.2	+0.8	-30.9
Steps (reduced)		24 (24)	38 (38)	56 (56)	68 (68)	83 (3)	89 (9)	98 (18)	102 (22)	109 (29)	117 (37)	119 (39)

Approximation of prime harmonics in 83ed11

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.4	-1.4	+14.6	-17.8	+0.0	+10.9	-3.4	+4.1	+23.5	+22.3	+6.9
	Relative (%)	+0.8	-2.7	+29.1	-35.5	+0.0	+21.8	-6.8	+8.2	+46.9	+44.5	+13.7
Steps (reduced)		24 (24)	38 (38)	56 (56)	67 (67)	83 (0)	89 (6)	98 (15)	102 (19)	109 (26)	117 (34)	119 (36)

Approximation of prime harmonics in 86ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.5	-1.1	+15.0	-17.3	+0.6	+11.5	-2.7	+4.8	+24.2	+23.1	+7.7
	Relative (%)	+1.1	-2.2	+29.9	-34.6	+1.1	+23.0	-5.5	+9.6	+48.4	+46.1	+15.3
Steps (reduced)		24 (24)	38 (38)	56 (56)	67 (67)	83 (83)	89 (3)	98 (12)	102 (16)	109 (23)	117 (31)	119 (33)

Approximation of prime harmonics in 89ed13

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.6	-6.0	+7.7	+23.9	-10.2	+0.0	-15.4	-8.4	+10.1	+8.0	-7.7
	Relative (%)	-5.1	-12.0	+15.5	+48.0	-20.3	+0.0	-30.8	-16.8	+20.3	+16.0	-15.4
Steps (reduced)		24 (24)	38 (38)	56 (56)	68 (68)	83 (83)	89 (0)	98 (9)	102 (13)	109 (20)	117 (28)	119 (30)

Approximation of prime harmonics in 14edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.4	+3.4	+21.5	-9.5	+10.3	+21.9	+8.7	+16.7	-13.2	-13.4	+21.6
	Relative (%)	+6.7	+6.7	+42.9	-18.9	+20.5	+43.7	+17.4	+33.4	-26.3	-26.7	+43.0
Steps (reduced)		24 (10)	38 (10)	56 (0)	67 (11)	83 (13)	89 (5)	98 (0)	102 (4)	108 (10)	116 (4)	119 (7)

Approximation of prime harmonics in 1ed49.942c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.4	-4.2	+10.4	-22.7	-6.1	+4.3	-10.6	-3.4	+15.4	+13.6	-1.9
	Relative (%)	-2.8	-8.3	+20.9	-45.5	-12.3	+8.6	-21.3	-6.9	+30.8	+27.3	-3.9
Step		24	38	56	67	83	89	98	102	109	117	119

Approximation of prime harmonics in 1ed50.017c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.4	-1.3	+14.6	-17.7	+0.1	+11.0	-3.3	+4.2	+23.6	+22.4	+7.0
	Relative (%)	+0.8	-2.6	+29.3	-35.4	+0.2	+22.0	-6.6	+8.4	+47.1	+44.8	+14.0
Step		24	38	56	67	83	89	98	102	109	117	119

Approximation of prime harmonics in 1ed49.988c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.3	-2.4	+13.0	-19.6	-2.3	+8.4	-6.1	+1.3	+20.4	+19.0	+3.5
	Relative (%)	-0.6	-4.8	+26.0	-39.3	-4.6	+16.8	-12.3	+2.5	+40.8	+38.0	+7.1
Step		24	38	56	67	83	89	98	102	109	117	119

5edo

• 8edt
• 13ed6
• 14ed7
• 18ed12
• 3edf
• 2.3.7 WE (239.426)
• 9zpi (238.357)

If one wishes to use 5edo as a 2.3.7 subgroup tuning, then it benefits from slight octave shrinking to improve its prime 3.

Approximation of prime harmonics in 5edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0	+18	+94	-9	-71	+119	-105	-58	+92	-70	+55
	Relative (%)	+0.0	+7.5	+39.0	-3.7	-29.7	+49.8	-43.7	-24.0	+38.2	-29.0	+22.9
Steps (reduced)		5 (0)	8 (3)	12 (2)	14 (4)	17 (2)	19 (4)	20 (0)	21 (1)	23 (3)	24 (4)	25 (0)

Approximation of prime harmonics in 8edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-11	+0	+67	-40	-110	+77	+88	-105	+40	+114	-1
	Relative (%)	-4.7	+0.0	+28.0	-17.0	-46.1	+32.2	+36.9	-44.1	+16.8	+48.0	-0.6
Steps (reduced)		5 (5)	8 (0)	12 (4)	14 (6)	17 (1)	19 (3)	21 (5)	21 (5)	23 (7)	25 (1)	25 (1)

Approximation of prime harmonics in 13ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-7	+7	+77	-28	-95	+93	+106	-87	+60	-103	+20
	Relative (%)	-2.9	+2.9	+32.3	-11.8	-39.8	+39.0	+44.4	-36.3	+25.1	-43.1	+8.5
Steps (reduced)		5 (5)	8 (8)	12 (12)	14 (1)	17 (4)	19 (6)	21 (8)	21 (8)	23 (10)	24 (11)	25 (12)

Approximation of prime harmonics in 14ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3	+23	+101	+0	-61	-109	-92	-44	+106	-54	+71
	Relative (%)	+1.3	+9.6	+42.1	+0.0	-25.2	-45.4	-38.4	-18.4	+44.1	-22.6	+29.4
Steps (reduced)		5 (5)	8 (8)	12 (12)	14 (0)	17 (3)	18 (4)	20 (6)	21 (7)	23 (9)	24 (10)	25 (11)

Approximation of prime harmonics in 18ed12

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5	+10	+82	-23	-88	+100	+114	-79	+69	-94	+30
	Relative (%)	-2.1	+4.2	+34.2	-9.6	-37.0	+42.0	+47.7	-32.9	+28.7	-39.2	+12.5
Steps (reduced)		5 (5)	8 (8)	12 (12)	14 (14)	17 (17)	19 (1)	21 (3)	21 (3)	23 (5)	24 (6)	25 (7)

Approximation of prime harmonics in 3edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-30	-30	+22	-93	+60	+5	+9	+50	-47	+20	-95
	Relative (%)	-12.9	-12.9	+9.2	-39.8	+25.8	+2.2	+3.7	+21.4	-19.9	+8.6	-40.8
Steps (reduced)		5 (2)	8 (2)	12 (0)	14 (2)	18 (0)	19 (1)	21 (0)	22 (1)	23 (2)	25 (1)	25 (1)

Approximation of prime harmonics in 1ed239.426c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-3	+13	+87	-17	-81	+109	-116	-70	+79	-83	+41
	Relative (%)	-1.2	+5.6	+36.3	-7.0	-33.9	+45.3	-48.6	-29.1	+32.8	-34.8	+17.0
Step		5	8	12	14	17	19	20	21	23	24	25

Approximation of prime harmonics in 1ed238.357c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-8	+5	+74	-32	-99	+88	+101	-92	+54	-109	+14
	Relative (%)	-3.4	+2.1	+31.0	-13.4	-41.6	+37.0	+42.2	-38.6	+22.6	-45.7	+5.8
Step		5	8	12	14	17	19	21	21	23	24	25

6edo

• 14ed5
• 17ed7
• 19ed9
• 20ed10
• 2.9.5 WE (199.736)
• 2.9.5.7 WE (199.329)
• 12zpi (198.843)

If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 sugroup tuning, then it benefits from octave shrinking.

Approximation of prime harmonics in 14ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.9	+88.3	+0.0	+14.6	+28.2	-62.0	+70.6	+77.1	-54.7	-57.9	+25.6
	Relative (%)	-2.9	+44.4	+0.0	+7.3	+14.1	-31.2	+35.5	+38.7	-27.5	-29.1	+12.9
Steps (reduced)		6 (6)	10 (10)	14 (0)	17 (3)	21 (7)	22 (8)	25 (11)	26 (12)	27 (13)	29 (1)	30 (2)

Approximation of prime harmonics in 17ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-11.0	+79.7	-12.0	+0.0	+10.2	-80.9	+49.2	+54.8	-77.8	-82.8	-0.0
	Relative (%)	-5.6	+40.2	-6.0	+0.0	+5.1	-40.8	+24.8	+27.7	-39.3	-41.8	-0.0
Steps (reduced)		6 (6)	10 (10)	14 (14)	17 (0)	21 (4)	22 (5)	25 (8)	26 (9)	27 (10)	29 (12)	30 (13)

Approximation of prime harmonics in 19ed9

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.2	+100.1	+16.6	+34.7	+53.0	-36.0	-100.0	-92.4	-22.7	-23.6	+61.1
	Relative (%)	+0.6	+50.0	+8.3	+17.3	+26.5	-18.0	-50.0	-46.1	-11.3	-11.8	+30.5
Steps (reduced)		6 (6)	10 (10)	14 (14)	17 (17)	21 (2)	22 (3)	24 (5)	25 (6)	27 (8)	29 (10)	30 (11)

{{harmonics in equal | 20 | 10 | 1 | intervals=prime}

Approximation of prime harmonics in 1ed199.736c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.6	+95.4	+10.0	+26.7	+43.1	-46.3	+88.4	+95.6	-35.4	-37.2	+47.0
	Relative (%)	-0.8	+47.8	+5.0	+13.4	+21.6	-23.2	+44.3	+47.9	-17.7	-18.6	+23.6
Step		6	10	14	17	21	22	25	26	27	29	30

Approximation of prime harmonics in 1ed199.329c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.0	+91.3	+4.3	+19.8	+34.6	-55.3	+78.3	+85.0	-46.4	-49.0	+34.8
	Relative (%)	-2.0	+45.8	+2.2	+9.9	+17.4	-27.7	+39.3	+42.7	-23.3	-24.6	+17.5
Step		6	10	14	17	21	22	25	26	27	29	30

Approximation of prime harmonics in 1ed198.843c

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-6.9	+86.5	-2.5	+11.5	+24.4	-66.0	+66.1	+72.4	-59.5	-63.1	+20.3
	Relative (%)	-3.5	+43.5	-1.3	+5.8	+12.3	-33.2	+33.3	+36.4	-29.9	-31.7	+10.2
Step		6	10	14	17	21	22	25	26	27	29	30

Low-priority

125edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

145edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

152edo

• 241edt
• 13-limit WE (7.894c)
• Best nearby ZPI(s)

159edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

166edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

182edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

198edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

212edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

243edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

247edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)