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

Revision as of 02:57, 7 April 2026

Approximations of odd harmonics

Approximation of odd harmonics in 9edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -35.3 +13.7 -35.5 +62.8 -18.0 -40.5 -21.6 +28.4 -30.8 +62.6 +38.4 +27.4 +27.5 +37.1 +55.0
Relative (%) -26.5 +10.3 -26.6 +47.1 -13.5 -30.4 -16.2 +21.3 -23.1 +46.9 +28.8 +20.5 +20.6 +27.8 +41.2
Steps
(reduced) 		14
(5) 		21
(3) 		25
(7) 		29
(2) 		31
(4) 		33
(6) 		35
(8) 		37
(1) 		38
(2) 		40
(4) 		41
(5) 		42
(6) 		43
(7) 		44
(8) 		45
(0)
Approximation of odd harmonics in 10edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +18.0 -26.3 -8.8 +36.1 +48.7 -0.5 -8.3 +15.0 -57.5 +9.2 -28.3 -52.6 +54.1 +50.4 +55.0
Relative (%) +15.0 -21.9 -7.4 +30.1 +40.6 -0.4 -6.9 +12.5 -47.9 +7.7 -23.6 -43.9 +45.1 +42.0 +45.8
Steps
(reduced) 		16
(6) 		23
(3) 		28
(8) 		32
(2) 		35
(5) 		37
(7) 		39
(9) 		41
(1) 		42
(2) 		44
(4) 		45
(5) 		46
(6) 		48
(8) 		49
(9) 		50
(0)
Approximation of odd harmonics in 11edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -47.4 +50.0 +13.0 +14.3 -5.9 +32.2 +2.6 +4.1 +29.8 -34.4 +26.3 -9.0 -33.1 -47.8 -54.1
Relative (%) -43.5 +45.9 +11.9 +13.1 -5.4 +29.5 +2.4 +3.8 +27.3 -31.5 +24.1 -8.2 -30.4 -43.8 -49.6
Steps
(reduced) 		17
(6) 		26
(4) 		31
(9) 		35
(2) 		38
(5) 		41
(8) 		43
(10) 		45
(1) 		47
(3) 		48
(4) 		50
(6) 		51
(7) 		52
(8) 		53
(9) 		54
(10)
Approximation of odd harmonics in 12edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -2.0 +13.7 +31.2 -3.9 +48.7 -40.5 +11.7 -5.0 +2.5 +29.2 -28.3 +27.4 -5.9 -29.6 -45.0
Relative (%) -2.0 +13.7 +31.2 -3.9 +48.7 -40.5 +11.7 -5.0 +2.5 +29.2 -28.3 +27.4 -5.9 -29.6 -45.0
Steps
(reduced) 		19
(7) 		28
(4) 		34
(10) 		38
(2) 		42
(6) 		44
(8) 		47
(11) 		49
(1) 		51
(3) 		53
(5) 		54
(6) 		56
(8) 		57
(9) 		58
(10) 		59
(11)
Approximation of odd harmonics in 13edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +36.5 -17.1 -45.7 -19.3 +2.5 -9.8 +19.4 -12.6 -20.6 -9.2 +17.9 -34.2 +17.2 -14.2 -37.3
Relative (%) +39.5 -18.5 -49.6 -20.9 +2.7 -10.6 +21.0 -13.7 -22.3 -10.0 +19.4 -37.0 +18.6 -15.4 -40.5
Steps
(reduced) 		21
(8) 		30
(4) 		36
(10) 		41
(2) 		45
(6) 		48
(9) 		51
(12) 		53
(1) 		55
(3) 		57
(5) 		59
(7) 		60
(8) 		62
(10) 		63
(11) 		64
(12)
Approximation of odd harmonics in 14edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -16.2 +42.3 -26.0 -32.5 -37.0 +16.6 +26.0 -19.2 -40.4 -42.2 -28.3 -1.2 +37.0 -1.0 -30.7
Relative (%) -18.9 +49.3 -30.3 -37.9 -43.2 +19.4 +30.4 -22.4 -47.1 -49.2 -33.0 -1.4 +43.2 -1.2 -35.9
Steps
(reduced) 		22
(8) 		33
(5) 		39
(11) 		44
(2) 		48
(6) 		52
(10) 		55
(13) 		57
(1) 		59
(3) 		61
(5) 		63
(7) 		65
(9) 		67
(11) 		68
(12) 		69
(13)
Approximation of odd harmonics in 15edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +18.0 +13.7 -8.8 +36.1 +8.7 +39.5 +31.7 -25.0 +22.5 +9.2 +11.7 +27.4 -25.9 +10.4 -25.0
Relative (%) +22.6 +17.1 -11.0 +45.1 +10.9 +49.3 +39.7 -31.2 +28.1 +11.5 +14.7 +34.2 -32.3 +13.0 -31.3
Steps
(reduced) 		24
(9) 		35
(5) 		42
(12) 		48
(3) 		52
(7) 		56
(11) 		59
(14) 		61
(1) 		64
(4) 		66
(6) 		68
(8) 		70
(10) 		71
(11) 		73
(13) 		74
(14)
Approximation of odd harmonics in 16edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -27.0 -11.3 +6.2 +21.1 -26.3 -15.5 +36.7 -30.0 +2.5 -20.8 -28.3 -22.6 -5.9 +20.4 -20.0
Relative (%) -35.9 -15.1 +8.2 +28.1 -35.1 -20.7 +49.0 -39.9 +3.3 -27.7 -37.7 -30.2 -7.8 +27.2 -26.7
Steps
(reduced) 		25
(9) 		37
(5) 		45
(13) 		51
(3) 		55
(7) 		59
(11) 		63
(15) 		65
(1) 		68
(4) 		70
(6) 		72
(8) 		74
(10) 		76
(12) 		78
(14) 		79
(15)
Approximation of odd harmonics in 17edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +3.9 -33.4 +19.4 +7.9 +13.4 +6.5 -29.4 -34.4 -15.2 +23.3 +7.0 +3.8 +11.8 +29.2 -15.6
Relative (%) +5.6 -47.3 +27.5 +11.1 +19.0 +9.3 -41.7 -48.7 -21.5 +33.1 +9.9 +5.4 +16.7 +41.4 -22.1
Steps
(reduced) 		27
(10) 		39
(5) 		48
(14) 		54
(3) 		59
(8) 		63
(12) 		66
(15) 		69
(1) 		72
(4) 		75
(7) 		77
(9) 		79
(11) 		81
(13) 		83
(15) 		84
(16)
Approximation of odd harmonics in 18edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +31.4 +13.7 +31.2 -3.9 -18.0 +26.1 -21.6 +28.4 -30.8 -4.1 -28.3 +27.4 +27.5 -29.6 -11.7
Relative (%) +47.1 +20.5 +46.8 -5.9 -27.0 +39.2 -32.4 +42.6 -46.3 -6.2 -42.4 +41.1 +41.2 -44.4 -17.6
Steps
(reduced) 		29
(11) 		42
(6) 		51
(15) 		57
(3) 		62
(8) 		67
(13) 		70
(16) 		74
(2) 		76
(4) 		79
(7) 		81
(9) 		84
(12) 		86
(14) 		87
(15) 		89
(17)
Approximation of odd harmonics in 19edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -7.2 -7.4 -21.5 -14.4 +17.1 -19.5 -14.6 +21.4 +18.3 -28.7 +3.3 -14.7 -21.7 -19.1 -8.2
Relative (%) -11.4 -11.7 -34.0 -22.9 +27.1 -30.8 -23.1 +33.8 +28.9 -45.4 +5.2 -23.3 -34.3 -30.2 -13.0
Steps
(reduced) 		30
(11) 		44
(6) 		53
(15) 		60
(3) 		66
(9) 		70
(13) 		74
(17) 		78
(2) 		81
(5) 		83
(7) 		86
(10) 		88
(12) 		90
(14) 		92
(16) 		94
(18)
Approximation of odd harmonics in 20edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +18.0 -26.3 -8.8 -23.9 -11.3 -0.5 -8.3 +15.0 +2.5 +9.2 -28.3 +7.4 -5.9 -9.6 -5.0
Relative (%) +30.1 -43.9 -14.7 -39.9 -18.9 -0.9 -13.8 +25.1 +4.1 +15.4 -47.1 +12.3 -9.8 -16.0 -8.4
Steps
(reduced) 		32
(12) 		46
(6) 		56
(16) 		63
(3) 		69
(9) 		74
(14) 		78
(18) 		82
(2) 		85
(5) 		88
(8) 		90
(10) 		93
(13) 		95
(15) 		97
(17) 		99
(19)
Approximation of odd harmonics in 21edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -16.2 +13.7 +2.6 +24.7 +20.1 +16.6 -2.6 +9.3 -11.8 -13.6 +0.3 +27.4 +8.4 -1.0 -2.2
Relative (%) -28.4 +24.0 +4.6 +43.2 +35.2 +29.1 -4.5 +16.3 -20.6 -23.9 +0.5 +47.9 +14.7 -1.8 -3.8
Steps
(reduced) 		33
(12) 		49
(7) 		59
(17) 		67
(4) 		73
(10) 		78
(15) 		82
(19) 		86
(2) 		89
(5) 		92
(8) 		95
(11) 		98
(14) 		100
(16) 		102
(18) 		104
(20)
Approximation of odd harmonics in 22edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +7.1 -4.5 +13.0 +14.3 -5.9 -22.3 +2.6 +4.1 -24.8 +20.1 +26.3 -9.0 +21.4 +6.8 +0.4
Relative (%) +13.1 -8.2 +23.8 +26.2 -10.7 -41.0 +4.8 +7.6 -45.4 +36.9 +48.2 -16.5 +39.2 +12.4 +0.8
Steps
(reduced) 		35
(13) 		51
(7) 		62
(18) 		70
(4) 		76
(10) 		81
(15) 		86
(20) 		90
(2) 		93
(5) 		97
(9) 		100
(12) 		102
(14) 		105
(17) 		107
(19) 		109
(21)
Approximation of odd harmonics in 23edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -23.7 -21.1 +22.5 +4.8 +22.6 -5.7 +7.4 -0.6 +15.5 -1.2 -2.2 +10.0 -18.9 +13.9 +2.8
Relative (%) -45.4 -40.4 +43.1 +9.2 +43.3 -11.0 +14.2 -1.2 +29.8 -2.3 -4.2 +19.1 -36.2 +26.6 +5.3
Steps
(reduced) 		36
(13) 		53
(7) 		65
(19) 		73
(4) 		80
(11) 		85
(16) 		90
(21) 		94
(2) 		98
(6) 		101
(9) 		104
(12) 		107
(15) 		109
(17) 		112
(20) 		114
(22)
Approximation of odd harmonics in 24edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -2.0 +13.7 -18.8 -3.9 -1.3 +9.5 +11.7 -5.0 +2.5 -20.8 +21.7 -22.6 -5.9 +20.4 +5.0
Relative (%) -3.9 +27.4 -37.7 -7.8 -2.6 +18.9 +23.5 -9.9 +5.0 -41.6 +43.5 -45.3 -11.7 +40.8 +9.9
Steps
(reduced) 		38
(14) 		56
(8) 		67
(19) 		76
(4) 		83
(11) 		89
(17) 		94
(22) 		98
(2) 		102
(6) 		105
(9) 		109
(13) 		111
(15) 		114
(18) 		117
(21) 		119
(23)
Approximation of odd harmonics in 25edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +18.0 -2.3 -8.8 -11.9 -23.3 +23.5 +15.7 -9.0 -9.5 +9.2 -4.3 -4.6 +6.1 -21.6 +7.0
Relative (%) +37.6 -4.8 -18.4 -24.8 -48.6 +48.9 +32.8 -18.7 -19.8 +19.2 -8.9 -9.6 +12.8 -45.0 +14.5
Steps
(reduced) 		40
(15) 		58
(8) 		70
(20) 		79
(4) 		86
(11) 		93
(18) 		98
(23) 		102
(2) 		106
(6) 		110
(10) 		113
(13) 		116
(16) 		119
(19) 		121
(21) 		124
(24)
Approximation of odd harmonics in 26edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -9.6 -17.1 +0.4 -19.3 +2.5 -9.8 +19.4 -12.6 -20.6 -9.2 +17.9 +12.0 +17.2 -14.2 +8.8
Relative (%) -20.9 -37.0 +0.9 -41.8 +5.5 -21.1 +42.1 -27.4 -44.6 -20.0 +38.7 +26.0 +37.3 -30.8 +19.1
Steps
(reduced) 		41
(15) 		60
(8) 		73
(21) 		82
(4) 		90
(12) 		96
(18) 		102
(24) 		106
(2) 		110
(6) 		114
(10) 		118
(14) 		121
(17) 		124
(20) 		126
(22) 		129
(25)
Approximation of odd harmonics in 27edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +9.2 +13.7 +9.0 +18.3 -18.0 +3.9 -21.6 -16.1 +13.6 +18.1 -6.1 -17.1 -17.0 -7.4 +10.5
Relative (%) +20.6 +30.8 +20.1 +41.2 -40.5 +8.8 -48.6 -36.1 +30.6 +40.7 -13.6 -38.4 -38.2 -16.5 +23.7
Steps
(reduced) 		43
(16) 		63
(9) 		76
(22) 		86
(5) 		93
(12) 		100
(19) 		105
(24) 		110
(2) 		115
(7) 		119
(11) 		122
(14) 		125
(17) 		128
(20) 		131
(23) 		134
(26)
Approximation of odd harmonics in 28edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -16.2 -0.6 +16.9 +10.4 +5.8 +16.6 -16.8 -19.2 +2.5 +0.6 +14.6 -1.2 -5.9 -1.0 +12.1
Relative (%) -37.9 -1.4 +39.4 +24.2 +13.6 +38.8 -39.3 -44.9 +5.8 +1.5 +34.0 -2.8 -13.7 -2.3 +28.3
Steps
(reduced) 		44
(16) 		65
(9) 		79
(23) 		89
(5) 		97
(13) 		104
(20) 		109
(25) 		114
(2) 		119
(7) 		123
(11) 		127
(15) 		130
(18) 		133
(21) 		136
(24) 		139
(27)
Approximation of odd harmonics in 29edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +1.5 -13.9 -17.1 +3.0 -13.4 -12.9 -12.4 +19.2 -7.9 -15.6 -7.6 +13.6 +4.5 +4.9 +13.6
Relative (%) +3.6 -33.6 -41.3 +7.2 -32.4 -31.3 -30.0 +46.4 -19.0 -37.7 -18.3 +32.8 +10.8 +11.9 +32.8
Steps
(reduced) 		46
(17) 		67
(9) 		81
(23) 		92
(5) 		100
(13) 		107
(20) 		113
(26) 		119
(3) 		123
(7) 		127
(11) 		131
(15) 		135
(19) 		138
(22) 		141
(25) 		144
(28)
Approximation of odd harmonics in 30edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +18.0 +13.7 -8.8 -3.9 +8.7 -0.5 -8.3 +15.0 -17.5 +9.2 +11.7 -12.6 +14.1 +10.4 +15.0
Relative (%) +45.1 +34.2 -22.1 -9.8 +21.7 -1.3 -20.7 +37.6 -43.8 +23.0 +29.3 -31.6 +35.3 +26.1 +37.4
Steps
(reduced) 		48
(18) 		70
(10) 		84
(24) 		95
(5) 		104
(14) 		111
(21) 		117
(27) 		123
(3) 		127
(7) 		132
(12) 		136
(16) 		139
(19) 		143
(23) 		146
(26) 		149
(29)
Approximation of odd harmonics in 31edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -5.2 +0.8 -1.1 -10.4 -9.4 +11.1 -4.4 +11.2 +12.2 -6.3 -8.9 +1.6 -15.5 +15.6 +16.3
Relative (%) -13.4 +2.0 -2.8 -26.8 -24.2 +28.6 -11.4 +28.9 +31.4 -16.2 -23.0 +4.0 -40.2 +40.3 +42.0
Steps
(reduced) 		49
(18) 		72
(10) 		87
(25) 		98
(5) 		107
(14) 		115
(22) 		121
(28) 		127
(3) 		132
(8) 		136
(12) 		140
(16) 		144
(20) 		147
(23) 		151
(27) 		154
(30)
Approximation of odd harmonics in 32edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +10.5 -11.3 +6.2 -16.4 +11.2 -15.5 -0.8 +7.5 +2.5 +16.7 +9.2 +14.9 -5.9 -17.1 +17.5
Relative (%) +28.1 -30.2 +16.5 -43.8 +29.8 -41.4 -2.0 +20.1 +6.6 +44.6 +24.6 +39.7 -15.6 -45.5 +46.6
Steps
(reduced) 		51
(19) 		74
(10) 		90
(26) 		101
(5) 		111
(15) 		118
(22) 		125
(29) 		131
(3) 		136
(8) 		141
(13) 		145
(17) 		149
(21) 		152
(24) 		155
(27) 		159
(31)
Approximation of odd harmonics in 33edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -11.0 +13.7 +13.0 +14.3 -5.9 -4.2 +2.6 +4.1 -6.6 +1.9 -10.1 -9.0 +3.2 -11.4 -17.8
Relative (%) -30.4 +37.6 +35.7 +39.2 -16.1 -11.5 +7.3 +11.4 -18.2 +5.4 -27.8 -24.7 +8.9 -31.3 -48.8
Steps
(reduced) 		52
(19) 		77
(11) 		93
(27) 		105
(6) 		114
(15) 		122
(23) 		129
(30) 		135
(3) 		140
(8) 		145
(13) 		149
(17) 		153
(21) 		157
(25) 		160
(28) 		163
(31)
Approximation of odd harmonics in 34edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +3.9 +1.9 -15.9 +7.9 +13.4 +6.5 +5.8 +0.9 -15.2 -12.0 +7.0 +3.8 +11.8 -6.0 -15.6
Relative (%) +11.1 +5.4 -45.0 +22.3 +37.9 +18.5 +16.6 +2.6 -43.0 -33.9 +19.9 +10.9 +33.4 -17.1 -44.3
Steps
(reduced) 		54
(20) 		79
(11) 		95
(27) 		108
(6) 		118
(16) 		126
(24) 		133
(31) 		139
(3) 		144
(8) 		149
(13) 		154
(18) 		158
(22) 		162
(26) 		165
(29) 		168
(32)
Approximation of odd harmonics in 35edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -16.2 -9.2 -8.8 +1.8 -2.7 +16.6 +8.9 -2.1 +11.1 +9.2 -11.1 +15.9 -14.4 -1.0 -13.6
Relative (%) -47.4 -26.7 -25.7 +5.3 -8.0 +48.5 +25.9 -6.1 +32.3 +26.9 -32.5 +46.5 -42.1 -2.9 -39.7
Steps
(reduced) 		55
(20) 		81
(11) 		98
(28) 		111
(6) 		121
(16) 		130
(25) 		137
(32) 		143
(3) 		149
(9) 		154
(14) 		158
(18) 		163
(23) 		166
(26) 		170
(30) 		173
(33)
Approximation of odd harmonics in 36edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -2.0 +13.7 -2.2 -3.9 +15.3 -7.2 +11.7 -5.0 +2.5 -4.1 +5.1 -6.0 -5.9 +3.8 -11.7
Relative (%) -5.9 +41.1 -6.5 -11.7 +46.0 -21.6 +35.2 -14.9 +7.5 -12.3 +15.2 -17.9 -17.6 +11.3 -35.1
Steps
(reduced) 		57
(21) 		84
(12) 		101
(29) 		114
(6) 		125
(17) 		133
(25) 		141
(33) 		147
(3) 		153
(9) 		158
(14) 		163
(19) 		167
(23) 		171
(27) 		175
(31) 		178
(34)
Approximation of odd harmonics in 37edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +11.6 +2.9 +4.1 -9.3 +0.0 +2.7 +14.4 -7.7 -5.6 +15.7 -12.1 +5.8 +2.2 +8.3 -9.9
Relative (%) +35.6 +8.9 +12.8 -28.7 +0.1 +8.4 +44.5 -23.6 -17.3 +48.4 -37.2 +17.7 +6.9 +25.5 -30.5
Steps
(reduced) 		59
(22) 		86
(12) 		104
(30) 		117
(6) 		128
(17) 		137
(26) 		145
(34) 		151
(3) 		157
(9) 		163
(15) 		167
(19) 		172
(24) 		176
(28) 		180
(32) 		183
(35)
Approximation of odd harmonics in 38edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -7.2 -7.4 +10.1 -14.4 -14.5 +12.1 -14.6 -10.2 -13.3 +2.9 +3.3 -14.7 +9.9 +12.5 -8.2
Relative (%) -22.9 -23.3 +32.1 -45.7 -45.8 +38.3 -46.2 -32.4 -42.1 +9.2 +10.5 -46.7 +31.4 +39.7 -25.9
Steps
(reduced) 		60
(22) 		88
(12) 		107
(31) 		120
(6) 		131
(17) 		141
(27) 		148
(34) 		155
(3) 		161
(9) 		167
(15) 		172
(20) 		176
(24) 		181
(29) 		185
(33) 		188
(36)
Approximation of odd harmonics in 39edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +5.7 +13.7 -15.0 +11.5 +2.5 -9.8 -11.3 -12.6 +10.2 -9.2 -12.9 -3.4 -13.6 -14.2 -6.6
Relative (%) +18.6 +44.5 -48.7 +37.3 +8.2 -31.7 -36.9 -41.1 +33.1 -30.0 -41.9 -11.0 -44.1 -46.1 -21.4
Steps
(reduced) 		62
(23) 		91
(13) 		109
(31) 		124
(7) 		135
(18) 		144
(27) 		152
(35) 		159
(3) 		166
(10) 		171
(15) 		176
(20) 		181
(25) 		185
(29) 		189
(33) 		193
(37)
Approximation of odd harmonics in 40edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -12.0 +3.7 -8.8 +6.1 -11.3 -0.5 -8.3 -15.0 +2.5 +9.2 +1.7 +7.4 -5.9 -9.6 -5.0
Relative (%) -39.9 +12.3 -29.4 +20.3 -37.7 -1.8 -27.6 -49.9 +8.3 +30.7 +5.8 +24.6 -19.6 -31.9 -16.8
Steps
(reduced) 		63
(23) 		93
(13) 		112
(32) 		127
(7) 		138
(18) 		148
(28) 		156
(36) 		163
(3) 		170
(10) 		176
(16) 		181
(21) 		186
(26) 		190
(30) 		194
(34) 		198
(38)
Approximation of odd harmonics in 41edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +0.5 -5.8 -3.0 +1.0 +4.8 +8.3 -5.3 +12.1 -4.8 -2.5 -13.6 -11.7 +1.5 -5.2 -3.6
Relative (%) +1.7 -19.9 -10.2 +3.3 +16.3 +28.2 -18.3 +41.4 -16.5 -8.5 -46.6 -39.8 +5.0 -17.7 -12.2
Steps
(reduced) 		65
(24) 		95
(13) 		115
(33) 		130
(7) 		142
(19) 		152
(29) 		160
(37) 		168
(4) 		174
(10) 		180
(16) 		185
(21) 		190
(26) 		195
(31) 		199
(35) 		203
(39)
Approximation of odd harmonics in 42edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +12.3 +13.7 +2.6 -3.9 -8.5 -12.0 -2.6 +9.3 -11.8 -13.6 +0.3 -1.2 +8.4 -1.0 -2.2
Relative (%) +43.2 +47.9 +9.1 -13.7 -29.6 -41.8 -8.9 +32.7 -41.3 -47.7 +1.0 -4.2 +29.5 -3.5 -7.6
Steps
(reduced) 		67
(25) 		98
(14) 		118
(34) 		133
(7) 		145
(19) 		155
(29) 		164
(38) 		172
(4) 		178
(10) 		184
(16) 		190
(22) 		195
(27) 		200
(32) 		204
(36) 		208
(40)
Approximation of odd harmonics in 43edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -4.3 +4.4 +7.9 -8.6 +6.8 -3.3 +0.1 +6.7 +9.5 +3.6 +13.6 +8.8 -12.8 +3.0 -0.8
Relative (%) -15.3 +15.7 +28.4 -30.7 +24.4 -11.9 +0.4 +23.9 +33.9 +13.0 +48.7 +31.4 -46.0 +10.7 -3.0
Steps
(reduced) 		68
(25) 		100
(14) 		121
(35) 		136
(7) 		149
(20) 		159
(30) 		168
(39) 		176
(4) 		183
(11) 		189
(17) 		195
(23) 		200
(28) 		204
(32) 		209
(37) 		213
(41)
Approximation of odd harmonics in 44edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +7.1 -4.5 +13.0 -13.0 -5.9 +4.9 +2.6 +4.1 +2.5 -7.1 -1.0 -9.0 -5.9 +6.8 +0.4
Relative (%) +26.2 -16.5 +47.6 -47.7 -21.5 +18.1 +9.7 +15.2 +9.1 -26.2 -3.7 -33.0 -21.5 +24.9 +1.5
Steps
(reduced) 		70
(26) 		102
(14) 		124
(36) 		139
(7) 		152
(20) 		163
(31) 		172
(40) 		180
(4) 		187
(11) 		193
(17) 		199
(23) 		204
(28) 		209
(33) 		214
(38) 		218
(42)
Approximation of odd harmonics in 45edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -8.6 -13.0 -8.8 +9.4 +8.7 +12.8 +5.1 +1.7 -4.2 +9.2 +11.7 +0.7 +0.8 +10.4 +1.6
Relative (%) -32.3 -48.7 -33.1 +35.3 +32.6 +48.0 +19.0 +6.4 -15.7 +34.6 +44.0 +2.6 +3.0 +39.1 +6.1
Steps
(reduced) 		71
(26) 		104
(14) 		126
(36) 		143
(8) 		156
(21) 		167
(32) 		176
(41) 		184
(4) 		191
(11) 		198
(18) 		204
(24) 		209
(29) 		214
(34) 		219
(39) 		223
(43)
Approximation of odd harmonics in 46edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +2.4 +5.0 -3.6 +4.8 -3.5 -5.7 +7.4 -0.6 -10.6 -1.2 -2.2 +10.0 +7.2 -12.2 +2.8
Relative (%) +9.2 +19.1 -13.8 +18.3 -13.4 -22.0 +28.3 -2.3 -40.5 -4.7 -8.4 +38.3 +27.5 -46.7 +10.7
Steps
(reduced) 		73
(27) 		107
(15) 		129
(37) 		146
(8) 		159
(21) 		170
(32) 		180
(42) 		188
(4) 		195
(11) 		202
(18) 		208
(24) 		214
(30) 		219
(35) 		223
(39) 		228
(44)
Approximation of odd harmonics in 47edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -12.6 -3.3 +1.4 +0.3 +10.4 +2.0 +9.6 -2.8 +8.9 -11.2 +10.0 -6.7 -12.2 -8.3 +3.9
Relative (%) -49.3 -13.1 +5.4 +1.4 +40.7 +7.9 +37.6 -11.1 +34.7 -43.9 +39.3 -26.1 -48.0 -32.5 +15.3
Steps
(reduced) 		74
(27) 		109
(15) 		132
(38) 		149
(8) 		163
(22) 		174
(33) 		184
(43) 		192
(4) 		200
(12) 		206
(18) 		213
(25) 		218
(30) 		223
(35) 		228
(40) 		233
(45)
Approximation of odd harmonics in 48edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -2.0 -11.3 +6.2 -3.9 -1.3 +9.5 +11.7 -5.0 +2.5 +4.2 -3.3 +2.4 -5.9 -4.6 +5.0
Relative (%) -7.8 -45.3 +24.7 -15.6 -5.3 +37.9 +46.9 -19.8 +9.9 +16.9 -13.1 +9.5 -23.5 -18.3 +19.9
Steps
(reduced) 		76
(28) 		111
(15) 		135
(39) 		152
(8) 		166
(22) 		178
(34) 		188
(44) 		196
(4) 		204
(12) 		211
(19) 		217
(25) 		223
(31) 		228
(36) 		233
(41) 		238
(46)
Approximation of odd harmonics in 49edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +8.2 +5.5 +10.8 -8.0 +11.9 -7.9 -10.7 -7.0 -3.6 -5.5 +8.5 +11.0 +0.3 -1.0 +6.0
Relative (%) +33.7 +22.6 +44.0 -32.6 +48.8 -32.2 -43.8 -28.6 -14.8 -22.4 +34.5 +45.1 +1.1 -4.1 +24.4
Steps
(reduced) 		78
(29) 		114
(16) 		138
(40) 		155
(8) 		170
(23) 		181
(34) 		191
(44) 		200
(4) 		208
(12) 		215
(19) 		222
(26) 		228
(32) 		233
(37) 		238
(42) 		243
(47)
Approximation of odd harmonics in 50edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -6.0 -2.3 -8.8 -11.9 +0.7 -0.5 -8.3 -9.0 -9.5 +9.2 -4.3 -4.6 +6.1 +2.4 +7.0
Relative (%) -24.8 -9.6 -36.8 -49.6 +2.8 -2.2 -34.5 -37.3 -39.6 +38.4 -17.8 -19.3 +25.6 +10.1 +29.0
Steps
(reduced) 		79
(29) 		116
(16) 		140
(40) 		158
(8) 		173
(23) 		185
(35) 		195
(45) 		204
(4) 		212
(12) 		220
(20) 		226
(26) 		232
(32) 		238
(38) 		243
(43) 		248
(48)
Approximation of odd harmonics in 51edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +3.9 -9.8 -4.1 +7.9 -10.1 +6.5 -5.9 -10.8 +8.4 -0.2 +7.0 +3.8 -11.7 +5.7 +7.9
Relative (%) +16.7 -41.8 -17.5 +33.4 -43.1 +27.8 -25.1 -46.1 +35.6 -0.8 +29.8 +16.3 -49.9 +24.3 +33.6
Steps
(reduced) 		81
(30) 		118
(16) 		143
(41) 		162
(9) 		176
(23) 		189
(36) 		199
(46) 		208
(4) 		217
(13) 		224
(20) 		231
(27) 		237
(33) 		242
(38) 		248
(44) 		253
(49)
Approximation of odd harmonics in 52edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -9.6 +6.0 +0.4 +3.8 +2.5 -9.8 -3.7 +10.4 +2.5 -9.2 -5.2 -11.1 -5.9 +8.9 +8.8
Relative (%) -41.8 +26.0 +1.8 +16.4 +11.0 -42.3 -15.8 +45.2 +10.8 -40.1 -22.5 -48.1 -25.4 +38.5 +38.2
Steps
(reduced) 		82
(30) 		121
(17) 		146
(42) 		165
(9) 		180
(24) 		192
(36) 		203
(47) 		213
(5) 		221
(13) 		228
(20) 		235
(27) 		241
(33) 		247
(39) 		253
(45) 		258
(50)
Approximation of odd harmonics in 53edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) -0.07 -1.41 +4.76 -0.14 -7.92 -2.79 -1.48 +8.25 -3.17 +4.69 +5.69 -2.82 -0.20 -10.71 +9.68
Relative (%) -0.3 -6.2 +21.0 -0.6 -35.0 -12.3 -6.5 +36.4 -14.0 +20.7 +25.1 -12.4 -0.9 -47.3 +42.8
Steps
(reduced) 		84
(31) 		123
(17) 		149
(43) 		168
(9) 		183
(24) 		196
(37) 		207
(48) 		217
(5) 		225
(13) 		233
(21) 		240
(28) 		246
(34) 		252
(40) 		257
(45) 		263
(51)
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