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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}}


== 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


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== 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 47zpi]]''
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 203: Line 173:
== 39ed255/128 ==
== 39ed255/128 ==
=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|39|255|128|intervals=integer}}
{{Harmonics in equal|39|255|128|intervals=prime}}




[[39edo]] for comparison:
[[39edo]] for comparison:
{{Harmonics in equal|39|intervals=integer|collapsed=1}}
{{Harmonics in equal|39|intervals=prime|collapsed=1}}




== 42ed255/128 ==
== 42ed255/128 ==
42ed255/128 is almost identical to [[191zpi]]. 191zpi does slightly better at approximating most harmonics so it usually sense to choose 191zpi over 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 ===
{{Harmonics in equal|42|255|128|intervals=integer}}
{{Harmonics in equal|42|255|128|intervals=prime}}




[[42edo]] for comparison:
[[42edo]] for comparison:
{{Harmonics in equal|42|intervals=integer|collapsed=1}}
{{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 ==
== 49ed255/128 ==
=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|49|255|128|intervals=integer}}
{{Harmonics in equal|49|255|128|intervals=prime}}




[[49edo]] for comparison:
[[49edo]] for comparison:
{{Harmonics in equal|49|intervals=integer|collapsed=1}}
{{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]]
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