Ploidacot/Enneacot: Difference between revisions
mNo edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 3: | Line 3: | ||
'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three. | '''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[tricot]] intervals, as the tricot generator is split further into three. | ||
Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves. | Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves. | ||
== Intervals and notation == | == Intervals and notation == | ||
Due to dividing the fifth into so many steps, standard notation becomes almost useless for enneacot. Regardless, notation has been provided for where [[Ploidacot/Monocot|monocot]] intervals appear in this system. | Due to dividing the fifth into so many steps, standard notation becomes almost useless for enneacot. Regardless, notation has been provided for where [[Ploidacot/Monocot|monocot]] intervals appear in this system. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Enneacot intervals (assuming pure fifth and octave) | |+ style="font-size: 105%;" | Enneacot intervals (assuming pure fifth and octave) | ||
!# | |- | ||
!Cents | ! # | ||
!Notation | ! Cents | ||
!Name | ! Notation | ||
! Name | |||
|- | |- | ||
| | | −9 | ||
|498.045 | | 498.045 | ||
|F | | F | ||
|perfect fourth | | perfect fourth | ||
|- | |- | ||
| | | −8 | ||
|576.04 | | 576.04 | ||
| | | | ||
| | | | ||
|- | |- | ||
| | | −7 | ||
|654.035 | | 654.035 | ||
| | | | ||
| | | | ||
|- | |- | ||
| | | −6 | ||
|732.03 | | 732.03 | ||
| | | | ||
| | | | ||
|- | |- | ||
| | | −5 | ||
|810.025 | | 810.025 | ||
| | | | ||
| | | | ||
|- | |- | ||
| | | −4 | ||
|888.02 | | 888.02 | ||
| | | | ||
| | | | ||
|- | |- | ||
| | | −3 | ||
|966.015 | | 966.015 | ||
| | | | ||
| | | | ||
|- | |- | ||
| | | −2 | ||
|1044.01 | | 1044.01 | ||
| | | | ||
| | | | ||
|- | |- | ||
| | | −1 | ||
|1122.005 | | 1122.005 | ||
| | | | ||
| | | | ||
|- | |- | ||
|0 | | 0 | ||
|0 | | 0 | ||
|C | | C | ||
|perfect unison | | perfect unison | ||
|- | |- | ||
|1 | | 1 | ||
|77.995 | | 77.995 | ||
| | | | ||
| | | | ||
|- | |- | ||
|2 | | 2 | ||
|155.99 | | 155.99 | ||
| | | | ||
| | | | ||
|- | |- | ||
|3 | | 3 | ||
|233.985 | | 233.985 | ||
| | | | ||
| | | | ||
|- | |- | ||
|4 | | 4 | ||
|311.98 | | 311.98 | ||
| | | | ||
| | | | ||
|- | |- | ||
|5 | | 5 | ||
|389.975 | | 389.975 | ||
| | | | ||
| | | | ||
|- | |- | ||
|6 | | 6 | ||
|467.97 | | 467.97 | ||
| | | | ||
| | | | ||
|- | |- | ||
|7 | | 7 | ||
|545.965 | | 545.965 | ||
| | | | ||
| | | | ||
|- | |- | ||
|8 | | 8 | ||
|623.96 | | 623.96 | ||
| | | | ||
| | | | ||
|- | |- | ||
|9 | | 9 | ||
|701.955 | | 701.955 | ||
|G | | G | ||
|perfect fifth | | perfect fifth | ||
|} | |} | ||
== Temperament interpretations == | == Temperament interpretations == | ||
=== Valentine === | |||
[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]]. | |||
{{Todo| unify precision }} | {{Todo| unify precision }} | ||