Ploidacot/Gamma-hexacot: Difference between revisions
Jump to navigation
Jump to search
Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=3|Cots=6|Pergen=[P8, ccP4/6]|Forms=17, 22, 27, 32, 37|Title=Gamma-hexacot|Wedgie=6}} '''Gamma-hexacot ''' is a temperament archetype where the generator is a grave fourth of about 482–484{{c}}, six of which make 16/3 (perfect eighteenth, two octaves above a perfect fourth), and the period is a 2/1 octave. Gamma-hexacot temperaments also include all alpha-dicot and Ploidacot/Tricot|tr..." Tags: Mobile edit Mobile web edit |
No edit summary Tags: Mobile edit Mobile web edit |
||
| (One intermediate revision by the same user not shown) | |||
| Line 4: | Line 4: | ||
== Intervals and notation == | == Intervals and notation == | ||
While there is no agreed-upon notation system for gamma-hexacot, the following is based on interpreting the generator as a grave fourth, and allowing for an ^ or v to stand for 1/6 of a diatonic semitone, so ^^^C and vvvDb are enharmonic. | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 21: | Line 21: | ||
| −23 | | −23 | ||
| 890.828 | | 890.828 | ||
| | | vA | ||
| | | | ||
|- | |- | ||
| −22 | | −22 | ||
| 173.835 | | 173.835 | ||
| | | vvD | ||
| | | | ||
|- | |- | ||
| −21 | | −21 | ||
| 656.843 | | 656.843 | ||
| | | ^^^F#/vvvG | ||
| | | | ||
|- | |- | ||
| −20 | | −20 | ||
| 1139.850 | | 1139.850 | ||
| | | ^^B | ||
| | | | ||
|- | |- | ||
| −19 | | −19 | ||
| 422.858 | | 422.858 | ||
| | | ^E | ||
| | | | ||
|- | |- | ||
| Line 51: | Line 51: | ||
| −17 | | −17 | ||
| 188.873 | | 188.873 | ||
| | | vD | ||
| | | | ||
|- | |- | ||
| −16 | | −16 | ||
| 671.880 | | 671.880 | ||
| | | vvG | ||
| | | | ||
|- | |- | ||
| −15 | | −15 | ||
| 1154.888 | | 1154.888 | ||
| | | ^^^B/vvvC | ||
| | | | ||
|- | |- | ||
| −14 | | −14 | ||
| 437.895 | | 437.895 | ||
| | | ^^E | ||
| | | | ||
|- | |- | ||
| −13 | | −13 | ||
| 920.903 | | 920.903 | ||
| | | ^A | ||
| | | | ||
|- | |- | ||
| Line 81: | Line 81: | ||
| −11 | | −11 | ||
| 686.918 | | 686.918 | ||
| | | vG | ||
| | | | ||
|- | |- | ||
| −10 | | −10 | ||
| 1169.925 | | 1169.925 | ||
| | | vvC | ||
| | | | ||
|- | |- | ||
| −9 | | −9 | ||
| 452.933 | | 452.933 | ||
| | | ^^^E/vvvF | ||
| | | | ||
|- | |- | ||
| −8 | | −8 | ||
| 935.940 | | 935.940 | ||
| | | ^^A | ||
| | | | ||
|- | |- | ||
| −7 | | −7 | ||
| 218.948 | | 218.948 | ||
| | | ^D | ||
| | | | ||
|- | |- | ||
| Line 111: | Line 111: | ||
| −5 | | −5 | ||
| 1184.963 | | 1184.963 | ||
| | | vC | ||
| | | | ||
|- | |- | ||
| −4 | | −4 | ||
| 467.970 | | 467.970 | ||
| | | vvF | ||
| | | | ||
|- | |- | ||
| −3 | | −3 | ||
| 950.978 | | 950.978 | ||
| | | ^^^A/vvvBb | ||
| | | | ||
|- | |- | ||
| −2 | | −2 | ||
| 233.985 | | 233.985 | ||
| | | ^^D | ||
| | | | ||
|- | |- | ||
| −1 | | −1 | ||
| 716.993 | | 716.993 | ||
| | | ^G | ||
| | | | ||
|- | |- | ||
| Line 141: | Line 141: | ||
| 1 | | 1 | ||
| 483.007 | | 483.007 | ||
| | | vF | ||
| | | | ||
|- | |- | ||
| 2 | | 2 | ||
| 966.015 | | 966.015 | ||
| | | vvBb | ||
| | | | ||
|- | |- | ||
| 3 | | 3 | ||
| 249.022 | | 249.022 | ||
| | | ^^^D/vvvEb | ||
| | | | ||
|- | |- | ||
| 4 | | 4 | ||
| 732.030 | | 732.030 | ||
| | | ^^G | ||
| | | | ||
|- | |- | ||
| 5 | | 5 | ||
| 15.037 | | 15.037 | ||
| | | ^C | ||
| | | | ||
|- | |- | ||
| Line 171: | Line 171: | ||
| 7 | | 7 | ||
| 981.052 | | 981.052 | ||
| | | vBb | ||
| | | | ||
|- | |- | ||
| 8 | | 8 | ||
| 264.060 | | 264.060 | ||
| | | vvEb | ||
| | | | ||
|- | |- | ||
| 9 | | 9 | ||
| 747.067 | | 747.067 | ||
| | | ^^^G/vvvAb | ||
| | | | ||
|- | |- | ||
| 10 | | 10 | ||
| 30.075 | | 30.075 | ||
| | | ^^C | ||
| | | | ||
|- | |- | ||
| 11 | | 11 | ||
| 513.082 | | 513.082 | ||
| | | ^F | ||
| | | | ||
|- | |- | ||
| Line 201: | Line 201: | ||
| 13 | | 13 | ||
| 279.097 | | 279.097 | ||
| | | vEb | ||
| | | | ||
|- | |- | ||
| 14 | | 14 | ||
| 762.105 | | 762.105 | ||
| | | vvAb | ||
| | | | ||
|- | |- | ||
| 15 | | 15 | ||
| 45.112 | | 45.112 | ||
| | | ^^^C/vvvDb | ||
| | | | ||
|- | |- | ||
| 16 | | 16 | ||
| 528.120 | | 528.120 | ||
| | | ^^F | ||
| | | | ||
|- | |- | ||
| 17 | | 17 | ||
| 1011.127 | | 1011.127 | ||
| | | ^Bb | ||
| | | | ||
|- | |- | ||
| Line 231: | Line 231: | ||
| 19 | | 19 | ||
| 777.142 | | 777.142 | ||
| | | vAb | ||
| | | | ||
|- | |- | ||
| 20 | | 20 | ||
| 60.150 | | 60.150 | ||
| | | vvDb | ||
| | | | ||
|- | |- | ||
| 21 | | 21 | ||
| 543.157 | | 543.157 | ||
| | | ^^^F/vvvGb | ||
| | | | ||
|- | |- | ||
| 22 | | 22 | ||
| 1026.165 | | 1026.165 | ||
| | | ^^Bb | ||
| | | | ||
|- | |- | ||
| 23 | | 23 | ||
| 309.172 | | 309.172 | ||
| | | ^Eb | ||
| | | | ||
|- | |- | ||
| Line 261: | Line 261: | ||
== Temperament interpretations == | == Temperament interpretations == | ||
An obvious interpretation for gamma-hexacot is [[hemiseven]], where the generator is [[45/34]], two of which make [[7/4]], four make {{nowrap|[[26/17]]~[[32/21]]}} above an octave, | An obvious interpretation for gamma-hexacot is [[hemiseven]], where the generator is [[45/34]], two of which make [[7/4]], three make [[15/13]] above an octave, four make {{nowrap|[[26/17]]~[[32/21]]}} above an octave, six make [[4/3]] above two octaves, seven make [[30/17]] above two octaves, seventeen make [[9/5]] above six octaves, and nineteen make [[11/7]] above seven octaves. | ||
[[Category:Ploidacots|Gamma-hexacot]] | [[Category:Ploidacots|Gamma-hexacot]] | ||
Latest revision as of 07:39, 26 January 2026
| Pergen | [P8, ccP4/6] |
| Numeral form | 3-sheared 6-cot |
| Pure generator size | 483.01 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 17, 22, 27, 32, 37 |
| Characteristic multival entry | 6 |
Gamma-hexacot is a temperament archetype where the generator is a grave fourth of about 482–484 ¢, six of which make 16/3 (perfect eighteenth, two octaves above a perfect fourth), and the period is a 2/1 octave. Gamma-hexacot temperaments also include all alpha-dicot and tricot intervals. Gamma-hexacot temperaments typically generate the 5L 7s, 5L 12s, and 5L 17s MOS scales.
Intervals and notation
While there is no agreed-upon notation system for gamma-hexacot, the following is based on interpreting the generator as a grave fourth, and allowing for an ^ or v to stand for 1/6 of a diatonic semitone, so ^^^C and vvvDb are enharmonic.
| # | Cents | Notation | Name |
|---|---|---|---|
| −24 | 407.820 | E | major third |
| −23 | 890.828 | vA | |
| −22 | 173.835 | vvD | |
| −21 | 656.843 | ^^^F#/vvvG | |
| −20 | 1139.850 | ^^B | |
| −19 | 422.858 | ^E | |
| −18 | 905.865 | A | major sixth |
| −17 | 188.873 | vD | |
| −16 | 671.880 | vvG | |
| −15 | 1154.888 | ^^^B/vvvC | |
| −14 | 437.895 | ^^E | |
| −13 | 920.903 | ^A | |
| −12 | 203.910 | D | major second |
| −11 | 686.918 | vG | |
| −10 | 1169.925 | vvC | |
| −9 | 452.933 | ^^^E/vvvF | |
| −8 | 935.940 | ^^A | |
| −7 | 218.948 | ^D | |
| −6 | 701.955 | G | perfect fifth |
| −5 | 1184.963 | vC | |
| −4 | 467.970 | vvF | |
| −3 | 950.978 | ^^^A/vvvBb | |
| −2 | 233.985 | ^^D | |
| −1 | 716.993 | ^G | |
| 0 | 0.000 | C | perfect unison |
| 1 | 483.007 | vF | |
| 2 | 966.015 | vvBb | |
| 3 | 249.022 | ^^^D/vvvEb | |
| 4 | 732.030 | ^^G | |
| 5 | 15.037 | ^C | |
| 6 | 498.045 | F | perfect fourth |
| 7 | 981.052 | vBb | |
| 8 | 264.060 | vvEb | |
| 9 | 747.067 | ^^^G/vvvAb | |
| 10 | 30.075 | ^^C | |
| 11 | 513.082 | ^F | |
| 12 | 996.090 | Bb | minor seventh |
| 13 | 279.097 | vEb | |
| 14 | 762.105 | vvAb | |
| 15 | 45.112 | ^^^C/vvvDb | |
| 16 | 528.120 | ^^F | |
| 17 | 1011.127 | ^Bb | |
| 18 | 294.135 | Eb | minor third |
| 19 | 777.142 | vAb | |
| 20 | 60.150 | vvDb | |
| 21 | 543.157 | ^^^F/vvvGb | |
| 22 | 1026.165 | ^^Bb | |
| 23 | 309.172 | ^Eb | |
| 24 | 792.180 | Ab | minor sixth |
Temperament interpretations
An obvious interpretation for gamma-hexacot is hemiseven, where the generator is 45/34, two of which make 7/4, three make 15/13 above an octave, four make 26/17~32/21 above an octave, six make 4/3 above two octaves, seven make 30/17 above two octaves, seventeen make 9/5 above six octaves, and nineteen make 11/7 above seven octaves.