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-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}}
+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]].
+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 [[ed257/128]]s.
+== 6ed255/128 ==
+=== Harmonics ===
+{{Harmonics in equal|6|255|128|intervals=odd}}
+edo for comparison:
+{{Harmonics in equal|6|intervals=odd|collapsed=1}}
+=== Intervals ===
+* 198.871
+* 397.741
+* 596.612
+* 795.483
+* 994.353
+* 1193.224
+== 11ed255/128 ==
+=== Harmonics ===
+{{Harmonics in equal|11|255|128|intervals=odd}}
+[[11edo]] for comparison:
+{{Harmonics in equal|11|intervals=odd|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 ==
+ed255/128 is very close to [[zpi|47zpi]]. The [[5- to 10-tone scales in 47zpi]] are also useable in 15ed255/128.
-== 5ed255/128 ==
 === Harmonics ===
-{{Harmonics in equal|5|255|128|intervals=integer}}
+{{Harmonics in equal|15|255|128|intervals=prime}}
-edo, [[8edt]], [[14ed7]] for comparison:
+[[15edo]] for comparison:
-{{Harmonics in equal|5|intervals=integer|collapsed=1}}
+{{Harmonics in equal|15|intervals=prime|collapsed=1}}
-{{Harmonics in equal|8|3|1|intervals=integer|collapsed=1}}
-{{Harmonics in equal|14|7|1|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=prime}}
+[[17edo]] for comparison:
+{{Harmonics in equal|17|intervals=prime|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=odd}}
+[[18edo]] for comparison:
+{{Harmonics in equal|18|intervals=odd|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=prime}}
+[[27edo]] for comparison:
+{{Harmonics in equal|27|intervals=prime|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
+== 39ed255/128 ==
+=== Harmonics ===
+{{Harmonics in equal|39|255|128|intervals=prime}}
+[[39edo]] for comparison:
+{{Harmonics in equal|39|intervals=prime|collapsed=1}}
+== 42ed255/128 ==
+ed255/128 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).
+ed255/128’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 ==
-* [[Ed257/128]]
 * [[Substitute harmonic]]
 * [[Equal-step tuning]]
-[[Category:Edonoi]][[Category:5edo]]
+[[Category:Edonoi]][[Category:5edo]][[Category:5-tone scales]]

User:BudjarnLambeth/Ed255/128: Difference between revisions