User:BudjarnLambeth/Ed255/128: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
mNo edit summary
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
mNo edit summary
 
(28 intermediate revisions by the same user not shown)
Line 1: Line 1:
An '''equal division of reduced harmonic 255''' ('''ed255/128''') is an [[equal-step tuning]] in which the octave-reduced 255th harmonic ([[255/128]]) is [[Just intonation|justly tuned]] and is divided in a given number of equal steps. 255/128 is very close to the [[octave]], 2/1, but it is slightly flatter. This makes it suitable as an alternative to edos whose consonances are too sharp, such as [[5edo]].
{{Editable user page}}


== 5ed255/128 ==
=== Harmonics ===
{{Harmonics in equal|5|255|128|intervals=integer}}


An '''equal division of reduced harmonic 255''' ('''ed255/128''') is an [[equal-step tuning]] in which the octave-reduced 255th harmonic ([[255/128]]) is [[Just intonation|justly tuned]] and is divided in a given number of equal steps. 255/128 is very close to the [[octave]], 2/1, but it is slightly flatter. This makes it suitable as an alternative to edos whose consonances are too sharp, such as [[6edo]].


5edo, [[8edt]], [[14ed7]] for comparison:
Ed255/128s really only make sense for that purpose with 65 or fewer tones per [[pseudo-octave]]. With more tones than that, the relative error on 2/1 becomes unacceptably high and it makes more sense to switch to a different tuning like a [[zpi]] or ed511/256.
{{Harmonics in equal|5|intervals=integer|collapsed=1}}
{{Harmonics in equal|8|3|1|intervals=integer|collapsed=1}}
{{Harmonics in equal|14|7|1|intervals=integer|collapsed=1}}
 
=== Intervals ===
* 238.645
* 477.29
* 715.934
* 954.579
* 1193.224


Ed255/128s are the complementary opposite of [[ed257/128]]s.


== 6ed255/128 ==
== 6ed255/128 ==
=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|6|255|128|intervals=integer}}
{{Harmonics in equal|6|255|128|intervals=odd}}




6edo for comparison:
6edo for comparison:
{{Harmonics in equal|6|intervals=integer|collapsed=1}}
{{Harmonics in equal|6|intervals=odd|collapsed=1}}


=== Intervals ===
=== Intervals ===
Line 33: Line 22:
* 795.483
* 795.483
* 994.353
* 994.353
* 1193.224
== 8ed255/128 ==
=== Harmonics ===
{{Harmonics in equal|8|255|128|intervals=integer}}
[[8edo]] for comparison:
{{Harmonics in equal|8|intervals=integer|collapsed=1}}
=== Intervals ===
* 149.153
* 298.306
* 447.459
* 596.612
* 745.765
* 894.918
* 1044.071
* 1193.224
* 1193.224


Line 57: Line 27:
== 11ed255/128 ==
== 11ed255/128 ==
=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|11|255|128|intervals=integer}}
{{Harmonics in equal|11|255|128|intervals=odd}}




[[11edo]] for comparison:
[[11edo]] for comparison:
{{Harmonics in equal|11|intervals=integer|collapsed=1}}
{{Harmonics in equal|11|intervals=odd|collapsed=1}}


=== Intervals ===
=== Intervals ===
Line 78: Line 48:


== 15ed255/128 ==
== 15ed255/128 ==
''See also: [[5- to 10-tone scales in zeta stretched 15edo]]''
15ed255/128 is very close to [[zpi|47zpi]]. The [[5- to 10-tone scales in 47zpi]] are also useable in 15ed255/128.
 


=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|15|255|128|intervals=integer}}
{{Harmonics in equal|15|255|128|intervals=prime}}




[[15edo]] for comparison:
[[15edo]] for comparison:
{{Harmonics in equal|15|intervals=integer|collapsed=1}}
{{Harmonics in equal|15|intervals=prime|collapsed=1}}


=== Intervals ===
=== Intervals ===
Line 104: Line 73:
* 1113.676
* 1113.676
* 1193.224
* 1193.224




== 17ed255/128 ==
== 17ed255/128 ==
=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|17|255|128|intervals=integer}}
{{Harmonics in equal|17|255|128|intervals=prime}}




[[17edo]] for comparison:
[[17edo]] for comparison:
{{Harmonics in equal|17|intervals=integer|collapsed=1}}
{{Harmonics in equal|17|intervals=prime|collapsed=1}}


=== Intervals ===
=== Intervals ===
Line 136: Line 106:
== 18ed255/128 ==
== 18ed255/128 ==
=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|18|255|128|intervals=integer}}
{{Harmonics in equal|18|255|128|intervals=odd}}




[[18edo]] for comparison:
[[18edo]] for comparison:
{{Harmonics in equal|18|intervals=integer|collapsed=1}}
{{Harmonics in equal|18|intervals=odd|collapsed=1}}


=== Intervals ===
=== Intervals ===
Line 165: Line 135:
== 27ed255/128 ==
== 27ed255/128 ==
=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|27|255|128|intervals=integer}}
{{Harmonics in equal|27|255|128|intervals=prime}}




[[27edo]] for comparison:
[[27edo]] for comparison:
{{Harmonics in equal|27|intervals=integer|collapsed=1}}
{{Harmonics in equal|27|intervals=prime|collapsed=1}}


=== Intervals ===
=== Intervals ===
Line 199: Line 169:
* 1149.031
* 1149.031
* 1193.224
* 1193.224
== 39ed255/128 ==
=== Harmonics ===
{{Harmonics in equal|39|255|128|intervals=prime}}
[[39edo]] for comparison:
{{Harmonics in equal|39|intervals=prime|collapsed=1}}
== 42ed255/128 ==
42ed255/128 is a kind of opposite twin to the scale [[42ed257/128]], as they improve 42edo’s [[JI]] approximation by about the same amount, but in opposite directions (those harmonics which are slightly sharp in one are slightly flat in the other).
42ed255/128’s step size is very close to that of [[1ed28.5c|APS715jot]] and [[191zpi]].
See [[Table of stretched 42edo tunings]] for more.
=== Harmonics ===
{{Harmonics in equal|42|255|128|intervals=prime}}
[[42edo]] for comparison:
{{Harmonics in equal|42|intervals=prime|collapsed=1}}
===Scales===
<br>
;[[MOS scale]]s
* Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3'''
* Eugene/Tritikleismic[15]: '''3 3 2 3 3 3 3 2 3 3 3 3 2 3 3'''
* Lemba[16]: '''3 2 3 2 3 3 2 3 3 2 3 2 3 3 2 3'''
* Qeema/Skateboard[15]: '''2 5 2 2 2 5 2 2 2 5 2 2 2 5 2'''
* Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''
* Seville/Sevond[14] 1st mode: '''1 5 1 5 1 5 1 5 1 5 1 5 1 5'''
* Seville/Sevond[14] 2nd mode: '''5 1 5 1 5 1 5 1 5 1 5 1 5 1'''
* Seville/Sevond[21]: '''1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4'''
; Subsets of MOS scales
''(Names used are [[Template:Idiosyncratic|idiosyncratic]].)''
* Eugene/Tritikleismic[9]
** Groovy aeolian pentatonic: '''11 6 8 3 14'''
** [[Otonal]] mixolydian pentatonic: '''14 3 8 11 6'''
** Pseudo-[[equipentatonic]]: '''11 6 8 6 11'''
** Septimal melodic minor pentatonic: '''8 3 14 14 3'''
** Septimal Picardy pentatonic: '''8 6 11 3 14'''
** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6'''
** Yokai pentatonic: '''3 14 8 3 14'''
== 49ed255/128 ==
=== Harmonics ===
{{Harmonics in equal|49|255|128|intervals=prime}}
[[49edo]] for comparison:
{{Harmonics in equal|49|intervals=prime|collapsed=1}}
== 54ed255/128 ==
=== Harmonics ===
{{Harmonics in equal|54|255|128|intervals=prime}}
[[54edo]] for comparison:
{{Harmonics in equal|54|intervals=prime|collapsed=1}}




== Related concepts ==
== Related concepts ==
* [[Ed257/128]]
* [[Substitute harmonic]]
* [[Substitute harmonic]]
* [[Equal-step tuning]]
* [[Equal-step tuning]]


[[Category:Edonoi]][[Category:5edo]][[Category:5-tone scales]]
[[Category:Edonoi]][[Category:5edo]][[Category:5-tone scales]]

Latest revision as of 13:13, 18 May 2025

This user page is editable by any wiki editor.

As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages.

However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits).


An equal division of reduced harmonic 255 (ed255/128) is an equal-step tuning in which the octave-reduced 255th harmonic (255/128) is justly tuned and is divided in a given number of equal steps. 255/128 is very close to the octave, 2/1, but it is slightly flatter. This makes it suitable as an alternative to edos whose consonances are too sharp, such as 6edo.

Ed255/128s really only make sense for that purpose with 65 or fewer tones per pseudo-octave. With more tones than that, the relative error on 2/1 becomes unacceptably high and it makes more sense to switch to a different tuning like a zpi or ed511/256.

Ed255/128s are the complementary opposite of ed257/128s.

6ed255/128

Harmonics

Approximation of odd harmonics in 6ed255/128
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +86.8 -2.1 +12.0 -25.4 +25.0 -65.4 +84.6 +66.8 +73.1 +98.7 -58.8
Relative (%) +43.6 -1.1 +6.0 -12.8 +12.6 -32.9 +42.6 +33.6 +36.8 +49.6 -29.5
Steps
(reduced) 		10
(4) 		14
(2) 		17
(5) 		19
(1) 		21
(3) 		22
(4) 		24
(0) 		25
(1) 		26
(2) 		27
(3) 		27
(3)


6edo for comparison:

Approximation of odd harmonics in 6edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +98.0 +13.7 +31.2 -3.9 +48.7 -40.5 -88.3 +95.0 -97.5 -70.8 -28.3
Relative (%) +49.0 +6.8 +15.6 -2.0 +24.3 -20.3 -44.1 +47.5 -48.8 -35.4 -14.1
Steps
(reduced) 		10
(4) 		14
(2) 		17
(5) 		19
(1) 		21
(3) 		22
(4) 		23
(5) 		25
(1) 		25
(1) 		26
(2) 		27
(3)

Intervals

  • 198.871
  • 397.741
  • 596.612
  • 795.483
  • 994.353
  • 1193.224


11ed255/128

Harmonics

Approximation of odd harmonics in 11ed255/128
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +50.6 +34.0 -6.1 -7.3 -29.3 +6.9 -23.8 -23.6 +0.8 +44.5 -4.5
Relative (%) +46.6 +31.4 -5.6 -6.7 -27.0 +6.4 -22.0 -21.7 +0.7 +41.0 -4.2
Steps
(reduced) 		18
(7) 		26
(4) 		31
(9) 		35
(2) 		38
(5) 		41
(8) 		43
(10) 		45
(1) 		47
(3) 		49
(5) 		50
(6)


11edo for comparison:

Approximation of odd harmonics in 11edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -47.4 +50.0 +13.0 +14.3 -5.9 +32.2 +2.6 +4.1 +29.8 -34.4 +26.3
Relative (%) -43.5 +45.9 +11.9 +13.1 -5.4 +29.5 +2.4 +3.8 +27.3 -31.5 +24.1
Steps
(reduced) 		17
(6) 		26
(4) 		31
(9) 		35
(2) 		38
(5) 		41
(8) 		43
(10) 		45
(1) 		47
(3) 		48
(4) 		50
(6)

Intervals

  • 108.475
  • 216.95
  • 325.425
  • 433.9
  • 542.375
  • 650.85
  • 759.324
  • 867.799
  • 976.274
  • 1084.749
  • 1193.224


15ed255/128

15ed255/128 is very close to 47zpi. The 5- to 10-tone scales in 47zpi are also useable in 15ed255/128.

Harmonics

Approximation of prime harmonics in 15ed255/128
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.8 +7.2 -2.1 -27.8 -14.8 +14.2 +27.0 -6.4 -19.0 -22.6 +21.1
Relative (%) -8.5 +9.1 -2.7 -34.9 -18.6 +17.8 +34.0 -8.1 -23.9 -28.4 +26.5
Steps
(reduced) 		15
(0) 		24
(9) 		35
(5) 		42
(12) 		52
(7) 		56
(11) 		62
(2) 		64
(4) 		68
(8) 		73
(13) 		75
(0)


15edo for comparison:

Approximation of prime harmonics in 15edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +18.0 +13.7 -8.8 +8.7 +39.5 -25.0 +22.5 +11.7 +10.4 -25.0
Relative (%) +0.0 +22.6 +17.1 -11.0 +10.9 +49.3 -31.2 +28.1 +14.7 +13.0 -31.3
Steps
(reduced) 		15
(0) 		24
(9) 		35
(5) 		42
(12) 		52
(7) 		56
(11) 		61
(1) 		64
(4) 		68
(8) 		73
(13) 		74
(14)

Intervals

  • 79.548
  • 159.097
  • 238.645
  • 318.193
  • 397.741
  • 477.29
  • 556.838
  • 636.386
  • 715.934
  • 795.483
  • 875.031
  • 954.579
  • 1034.128
  • 1113.676
  • 1193.224


17ed255/128

Harmonics

Approximation of prime harmonics in 17ed255/128
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.8 -6.8 +21.3 +0.3 -10.1 -18.6 +8.3 +26.3 -23.7 -3.8 +21.1
Relative (%) -9.7 -9.7 +30.3 +0.4 -14.4 -26.5 +11.9 +37.5 -33.7 -5.5 +30.0
Steps
(reduced) 		17
(0) 		27
(10) 		40
(6) 		48
(14) 		59
(8) 		63
(12) 		70
(2) 		73
(5) 		77
(9) 		83
(15) 		85
(0)


17edo for comparison:

Approximation of prime harmonics in 17edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +3.9 -33.4 +19.4 +13.4 +6.5 -34.4 -15.2 +7.0 +29.2 -15.6
Relative (%) +0.0 +5.6 -47.3 +27.5 +19.0 +9.3 -48.7 -21.5 +9.9 +41.4 -22.1
Steps
(reduced) 		17
(0) 		27
(10) 		39
(5) 		48
(14) 		59
(8) 		63
(12) 		69
(1) 		72
(4) 		77
(9) 		83
(15) 		84
(16)

Intervals

  • 70.19
  • 140.379
  • 210.569
  • 280.759
  • 350.948
  • 421.138
  • 491.328
  • 561.517
  • 631.707
  • 701.897
  • 772.086
  • 842.276
  • 912.466
  • 982.655
  • 1052.845
  • 1123.034
  • 1193.224


18ed255/128

Harmonics

Approximation of odd harmonics in 18ed255/128
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +20.5 -2.1 +12.0 -25.4 +25.0 +0.9 +18.3 +0.5 +6.8 +32.4 +7.5
Relative (%) +30.9 -3.2 +18.1 -38.3 +37.7 +1.4 +27.7 +0.8 +10.3 +48.9 +11.4
Steps
(reduced) 		29
(11) 		42
(6) 		51
(15) 		57
(3) 		63
(9) 		67
(13) 		71
(17) 		74
(2) 		77
(5) 		80
(8) 		82
(10)


18edo for comparison:

Approximation of odd harmonics in 18edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +31.4 +13.7 +31.2 -3.9 -18.0 +26.1 -21.6 +28.4 -30.8 -4.1 -28.3
Relative (%) +47.1 +20.5 +46.8 -5.9 -27.0 +39.2 -32.4 +42.6 -46.3 -6.2 -42.4
Steps
(reduced) 		29
(11) 		42
(6) 		51
(15) 		57
(3) 		62
(8) 		67
(13) 		70
(16) 		74
(2) 		76
(4) 		79
(7) 		81
(9)

Intervals

  • 66.29
  • 132.58
  • 198.871
  • 265.161
  • 331.451
  • 397.741
  • 464.032
  • 530.322
  • 596.612
  • 662.902
  • 729.193
  • 795.483
  • 861.773
  • 928.063
  • 994.353
  • 1060.644
  • 1126.934
  • 1193.224


27ed255/128

Harmonics

Approximation of prime harmonics in 27ed255/128
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.8 -1.6 -2.1 -10.1 +2.9 -21.2 +0.5 -15.3 +7.5 +4.0 +21.1
Relative (%) -15.3 -3.7 -4.8 -22.9 +6.5 -47.9 +1.2 -34.5 +17.0 +9.0 +47.7
Steps
(reduced) 		27
(0) 		43
(16) 		63
(9) 		76
(22) 		94
(13) 		100
(19) 		111
(3) 		115
(7) 		123
(15) 		132
(24) 		135
(0)


27edo for comparison:

Approximation of prime harmonics in 27edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +9.2 +13.7 +9.0 -18.0 +3.9 -16.1 +13.6 -6.1 -7.4 +10.5
Relative (%) +0.0 +20.6 +30.8 +20.1 -40.5 +8.8 -36.1 +30.6 -13.6 -16.5 +23.7
Steps
(reduced) 		27
(0) 		43
(16) 		63
(9) 		76
(22) 		93
(12) 		100
(19) 		110
(2) 		115
(7) 		122
(14) 		131
(23) 		134
(26)

Intervals

  • 44.193
  • 88.387
  • 132.58
  • 176.774
  • 220.967
  • 265.161
  • 309.354
  • 353.548
  • 397.741
  • 441.935
  • 486.128
  • 530.322
  • 574.515
  • 618.709
  • 662.902
  • 707.096
  • 751.289
  • 795.483
  • 839.676
  • 883.87
  • 928.063
  • 972.257
  • 1016.45
  • 1060.644
  • 1104.837
  • 1149.031
  • 1193.224


39ed255/128

Harmonics

Approximation of prime harmonics in 39ed255/128
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.8 -5.0 -2.1 -3.3 +9.7 -4.2 -9.7 +11.9 -12.9 +14.2 -9.5
Relative (%) -22.1 -16.5 -6.9 -10.9 +31.6 -13.7 -31.6 +39.0 -42.1 +46.3 -31.1
Steps
(reduced) 		39
(0) 		62
(23) 		91
(13) 		110
(32) 		136
(19) 		145
(28) 		160
(4) 		167
(11) 		177
(21) 		191
(35) 		194
(38)


39edo for comparison:

Approximation of prime harmonics in 39edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +5.7 +13.7 -15.0 +2.5 -9.8 -12.6 +10.2 -12.9 -14.2 -6.6
Relative (%) +0.0 +18.6 +44.5 -48.7 +8.2 -31.7 -41.1 +33.1 -41.9 -46.1 -21.4
Steps
(reduced) 		39
(0) 		62
(23) 		91
(13) 		109
(31) 		135
(18) 		144
(27) 		159
(3) 		166
(10) 		176
(20) 		189
(33) 		193
(37)


42ed255/128

42ed255/128 is a kind of opposite twin to the scale 42ed257/128, as they improve 42edo’s JI approximation by about the same amount, but in opposite directions (those harmonics which are slightly sharp in one are slightly flat in the other).

42ed255/128’s step size is very close to that of APS715jot and 191zpi.

See Table of stretched 42edo tunings for more.

Harmonics

Approximation of prime harmonics in 42ed255/128
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.8 +1.5 -2.1 +12.0 -3.4 -8.6 +10.0 -12.1 -1.9 -5.5 -7.3
Relative (%) -23.9 +5.4 -7.5 +42.2 -12.1 -30.1 +35.2 -42.6 -6.8 -19.4 -25.8
Steps
(reduced) 		42
(0) 		67
(25) 		98
(14) 		119
(35) 		146
(20) 		156
(30) 		173
(5) 		179
(11) 		191
(23) 		205
(37) 		209
(41)


42edo for comparison:

Approximation of prime harmonics in 42edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +12.3 +13.7 +2.6 -8.5 -12.0 +9.3 -11.8 +0.3 -1.0 -2.2
Relative (%) +0.0 +43.2 +47.9 +9.1 -29.6 -41.8 +32.7 -41.3 +1.0 -3.5 -7.6
Steps
(reduced) 		42
(0) 		67
(25) 		98
(14) 		118
(34) 		145
(19) 		155
(29) 		172
(4) 		178
(10) 		190
(22) 		204
(36) 		208
(40)

Scales


MOS scales
  • Eugene/Tritikleismic[9]: 3 8 3 3 8 3 3 8 3
  • Eugene/Tritikleismic[15]: 3 3 2 3 3 3 3 2 3 3 3 3 2 3 3
  • Lemba[16]: 3 2 3 2 3 3 2 3 3 2 3 2 3 3 2 3
  • Qeema/Skateboard[15]: 2 5 2 2 2 5 2 2 2 5 2 2 2 5 2
  • Qeema/Skateboard[19]: 2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2
  • Seville/Sevond[14] 1st mode: 1 5 1 5 1 5 1 5 1 5 1 5 1 5
  • Seville/Sevond[14] 2nd mode: 5 1 5 1 5 1 5 1 5 1 5 1 5 1
  • Seville/Sevond[21]: 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4


Subsets of MOS scales

(Names used are idiosyncratic.)

  • Eugene/Tritikleismic[9]
    • Groovy aeolian pentatonic: 11 6 8 3 14
    • Otonal mixolydian pentatonic: 14 3 8 11 6
    • Pseudo-equipentatonic: 11 6 8 6 11
    • Septimal melodic minor pentatonic: 8 3 14 14 3
    • Septimal Picardy pentatonic: 8 6 11 3 14
    • Undecimal lydian-aeolian pentatonic: 8 14 3 11 6
    • Yokai pentatonic: 3 14 8 3 14


49ed255/128

Harmonics

Approximation of prime harmonics in 49ed255/128
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.8 -2.5 -10.2 -8.3 -11.6 -8.6 -10.3 -8.0 +2.1 -9.6 -3.3
Relative (%) -27.8 -10.4 -42.1 -34.2 -47.5 -35.1 -42.3 -33.0 +8.7 -39.3 -13.4
Steps
(reduced) 		49
(0) 		78
(29) 		114
(16) 		138
(40) 		170
(23) 		182
(35) 		201
(5) 		209
(13) 		223
(27) 		239
(43) 		244
(48)


49edo for comparison:

Approximation of prime harmonics in 49edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +8.2 +5.5 +10.8 +11.9 -7.9 -7.0 -3.6 +8.5 -1.0 +6.0
Relative (%) +0.0 +33.7 +22.6 +44.0 +48.8 -32.2 -28.6 -14.8 +34.5 -4.1 +24.4
Steps
(reduced) 		49
(0) 		78
(29) 		114
(16) 		138
(40) 		170
(23) 		181
(34) 		200
(4) 		208
(12) 		222
(26) 		238
(42) 		243
(47)


54ed255/128

Harmonics

Approximation of prime harmonics in 54ed255/128
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.78 -1.64 -2.12 -10.12 +2.87 +0.92 +0.52 +6.83 +7.52 +3.96 -1.01
Relative (%) -30.7 -7.4 -9.6 -45.8 +13.0 +4.2 +2.4 +30.9 +34.1 +17.9 -4.6
Steps
(reduced) 		54
(0) 		86
(32) 		126
(18) 		152
(44) 		188
(26) 		201
(39) 		222
(6) 		231
(15) 		246
(30) 		264
(48) 		269
(53)


54edo for comparison:

Approximation of prime harmonics in 54edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +9.16 -8.54 +8.95 +4.24 +3.92 +6.16 -8.62 -6.05 -7.35 +10.52
Relative (%) +0.0 +41.2 -38.4 +40.3 +19.1 +17.6 +27.7 -38.8 -27.2 -33.1 +47.3
Steps
(reduced) 		54
(0) 		86
(32) 		125
(17) 		152
(44) 		187
(25) 		200
(38) 		221
(5) 		229
(13) 		244
(28) 		262
(46) 		268
(52)


Related concepts

Retrieved from "https://en.xen.wiki/index.php?title=User:BudjarnLambeth/Ed255/128&oldid=196589"