256ed5: Difference between revisions

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-'''256 equal divisions of the 5th harmonic''' is an equal-step tuning of 10.884 cents per each step. It is equivalent to 110.2532 EDO.
+{{Infobox ET}}
+'''256 equal divisions of the 5th harmonic''' is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.
-ed5 combines [[dual-fifth temperaments]] with [[quarter-comma meantone]].
+ed5 combines [[Dual-fifth system|dual-fifth systems]] with [[quarter-comma meantone]].
 == Theory ==
-{| class="wikitable center-all"
+In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.
+Uniquely, [[6/5]] is nearly perfect.
+== Harmonics ==
+{{Harmonics in equal
+| steps = 256
+| num = 5
+| denom = 1
+}}
+{{Harmonics in equal
+| steps = 256
+| num = 5
+| denom = 1
+| start = 12
+| collapsed = 1
+}}
+== Table of intervals ==
+{| class="wikitable"
+|+
+!Step
+!Name
+!Size (cents)
+!Size (millipentaves)
+!Associated ratio
+|-
+|0
+|prime, unison
+|0
+|0
+|exact 1/1
+|-
+|29
+|classical minor third
+|315.63710
+|113.28125
+|6/5
 |-
-|+Approximation of prime harmonics in 256 e.d. 5
+|64
+|minor fifth
+|[[Quarter-comma meantone|696.57843]]
+|250
+|3/2 I, exact 4th root of(5)
 |-
-! style="text-align:right" | Prime
+|65
-! 2
+|major fifth
-! 3
+|
-! 5
+|253.90625
-! 7
+|
-! 11
-! 13
-! 17
-! 19
-! 23
 |-
-! style="text-align:right" | Error (rc)
+|128
-| +25
+|octitone, symmetric ninth
-| -26
+|1393.15686
-| 0
+|500
-| -48
+|
-| +41
-| -1
-| -34
-| +35
-| -26
 |-
-! style="text-align:right" | Steps (reduced)
+|256
-| 110 (110)
+|pentave, fifth harmonic
-| 175 (175)
+|2786.31371
-| 256 (0)
+|1000
-| 310 (54)
+|exact 5/1
-| 381 (125)
-| 408 (152)
-| 451 (195)
-| 468 (212)
-| 499 (243)
 |}
-In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.
-[[Category:Ed5]]
+== See also ==
+* [[Ed5]]
+* [[110edo]]
+{{todo|expand}}