User:BudjarnLambeth/Ed255/128: Difference between revisions

← Older edit

VisualWikitext

@@ 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=prime}}
+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]].
-edo, [[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=prime|collapsed=1}}
-{{Harmonics in equal|8|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|14|7|1|intervals=prime|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 ==
@@ Line 24: / Line 13: @@
-[[6edo]] for comparison:
+edo for comparison:
 {{Harmonics in equal|6|intervals=odd|collapsed=1}}
@@ Line 33: / Line 22: @@
 * 795.483
 * 994.353
-* 1193.224
-== 8ed255/128 ==
-=== Harmonics ===
-{{Harmonics in equal|8|255|128|intervals=odd}}
-[[8edo]] for comparison:
-{{Harmonics in equal|8|intervals=odd|collapsed=1}}
-=== Intervals ===
-* 149.153
-* 298.306
-* 447.459
-* 596.612
-* 745.765
-* 894.918
-* 1044.071
 * 1193.224
@@ Line 246: / Line 217: @@
 ** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6'''
 ** Yokai pentatonic: '''3 14 8 3 14'''
 == 49ed255/128 ==
@@ Line 254: / Line 227: @@
 [[49edo]] for comparison:
 {{Harmonics in equal|49|intervals=prime|collapsed=1}}
 == 54ed255/128 ==
@@ Line 262: / Line 237: @@
 [[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:5-tone scales]]