Ploidacot/Enneacot: Difference between revisions
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{{Infobox ploidacot|Ploids=1|Shears=0|Cots=9|Pergen=[P8, P5/9]|Forms=15, 16, 31|Title=Enneacot|Wedgie=9}} | {{Infobox ploidacot|Ploids=1|Shears=0|Cots=9|Pergen=[P8, P5/9]|Forms=15, 16, 31|Title=Enneacot|Wedgie=9}} | ||
'''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 [[Ploidacot/Tricot|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. | ||
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[[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]]. | [[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]]. | ||
[[Category:Ploidacots]] | [[Category:Ploidacots|Enneacot]] | ||
Latest revision as of 10:33, 8 January 2026
| Pergen | [P8, P5/9] |
| Numeral form | 9-cot |
| Pure generator size | 78 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 15, 16, 31 |
| Characteristic multival entry | 9 |
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.
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 monocot intervals appear in this system.
| # | Cents | Notation | Name |
|---|---|---|---|
| −9 | 498.045 | F | perfect fourth |
| −8 | 576.040 | ||
| −7 | 654.035 | ||
| −6 | 732.030 | ||
| −5 | 810.025 | ||
| −4 | 888.020 | ||
| −3 | 966.015 | ||
| −2 | 1044.010 | ||
| −1 | 1122.005 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 77.995 | ||
| 2 | 155.990 | ||
| 3 | 233.985 | ||
| 4 | 311.980 | ||
| 5 | 389.975 | ||
| 6 | 467.970 | ||
| 7 | 545.965 | ||
| 8 | 623.960 | ||
| 9 | 701.955 | G | perfect fifth |
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; a few mappings of 13 are possible, the most accurate of which maps 20 generators to 32/13.