Ploidacot/Gamma-pentacot: Difference between revisions
Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=3|Cots=5|Pergen=[P8, P11/5]|Forms=7, 11, 18, 25|Title=Gamma-pentacot|Wedgie=5}} '''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Gamma-pentacot temperaments typically generate the 4L 3s and 7L 4s MOS scales, and they split the chromatic semitone into five equal parts, creating..." Tags: Mobile edit Mobile web edit |
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{{Infobox ploidacot|Ploids=1|Shears=3|Cots=5|Pergen=[P8, P11/5]|Forms=7, 11, 18, 25|Title=Gamma-pentacot|Wedgie=5}} | {{Infobox ploidacot|Ploids=1|Shears=3|Cots=5|Pergen=[P8, P11/5]|Forms=7, 11, 18, 25, 32|Title=Gamma-pentacot|Wedgie=5}} | ||
'''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Gamma-pentacot temperaments typically generate the [[4L 3s]] and [[7L 4s]] MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals. | '''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Gamma-pentacot temperaments typically generate the [[4L 3s]] and [[7L 4s]] MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals. | ||
Gamma-pentacot temperaments often generate [[7L 11s]], 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly | Gamma-pentacot temperaments often generate [[7L 11s]], 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly 18L 7s, 25L 7s, 32L 7s, or 39L 7s. | ||
== Intervals and notation == | == Intervals and notation == | ||
Revision as of 12:48, 5 January 2026
| Pergen | [P8, P11/5] |
| Numeral form | 3-sheared 5-cot |
| Pure generator size | 339.61 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 7, 11, 18, 25, 32 |
| Characteristic multival entry | 5 |
Gamma-pentacot is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Gamma-pentacot temperaments typically generate the 4L 3s and 7L 4s MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals.
Gamma-pentacot temperaments often generate 7L 11s, 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly 18L 7s, 25L 7s, 32L 7s, or 39L 7s.
Intervals and notation
While there is no agreed-upon notation system for gamma-pentacot, the notation provided here is based on interpreting the generator as a subneutral third, and allowing for an ^ or v to stand for 1/5 of a chromatic semitone, so ^^^C and vvC# are enharmonic.
| # | Cents | Notation | Name |
|---|---|---|---|
| −30 | 611.730 | F# | augmented fourth |
| −29 | 951.339 | ^^A | |
| −28 | 90.948 | vC# | |
| −27 | 430.557 | ^E | |
| −26 | 770.166 | vvG# | |
| −25 | 1109.775 | B | major seventh |
| −24 | 249.384 | ^^D | |
| −23 | 588.993 | vF# | |
| −22 | 928.602 | ^A | |
| −21 | 68.211 | vvC# | |
| −20 | 407.820 | E | major third |
| −19 | 747.429 | ^^G | |
| −18 | 1087.038 | vB | |
| −17 | 226.647 | ^D | |
| −16 | 566.256 | vvF# | |
| −15 | 905.865 | A | major sixth |
| −14 | 45.474 | ^^C | |
| −13 | 385.083 | vE | |
| −12 | 724.692 | ^G | |
| −11 | 1064.301 | vvB | |
| −10 | 203.910 | D | major second |
| −9 | 543.519 | ^^F | |
| −8 | 883.128 | vA | |
| −7 | 22.737 | ^C | |
| −6 | 362.346 | vvE | |
| −5 | 701.955 | G | perfect fifth |
| −4 | 1041.564 | ^^Bb | |
| −3 | 181.173 | vD | |
| −2 | 520.782 | ^F | |
| −1 | 860.391 | vvA | |
| 0 | 0.000 | C | perfect unison |
| 1 | 339.609 | ^^Eb | |
| 2 | 679.218 | vG | |
| 3 | 1018.827 | ^Bb | |
| 4 | 158.436 | vvD | |
| 5 | 498.045 | F | perfect fourth |
| 6 | 837.654 | ^^Ab | |
| 7 | 1177.263 | vC | |
| 8 | 316.872 | ^Eb | |
| 9 | 656.481 | vvG | |
| 10 | 996.090 | Bb | minor seventh |
| 11 | 135.699 | ^^Db | |
| 12 | 475.308 | vF | |
| 13 | 814.917 | ^Ab | |
| 14 | 1174.526 | vvC | |
| 15 | 294.135 | Eb | minor third |
| 16 | 633.744 | ^^Gb | |
| 17 | 973.353 | vBb | |
| 18 | 112.962 | ^Db | |
| 19 | 452.571 | vvF | |
| 20 | 792.180 | Ab | minor sixth |
| 21 | 1131.789 | ^^Cb | |
| 22 | 271.398 | vEb | |
| 23 | 611.007 | ^Gb | |
| 24 | 950.616 | vvBb | |
| 25 | 90.225 | Db | minor second |
| 26 | 429.834 | ^^Fb | |
| 27 | 769.443 | vAb | |
| 28 | 1109.052 | ^Cb | |
| 29 | 248.661 | vvEb | |
| 30 | 588.270 | Gb | diminished fifth |
Temperament interpretations
An obvious interpretation for gamma-pentacot is amity, 5/4 is equated to 4 octaves minus 13 generators, and 7/4 is equated to 17 generators minus 4 octaves. Other interpretations include sixix, which interprets 6/5 as a generator.