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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.


256ed5 combines [[dual-fifth temperaments]] with [[quarter-comma meantone]].
256ed5 combines [[Dual-fifth system|dual-fifth systems]] with [[quarter-comma meantone]].


== Theory ==
== Theory ==
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"
{| class="wikitable"
|+Approximation of prime harmonics in 256 e.d. 5
|+
|'''P'''
!Step
|2
!Name
|3
!Size (cents)
|5
!Size (millipentaves)
|7
!Associated ratio
|11
|13
|17
|19
|23
|-
|-
|'''Error (rc)'''
|25
| -26
|0
|0
| -48
|prime, unison
|41
|0
| -1
|0
| -34
|exact 1/1
|35
| -26
|-
|-
|'''Steps (reduced)'''
|29
|110 (110)
|classical minor third
|175 (175)
|315.63710
|256 (256)
|113.28125
|310 (54)
|6/5
|381 (125)
|-
|408 (152)
|64
|451 (195)
|minor fifth
|468 (212)
|[[Quarter-comma meantone|696.57843]]
|499 (243)
|250
|3/2 I, exact 4th root of(5)
|-
|65
|major fifth
|
|253.90625
|
|-
|128
|octitone, symmetric ninth
|1393.15686
|500
|
|-
|256
|pentave, fifth harmonic
|2786.31371
|1000
|exact 5/1
|}
|}
In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occuring almost halfway between the [[quarter-comma meantone]] fifth and it's next step.
 
== See also ==
* [[Ed5]]
* [[110edo]]
 
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/256ed5"