User:BudjarnLambeth/Ed255/128: Difference between revisions

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* 954.579
* 954.579
* 1193.224
* 1193.224
== 6ed255/128 ==
=== Harmonics ===
{{Harmonics in equal|6|255|128|intervals=integer}}
6edo for comparison:
{{Harmonics in equal|6|intervals=integer|collapsed=1}}
=== Intervals ===
* 198.871
* 397.741
* 596.612
* 795.483
* 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
== 11ed255/128 ==
=== Harmonics ===
{{Harmonics in equal|11|255|128|intervals=integer}}
[[11edo]] for comparison:
{{Harmonics in equal|11|intervals=integer|collapsed=1}}
=== 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 ==
''See also: [[5- to 10-tone scales in zeta stretched 15edo]]''
=== Harmonics ===
{{Harmonics in equal|15|255|128|intervals=integer}}
[[15edo]] for comparison:
{{Harmonics in equal|15|intervals=integer|collapsed=1}}
=== 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 ===
{{Harmonics in equal|17|255|128|intervals=integer}}
[[17edo]] for comparison:
{{Harmonics in equal|17|intervals=integer|collapsed=1}}
=== 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 ===
{{Harmonics in equal|18|255|128|intervals=integer}}
[[18edo]] for comparison:
{{Harmonics in equal|18|intervals=integer|collapsed=1}}
=== 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 ===
{{Harmonics in equal|27|255|128|intervals=integer}}
[[27edo]] for comparison:
{{Harmonics in equal|27|intervals=integer|collapsed=1}}
=== 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


== Related concepts ==
== Related concepts ==

Revision as of 11:36, 4 February 2024

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 5edo.

5ed255/128

Harmonics

Approximation of harmonics in 5ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -7 +7 -14 +77 +0 -28 -20 +14 +71 -94 -6
Relative (%) -2.8 +3.0 -5.7 +32.4 +0.2 -11.6 -8.5 +6.0 +29.6 -39.5 -2.7
Steps
(reduced) 		5
(0) 		8
(3) 		10
(0) 		12
(2) 		13
(3) 		14
(4) 		15
(0) 		16
(1) 		17
(2) 		17
(2) 		18
(3)


5edo, 8edt, 14ed7 for comparison:

Approximation of harmonics in 5edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0 +18 +0 +94 +18 -9 +0 +36 +94 -71 +18
Relative (%) +0.0 +7.5 +0.0 +39.0 +7.5 -3.7 +0.0 +15.0 +39.0 -29.7 +7.5
Steps
(reduced) 		5
(0) 		8
(3) 		10
(0) 		12
(2) 		13
(3) 		14
(4) 		15
(0) 		16
(1) 		17
(2) 		17
(2) 		18
(3)
Approximation of harmonics in 8edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -11 +0 -23 +67 -11 -40 -34 +0 +55 -110 -23
Relative (%) -4.7 +0.0 -9.5 +28.0 -4.7 -17.0 -14.2 +0.0 +23.3 -46.1 -9.5
Steps
(reduced) 		5
(5) 		8
(0) 		10
(2) 		12
(4) 		13
(5) 		14
(6) 		15
(7) 		16
(0) 		17
(1) 		17
(1) 		18
(2)
Approximation of harmonics in 14ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3 +23 +6 +101 +26 +0 +9 +46 +104 -61 +29
Relative (%) +1.3 +9.6 +2.6 +42.1 +10.9 +0.0 +3.9 +19.2 +43.4 -25.2 +12.2
Steps
(reduced) 		5
(5) 		8
(8) 		10
(10) 		12
(12) 		13
(13) 		14
(0) 		15
(1) 		16
(2) 		17
(3) 		17
(3) 		18
(4)

Intervals

  • 238.645
  • 477.29
  • 715.934
  • 954.579
  • 1193.224


6ed255/128

Harmonics

Approximation of harmonics in 6ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.8 +86.8 -13.6 -2.1 +80.0 +12.0 -20.3 -25.4 -8.9 +25.0 +73.2
Relative (%) -3.4 +43.6 -6.8 -1.1 +40.2 +6.0 -10.2 -12.8 -4.5 +12.6 +36.8
Steps
(reduced) 		6
(0) 		10
(4) 		12
(0) 		14
(2) 		16
(4) 		17
(5) 		18
(0) 		19
(1) 		20
(2) 		21
(3) 		22
(4)


6edo for comparison:

Approximation of harmonics in 6edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 +98.0 +0.0 +13.7 +98.0 +31.2 +0.0 -3.9 +13.7 +48.7 +98.0
Relative (%) +0.0 +49.0 +0.0 +6.8 +49.0 +15.6 +0.0 -2.0 +6.8 +24.3 +49.0
Steps
(reduced) 		6
(0) 		10
(4) 		12
(0) 		14
(2) 		16
(4) 		17
(5) 		18
(0) 		19
(1) 		20
(2) 		21
(3) 		22
(4)

Intervals

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


8ed255/128

Harmonics

Approximation of harmonics in 8ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.8 +37.0 -13.6 +47.6 +30.3 +61.7 -20.3 +74.1 +40.8 +25.0 +23.5
Relative (%) -4.5 +24.8 -9.1 +31.9 +20.3 +41.4 -13.6 +49.7 +27.4 +16.7 +15.7
Steps
(reduced) 		8
(0) 		13
(5) 		16
(0) 		19
(3) 		21
(5) 		23
(7) 		24
(0) 		26
(2) 		27
(3) 		28
(4) 		29
(5)


8edo for comparison:

Approximation of harmonics in 8edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 +48.0 +0.0 +63.7 +48.0 -68.8 +0.0 -53.9 +63.7 +48.7 +48.0
Relative (%) +0.0 +32.0 +0.0 +42.5 +32.0 -45.9 +0.0 -35.9 +42.5 +32.5 +32.0
Steps
(reduced) 		8
(0) 		13
(5) 		16
(0) 		19
(3) 		21
(5) 		22
(6) 		24
(0) 		25
(1) 		27
(3) 		28
(4) 		29
(5)

Intervals

  • 149.153
  • 298.306
  • 447.459
  • 596.612
  • 745.765
  • 894.918
  • 1044.071
  • 1193.224


11ed255/128

Harmonics

Approximation of harmonics in 11ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.8 +50.6 -13.6 +34.0 +43.8 -6.1 -20.3 -7.3 +27.3 -29.3 +37.0
Relative (%) -6.2 +46.6 -12.5 +31.4 +40.4 -5.6 -18.7 -6.7 +25.1 -27.0 +34.1
Steps
(reduced) 		11
(0) 		18
(7) 		22
(0) 		26
(4) 		29
(7) 		31
(9) 		33
(0) 		35
(2) 		37
(4) 		38
(5) 		40
(7)


11edo for comparison:

Approximation of harmonics in 11edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -47.4 +0.0 +50.0 -47.4 +13.0 +0.0 +14.3 +50.0 -5.9 -47.4
Relative (%) +0.0 -43.5 +0.0 +45.9 -43.5 +11.9 +0.0 +13.1 +45.9 -5.4 -43.5
Steps
(reduced) 		11
(0) 		17
(6) 		22
(0) 		26
(4) 		28
(6) 		31
(9) 		33
(0) 		35
(2) 		37
(4) 		38
(5) 		39
(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

See also: 5- to 10-tone scales in zeta stretched 15edo


Harmonics

Approximation of harmonics in 15ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.8 +7.2 -13.6 -2.1 +0.4 -27.8 -20.3 +14.4 -8.9 -14.8 -6.3
Relative (%) -8.5 +9.1 -17.0 -2.7 +0.5 -34.9 -25.6 +18.1 -11.2 -18.6 -8.0
Steps
(reduced) 		15
(0) 		24
(9) 		30
(0) 		35
(5) 		39
(9) 		42
(12) 		45
(0) 		48
(3) 		50
(5) 		52
(7) 		54
(9)


15edo for comparison:

Approximation of harmonics in 15edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 +36.1 +13.7 +8.7 +18.0
Relative (%) +0.0 +22.6 +0.0 +17.1 +22.6 -11.0 +0.0 +45.1 +17.1 +10.9 +22.6
Steps
(reduced) 		15
(0) 		24
(9) 		30
(0) 		35
(5) 		39
(9) 		42
(12) 		45
(0) 		48
(3) 		50
(5) 		52
(7) 		54
(9)

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 harmonics in 17ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.8 -6.8 -13.6 +21.3 -13.6 +0.3 -20.3 -13.7 +14.5 -10.1 -20.4
Relative (%) -9.7 -9.7 -19.3 +30.3 -19.4 +0.4 -29.0 -19.5 +20.7 -14.4 -29.0
Steps
(reduced) 		17
(0) 		27
(10) 		34
(0) 		40
(6) 		44
(10) 		48
(14) 		51
(0) 		54
(3) 		57
(6) 		59
(8) 		61
(10)


17edo for comparison:

Approximation of harmonics in 17edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 +3.9 +0.0 -33.4 +3.9 +19.4 +0.0 +7.9 -33.4 +13.4 +3.9
Relative (%) +0.0 +5.6 +0.0 -47.3 +5.6 +27.5 +0.0 +11.1 -47.3 +19.0 +5.6
Steps
(reduced) 		17
(0) 		27
(10) 		34
(0) 		39
(5) 		44
(10) 		48
(14) 		51
(0) 		54
(3) 		56
(5) 		59
(8) 		61
(10)

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 harmonics in 18ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.8 +20.5 -13.6 -2.1 +13.7 +12.0 -20.3 -25.4 -8.9 +25.0 +6.9
Relative (%) -10.2 +30.9 -20.4 -3.2 +20.6 +18.1 -30.7 -38.3 -13.4 +37.7 +10.4
Steps
(reduced) 		18
(0) 		29
(11) 		36
(0) 		42
(6) 		47
(11) 		51
(15) 		54
(0) 		57
(3) 		60
(6) 		63
(9) 		65
(11)


18edo for comparison:

Approximation of harmonics in 18edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 +31.4 +0.0 +13.7 +31.4 +31.2 +0.0 -3.9 +13.7 -18.0 +31.4
Relative (%) +0.0 +47.1 +0.0 +20.5 +47.1 +46.8 +0.0 -5.9 +20.5 -27.0 +47.1
Steps
(reduced) 		18
(0) 		29
(11) 		36
(0) 		42
(6) 		47
(11) 		51
(15) 		54
(0) 		57
(3) 		60
(6) 		62
(8) 		65
(11)

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 harmonics in 27ed255/128
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.8 -1.6 -13.6 -2.1 -8.4 -10.1 -20.3 -3.3 -8.9 +2.9 -15.2
Relative (%) -15.3 -3.7 -30.7 -4.8 -19.0 -22.9 -46.0 -7.4 -20.1 +6.5 -34.4
Steps
(reduced) 		27
(0) 		43
(16) 		54
(0) 		63
(9) 		70
(16) 		76
(22) 		81
(0) 		86
(5) 		90
(9) 		94
(13) 		97
(16)


27edo for comparison:

Approximation of harmonics in 27edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 +9.2 +0.0 +13.7 +9.2 +9.0 +0.0 +18.3 +13.7 -18.0 +9.2
Relative (%) +0.0 +20.6 +0.0 +30.8 +20.6 +20.1 +0.0 +41.2 +30.8 -40.5 +20.6
Steps
(reduced) 		27
(0) 		43
(16) 		54
(0) 		63
(9) 		70
(16) 		76
(22) 		81
(0) 		86
(5) 		90
(9) 		93
(12) 		97
(16)

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


Related concepts

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