6ed5: Difference between revisions
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Expand stub page with a couple short paragraphs about harmonics and subgroups, and a manually curated interval table |
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{{ED intro}} | {{ED intro}} | ||
== | == Harmonics == | ||
6ed5 does not approximate any sensible [[subgroup]] of integer [[harmonic]]s. If one does try to interpret it using an integer subgroup, then it looks something like a 5.19.33 subgroup: which has severely limited use cases. | |||
6ed5 does however have some [[chord]]s and [[interval]]s that sound good for its size, despite its poor approximations of pure harmonics. These shine when it is interpreted using a [[Subgroup temperaments#Fractional subgroup temperaments|fractional subgroup]]. | |||
{{Harmonics in equal | {{Harmonics in equal | ||
| steps = 6 | | steps = 6 | ||
| Line 15: | Line 15: | ||
| num = 5 | | num = 5 | ||
| denom = 1 | | denom = 1 | ||
| collapsed = yes | |||
| start = 12 | | start = 12 | ||
| | | columns = 14 | ||
| title = (higher harmonics) | |||
}} | }} | ||
== Intervals == | |||
{| class="wikitable mw-collapsible" | |||
|+ | |||
!Step | |||
!Interval (¢) | |||
!JI approximated <br>(subgroup A) | |||
!JI approximated <br>(subgroup B) | |||
!JI approximated <br>(subgroup C) | |||
|- | |||
|1 | |||
|424.39 | |||
|9/7 | |||
|14/11 | |||
|23/18 | |||
|- | |||
|2 | |||
|928.77 | |||
|12/7 | |||
|12/7 | |||
|53/31 | |||
|- | |||
|3 | |||
|1393.16 | |||
|9/4 | |||
|29/13 | |||
|38/17 | |||
|- | |||
|4 | |||
|1857.54 | |||
|29/10 | |||
|35/12 | |||
|38/13 | |||
|- | |||
|5 | |||
|2321.93 | |||
|19/5 | |||
|23/6 | |||
|65/17 | |||
|- | |||
|6 | |||
|2786.31 | |||
|5/1 | |||
|5/1 | |||
|5/1 | |||
|} | |||
* Subgroup A = low complexity subgroup: 5/1.9/4.9/7.12/7.19/5.29/10 | |||
* Subgroup B = compromise subgroup: 5/1.12/7.14/11.23/6.29/13.35/12 | |||
* Subgroup C = low error subgroup: 5/1.23/18.38/13.38/17.53/31.65/17 | |||
Other interpretations are possible. | |||
{{todo|expand|intro}} | |||