Xenharmonic Wiki

User:BudjarnLambeth/Sandbox

< User:BudjarnLambeth
Revision as of 23:14, 21 September 2025 by BudjarnLambeth (talk | contribs) (→Sandbox)

This is a working out sandbox page, not a content page.


Sandbox

Approximation of harmonics in 1ed15/14
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -5.6 +9.1 -11.1 -39.1 +3.6 -24.4 -16.7 +18.3 -44.7 +29.2 -2.0 -21.1
Relative (%) -4.7 +7.6 -9.3 -32.8 +3.0 -20.5 -14.0 +15.3 -37.4 +24.4 -1.7 -17.7
Step 10 16 20 23 26 28 30 32 33 35 36 37
Approximation of harmonics in 10edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
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
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
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)



Approximation of harmonics in 1ed16/15
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +29.0 -2.5 -53.6 +7.0 +26.5 -16.9 -24.6 -5.0 +36.0 -17.3 +55.6 +28.7
Relative (%) +26.0 -2.3 -48.0 +6.2 +23.7 -15.1 -22.0 -4.5 +32.2 -15.4 +49.7 +25.7
Step 11 17 21 25 28 30 32 34 36 37 39 40
Approximation of harmonics in 17edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +30.7 +0.0 -50.5 +10.7 +30.7 -12.4 -19.8 +0.0 +41.4 -11.8 -50.5 +34.7
Relative (%) +27.4 +0.0 -45.2 +9.5 +27.4 -11.1 -17.7 +0.0 +37.0 -10.5 -45.2 +31.0
Steps
(reduced) 		11
(11) 		17
(0) 		21
(4) 		25
(8) 		28
(11) 		30
(13) 		32
(15) 		34
(0) 		36
(2) 		37
(3) 		38
(4) 		40
(6)



Approximation of harmonics in 1ed17/16
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -45.5 -12.8 +14.0 +47.5 +46.7 -10.3 -31.5 -25.5 +2.0 +46.9 +1.2 -32.4
Relative (%) -43.3 -12.2 +13.3 +45.2 +44.5 -9.8 -30.0 -24.3 +1.9 +44.7 +1.2 -30.9
Step 11 18 23 27 30 32 34 36 38 40 41 42



Approximation of harmonics in 1ed18/17
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -12.5 -21.8 -25.1 -15.6 -34.4 -4.4 -37.6 -43.6 -28.1 +4.8 -46.9 +12.4
Relative (%) -12.7 -22.0 -25.4 -15.7 -34.7 -4.4 -38.0 -44.1 -28.4 +4.8 -47.4 +12.6
Step 12 19 24 28 31 34 36 38 40 42 43 45
Approximation of harmonics in 34ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -11.0 -19.4 -22.0 -12.0 -30.4 +0.0 -33.0 -38.8 -23.0 +10.2 -41.4 +18.2
Relative (%) -11.1 -19.6 -22.2 -12.1 -30.7 +0.0 -33.3 -39.1 -23.2 +10.3 -41.8 +18.4
Steps
(reduced) 		12
(12) 		19
(19) 		24
(24) 		28
(28) 		31
(31) 		34
(0) 		36
(2) 		38
(4) 		40
(6) 		42
(8) 		43
(9) 		45
(11)



Approximation of harmonics in 1ed19/18
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +16.8 -29.9 +33.7 +21.8 -13.1 +0.9 -43.1 +33.8 +38.6 -32.8 +3.8 -41.2
Relative (%) +18.0 -31.9 +36.0 +23.3 -13.9 +0.9 -46.0 +36.1 +41.3 -35.0 +4.0 -44.0
Step 13 20 26 30 33 36 38 41 43 44 46 47
Approximation of harmonics in 36ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +16.5 -30.4 +33.0 +21.0 -13.9 +0.0 -44.0 +32.8 +37.6 -33.9 +2.7 -42.3
Relative (%) +17.7 -32.5 +35.3 +22.5 -14.8 +0.0 -47.0 +35.1 +40.1 -36.2 +2.8 -45.2
Steps
(reduced) 		13
(13) 		20
(20) 		26
(26) 		30
(30) 		33
(33) 		36
(0) 		38
(2) 		41
(5) 		43
(7) 		44
(8) 		46
(10) 		47
(11)



Approximation of harmonics in 1ed20/19
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +43.2 -37.1 -2.4 -33.5 +6.1 +5.6 +40.8 +14.5 +9.7 +22.3 -39.5 -0.5
Relative (%) +48.7 -41.8 -2.7 -37.7 +6.8 +6.3 +46.0 +16.4 +10.9 +25.1 -44.5 -0.6
Step 14 21 27 31 35 38 41 43 45 47 48 50
Approximation of harmonics in 27ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +44.4 -35.3 +0.0 -30.8 +9.2 +9.0 +44.4 +18.3 +13.7 +26.5 -35.3 +3.9
Relative (%) +50.0 -39.7 +0.0 -34.6 +10.3 +10.1 +50.0 +20.6 +15.4 +29.8 -39.7 +4.4
Steps
(reduced) 		14
(14) 		21
(21) 		27
(0) 		31
(4) 		35
(8) 		38
(11) 		41
(14) 		43
(16) 		45
(18) 		47
(20) 		48
(21) 		50
(23)



Approximation of harmonics in 1ed21/20
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -17.5 +40.8 -34.9 +1.1 +23.3 +9.9 +32.1 -2.9 -16.4 -12.4 +5.9 +36.2
Relative (%) -20.7 +48.3 -41.3 +1.3 +27.6 +11.7 +38.0 -3.4 -19.4 -14.7 +7.0 +42.9
Step 14 23 28 33 37 40 43 45 47 49 51 53
Approximation of harmonics in 33ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -17.9 +40.0 -35.9 +0.0 +22.1 +8.5 +30.7 -4.4 -17.9 -14.1 +4.2 +34.5
Relative (%) -21.2 +47.4 -42.5 +0.0 +26.2 +10.1 +36.3 -5.2 -21.2 -16.7 +4.9 +40.8
Steps
(reduced) 		14
(14) 		23
(23) 		28
(28) 		33
(0) 		37
(4) 		40
(7) 		43
(10) 		45
(12) 		47
(14) 		49
(16) 		51
(18) 		53
(20)



Approximation of harmonics in 1ed22/21
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +8.1 +30.9 +16.1 +32.5 +39.0 +13.7 +24.2 -18.7 -40.0 +36.6 -33.5 -11.0
Relative (%) +10.0 +38.4 +20.0 +40.3 +48.4 +17.0 +30.0 -23.2 -49.7 +45.5 -41.6 -13.6
Step 15 24 30 35 39 42 45 47 49 52 53 55



Approximation of harmonics in 1ed23/22
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +31.3 +22.0 -14.4 -15.9 -23.7 +17.3 +17.0 -33.0 +15.4 +4.3 +7.6 +22.9
Relative (%) +40.7 +28.5 -18.6 -20.6 -30.8 +22.4 +22.0 -42.9 +20.0 +5.6 +9.9 +29.8
Step 16 25 31 36 40 44 47 49 52 54 56 58



Approximation of harmonics in 1ed24/23
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -21.1 +13.7 +31.5 +13.6 -7.4 +20.5 +10.4 +27.5 -7.6 -25.2 -28.5 -19.7
Relative (%) -28.7 +18.7 +42.7 +18.4 -10.0 +27.8 +14.0 +37.3 -10.3 -34.2 -38.6 -26.7
Step 16 26 33 38 42 46 49 52 54 56 58 60
Approximation of harmonics in 42ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -18.3 +18.3 -36.6 +20.2 +0.0 +28.6 +18.9 +36.6 +1.9 -15.4 -18.3 -9.2
Relative (%) -24.8 +24.8 -49.6 +27.4 +0.0 +38.7 +25.7 +49.6 +2.6 -20.8 -24.8 -12.4
Steps
(reduced) 		16
(16) 		26
(26) 		32
(32) 		38
(38) 		42
(0) 		46
(4) 		49
(7) 		52
(10) 		54
(12) 		56
(14) 		58
(16) 		60
(18)



Approximation of harmonics in 1ed25/24
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +1.4 +6.2 +2.9 -30.1 +7.6 +23.5 +4.3 +12.4 -28.7 +18.4 +9.1 +11.8
Relative (%) +2.0 +8.8 +4.1 -42.6 +10.8 +33.2 +6.1 +17.5 -40.6 +26.0 +12.8 +16.7
Step 17 27 34 39 44 48 51 54 56 59 61 63
Approximation of harmonics in 17edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
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
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
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)



Approximation of harmonics in 1ed26/25
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +22.2 -0.7 -23.5 -2.4 +21.5 +26.2 -1.3 -1.5 +19.8 -9.4 -24.2 -27.0
Relative (%) +32.7 -1.1 -34.6 -3.5 +31.6 +38.6 -1.9 -2.2 +29.2 -13.8 -35.7 -39.8
Step 18 28 35 41 46 50 53 56 59 61 63 65
Approximation of harmonics in 28edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +22.7 +0.0 -22.6 -1.3 +22.7 +27.5 +0.1 +0.0 +21.4 -7.8 -22.6 -25.3
Relative (%) +33.4 +0.0 -33.2 -1.9 +33.4 +40.5 +0.2 +0.0 +31.5 -11.4 -33.2 -37.2
Steps
(reduced) 		18
(18) 		28
(0) 		35
(7) 		41
(13) 		46
(18) 		50
(22) 		53
(25) 		56
(0) 		59
(3) 		61
(5) 		63
(7) 		65
(9)



Approximation of harmonics in 1ed27/26
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -23.9 -7.2 +17.5 +23.2 -31.1 +28.7 -6.4 -14.3 -0.7 +30.3 +10.3 +2.4
Relative (%) -36.6 -11.0 +26.8 +35.5 -47.6 +44.0 -9.9 -22.0 -1.1 +46.3 +15.8 +3.7
Step 18 29 37 43 47 52 55 58 61 64 66 68
Approximation of harmonics in 61ed10
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -23.7 -6.8 +17.9 +23.7 -30.5 +29.3 -5.8 -13.6 +0.0 +31.0 +11.1 +3.2
Relative (%) -36.3 -10.4 +27.4 +36.3 -46.7 +44.9 -8.8 -20.9 +0.0 +47.5 +17.0 +4.9
Steps
(reduced) 		18
(18) 		29
(29) 		37
(37) 		43
(43) 		47
(47) 		52
(52) 		55
(55) 		58
(58) 		61
(0) 		64
(3) 		66
(5) 		68
(7)



Approximation of harmonics in 1ed28/27
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -3.7 -13.1 -7.5 -16.0 -16.9 +31.1 -11.2 -26.3 -19.8 +4.1 -20.6 +29.7
Relative (%) -5.9 -20.9 -11.9 -25.5 -26.8 +49.3 -17.8 -41.7 -31.4 +6.5 -32.7 +47.2
Step 19 30 38 44 49 54 57 60 63 66 68 71
Approximation of harmonics in 19edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
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
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
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)



Approximation of harmonics in 1ed29/28
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +15.0 -18.7 +30.1 +8.2 -3.6 -27.5 -15.7 +23.4 +23.3 -20.2 +11.4 -5.7
Relative (%) +24.7 -30.7 +49.5 +13.6 -6.0 -45.3 -25.8 +38.6 +38.3 -33.3 +18.7 -9.4
Step 20 31 40 46 51 55 59 63 66 68 71 73
Approximation of harmonics in 51ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +16.5 -16.5 -27.9 +11.5 +0.0 -23.6 -11.5 +27.9 +28.0 -15.4 +16.5 -0.5
Relative (%) +27.1 -27.1 -45.9 +19.0 +0.0 -38.8 -18.8 +45.9 +46.0 -25.3 +27.1 -0.8
Steps
(reduced) 		20
(20) 		31
(31) 		39
(39) 		46
(46) 		51
(0) 		55
(4) 		59
(8) 		63
(12) 		66
(15) 		68
(17) 		71
(20) 		73
(22)



Approximation of harmonics in 1ed30/29
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -26.2 -23.8 +6.4 -27.8 +8.7 -23.4 -19.8 +11.0 +4.7 +15.8 -17.5 +20.0
Relative (%) -44.6 -40.6 +10.8 -47.4 +14.8 -39.9 -33.8 +18.8 +8.0 +26.9 -29.8 +34.1
Step 20 32 41 47 53 57 61 65 68 71 73 76
Approximation of harmonics in 41ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +29.3 -28.8 +0.0 +23.4 +0.5 +26.3 +29.3 +1.0 -5.8 +4.8 -28.8 +8.3
Relative (%) +50.0 -49.2 +0.0 +40.0 +0.8 +44.9 +50.0 +1.7 -10.0 +8.2 -49.2 +14.1
Steps
(reduced) 		21
(21) 		32
(32) 		41
(0) 		48
(7) 		53
(12) 		58
(17) 		62
(21) 		65
(24) 		68
(27) 		71
(30) 		73
(32) 		76
(35)
Retrieved from "https://en.xen.wiki/index.php?title=User:BudjarnLambeth/Sandbox&oldid=210377"