9edf: Difference between revisions
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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 | ||
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== Scales == | == Scales == | ||
{{Idiosyncratic terms}} | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ | |+ | ||
! rowspan="2" |Name | ! rowspan="2" | Name | ||
! rowspan="2" |Step pattern within 1 period | ! rowspan="2" | Step pattern within 1 period | ||
! colspan="3" |Interval of repetition | ! colspan="3" | Interval of repetition | ||
! rowspan="2" |First described by | ! rowspan="2" | First described by | ||
|- | |- | ||
!( | ! (In 9edf steps) | ||
!( | ! (In cents) | ||
!( | ! (Nearby JI) | ||
|- | |- | ||
|Molten [[slendro]] | | Molten [[slendro]] | ||
|3 | | 3 | ||
|3 | | 3 | ||
|234.0 | | 234.0 | ||
|[[8/7]] | | [[8/7]] | ||
|''[[Budjarn Lambeth]] (2023)'' | | ''[[Budjarn Lambeth]] (2023)'' | ||
|- | |- | ||
|Pylon | | Pylon | ||
|6 3 | | 6 3 | ||
|9 | | 9 | ||
|702.0 | | 702.0 | ||
|[[3/2]] | | [[3/2]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Quest | | Quest | ||
|7 2 | | 7 2 | ||
|9 | | 9 | ||
|702.0 | | 702.0 | ||
|[[3/2]] | | [[3/2]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Snowcone | | Snowcone | ||
|3 6 | | 3 6 | ||
|9 | | 9 | ||
|702.0 | | 702.0 | ||
|[[3/2]] | | [[3/2]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Molten [[pelog]] | | Molten [[pelog]] | ||
|2 2 5 2 5 | | 2 2 5 2 5 | ||
|16 | | 16 | ||
|1247.9 | | 1247.9 | ||
| | | [[33/16]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Swan | | Swan | ||
|4 5 4 5 4 5 4 | | 4 5 4 5 4 5 4 | ||
|31 | | 31 | ||
|2417.8 | | 2417.8 | ||
|[[4/1]] | | [[4/1]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Livewire | | Livewire | ||
|1 8 1 8 1 8 1 8 1 8 1 | | 1 8 1 8 1 8 1 8 1 8 1 | ||
|46 | | 46 | ||
|3587.8 | | 3587.8 | ||
|[[8/1]] | | [[8/1]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Purgatory | | Purgatory | ||
|8 1 8 1 8 1 8 1 8 1 8 1 8 | | 8 1 8 1 8 1 8 1 8 1 8 1 8 | ||
|62 | | 62 | ||
|4835.7 | | 4835.7 | ||
|[[16/1]] | | [[16/1]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Cloudscape | | Cloudscape | ||
|5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 | | 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 | ||
|72 | | 72 | ||
|5615.6 | | 5615.6 | ||
| | | [[128/5]] | ||
|''Budjarn Lambeth (2023)'' | | ''Budjarn Lambeth (2023)'' | ||
|- | |- | ||
|Corrugated | | 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 | | 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 | | 135 | ||
|10529.3 | | 10529.3 | ||
| | | [[437/1]] | ||
|''Budjarn Lambeth (2023)'' | | ''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]]. | None of these scales are approximated from another tuning unless specified otherwise. For exact [[cents]] values see [[User:BudjarnLambeth/Longer versions of scales#9edf]]. | ||
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== 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]] | ||