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# | {{Infobox ET}} | ||
{{ED intro}} | |||
== Theory == | |||
9edf corresponds to 15.385602edo. It is closely related to [[Carlos Alpha]], and can be used as a temperament of the [[Half-prime subgroup|3/2.5/4.7/8.11/8 subgroup]]. Carlos Alpha can be seen as 9edf with an independent dimension for 2. | |||
=== Harmonics === | |||
{{Harmonics in equal|9|3|2|columns=11}} | |||
{{Harmonics in equal|9|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 9edf (continued)}} | |||
== Intervals == | |||
{|class="wikitable center-1 right-2" | |||
|- | |||
! # | |||
! Cents | |||
! Approximate ratios | |||
! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 7\9edf | |||
|- | |||
| 0 | |||
| 0.0 | |||
| [[1/1]] | |||
| C | |||
|- | |||
| 1 | |||
| 78.0 | |||
| [[21/20]], [[22/21]], [[25/24]] | |||
| C# | |||
|- | |||
| 2 | |||
| 156.0 | |||
| [[11/10]], [[12/11]] | |||
| Db | |||
|- | |||
| 3 | |||
| 234.0 | |||
| [[8/7]] | |||
| D | |||
|- | |||
| 4 | |||
| 312.0 | |||
| [[6/5]] | |||
| D#, Eb | |||
|- | |||
| 5 | |||
| 390.0 | |||
| [[5/4]] | |||
| E | |||
|- | |||
| 6 | |||
| 468.0 | |||
| [[21/16]] | |||
| E#, Fb | |||
|- | |||
| 7 | |||
| 546.0 | |||
| [[11/8]], [[15/11]] | |||
| F | |||
|- | |||
| 8 | |||
| 624.0 | |||
| [[10/7]], [[36/25]] | |||
| F#, Cb | |||
|- | |||
| 9 | |||
| 701.9 | |||
| [[3/2]] | |||
| C | |||
|} | |||
== Scales == | |||
{| 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 | |||
|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 == | |||
See [[Carlos Alpha #Music]]. Many are tuned to exactly 9edf. | |||
[[Category:Listen]] | |||