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== Approximations of integer harmonics ==
{{harmonics in equal|9|intervals=integer|columns=16}}
{{harmonics in equal|10|intervals=integer|columns=16}}
{{harmonics in equal|11|intervals=integer|columns=16}}
{{harmonics in equal|12|intervals=integer|columns=16}}
{{harmonics in equal|13|intervals=integer|columns=16}}
{{harmonics in equal|14|intervals=integer|columns=16}}
{{harmonics in equal|15|intervals=integer|columns=16}}
{{harmonics in equal|16|intervals=integer|columns=16}}
{{harmonics in equal|17|intervals=integer|columns=16}}
{{harmonics in equal|18|intervals=integer|columns=16}}
{{harmonics in equal|19|intervals=integer|columns=16}}
{{harmonics in equal|20|intervals=integer|columns=16}}
{{harmonics in equal|21|intervals=integer|columns=16}}
{{harmonics in equal|22|intervals=integer|columns=16}}
{{harmonics in equal|23|intervals=integer|columns=16}}
{{harmonics in equal|24|intervals=integer|columns=16}}
{{harmonics in equal|25|intervals=integer|columns=16}}
{{harmonics in equal|26|intervals=integer|columns=16}}
{{harmonics in equal|27|intervals=integer|columns=16}}
{{harmonics in equal|28|intervals=integer|columns=16}}
{{harmonics in equal|29|intervals=integer|columns=16}}
{{harmonics in equal|30|intervals=integer|columns=16}}
{{harmonics in equal|31|intervals=integer|columns=16}}
{{harmonics in equal|32|intervals=integer|columns=16}}
{{harmonics in equal|33|intervals=integer|columns=16}}
{{harmonics in equal|34|intervals=integer|columns=16}}
{{harmonics in equal|35|intervals=integer|columns=16}}
{{harmonics in equal|36|intervals=integer|columns=16}}
{{harmonics in equal|37|intervals=integer|columns=16}}
{{harmonics in equal|38|intervals=integer|columns=16}}
{{harmonics in equal|39|intervals=integer|columns=16}}
{{harmonics in equal|40|intervals=integer|columns=16}}
{{harmonics in equal|41|intervals=integer|columns=16}}
{{harmonics in equal|42|intervals=integer|columns=16}}
{{harmonics in equal|43|intervals=integer|columns=16}}
{{harmonics in equal|44|intervals=integer|columns=16}}
{{harmonics in equal|45|intervals=integer|columns=16}}
{{harmonics in equal|46|intervals=integer|columns=16}}
{{harmonics in equal|47|intervals=integer|columns=16}}
{{harmonics in equal|48|intervals=integer|columns=16}}
{{harmonics in equal|49|intervals=integer|columns=16}}
{{harmonics in equal|50|intervals=integer|columns=16}}
{{harmonics in equal|51|intervals=integer|columns=16}}
{{harmonics in equal|52|intervals=integer|columns=16}}
{{harmonics in equal|53|intervals=integer|columns=16}}
== Approximations of prime harmonics ==
{{harmonics in equal|9|intervals=prime|columns=9}}
{{harmonics in equal|9|intervals=prime|columns=9}}
{{harmonics in equal|10|intervals=prime|columns=9}}
{{harmonics in equal|10|intervals=prime|columns=9}}

Revision as of 13:27, 21 February 2026

Approximations of integer harmonics

Approximation of harmonics in 9edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -35.3 +0.0 +13.7 -35.3 -35.5 +0.0 +62.8 +13.7 -18.0 -35.3 -40.5 -35.5 -21.6 +0.0 +28.4
Relative (%) +0.0 -26.5 +0.0 +10.3 -26.5 -26.6 +0.0 +47.1 +10.3 -13.5 -26.5 -30.4 -26.6 -16.2 +0.0 +21.3
Steps
(reduced) 		9
(0) 		14
(5) 		18
(0) 		21
(3) 		23
(5) 		25
(7) 		27
(0) 		29
(2) 		30
(3) 		31
(4) 		32
(5) 		33
(6) 		34
(7) 		35
(8) 		36
(0) 		37
(1)
Approximation of harmonics in 10edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +18.0 +0.0 -26.3 +18.0 -8.8 +0.0 +36.1 -26.3 +48.7 +18.0 -0.5 -8.8 -8.3 +0.0 +15.0
Relative (%) +0.0 +15.0 +0.0 -21.9 +15.0 -7.4 +0.0 +30.1 -21.9 +40.6 +15.0 -0.4 -7.4 -6.9 +0.0 +12.5
Steps
(reduced) 		10
(0) 		16
(6) 		20
(0) 		23
(3) 		26
(6) 		28
(8) 		30
(0) 		32
(2) 		33
(3) 		35
(5) 		36
(6) 		37
(7) 		38
(8) 		39
(9) 		40
(0) 		41
(1)
Approximation of harmonics in 11edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -47.4 +0.0 +50.0 -47.4 +13.0 +0.0 +14.3 +50.0 -5.9 -47.4 +32.2 +13.0 +2.6 +0.0 +4.1
Relative (%) +0.0 -43.5 +0.0 +45.9 -43.5 +11.9 +0.0 +13.1 +45.9 -5.4 -43.5 +29.5 +11.9 +2.4 +0.0 +3.8
Steps
(reduced) 		11
(0) 		17
(6) 		22
(0) 		26
(4) 		28
(6) 		31
(9) 		33
(0) 		35
(2) 		37
(4) 		38
(5) 		39
(6) 		41
(8) 		42
(9) 		43
(10) 		44
(0) 		45
(1)
Approximation of harmonics in 12edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 +31.2 +0.0 -3.9 +13.7 +48.7 -2.0 -40.5 +31.2 +11.7 +0.0 -5.0
Relative (%) +0.0 -2.0 +0.0 +13.7 -2.0 +31.2 +0.0 -3.9 +13.7 +48.7 -2.0 -40.5 +31.2 +11.7 +0.0 -5.0
Steps
(reduced) 		12
(0) 		19
(7) 		24
(0) 		28
(4) 		31
(7) 		34
(10) 		36
(0) 		38
(2) 		40
(4) 		42
(6) 		43
(7) 		44
(8) 		46
(10) 		47
(11) 		48
(0) 		49
(1)
Approximation of harmonics in 13edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +36.5 +0.0 -17.1 +36.5 -45.7 +0.0 -19.3 -17.1 +2.5 +36.5 -9.8 -45.7 +19.4 +0.0 -12.6
Relative (%) +0.0 +39.5 +0.0 -18.5 +39.5 -49.6 +0.0 -20.9 -18.5 +2.7 +39.5 -10.6 -49.6 +21.0 +0.0 -13.7
Steps
(reduced) 		13
(0) 		21
(8) 		26
(0) 		30
(4) 		34
(8) 		36
(10) 		39
(0) 		41
(2) 		43
(4) 		45
(6) 		47
(8) 		48
(9) 		49
(10) 		51
(12) 		52
(0) 		53
(1)
Approximation of harmonics in 14edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -16.2 +0.0 +42.3 -16.2 -26.0 +0.0 -32.5 +42.3 -37.0 -16.2 +16.6 -26.0 +26.0 +0.0 -19.2
Relative (%) +0.0 -18.9 +0.0 +49.3 -18.9 -30.3 +0.0 -37.9 +49.3 -43.2 -18.9 +19.4 -30.3 +30.4 +0.0 -22.4
Steps
(reduced) 		14
(0) 		22
(8) 		28
(0) 		33
(5) 		36
(8) 		39
(11) 		42
(0) 		44
(2) 		47
(5) 		48
(6) 		50
(8) 		52
(10) 		53
(11) 		55
(13) 		56
(0) 		57
(1)
Approximation of harmonics in 15edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 +36.1 +13.7 +8.7 +18.0 +39.5 -8.8 +31.7 +0.0 -25.0
Relative (%) +0.0 +22.6 +0.0 +17.1 +22.6 -11.0 +0.0 +45.1 +17.1 +10.9 +22.6 +49.3 -11.0 +39.7 +0.0 -31.2
Steps
(reduced) 		15
(0) 		24
(9) 		30
(0) 		35
(5) 		39
(9) 		42
(12) 		45
(0) 		48
(3) 		50
(5) 		52
(7) 		54
(9) 		56
(11) 		57
(12) 		59
(14) 		60
(0) 		61
(1)
Approximation of harmonics in 16edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -27.0 +0.0 -11.3 -27.0 +6.2 +0.0 +21.1 -11.3 -26.3 -27.0 -15.5 +6.2 +36.7 +0.0 -30.0
Relative (%) +0.0 -35.9 +0.0 -15.1 -35.9 +8.2 +0.0 +28.1 -15.1 -35.1 -35.9 -20.7 +8.2 +49.0 +0.0 -39.9
Steps
(reduced) 		16
(0) 		25
(9) 		32
(0) 		37
(5) 		41
(9) 		45
(13) 		48
(0) 		51
(3) 		53
(5) 		55
(7) 		57
(9) 		59
(11) 		61
(13) 		63
(15) 		64
(0) 		65
(1)
Approximation of harmonics in 17edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +3.9 +0.0 -33.4 +3.9 +19.4 +0.0 +7.9 -33.4 +13.4 +3.9 +6.5 +19.4 -29.4 +0.0 -34.4
Relative (%) +0.0 +5.6 +0.0 -47.3 +5.6 +27.5 +0.0 +11.1 -47.3 +19.0 +5.6 +9.3 +27.5 -41.7 +0.0 -48.7
Steps
(reduced) 		17
(0) 		27
(10) 		34
(0) 		39
(5) 		44
(10) 		48
(14) 		51
(0) 		54
(3) 		56
(5) 		59
(8) 		61
(10) 		63
(12) 		65
(14) 		66
(15) 		68
(0) 		69
(1)
Approximation of harmonics in 18edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +31.4 +0.0 +13.7 +31.4 +31.2 +0.0 -3.9 +13.7 -18.0 +31.4 +26.1 +31.2 -21.6 +0.0 +28.4
Relative (%) +0.0 +47.1 +0.0 +20.5 +47.1 +46.8 +0.0 -5.9 +20.5 -27.0 +47.1 +39.2 +46.8 -32.4 +0.0 +42.6
Steps
(reduced) 		18
(0) 		29
(11) 		36
(0) 		42
(6) 		47
(11) 		51
(15) 		54
(0) 		57
(3) 		60
(6) 		62
(8) 		65
(11) 		67
(13) 		69
(15) 		70
(16) 		72
(0) 		74
(2)
Approximation of harmonics in 19edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -7.2 +0.0 -7.4 -7.2 -21.5 +0.0 -14.4 -7.4 +17.1 -7.2 -19.5 -21.5 -14.6 +0.0 +21.4
Relative (%) +0.0 -11.4 +0.0 -11.7 -11.4 -34.0 +0.0 -22.9 -11.7 +27.1 -11.4 -30.8 -34.0 -23.1 +0.0 +33.8
Steps
(reduced) 		19
(0) 		30
(11) 		38
(0) 		44
(6) 		49
(11) 		53
(15) 		57
(0) 		60
(3) 		63
(6) 		66
(9) 		68
(11) 		70
(13) 		72
(15) 		74
(17) 		76
(0) 		78
(2)
Approximation of harmonics in 20edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +18.0 +0.0 -26.3 +18.0 -8.8 +0.0 -23.9 -26.3 -11.3 +18.0 -0.5 -8.8 -8.3 +0.0 +15.0
Relative (%) +0.0 +30.1 +0.0 -43.9 +30.1 -14.7 +0.0 -39.9 -43.9 -18.9 +30.1 -0.9 -14.7 -13.8 +0.0 +25.1
Steps
(reduced) 		20
(0) 		32
(12) 		40
(0) 		46
(6) 		52
(12) 		56
(16) 		60
(0) 		63
(3) 		66
(6) 		69
(9) 		72
(12) 		74
(14) 		76
(16) 		78
(18) 		80
(0) 		82
(2)
Approximation of harmonics in 21edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -16.2 +0.0 +13.7 -16.2 +2.6 +0.0 +24.7 +13.7 +20.1 -16.2 +16.6 +2.6 -2.6 +0.0 +9.3
Relative (%) +0.0 -28.4 +0.0 +24.0 -28.4 +4.6 +0.0 +43.2 +24.0 +35.2 -28.4 +29.1 +4.6 -4.5 +0.0 +16.3
Steps
(reduced) 		21
(0) 		33
(12) 		42
(0) 		49
(7) 		54
(12) 		59
(17) 		63
(0) 		67
(4) 		70
(7) 		73
(10) 		75
(12) 		78
(15) 		80
(17) 		82
(19) 		84
(0) 		86
(2)
Approximation of harmonics in 22edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +7.1 +0.0 -4.5 +7.1 +13.0 +0.0 +14.3 -4.5 -5.9 +7.1 -22.3 +13.0 +2.6 +0.0 +4.1
Relative (%) +0.0 +13.1 +0.0 -8.2 +13.1 +23.8 +0.0 +26.2 -8.2 -10.7 +13.1 -41.0 +23.8 +4.8 +0.0 +7.6
Steps
(reduced) 		22
(0) 		35
(13) 		44
(0) 		51
(7) 		57
(13) 		62
(18) 		66
(0) 		70
(4) 		73
(7) 		76
(10) 		79
(13) 		81
(15) 		84
(18) 		86
(20) 		88
(0) 		90
(2)
Approximation of harmonics in 23edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -23.7 +0.0 -21.1 -23.7 +22.5 +0.0 +4.8 -21.1 +22.6 -23.7 -5.7 +22.5 +7.4 +0.0 -0.6
Relative (%) +0.0 -45.4 +0.0 -40.4 -45.4 +43.1 +0.0 +9.2 -40.4 +43.3 -45.4 -11.0 +43.1 +14.2 +0.0 -1.2
Steps
(reduced) 		23
(0) 		36
(13) 		46
(0) 		53
(7) 		59
(13) 		65
(19) 		69
(0) 		73
(4) 		76
(7) 		80
(11) 		82
(13) 		85
(16) 		88
(19) 		90
(21) 		92
(0) 		94
(2)
Approximation of harmonics in 24edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -18.8 +0.0 -3.9 +13.7 -1.3 -2.0 +9.5 -18.8 +11.7 +0.0 -5.0
Relative (%) +0.0 -3.9 +0.0 +27.4 -3.9 -37.7 +0.0 -7.8 +27.4 -2.6 -3.9 +18.9 -37.7 +23.5 +0.0 -9.9
Steps
(reduced) 		24
(0) 		38
(14) 		48
(0) 		56
(8) 		62
(14) 		67
(19) 		72
(0) 		76
(4) 		80
(8) 		83
(11) 		86
(14) 		89
(17) 		91
(19) 		94
(22) 		96
(0) 		98
(2)
Approximation of harmonics in 25edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +18.0 +0.0 -2.3 +18.0 -8.8 +0.0 -11.9 -2.3 -23.3 +18.0 +23.5 -8.8 +15.7 +0.0 -9.0
Relative (%) +0.0 +37.6 +0.0 -4.8 +37.6 -18.4 +0.0 -24.8 -4.8 -48.6 +37.6 +48.9 -18.4 +32.8 +0.0 -18.7
Steps
(reduced) 		25
(0) 		40
(15) 		50
(0) 		58
(8) 		65
(15) 		70
(20) 		75
(0) 		79
(4) 		83
(8) 		86
(11) 		90
(15) 		93
(18) 		95
(20) 		98
(23) 		100
(0) 		102
(2)
Approximation of harmonics in 26edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -9.6 +0.0 -17.1 -9.6 +0.4 +0.0 -19.3 -17.1 +2.5 -9.6 -9.8 +0.4 +19.4 +0.0 -12.6
Relative (%) +0.0 -20.9 +0.0 -37.0 -20.9 +0.9 +0.0 -41.8 -37.0 +5.5 -20.9 -21.1 +0.9 +42.1 +0.0 -27.4
Steps
(reduced) 		26
(0) 		41
(15) 		52
(0) 		60
(8) 		67
(15) 		73
(21) 		78
(0) 		82
(4) 		86
(8) 		90
(12) 		93
(15) 		96
(18) 		99
(21) 		102
(24) 		104
(0) 		106
(2)
Approximation of harmonics in 27edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +9.2 +0.0 +13.7 +9.2 +9.0 +0.0 +18.3 +13.7 -18.0 +9.2 +3.9 +9.0 -21.6 +0.0 -16.1
Relative (%) +0.0 +20.6 +0.0 +30.8 +20.6 +20.1 +0.0 +41.2 +30.8 -40.5 +20.6 +8.8 +20.1 -48.6 +0.0 -36.1
Steps
(reduced) 		27
(0) 		43
(16) 		54
(0) 		63
(9) 		70
(16) 		76
(22) 		81
(0) 		86
(5) 		90
(9) 		93
(12) 		97
(16) 		100
(19) 		103
(22) 		105
(24) 		108
(0) 		110
(2)
Approximation of harmonics in 28edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -16.2 +0.0 -0.6 -16.2 +16.9 +0.0 +10.4 -0.6 +5.8 -16.2 +16.6 +16.9 -16.8 +0.0 -19.2
Relative (%) +0.0 -37.9 +0.0 -1.4 -37.9 +39.4 +0.0 +24.2 -1.4 +13.6 -37.9 +38.8 +39.4 -39.3 +0.0 -44.9
Steps
(reduced) 		28
(0) 		44
(16) 		56
(0) 		65
(9) 		72
(16) 		79
(23) 		84
(0) 		89
(5) 		93
(9) 		97
(13) 		100
(16) 		104
(20) 		107
(23) 		109
(25) 		112
(0) 		114
(2)
Approximation of harmonics in 29edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +1.5 +0.0 -13.9 +1.5 -17.1 +0.0 +3.0 -13.9 -13.4 +1.5 -12.9 -17.1 -12.4 +0.0 +19.2
Relative (%) +0.0 +3.6 +0.0 -33.6 +3.6 -41.3 +0.0 +7.2 -33.6 -32.4 +3.6 -31.3 -41.3 -30.0 +0.0 +46.4
Steps
(reduced) 		29
(0) 		46
(17) 		58
(0) 		67
(9) 		75
(17) 		81
(23) 		87
(0) 		92
(5) 		96
(9) 		100
(13) 		104
(17) 		107
(20) 		110
(23) 		113
(26) 		116
(0) 		119
(3)
Approximation of harmonics in 30edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 -3.9 +13.7 +8.7 +18.0 -0.5 -8.8 -8.3 +0.0 +15.0
Relative (%) +0.0 +45.1 +0.0 +34.2 +45.1 -22.1 +0.0 -9.8 +34.2 +21.7 +45.1 -1.3 -22.1 -20.7 +0.0 +37.6
Steps
(reduced) 		30
(0) 		48
(18) 		60
(0) 		70
(10) 		78
(18) 		84
(24) 		90
(0) 		95
(5) 		100
(10) 		104
(14) 		108
(18) 		111
(21) 		114
(24) 		117
(27) 		120
(0) 		123
(3)
Approximation of harmonics in 31edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -5.2 +0.0 +0.8 -5.2 -1.1 +0.0 -10.4 +0.8 -9.4 -5.2 +11.1 -1.1 -4.4 +0.0 +11.2
Relative (%) +0.0 -13.4 +0.0 +2.0 -13.4 -2.8 +0.0 -26.8 +2.0 -24.2 -13.4 +28.6 -2.8 -11.4 +0.0 +28.9
Steps
(reduced) 		31
(0) 		49
(18) 		62
(0) 		72
(10) 		80
(18) 		87
(25) 		93
(0) 		98
(5) 		103
(10) 		107
(14) 		111
(18) 		115
(22) 		118
(25) 		121
(28) 		124
(0) 		127
(3)
Approximation of harmonics in 32edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +10.5 +0.0 -11.3 +10.5 +6.2 +0.0 -16.4 -11.3 +11.2 +10.5 -15.5 +6.2 -0.8 +0.0 +7.5
Relative (%) +0.0 +28.1 +0.0 -30.2 +28.1 +16.5 +0.0 -43.8 -30.2 +29.8 +28.1 -41.4 +16.5 -2.0 +0.0 +20.1
Steps
(reduced) 		32
(0) 		51
(19) 		64
(0) 		74
(10) 		83
(19) 		90
(26) 		96
(0) 		101
(5) 		106
(10) 		111
(15) 		115
(19) 		118
(22) 		122
(26) 		125
(29) 		128
(0) 		131
(3)
Approximation of harmonics in 33edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -11.0 +0.0 +13.7 -11.0 +13.0 +0.0 +14.3 +13.7 -5.9 -11.0 -4.2 +13.0 +2.6 +0.0 +4.1
Relative (%) +0.0 -30.4 +0.0 +37.6 -30.4 +35.7 +0.0 +39.2 +37.6 -16.1 -30.4 -11.5 +35.7 +7.3 +0.0 +11.4
Steps
(reduced) 		33
(0) 		52
(19) 		66
(0) 		77
(11) 		85
(19) 		93
(27) 		99
(0) 		105
(6) 		110
(11) 		114
(15) 		118
(19) 		122
(23) 		126
(27) 		129
(30) 		132
(0) 		135
(3)
Approximation of harmonics in 34edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +3.9 +0.0 +1.9 +3.9 -15.9 +0.0 +7.9 +1.9 +13.4 +3.9 +6.5 -15.9 +5.8 +0.0 +0.9
Relative (%) +0.0 +11.1 +0.0 +5.4 +11.1 -45.0 +0.0 +22.3 +5.4 +37.9 +11.1 +18.5 -45.0 +16.6 +0.0 +2.6
Steps
(reduced) 		34
(0) 		54
(20) 		68
(0) 		79
(11) 		88
(20) 		95
(27) 		102
(0) 		108
(6) 		113
(11) 		118
(16) 		122
(20) 		126
(24) 		129
(27) 		133
(31) 		136
(0) 		139
(3)
Approximation of harmonics in 35edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -16.2 +0.0 -9.2 -16.2 -8.8 +0.0 +1.8 -9.2 -2.7 -16.2 +16.6 -8.8 +8.9 +0.0 -2.1
Relative (%) +0.0 -47.4 +0.0 -26.7 -47.4 -25.7 +0.0 +5.3 -26.7 -8.0 -47.4 +48.5 -25.7 +25.9 +0.0 -6.1
Steps
(reduced) 		35
(0) 		55
(20) 		70
(0) 		81
(11) 		90
(20) 		98
(28) 		105
(0) 		111
(6) 		116
(11) 		121
(16) 		125
(20) 		130
(25) 		133
(28) 		137
(32) 		140
(0) 		143
(3)
Approximation of harmonics in 36edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -2.2 +0.0 -3.9 +13.7 +15.3 -2.0 -7.2 -2.2 +11.7 +0.0 -5.0
Relative (%) +0.0 -5.9 +0.0 +41.1 -5.9 -6.5 +0.0 -11.7 +41.1 +46.0 -5.9 -21.6 -6.5 +35.2 +0.0 -14.9
Steps
(reduced) 		36
(0) 		57
(21) 		72
(0) 		84
(12) 		93
(21) 		101
(29) 		108
(0) 		114
(6) 		120
(12) 		125
(17) 		129
(21) 		133
(25) 		137
(29) 		141
(33) 		144
(0) 		147
(3)
Approximation of harmonics in 37edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +11.6 +0.0 +2.9 +11.6 +4.1 +0.0 -9.3 +2.9 +0.0 +11.6 +2.7 +4.1 +14.4 +0.0 -7.7
Relative (%) +0.0 +35.6 +0.0 +8.9 +35.6 +12.8 +0.0 -28.7 +8.9 +0.1 +35.6 +8.4 +12.8 +44.5 +0.0 -23.6
Steps
(reduced) 		37
(0) 		59
(22) 		74
(0) 		86
(12) 		96
(22) 		104
(30) 		111
(0) 		117
(6) 		123
(12) 		128
(17) 		133
(22) 		137
(26) 		141
(30) 		145
(34) 		148
(0) 		151
(3)
Approximation of harmonics in 38edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -7.2 +0.0 -7.4 -7.2 +10.1 +0.0 -14.4 -7.4 -14.5 -7.2 +12.1 +10.1 -14.6 +0.0 -10.2
Relative (%) +0.0 -22.9 +0.0 -23.3 -22.9 +32.1 +0.0 -45.7 -23.3 -45.8 -22.9 +38.3 +32.1 -46.2 +0.0 -32.4
Steps
(reduced) 		38
(0) 		60
(22) 		76
(0) 		88
(12) 		98
(22) 		107
(31) 		114
(0) 		120
(6) 		126
(12) 		131
(17) 		136
(22) 		141
(27) 		145
(31) 		148
(34) 		152
(0) 		155
(3)
Approximation of harmonics in 39edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +5.7 +0.0 +13.7 +5.7 -15.0 +0.0 +11.5 +13.7 +2.5 +5.7 -9.8 -15.0 -11.3 +0.0 -12.6
Relative (%) +0.0 +18.6 +0.0 +44.5 +18.6 -48.7 +0.0 +37.3 +44.5 +8.2 +18.6 -31.7 -48.7 -36.9 +0.0 -41.1
Steps
(reduced) 		39
(0) 		62
(23) 		78
(0) 		91
(13) 		101
(23) 		109
(31) 		117
(0) 		124
(7) 		130
(13) 		135
(18) 		140
(23) 		144
(27) 		148
(31) 		152
(35) 		156
(0) 		159
(3)
Approximation of harmonics in 40edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -12.0 +0.0 +3.7 -12.0 -8.8 +0.0 +6.1 +3.7 -11.3 -12.0 -0.5 -8.8 -8.3 +0.0 -15.0
Relative (%) +0.0 -39.9 +0.0 +12.3 -39.9 -29.4 +0.0 +20.3 +12.3 -37.7 -39.9 -1.8 -29.4 -27.6 +0.0 -49.9
Steps
(reduced) 		40
(0) 		63
(23) 		80
(0) 		93
(13) 		103
(23) 		112
(32) 		120
(0) 		127
(7) 		133
(13) 		138
(18) 		143
(23) 		148
(28) 		152
(32) 		156
(36) 		160
(0) 		163
(3)
Approximation of harmonics in 41edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +0.5 +0.0 -5.8 +0.5 -3.0 +0.0 +1.0 -5.8 +4.8 +0.5 +8.3 -3.0 -5.3 +0.0 +12.1
Relative (%) +0.0 +1.7 +0.0 -19.9 +1.7 -10.2 +0.0 +3.3 -19.9 +16.3 +1.7 +28.2 -10.2 -18.3 +0.0 +41.4
Steps
(reduced) 		41
(0) 		65
(24) 		82
(0) 		95
(13) 		106
(24) 		115
(33) 		123
(0) 		130
(7) 		136
(13) 		142
(19) 		147
(24) 		152
(29) 		156
(33) 		160
(37) 		164
(0) 		168
(4)
Approximation of harmonics in 42edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +12.3 +0.0 +13.7 +12.3 +2.6 +0.0 -3.9 +13.7 -8.5 +12.3 -12.0 +2.6 -2.6 +0.0 +9.3
Relative (%) +0.0 +43.2 +0.0 +47.9 +43.2 +9.1 +0.0 -13.7 +47.9 -29.6 +43.2 -41.8 +9.1 -8.9 +0.0 +32.7
Steps
(reduced) 		42
(0) 		67
(25) 		84
(0) 		98
(14) 		109
(25) 		118
(34) 		126
(0) 		133
(7) 		140
(14) 		145
(19) 		151
(25) 		155
(29) 		160
(34) 		164
(38) 		168
(0) 		172
(4)
Approximation of harmonics in 43edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -4.3 +0.0 +4.4 -4.3 +7.9 +0.0 -8.6 +4.4 +6.8 -4.3 -3.3 +7.9 +0.1 +0.0 +6.7
Relative (%) +0.0 -15.3 +0.0 +15.7 -15.3 +28.4 +0.0 -30.7 +15.7 +24.4 -15.3 -11.9 +28.4 +0.4 +0.0 +23.9
Steps
(reduced) 		43
(0) 		68
(25) 		86
(0) 		100
(14) 		111
(25) 		121
(35) 		129
(0) 		136
(7) 		143
(14) 		149
(20) 		154
(25) 		159
(30) 		164
(35) 		168
(39) 		172
(0) 		176
(4)
Approximation of harmonics in 44edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +7.1 +0.0 -4.5 +7.1 +13.0 +0.0 -13.0 -4.5 -5.9 +7.1 +4.9 +13.0 +2.6 +0.0 +4.1
Relative (%) +0.0 +26.2 +0.0 -16.5 +26.2 +47.6 +0.0 -47.7 -16.5 -21.5 +26.2 +18.1 +47.6 +9.7 +0.0 +15.2
Steps
(reduced) 		44
(0) 		70
(26) 		88
(0) 		102
(14) 		114
(26) 		124
(36) 		132
(0) 		139
(7) 		146
(14) 		152
(20) 		158
(26) 		163
(31) 		168
(36) 		172
(40) 		176
(0) 		180
(4)
Approximation of harmonics in 45edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -8.6 +0.0 -13.0 -8.6 -8.8 +0.0 +9.4 -13.0 +8.7 -8.6 +12.8 -8.8 +5.1 +0.0 +1.7
Relative (%) +0.0 -32.3 +0.0 -48.7 -32.3 -33.1 +0.0 +35.3 -48.7 +32.6 -32.3 +48.0 -33.1 +19.0 +0.0 +6.4
Steps
(reduced) 		45
(0) 		71
(26) 		90
(0) 		104
(14) 		116
(26) 		126
(36) 		135
(0) 		143
(8) 		149
(14) 		156
(21) 		161
(26) 		167
(32) 		171
(36) 		176
(41) 		180
(0) 		184
(4)
Approximation of harmonics in 46edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +2.4 +0.0 +5.0 +2.4 -3.6 +0.0 +4.8 +5.0 -3.5 +2.4 -5.7 -3.6 +7.4 +0.0 -0.6
Relative (%) +0.0 +9.2 +0.0 +19.1 +9.2 -13.8 +0.0 +18.3 +19.1 -13.4 +9.2 -22.0 -13.8 +28.3 +0.0 -2.3
Steps
(reduced) 		46
(0) 		73
(27) 		92
(0) 		107
(15) 		119
(27) 		129
(37) 		138
(0) 		146
(8) 		153
(15) 		159
(21) 		165
(27) 		170
(32) 		175
(37) 		180
(42) 		184
(0) 		188
(4)
Approximation of harmonics in 47edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -12.6 +0.0 -3.3 -12.6 +1.4 +0.0 +0.3 -3.3 +10.4 -12.6 +2.0 +1.4 +9.6 +0.0 -2.8
Relative (%) +0.0 -49.3 +0.0 -13.1 -49.3 +5.4 +0.0 +1.4 -13.1 +40.7 -49.3 +7.9 +5.4 +37.6 +0.0 -11.1
Steps
(reduced) 		47
(0) 		74
(27) 		94
(0) 		109
(15) 		121
(27) 		132
(38) 		141
(0) 		149
(8) 		156
(15) 		163
(22) 		168
(27) 		174
(33) 		179
(38) 		184
(43) 		188
(0) 		192
(4)
Approximation of harmonics in 48edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -2.0 +0.0 -11.3 -2.0 +6.2 +0.0 -3.9 -11.3 -1.3 -2.0 +9.5 +6.2 +11.7 +0.0 -5.0
Relative (%) +0.0 -7.8 +0.0 -45.3 -7.8 +24.7 +0.0 -15.6 -45.3 -5.3 -7.8 +37.9 +24.7 +46.9 +0.0 -19.8
Steps
(reduced) 		48
(0) 		76
(28) 		96
(0) 		111
(15) 		124
(28) 		135
(39) 		144
(0) 		152
(8) 		159
(15) 		166
(22) 		172
(28) 		178
(34) 		183
(39) 		188
(44) 		192
(0) 		196
(4)
Approximation of harmonics in 49edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +8.2 +0.0 +5.5 +8.2 +10.8 +0.0 -8.0 +5.5 +11.9 +8.2 -7.9 +10.8 -10.7 +0.0 -7.0
Relative (%) +0.0 +33.7 +0.0 +22.6 +33.7 +44.0 +0.0 -32.6 +22.6 +48.8 +33.7 -32.2 +44.0 -43.8 +0.0 -28.6
Steps
(reduced) 		49
(0) 		78
(29) 		98
(0) 		114
(16) 		127
(29) 		138
(40) 		147
(0) 		155
(8) 		163
(16) 		170
(23) 		176
(29) 		181
(34) 		187
(40) 		191
(44) 		196
(0) 		200
(4)
Approximation of harmonics in 50edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -6.0 +0.0 -2.3 -6.0 -8.8 +0.0 -11.9 -2.3 +0.7 -6.0 -0.5 -8.8 -8.3 +0.0 -9.0
Relative (%) +0.0 -24.8 +0.0 -9.6 -24.8 -36.8 +0.0 -49.6 -9.6 +2.8 -24.8 -2.2 -36.8 -34.5 +0.0 -37.3
Steps
(reduced) 		50
(0) 		79
(29) 		100
(0) 		116
(16) 		129
(29) 		140
(40) 		150
(0) 		158
(8) 		166
(16) 		173
(23) 		179
(29) 		185
(35) 		190
(40) 		195
(45) 		200
(0) 		204
(4)
Approximation of harmonics in 51edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 +3.9 +0.0 -9.8 +3.9 -4.1 +0.0 +7.9 -9.8 -10.1 +3.9 +6.5 -4.1 -5.9 +0.0 -10.8
Relative (%) +0.0 +16.7 +0.0 -41.8 +16.7 -17.5 +0.0 +33.4 -41.8 -43.1 +16.7 +27.8 -17.5 -25.1 +0.0 -46.1
Steps
(reduced) 		51
(0) 		81
(30) 		102
(0) 		118
(16) 		132
(30) 		143
(41) 		153
(0) 		162
(9) 		169
(16) 		176
(23) 		183
(30) 		189
(36) 		194
(41) 		199
(46) 		204
(0) 		208
(4)
Approximation of harmonics in 52edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.0 -9.6 +0.0 +6.0 -9.6 +0.4 +0.0 +3.8 +6.0 +2.5 -9.6 -9.8 +0.4 -3.7 +0.0 +10.4
Relative (%) +0.0 -41.8 +0.0 +26.0 -41.8 +1.8 +0.0 +16.4 +26.0 +11.0 -41.8 -42.3 +1.8 -15.8 +0.0 +45.2
Steps
(reduced) 		52
(0) 		82
(30) 		104
(0) 		121
(17) 		134
(30) 		146
(42) 		156
(0) 		165
(9) 		173
(17) 		180
(24) 		186
(30) 		192
(36) 		198
(42) 		203
(47) 		208
(0) 		213
(5)
Approximation of harmonics in 53edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +0.00 -0.07 +0.00 -1.41 -0.07 +4.76 +0.00 -0.14 -1.41 -7.92 -0.07 -2.79 +4.76 -1.48 +0.00 +8.25
Relative (%) +0.0 -0.3 +0.0 -6.2 -0.3 +21.0 +0.0 -0.6 -6.2 -35.0 -0.3 -12.3 +21.0 -6.5 +0.0 +36.4
Steps
(reduced) 		53
(0) 		84
(31) 		106
(0) 		123
(17) 		137
(31) 		149
(43) 		159
(0) 		168
(9) 		176
(17) 		183
(24) 		190
(31) 		196
(37) 		202
(43) 		207
(48) 		212
(0) 		217
(5)

Approximations of prime harmonics

Approximation of prime harmonics in 9edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -35.3 +13.7 -35.5 -18.0 -40.5 +28.4 -30.8 +38.4
Relative (%) +0.0 -26.5 +10.3 -26.6 -13.5 -30.4 +21.3 -23.1 +28.8
Steps
(reduced) 		9
(0) 		14
(5) 		21
(3) 		25
(7) 		31
(4) 		33
(6) 		37
(1) 		38
(2) 		41
(5)
Approximation of prime harmonics in 10edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +18.0 -26.3 -8.8 +48.7 -0.5 +15.0 -57.5 -28.3
Relative (%) +0.0 +15.0 -21.9 -7.4 +40.6 -0.4 +12.5 -47.9 -23.6
Steps
(reduced) 		10
(0) 		16
(6) 		23
(3) 		28
(8) 		35
(5) 		37
(7) 		41
(1) 		42
(2) 		45
(5)
Approximation of prime harmonics in 11edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -47.4 +50.0 +13.0 -5.9 +32.2 +4.1 +29.8 +26.3
Relative (%) +0.0 -43.5 +45.9 +11.9 -5.4 +29.5 +3.8 +27.3 +24.1
Steps
(reduced) 		11
(0) 		17
(6) 		26
(4) 		31
(9) 		38
(5) 		41
(8) 		45
(1) 		47
(3) 		50
(6)
Approximation of prime harmonics in 12edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -2.0 +13.7 +31.2 +48.7 -40.5 -5.0 +2.5 -28.3
Relative (%) +0.0 -2.0 +13.7 +31.2 +48.7 -40.5 -5.0 +2.5 -28.3
Steps
(reduced) 		12
(0) 		19
(7) 		28
(4) 		34
(10) 		42
(6) 		44
(8) 		49
(1) 		51
(3) 		54
(6)
Approximation of prime harmonics in 13edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +36.5 -17.1 -45.7 +2.5 -9.8 -12.6 -20.6 +17.9
Relative (%) +0.0 +39.5 -18.5 -49.6 +2.7 -10.6 -13.7 -22.3 +19.4
Steps
(reduced) 		13
(0) 		21
(8) 		30
(4) 		36
(10) 		45
(6) 		48
(9) 		53
(1) 		55
(3) 		59
(7)
Approximation of prime harmonics in 14edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -16.2 +42.3 -26.0 -37.0 +16.6 -19.2 -40.4 -28.3
Relative (%) +0.0 -18.9 +49.3 -30.3 -43.2 +19.4 -22.4 -47.1 -33.0
Steps
(reduced) 		14
(0) 		22
(8) 		33
(5) 		39
(11) 		48
(6) 		52
(10) 		57
(1) 		59
(3) 		63
(7)
Approximation of prime harmonics in 15edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +18.0 +13.7 -8.8 +8.7 +39.5 -25.0 +22.5 +11.7
Relative (%) +0.0 +22.6 +17.1 -11.0 +10.9 +49.3 -31.2 +28.1 +14.7
Steps
(reduced) 		15
(0) 		24
(9) 		35
(5) 		42
(12) 		52
(7) 		56
(11) 		61
(1) 		64
(4) 		68
(8)
Approximation of prime harmonics in 16edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -27.0 -11.3 +6.2 -26.3 -15.5 -30.0 +2.5 -28.3
Relative (%) +0.0 -35.9 -15.1 +8.2 -35.1 -20.7 -39.9 +3.3 -37.7
Steps
(reduced) 		16
(0) 		25
(9) 		37
(5) 		45
(13) 		55
(7) 		59
(11) 		65
(1) 		68
(4) 		72
(8)
Approximation of prime harmonics in 17edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +3.9 -33.4 +19.4 +13.4 +6.5 -34.4 -15.2 +7.0
Relative (%) +0.0 +5.6 -47.3 +27.5 +19.0 +9.3 -48.7 -21.5 +9.9
Steps
(reduced) 		17
(0) 		27
(10) 		39
(5) 		48
(14) 		59
(8) 		63
(12) 		69
(1) 		72
(4) 		77
(9)
Approximation of prime harmonics in 18edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +31.4 +13.7 +31.2 -18.0 +26.1 +28.4 -30.8 -28.3
Relative (%) +0.0 +47.1 +20.5 +46.8 -27.0 +39.2 +42.6 -46.3 -42.4
Steps
(reduced) 		18
(0) 		29
(11) 		42
(6) 		51
(15) 		62
(8) 		67
(13) 		74
(2) 		76
(4) 		81
(9)
Approximation of prime harmonics in 19edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -7.2 -7.4 -21.5 +17.1 -19.5 +21.4 +18.3 +3.3
Relative (%) +0.0 -11.4 -11.7 -34.0 +27.1 -30.8 +33.8 +28.9 +5.2
Steps
(reduced) 		19
(0) 		30
(11) 		44
(6) 		53
(15) 		66
(9) 		70
(13) 		78
(2) 		81
(5) 		86
(10)
Approximation of prime harmonics in 20edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +18.0 -26.3 -8.8 -11.3 -0.5 +15.0 +2.5 -28.3
Relative (%) +0.0 +30.1 -43.9 -14.7 -18.9 -0.9 +25.1 +4.1 -47.1
Steps
(reduced) 		20
(0) 		32
(12) 		46
(6) 		56
(16) 		69
(9) 		74
(14) 		82
(2) 		85
(5) 		90
(10)
Approximation of prime harmonics in 21edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -16.2 +13.7 +2.6 +20.1 +16.6 +9.3 -11.8 +0.3
Relative (%) +0.0 -28.4 +24.0 +4.6 +35.2 +29.1 +16.3 -20.6 +0.5
Steps
(reduced) 		21
(0) 		33
(12) 		49
(7) 		59
(17) 		73
(10) 		78
(15) 		86
(2) 		89
(5) 		95
(11)
Approximation of prime harmonics in 22edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +7.1 -4.5 +13.0 -5.9 -22.3 +4.1 -24.8 +26.3
Relative (%) +0.0 +13.1 -8.2 +23.8 -10.7 -41.0 +7.6 -45.4 +48.2
Steps
(reduced) 		22
(0) 		35
(13) 		51
(7) 		62
(18) 		76
(10) 		81
(15) 		90
(2) 		93
(5) 		100
(12)
Approximation of prime harmonics in 23edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -23.7 -21.1 +22.5 +22.6 -5.7 -0.6 +15.5 -2.2
Relative (%) +0.0 -45.4 -40.4 +43.1 +43.3 -11.0 -1.2 +29.8 -4.2
Steps
(reduced) 		23
(0) 		36
(13) 		53
(7) 		65
(19) 		80
(11) 		85
(16) 		94
(2) 		98
(6) 		104
(12)
Approximation of prime harmonics in 24edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -2.0 +13.7 -18.8 -1.3 +9.5 -5.0 +2.5 +21.7
Relative (%) +0.0 -3.9 +27.4 -37.7 -2.6 +18.9 -9.9 +5.0 +43.5
Steps
(reduced) 		24
(0) 		38
(14) 		56
(8) 		67
(19) 		83
(11) 		89
(17) 		98
(2) 		102
(6) 		109
(13)
Approximation of prime harmonics in 25edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +18.0 -2.3 -8.8 -23.3 +23.5 -9.0 -9.5 -4.3
Relative (%) +0.0 +37.6 -4.8 -18.4 -48.6 +48.9 -18.7 -19.8 -8.9
Steps
(reduced) 		25
(0) 		40
(15) 		58
(8) 		70
(20) 		86
(11) 		93
(18) 		102
(2) 		106
(6) 		113
(13)
Approximation of prime harmonics in 26edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -9.6 -17.1 +0.4 +2.5 -9.8 -12.6 -20.6 +17.9
Relative (%) +0.0 -20.9 -37.0 +0.9 +5.5 -21.1 -27.4 -44.6 +38.7
Steps
(reduced) 		26
(0) 		41
(15) 		60
(8) 		73
(21) 		90
(12) 		96
(18) 		106
(2) 		110
(6) 		118
(14)
Approximation of prime harmonics in 27edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +9.2 +13.7 +9.0 -18.0 +3.9 -16.1 +13.6 -6.1
Relative (%) +0.0 +20.6 +30.8 +20.1 -40.5 +8.8 -36.1 +30.6 -13.6
Steps
(reduced) 		27
(0) 		43
(16) 		63
(9) 		76
(22) 		93
(12) 		100
(19) 		110
(2) 		115
(7) 		122
(14)
Approximation of prime harmonics in 28edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -16.2 -0.6 +16.9 +5.8 +16.6 -19.2 +2.5 +14.6
Relative (%) +0.0 -37.9 -1.4 +39.4 +13.6 +38.8 -44.9 +5.8 +34.0
Steps
(reduced) 		28
(0) 		44
(16) 		65
(9) 		79
(23) 		97
(13) 		104
(20) 		114
(2) 		119
(7) 		127
(15)
Approximation of prime harmonics in 29edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +1.5 -13.9 -17.1 -13.4 -12.9 +19.2 -7.9 -7.6
Relative (%) +0.0 +3.6 -33.6 -41.3 -32.4 -31.3 +46.4 -19.0 -18.3
Steps
(reduced) 		29
(0) 		46
(17) 		67
(9) 		81
(23) 		100
(13) 		107
(20) 		119
(3) 		123
(7) 		131
(15)
Approximation of prime harmonics in 30edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +18.0 +13.7 -8.8 +8.7 -0.5 +15.0 -17.5 +11.7
Relative (%) +0.0 +45.1 +34.2 -22.1 +21.7 -1.3 +37.6 -43.8 +29.3
Steps
(reduced) 		30
(0) 		48
(18) 		70
(10) 		84
(24) 		104
(14) 		111
(21) 		123
(3) 		127
(7) 		136
(16)
Approximation of prime harmonics in 31edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -5.2 +0.8 -1.1 -9.4 +11.1 +11.2 +12.2 -8.9
Relative (%) +0.0 -13.4 +2.0 -2.8 -24.2 +28.6 +28.9 +31.4 -23.0
Steps
(reduced) 		31
(0) 		49
(18) 		72
(10) 		87
(25) 		107
(14) 		115
(22) 		127
(3) 		132
(8) 		140
(16)
Approximation of prime harmonics in 32edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +10.5 -11.3 +6.2 +11.2 -15.5 +7.5 +2.5 +9.2
Relative (%) +0.0 +28.1 -30.2 +16.5 +29.8 -41.4 +20.1 +6.6 +24.6
Steps
(reduced) 		32
(0) 		51
(19) 		74
(10) 		90
(26) 		111
(15) 		118
(22) 		131
(3) 		136
(8) 		145
(17)
Approximation of prime harmonics in 33edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -11.0 +13.7 +13.0 -5.9 -4.2 +4.1 -6.6 -10.1
Relative (%) +0.0 -30.4 +37.6 +35.7 -16.1 -11.5 +11.4 -18.2 -27.8
Steps
(reduced) 		33
(0) 		52
(19) 		77
(11) 		93
(27) 		114
(15) 		122
(23) 		135
(3) 		140
(8) 		149
(17)
Approximation of prime harmonics in 34edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +3.9 +1.9 -15.9 +13.4 +6.5 +0.9 -15.2 +7.0
Relative (%) +0.0 +11.1 +5.4 -45.0 +37.9 +18.5 +2.6 -43.0 +19.9
Steps
(reduced) 		34
(0) 		54
(20) 		79
(11) 		95
(27) 		118
(16) 		126
(24) 		139
(3) 		144
(8) 		154
(18)
Approximation of prime harmonics in 35edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -16.2 -9.2 -8.8 -2.7 +16.6 -2.1 +11.1 -11.1
Relative (%) +0.0 -47.4 -26.7 -25.7 -8.0 +48.5 -6.1 +32.3 -32.5
Steps
(reduced) 		35
(0) 		55
(20) 		81
(11) 		98
(28) 		121
(16) 		130
(25) 		143
(3) 		149
(9) 		158
(18)
Approximation of prime harmonics in 36edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -2.0 +13.7 -2.2 +15.3 -7.2 -5.0 +2.5 +5.1
Relative (%) +0.0 -5.9 +41.1 -6.5 +46.0 -21.6 -14.9 +7.5 +15.2
Steps
(reduced) 		36
(0) 		57
(21) 		84
(12) 		101
(29) 		125
(17) 		133
(25) 		147
(3) 		153
(9) 		163
(19)
Approximation of prime harmonics in 37edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +11.6 +2.9 +4.1 +0.0 +2.7 -7.7 -5.6 -12.1
Relative (%) +0.0 +35.6 +8.9 +12.8 +0.1 +8.4 -23.6 -17.3 -37.2
Steps
(reduced) 		37
(0) 		59
(22) 		86
(12) 		104
(30) 		128
(17) 		137
(26) 		151
(3) 		157
(9) 		167
(19)
Approximation of prime harmonics in 38edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -7.2 -7.4 +10.1 -14.5 +12.1 -10.2 -13.3 +3.3
Relative (%) +0.0 -22.9 -23.3 +32.1 -45.8 +38.3 -32.4 -42.1 +10.5
Steps
(reduced) 		38
(0) 		60
(22) 		88
(12) 		107
(31) 		131
(17) 		141
(27) 		155
(3) 		161
(9) 		172
(20)
Approximation of prime harmonics in 39edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +5.7 +13.7 -15.0 +2.5 -9.8 -12.6 +10.2 -12.9
Relative (%) +0.0 +18.6 +44.5 -48.7 +8.2 -31.7 -41.1 +33.1 -41.9
Steps
(reduced) 		39
(0) 		62
(23) 		91
(13) 		109
(31) 		135
(18) 		144
(27) 		159
(3) 		166
(10) 		176
(20)
Approximation of prime harmonics in 40edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -12.0 +3.7 -8.8 -11.3 -0.5 -15.0 +2.5 +1.7
Relative (%) +0.0 -39.9 +12.3 -29.4 -37.7 -1.8 -49.9 +8.3 +5.8
Steps
(reduced) 		40
(0) 		63
(23) 		93
(13) 		112
(32) 		138
(18) 		148
(28) 		163
(3) 		170
(10) 		181
(21)
Approximation of prime harmonics in 41edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +0.5 -5.8 -3.0 +4.8 +8.3 +12.1 -4.8 -13.6
Relative (%) +0.0 +1.7 -19.9 -10.2 +16.3 +28.2 +41.4 -16.5 -46.6
Steps
(reduced) 		41
(0) 		65
(24) 		95
(13) 		115
(33) 		142
(19) 		152
(29) 		168
(4) 		174
(10) 		185
(21)
Approximation of prime harmonics in 42edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +12.3 +13.7 +2.6 -8.5 -12.0 +9.3 -11.8 +0.3
Relative (%) +0.0 +43.2 +47.9 +9.1 -29.6 -41.8 +32.7 -41.3 +1.0
Steps
(reduced) 		42
(0) 		67
(25) 		98
(14) 		118
(34) 		145
(19) 		155
(29) 		172
(4) 		178
(10) 		190
(22)
Approximation of prime harmonics in 43edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -4.3 +4.4 +7.9 +6.8 -3.3 +6.7 +9.5 +13.6
Relative (%) +0.0 -15.3 +15.7 +28.4 +24.4 -11.9 +23.9 +33.9 +48.7
Steps
(reduced) 		43
(0) 		68
(25) 		100
(14) 		121
(35) 		149
(20) 		159
(30) 		176
(4) 		183
(11) 		195
(23)
Approximation of prime harmonics in 44edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +7.1 -4.5 +13.0 -5.9 +4.9 +4.1 +2.5 -1.0
Relative (%) +0.0 +26.2 -16.5 +47.6 -21.5 +18.1 +15.2 +9.1 -3.7
Steps
(reduced) 		44
(0) 		70
(26) 		102
(14) 		124
(36) 		152
(20) 		163
(31) 		180
(4) 		187
(11) 		199
(23)
Approximation of prime harmonics in 45edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -8.6 -13.0 -8.8 +8.7 +12.8 +1.7 -4.2 +11.7
Relative (%) +0.0 -32.3 -48.7 -33.1 +32.6 +48.0 +6.4 -15.7 +44.0
Steps
(reduced) 		45
(0) 		71
(26) 		104
(14) 		126
(36) 		156
(21) 		167
(32) 		184
(4) 		191
(11) 		204
(24)
Approximation of prime harmonics in 46edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +2.4 +5.0 -3.6 -3.5 -5.7 -0.6 -10.6 -2.2
Relative (%) +0.0 +9.2 +19.1 -13.8 -13.4 -22.0 -2.3 -40.5 -8.4
Steps
(reduced) 		46
(0) 		73
(27) 		107
(15) 		129
(37) 		159
(21) 		170
(32) 		188
(4) 		195
(11) 		208
(24)
Approximation of prime harmonics in 47edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -12.6 -3.3 +1.4 +10.4 +2.0 -2.8 +8.9 +10.0
Relative (%) +0.0 -49.3 -13.1 +5.4 +40.7 +7.9 -11.1 +34.7 +39.3
Steps
(reduced) 		47
(0) 		74
(27) 		109
(15) 		132
(38) 		163
(22) 		174
(33) 		192
(4) 		200
(12) 		213
(25)
Approximation of prime harmonics in 48edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -2.0 -11.3 +6.2 -1.3 +9.5 -5.0 +2.5 -3.3
Relative (%) +0.0 -7.8 -45.3 +24.7 -5.3 +37.9 -19.8 +9.9 -13.1
Steps
(reduced) 		48
(0) 		76
(28) 		111
(15) 		135
(39) 		166
(22) 		178
(34) 		196
(4) 		204
(12) 		217
(25)
Approximation of prime harmonics in 49edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +8.2 +5.5 +10.8 +11.9 -7.9 -7.0 -3.6 +8.5
Relative (%) +0.0 +33.7 +22.6 +44.0 +48.8 -32.2 -28.6 -14.8 +34.5
Steps
(reduced) 		49
(0) 		78
(29) 		114
(16) 		138
(40) 		170
(23) 		181
(34) 		200
(4) 		208
(12) 		222
(26)
Approximation of prime harmonics in 50edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -6.0 -2.3 -8.8 +0.7 -0.5 -9.0 -9.5 -4.3
Relative (%) +0.0 -24.8 -9.6 -36.8 +2.8 -2.2 -37.3 -39.6 -17.8
Steps
(reduced) 		50
(0) 		79
(29) 		116
(16) 		140
(40) 		173
(23) 		185
(35) 		204
(4) 		212
(12) 		226
(26)
Approximation of prime harmonics in 51edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 +3.9 -9.8 -4.1 -10.1 +6.5 -10.8 +8.4 +7.0
Relative (%) +0.0 +16.7 -41.8 -17.5 -43.1 +27.8 -46.1 +35.6 +29.8
Steps
(reduced) 		51
(0) 		81
(30) 		118
(16) 		143
(41) 		176
(23) 		189
(36) 		208
(4) 		217
(13) 		231
(27)
Approximation of prime harmonics in 52edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.0 -9.6 +6.0 +0.4 +2.5 -9.8 +10.4 +2.5 -5.2
Relative (%) +0.0 -41.8 +26.0 +1.8 +11.0 -42.3 +45.2 +10.8 -22.5
Steps
(reduced) 		52
(0) 		82
(30) 		121
(17) 		146
(42) 		180
(24) 		192
(36) 		213
(5) 		221
(13) 		235
(27)
Approximation of prime harmonics in 53edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.00 -0.07 -1.41 +4.76 -7.92 -2.79 +8.25 -3.17 +5.69
Relative (%) +0.0 -0.3 -6.2 +21.0 -35.0 -12.3 +36.4 -14.0 +25.1
Steps
(reduced) 		53
(0) 		84
(31) 		123
(17) 		149
(43) 		183
(24) 		196
(37) 		217
(5) 		225
(13) 		240
(28)
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