256ed5: Difference between revisions
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'''256 equal divisions of the 5th harmonic''' is an equal-step tuning of 10.884 cents | {{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 | 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. | 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. | 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 | |||
|- | |||
|64 | |||
|minor fifth | |||
|[[Quarter-comma meantone|696.57843]] | |||
|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 | |||
|} | |||
== See also == | == See also == | ||
| Line 13: | Line 73: | ||
* [[110edo]] | * [[110edo]] | ||
{{todo|expand}} | |||