9edf: Difference between revisions
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→Theory: mention difference with Carlos Alpha |
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== Theory == | == Theory == | ||
9edf corresponds to 15. | 9edf corresponds to 15.385602edo. It is closely related to [[Carlos Alpha]] (though the Carlos Alpha generator is 0.03{{C}} narrower at 77.965{{C}}), and can be used as a temperament of the 3/2.5/4.8/7.11/8 subgroup. [[Valentine]] can be seen as 9edf with an independent dimension for 2. | ||
=== Harmonics === | === Harmonics === | ||
| Line 63: | Line 63: | ||
|- | |- | ||
| 9 | | 9 | ||
| | | 702.0 | ||
| [[3/2]] | | [[3/2]] | ||
| C | | C | ||
| Line 69: | Line 69: | ||
== Scales == | == Scales == | ||
{{Idiosyncratic terms}} | |||
{| class="wikitable sortable" | |||
|+ | |||
! rowspan="2" | Name | |||
! rowspan="2" | Step pattern within 1 period | |||
! colspan="3" | Interval of repetition | |||
! rowspan="2" | First described by | |||
|- | |||
! (In 9edf steps) | |||
! (In cents) | |||
! (Nearby JI) | |||
|- | |||
| Molten [[slendro]] | |||
| 3 | |||
For exact [[cents]] values see [[User:BudjarnLambeth/Longer versions of scales#9edf]]. | | 3 | ||
| 234.0 | |||
| [[8/7]] | |||
| ''[[Budjarn Lambeth]] (2023)'' | |||
|- | |||
| Pylon | |||
| 6 3 | |||
| 9 | |||
| 702.0 | |||
| [[3/2]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Quest | |||
| 7 2 | |||
| 9 | |||
| 702.0 | |||
| [[3/2]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Snowcone | |||
| 3 6 | |||
| 9 | |||
| 702.0 | |||
| [[3/2]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Molten [[pelog]] | |||
| 2 2 5 2 5 | |||
| 16 | |||
| 1247.9 | |||
| [[33/16]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Swan | |||
| 4 5 4 5 4 5 4 | |||
| 31 | |||
| 2417.8 | |||
| [[4/1]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Livewire | |||
| 1 8 1 8 1 8 1 8 1 8 1 | |||
| 46 | |||
| 3587.8 | |||
| [[8/1]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Purgatory | |||
| 8 1 8 1 8 1 8 1 8 1 8 1 8 | |||
| 62 | |||
| 4835.7 | |||
| [[16/1]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Cloudscape | |||
| 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 | |||
| 72 | |||
| 5615.6 | |||
| [[128/5]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|- | |||
| Corrugated | |||
| 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 | |||
| 135 | |||
| 10529.3 | |||
| [[437/1]] | |||
| ''Budjarn Lambeth (2023)'' | |||
|} | |||
None of these scales are approximated from another tuning unless specified otherwise. For exact [[cents]] values see [[User:BudjarnLambeth/Longer versions of scales#9edf]]. | |||
== Music == | == Music == | ||
See [[Carlos Alpha #Music]]. Many are tuned to exactly 9edf. | See [[Carlos Alpha #Music]]. Many are tuned to exactly 9edf. | ||
== See also == | |||
* [[Alpha, beta, and gamma family of equal divisions]] | |||
[[Category:Listen]] | [[Category:Listen]] | ||