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= Title1 =
== Approximations of odd harmonics ==
{{Harmonics in equal|40|10|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
{{harmonics in equal|1|intervals=odd|columns=7}}
{{Harmonics in equal|7|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}  
{{harmonics in equal|2|intervals=odd|columns=7}}
{{Harmonics in equal|19|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}  
{{harmonics in equal|3|intervals=odd|columns=7}}
{{Harmonics in equal|31|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
{{harmonics in equal|4|intervals=odd|columns=7}}
 
{{harmonics in equal|5|intervals=odd|columns=7}}
= Title2 =
{{harmonics in equal|6|intervals=odd|columns=7}}
== Octave compression ==
{{harmonics in equal|7|intervals=odd|columns=7}}
What follows is a comparison of compressed-octave 17edo tunings.
{{harmonics in equal|8|intervals=odd|columns=7}}
 
{{harmonics in equal|9|intervals=odd|columns=7}}
; 17edo
{{harmonics in equal|10|intervals=odd|columns=7}}
* Step size: 70.588{{c}}, octave size: 1200.0{{c}}  
{{harmonics in equal|11|intervals=odd|columns=7}}
Pure-octaves 17edo approximates the 2.3.11 subgroup well, it arguably might approximate 7, but not well, and it doesn't really approximate 5. It might make tuning for exploring new harmonies with the 7th, 11th and 13th harmonics not found in 12edo, but its very sharp 7th harmonic might arguably hamper that use case.
{{harmonics in equal|12|intervals=odd|columns=7}}
{{Harmonics in equal|17|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 17edo}}
{{harmonics in equal|13|intervals=odd|columns=7}}
{{Harmonics in equal|17|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 17edo (continued)}}
{{harmonics in equal|14|intervals=odd|columns=7}}
 
{{harmonics in equal|15|intervals=odd|columns=7}}
; [[44ed6]]
{{harmonics in equal|16|intervals=odd|columns=7}}
* Step size: NNN{{c}}, octave size: 1198.5{{c}}
{{harmonics in equal|17|intervals=odd|columns=7}}
Compressing the octave of 17edo by around 1.5{{c}} results in greatly improved primes 3, 7, 11 and 13, but a slightly worse prime 2. The tuning 44ed6 does this. Its primary purpose is to greatly improve 17edo's approximation of harmonic 7, to make it into an exceptional no-5s [[13-limit]] tuning for its size.
{{harmonics in equal|18|intervals=odd|columns=7}}
{{Harmonics in equal|44|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 44ed6}}
{{harmonics in equal|19|intervals=odd|columns=7}}
{{Harmonics in equal|44|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 44ed6 (continued)}}
{{harmonics in equal|20|intervals=odd|columns=7}}
 
{{harmonics in equal|21|intervals=odd|columns=7}}
; [[27edt]]
{{harmonics in equal|22|intervals=odd|columns=7}}
* Step size: NNN{{c}}, octave size: 1197.5{{c}}
{{harmonics in equal|23|intervals=odd|columns=7}}
Compressing the octave of 17edo by around 2.5{{c}} results in improved primes NNN, but worse primes NNN. The tuning 27edt does this. Its primary purpose is to greatly improve 17edo's approximation of harmonic 7, to make it into an exceptional no-5s [[13-limit]] tuning for its size.
{{harmonics in equal|24|intervals=odd|columns=7}}
{{Harmonics in equal|27|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 27edt}}
{{harmonics in equal|25|intervals=odd|columns=7}}
{{Harmonics in equal|27|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 27edt (continued)}}
{{harmonics in equal|26|intervals=odd|columns=7}}
 
{{harmonics in equal|27|intervals=odd|columns=7}}
; [[zpi|56zpi]] / [[WE|17et, 2.3.7.11.13 WE tuning]]
{{harmonics in equal|28|intervals=odd|columns=7}}
* Step size: 70.403{{c}}, octave size: 1296.9{{c}}
{{harmonics in equal|29|intervals=odd|columns=7}}
Compressing the octave of 17edo by around 3{{c}} results in improved primes NNN, but worse primes NNN. The tunings: 56zpi, [[TE|17et, 2.3.7.11.13 TE]] and [[WE|17et, 2.3.7.11.13 WE]] all do this. Their primary purpose is to greatly improve 17edo's approximation of harmonic 7, to make it into an exceptional no-5s [[13-limit]] tuning for its size.
{{harmonics in equal|30|intervals=odd|columns=7}}
{{Harmonics in cet|70.403|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 56zpi}}
{{harmonics in equal|31|intervals=odd|columns=7}}
{{Harmonics in cet|70.403|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 56zpi (continued)}}
{{harmonics in equal|32|intervals=odd|columns=7}}
 
{{harmonics in equal|33|intervals=odd|columns=7}}
; [[WE|17et, 2.3.7.11 WE tuning]]
{{harmonics in equal|34|intervals=odd|columns=7}}
* Step size: 70.392{{c}}, octave size: 1296.7{{c}}
{{harmonics in equal|35|intervals=odd|columns=7}}
Compressing the octave of 17edo by just over 3{{c}} results in improved primes NNN, but worse primes NNN. Its 2.3.7.11 WE tuning and 2.3.7.11 [[TE]] tuning both do this. Their primary purpose is to greatly improve 17edo's approximation of harmonic 7, to make it into an exceptional no-5s [[13-limit]] tuning for its size.
{{harmonics in equal|36|intervals=odd|columns=7}}
{{Harmonics in cet|70.392|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 17et, 2.3.7.11 WE tuning}}
{{harmonics in equal|37|intervals=odd|columns=7}}
{{Harmonics in cet|70.392|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 17et, 2.3.7.11 WE tuning (continued)}}
{{harmonics in equal|38|intervals=odd|columns=7}}
{{harmonics in equal|39|intervals=odd|columns=7}}
{{harmonics in equal|40|intervals=odd|columns=7}}
{{harmonics in equal|41|intervals=odd|columns=7}}
{{harmonics in equal|42|intervals=odd|columns=7}}
{{harmonics in equal|43|intervals=odd|columns=7}}
{{harmonics in equal|44|intervals=odd|columns=7}}
{{harmonics in equal|45|intervals=odd|columns=7}}
{{harmonics in equal|46|intervals=odd|columns=7}}
{{harmonics in equal|47|intervals=odd|columns=7}}
{{harmonics in equal|48|intervals=odd|columns=7}}
{{harmonics in equal|49|intervals=odd|columns=7}}
{{harmonics in equal|50|intervals=odd|columns=7}}
{{harmonics in equal|51|intervals=odd|columns=7}}
{{harmonics in equal|52|intervals=odd|columns=7}}
{{harmonics in equal|53|intervals=odd|columns=7}}

Latest revision as of 03:35, 27 April 2026

Approximations of odd harmonics

Approximation of odd harmonics in 1edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +498 -386 +231 -204 -551 +359 +112
Relative (%) +41.5 -32.2 +19.3 -17.0 -45.9 +30.0 +9.3
Step 2 2 3 3 3 4 4
Approximation of odd harmonics in 2edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -102 +214 +231 -204 +49 -241 +112
Relative (%) -17.0 +35.6 +38.5 -34.0 +8.1 -40.1 +18.6
Steps
(reduced) 		3
(1) 		5
(1) 		6
(0) 		6
(0) 		7
(1) 		7
(1) 		8
(0)
Approximation of odd harmonics in 3edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +98 +14 -169 +196 -151 -41 +112
Relative (%) +24.5 +3.4 -42.2 +49.0 -37.8 -10.1 +27.9
Steps
(reduced) 		5
(2) 		7
(1) 		8
(2) 		10
(1) 		10
(1) 		11
(2) 		12
(0)
Approximation of odd harmonics in 4edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -102 -86 -69 +96 +49 +59 +112
Relative (%) -34.0 -28.8 -22.9 +32.0 +16.2 +19.8 +37.2
Steps
(reduced) 		6
(2) 		9
(1) 		11
(3) 		13
(1) 		14
(2) 		15
(3) 		16
(0)
Approximation of odd harmonics in 5edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +18 +94 -9 +36 -71 +119 +112
Relative (%) +7.5 +39.0 -3.7 +15.0 -29.7 +49.8 +46.6
Steps
(reduced) 		8
(3) 		12
(2) 		14
(4) 		16
(1) 		17
(2) 		19
(4) 		20
(0)
Approximation of odd harmonics in 6edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +98.0 +13.7 +31.2 -3.9 +48.7 -40.5 -88.3
Relative (%) +49.0 +6.8 +15.6 -2.0 +24.3 -20.3 -44.1
Steps
(reduced) 		10
(4) 		14
(2) 		17
(5) 		19
(1) 		21
(3) 		22
(4) 		23
(5)
Approximation of odd harmonics in 7edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -16.2 -43.5 +59.7 -32.5 -37.0 +16.6 -59.7
Relative (%) -9.5 -25.3 +34.9 -18.9 -21.6 +9.7 -34.8
Steps
(reduced) 		11
(4) 		16
(2) 		20
(6) 		22
(1) 		24
(3) 		26
(5) 		27
(6)
Approximation of odd harmonics in 8edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +48.0 +63.7 -68.8 -53.9 +48.7 +59.5 -38.3
Relative (%) +32.0 +42.5 -45.9 -35.9 +32.5 +39.6 -25.5
Steps
(reduced) 		13
(5) 		19
(3) 		22
(6) 		25
(1) 		28
(4) 		30
(6) 		31
(7)
Approximation of odd harmonics in 9edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -35.3 +13.7 -35.5 +62.8 -18.0 -40.5 -21.6
Relative (%) -26.5 +10.3 -26.6 +47.1 -13.5 -30.4 -16.2
Steps
(reduced) 		14
(5) 		21
(3) 		25
(7) 		29
(2) 		31
(4) 		33
(6) 		35
(8)
Approximation of odd harmonics in 10edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +18.0 -26.3 -8.8 +36.1 +48.7 -0.5 -8.3
Relative (%) +15.0 -21.9 -7.4 +30.1 +40.6 -0.4 -6.9
Steps
(reduced) 		16
(6) 		23
(3) 		28
(8) 		32
(2) 		35
(5) 		37
(7) 		39
(9)
Approximation of odd harmonics in 11edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -47.4 +50.0 +13.0 +14.3 -5.9 +32.2 +2.6
Relative (%) -43.5 +45.9 +11.9 +13.1 -5.4 +29.5 +2.4
Steps
(reduced) 		17
(6) 		26
(4) 		31
(9) 		35
(2) 		38
(5) 		41
(8) 		43
(10)
Approximation of odd harmonics in 12edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -2.0 +13.7 +31.2 -3.9 +48.7 -40.5 +11.7
Relative (%) -2.0 +13.7 +31.2 -3.9 +48.7 -40.5 +11.7
Steps
(reduced) 		19
(7) 		28
(4) 		34
(10) 		38
(2) 		42
(6) 		44
(8) 		47
(11)
Approximation of odd harmonics in 13edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +36.5 -17.1 -45.7 -19.3 +2.5 -9.8 +19.4
Relative (%) +39.5 -18.5 -49.6 -20.9 +2.7 -10.6 +21.0
Steps
(reduced) 		21
(8) 		30
(4) 		36
(10) 		41
(2) 		45
(6) 		48
(9) 		51
(12)
Approximation of odd harmonics in 14edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -16.2 +42.3 -26.0 -32.5 -37.0 +16.6 +26.0
Relative (%) -18.9 +49.3 -30.3 -37.9 -43.2 +19.4 +30.4
Steps
(reduced) 		22
(8) 		33
(5) 		39
(11) 		44
(2) 		48
(6) 		52
(10) 		55
(13)
Approximation of odd harmonics in 15edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +18.0 +13.7 -8.8 +36.1 +8.7 +39.5 +31.7
Relative (%) +22.6 +17.1 -11.0 +45.1 +10.9 +49.3 +39.7
Steps
(reduced) 		24
(9) 		35
(5) 		42
(12) 		48
(3) 		52
(7) 		56
(11) 		59
(14)
Approximation of odd harmonics in 16edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -27.0 -11.3 +6.2 +21.1 -26.3 -15.5 +36.7
Relative (%) -35.9 -15.1 +8.2 +28.1 -35.1 -20.7 +49.0
Steps
(reduced) 		25
(9) 		37
(5) 		45
(13) 		51
(3) 		55
(7) 		59
(11) 		63
(15)
Approximation of odd harmonics in 17edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +3.9 -33.4 +19.4 +7.9 +13.4 +6.5 -29.4
Relative (%) +5.6 -47.3 +27.5 +11.1 +19.0 +9.3 -41.7
Steps
(reduced) 		27
(10) 		39
(5) 		48
(14) 		54
(3) 		59
(8) 		63
(12) 		66
(15)
Approximation of odd harmonics in 18edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +31.4 +13.7 +31.2 -3.9 -18.0 +26.1 -21.6
Relative (%) +47.1 +20.5 +46.8 -5.9 -27.0 +39.2 -32.4
Steps
(reduced) 		29
(11) 		42
(6) 		51
(15) 		57
(3) 		62
(8) 		67
(13) 		70
(16)
Approximation of odd harmonics in 19edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -7.2 -7.4 -21.5 -14.4 +17.1 -19.5 -14.6
Relative (%) -11.4 -11.7 -34.0 -22.9 +27.1 -30.8 -23.1
Steps
(reduced) 		30
(11) 		44
(6) 		53
(15) 		60
(3) 		66
(9) 		70
(13) 		74
(17)
Approximation of odd harmonics in 20edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +18.0 -26.3 -8.8 -23.9 -11.3 -0.5 -8.3
Relative (%) +30.1 -43.9 -14.7 -39.9 -18.9 -0.9 -13.8
Steps
(reduced) 		32
(12) 		46
(6) 		56
(16) 		63
(3) 		69
(9) 		74
(14) 		78
(18)
Approximation of odd harmonics in 21edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -16.2 +13.7 +2.6 +24.7 +20.1 +16.6 -2.6
Relative (%) -28.4 +24.0 +4.6 +43.2 +35.2 +29.1 -4.5
Steps
(reduced) 		33
(12) 		49
(7) 		59
(17) 		67
(4) 		73
(10) 		78
(15) 		82
(19)
Approximation of odd harmonics in 22edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +7.1 -4.5 +13.0 +14.3 -5.9 -22.3 +2.6
Relative (%) +13.1 -8.2 +23.8 +26.2 -10.7 -41.0 +4.8
Steps
(reduced) 		35
(13) 		51
(7) 		62
(18) 		70
(4) 		76
(10) 		81
(15) 		86
(20)
Approximation of odd harmonics in 23edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -23.7 -21.1 +22.5 +4.8 +22.6 -5.7 +7.4
Relative (%) -45.4 -40.4 +43.1 +9.2 +43.3 -11.0 +14.2
Steps
(reduced) 		36
(13) 		53
(7) 		65
(19) 		73
(4) 		80
(11) 		85
(16) 		90
(21)
Approximation of odd harmonics in 24edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -2.0 +13.7 -18.8 -3.9 -1.3 +9.5 +11.7
Relative (%) -3.9 +27.4 -37.7 -7.8 -2.6 +18.9 +23.5
Steps
(reduced) 		38
(14) 		56
(8) 		67
(19) 		76
(4) 		83
(11) 		89
(17) 		94
(22)
Approximation of odd harmonics in 25edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +18.0 -2.3 -8.8 -11.9 -23.3 +23.5 +15.7
Relative (%) +37.6 -4.8 -18.4 -24.8 -48.6 +48.9 +32.8
Steps
(reduced) 		40
(15) 		58
(8) 		70
(20) 		79
(4) 		86
(11) 		93
(18) 		98
(23)
Approximation of odd harmonics in 26edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -9.6 -17.1 +0.4 -19.3 +2.5 -9.8 +19.4
Relative (%) -20.9 -37.0 +0.9 -41.8 +5.5 -21.1 +42.1
Steps
(reduced) 		41
(15) 		60
(8) 		73
(21) 		82
(4) 		90
(12) 		96
(18) 		102
(24)
Approximation of odd harmonics in 27edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +9.2 +13.7 +9.0 +18.3 -18.0 +3.9 -21.6
Relative (%) +20.6 +30.8 +20.1 +41.2 -40.5 +8.8 -48.6
Steps
(reduced) 		43
(16) 		63
(9) 		76
(22) 		86
(5) 		93
(12) 		100
(19) 		105
(24)
Approximation of odd harmonics in 28edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -16.2 -0.6 +16.9 +10.4 +5.8 +16.6 -16.8
Relative (%) -37.9 -1.4 +39.4 +24.2 +13.6 +38.8 -39.3
Steps
(reduced) 		44
(16) 		65
(9) 		79
(23) 		89
(5) 		97
(13) 		104
(20) 		109
(25)
Approximation of odd harmonics in 29edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +1.5 -13.9 -17.1 +3.0 -13.4 -12.9 -12.4
Relative (%) +3.6 -33.6 -41.3 +7.2 -32.4 -31.3 -30.0
Steps
(reduced) 		46
(17) 		67
(9) 		81
(23) 		92
(5) 		100
(13) 		107
(20) 		113
(26)
Approximation of odd harmonics in 30edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +18.0 +13.7 -8.8 -3.9 +8.7 -0.5 -8.3
Relative (%) +45.1 +34.2 -22.1 -9.8 +21.7 -1.3 -20.7
Steps
(reduced) 		48
(18) 		70
(10) 		84
(24) 		95
(5) 		104
(14) 		111
(21) 		117
(27)
Approximation of odd harmonics in 31edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -5.2 +0.8 -1.1 -10.4 -9.4 +11.1 -4.4
Relative (%) -13.4 +2.0 -2.8 -26.8 -24.2 +28.6 -11.4
Steps
(reduced) 		49
(18) 		72
(10) 		87
(25) 		98
(5) 		107
(14) 		115
(22) 		121
(28)
Approximation of odd harmonics in 32edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +10.5 -11.3 +6.2 -16.4 +11.2 -15.5 -0.8
Relative (%) +28.1 -30.2 +16.5 -43.8 +29.8 -41.4 -2.0
Steps
(reduced) 		51
(19) 		74
(10) 		90
(26) 		101
(5) 		111
(15) 		118
(22) 		125
(29)
Approximation of odd harmonics in 33edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -11.0 +13.7 +13.0 +14.3 -5.9 -4.2 +2.6
Relative (%) -30.4 +37.6 +35.7 +39.2 -16.1 -11.5 +7.3
Steps
(reduced) 		52
(19) 		77
(11) 		93
(27) 		105
(6) 		114
(15) 		122
(23) 		129
(30)
Approximation of odd harmonics in 34edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +3.9 +1.9 -15.9 +7.9 +13.4 +6.5 +5.8
Relative (%) +11.1 +5.4 -45.0 +22.3 +37.9 +18.5 +16.6
Steps
(reduced) 		54
(20) 		79
(11) 		95
(27) 		108
(6) 		118
(16) 		126
(24) 		133
(31)
Approximation of odd harmonics in 35edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -16.2 -9.2 -8.8 +1.8 -2.7 +16.6 +8.9
Relative (%) -47.4 -26.7 -25.7 +5.3 -8.0 +48.5 +25.9
Steps
(reduced) 		55
(20) 		81
(11) 		98
(28) 		111
(6) 		121
(16) 		130
(25) 		137
(32)
Approximation of odd harmonics in 36edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -2.0 +13.7 -2.2 -3.9 +15.3 -7.2 +11.7
Relative (%) -5.9 +41.1 -6.5 -11.7 +46.0 -21.6 +35.2
Steps
(reduced) 		57
(21) 		84
(12) 		101
(29) 		114
(6) 		125
(17) 		133
(25) 		141
(33)
Approximation of odd harmonics in 37edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +11.6 +2.9 +4.1 -9.3 +0.0 +2.7 +14.4
Relative (%) +35.6 +8.9 +12.8 -28.7 +0.1 +8.4 +44.5
Steps
(reduced) 		59
(22) 		86
(12) 		104
(30) 		117
(6) 		128
(17) 		137
(26) 		145
(34)
Approximation of odd harmonics in 38edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -7.2 -7.4 +10.1 -14.4 -14.5 +12.1 -14.6
Relative (%) -22.9 -23.3 +32.1 -45.7 -45.8 +38.3 -46.2
Steps
(reduced) 		60
(22) 		88
(12) 		107
(31) 		120
(6) 		131
(17) 		141
(27) 		148
(34)
Approximation of odd harmonics in 39edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +5.7 +13.7 -15.0 +11.5 +2.5 -9.8 -11.3
Relative (%) +18.6 +44.5 -48.7 +37.3 +8.2 -31.7 -36.9
Steps
(reduced) 		62
(23) 		91
(13) 		109
(31) 		124
(7) 		135
(18) 		144
(27) 		152
(35)
Approximation of odd harmonics in 40edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -12.0 +3.7 -8.8 +6.1 -11.3 -0.5 -8.3
Relative (%) -39.9 +12.3 -29.4 +20.3 -37.7 -1.8 -27.6
Steps
(reduced) 		63
(23) 		93
(13) 		112
(32) 		127
(7) 		138
(18) 		148
(28) 		156
(36)
Approximation of odd harmonics in 41edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +0.5 -5.8 -3.0 +1.0 +4.8 +8.3 -5.3
Relative (%) +1.7 -19.9 -10.2 +3.3 +16.3 +28.2 -18.3
Steps
(reduced) 		65
(24) 		95
(13) 		115
(33) 		130
(7) 		142
(19) 		152
(29) 		160
(37)
Approximation of odd harmonics in 42edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +12.3 +13.7 +2.6 -3.9 -8.5 -12.0 -2.6
Relative (%) +43.2 +47.9 +9.1 -13.7 -29.6 -41.8 -8.9
Steps
(reduced) 		67
(25) 		98
(14) 		118
(34) 		133
(7) 		145
(19) 		155
(29) 		164
(38)
Approximation of odd harmonics in 43edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -4.3 +4.4 +7.9 -8.6 +6.8 -3.3 +0.1
Relative (%) -15.3 +15.7 +28.4 -30.7 +24.4 -11.9 +0.4
Steps
(reduced) 		68
(25) 		100
(14) 		121
(35) 		136
(7) 		149
(20) 		159
(30) 		168
(39)
Approximation of odd harmonics in 44edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +7.1 -4.5 +13.0 -13.0 -5.9 +4.9 +2.6
Relative (%) +26.2 -16.5 +47.6 -47.7 -21.5 +18.1 +9.7
Steps
(reduced) 		70
(26) 		102
(14) 		124
(36) 		139
(7) 		152
(20) 		163
(31) 		172
(40)
Approximation of odd harmonics in 45edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -8.6 -13.0 -8.8 +9.4 +8.7 +12.8 +5.1
Relative (%) -32.3 -48.7 -33.1 +35.3 +32.6 +48.0 +19.0
Steps
(reduced) 		71
(26) 		104
(14) 		126
(36) 		143
(8) 		156
(21) 		167
(32) 		176
(41)
Approximation of odd harmonics in 46edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +2.4 +5.0 -3.6 +4.8 -3.5 -5.7 +7.4
Relative (%) +9.2 +19.1 -13.8 +18.3 -13.4 -22.0 +28.3
Steps
(reduced) 		73
(27) 		107
(15) 		129
(37) 		146
(8) 		159
(21) 		170
(32) 		180
(42)
Approximation of odd harmonics in 47edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -12.6 -3.3 +1.4 +0.3 +10.4 +2.0 +9.6
Relative (%) -49.3 -13.1 +5.4 +1.4 +40.7 +7.9 +37.6
Steps
(reduced) 		74
(27) 		109
(15) 		132
(38) 		149
(8) 		163
(22) 		174
(33) 		184
(43)
Approximation of odd harmonics in 48edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -2.0 -11.3 +6.2 -3.9 -1.3 +9.5 +11.7
Relative (%) -7.8 -45.3 +24.7 -15.6 -5.3 +37.9 +46.9
Steps
(reduced) 		76
(28) 		111
(15) 		135
(39) 		152
(8) 		166
(22) 		178
(34) 		188
(44)
Approximation of odd harmonics in 49edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +8.2 +5.5 +10.8 -8.0 +11.9 -7.9 -10.7
Relative (%) +33.7 +22.6 +44.0 -32.6 +48.8 -32.2 -43.8
Steps
(reduced) 		78
(29) 		114
(16) 		138
(40) 		155
(8) 		170
(23) 		181
(34) 		191
(44)
Approximation of odd harmonics in 50edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -6.0 -2.3 -8.8 -11.9 +0.7 -0.5 -8.3
Relative (%) -24.8 -9.6 -36.8 -49.6 +2.8 -2.2 -34.5
Steps
(reduced) 		79
(29) 		116
(16) 		140
(40) 		158
(8) 		173
(23) 		185
(35) 		195
(45)
Approximation of odd harmonics in 51edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) +3.9 -9.8 -4.1 +7.9 -10.1 +6.5 -5.9
Relative (%) +16.7 -41.8 -17.5 +33.4 -43.1 +27.8 -25.1
Steps
(reduced) 		81
(30) 		118
(16) 		143
(41) 		162
(9) 		176
(23) 		189
(36) 		199
(46)
Approximation of odd harmonics in 52edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -9.6 +6.0 +0.4 +3.8 +2.5 -9.8 -3.7
Relative (%) -41.8 +26.0 +1.8 +16.4 +11.0 -42.3 -15.8
Steps
(reduced) 		82
(30) 		121
(17) 		146
(42) 		165
(9) 		180
(24) 		192
(36) 		203
(47)
Approximation of odd harmonics in 53edo
Harmonic 3 5 7 9 11 13 15
Error Absolute (¢) -0.07 -1.41 +4.76 -0.14 -7.92 -2.79 -1.48
Relative (%) -0.3 -6.2 +21.0 -0.6 -35.0 -12.3 -6.5
Steps
(reduced) 		84
(31) 		123
(17) 		149
(43) 		168
(9) 		183
(24) 		196
(37) 		207
(48)
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