Ploidacot/Diploid alpha-tricot: Difference between revisions
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{{Infobox ploidacot|Ploids=2|Shears=1|Cots=3|Pergen=[P8/2, P4/3]|Forms=6, 8, 14|Title=Diploid alpha-tricot|Wedgie=6}} | {{Infobox ploidacot|Ploids=2|Shears=1|Cots=3|Pergen=[P8/2, P4/3]|Forms=6, 8, 14, 22|Title=Diploid alpha-tricot|Wedgie=6}} | ||
'''Diploid alpha-tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a stack of a period and a perfect fifth (433.98{{c}}), but the alternative generator with size a third of a perfect fourth is rather easier to grasp. | '''Diploid alpha-tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a stack of a period and a perfect fifth (433.98{{c}}), but the alternative generator with size a third of a perfect fourth is rather easier to grasp. | ||
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== Intervals and notation == | == Intervals and notation == | ||
Diploid alpha-tricot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. | Diploid alpha-tricot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. Note and interval names are provided where diploid alpha-dicot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]). | ||
{| class="wikitable" | |||
|- | |||
! rowspan="2" | # | |||
! colspan="3" | Ploid 1 | |||
! colspan="3" | Ploid 2 | |||
|- | |||
! Cents | |||
! Notation | |||
! Name | |||
! Cents | |||
! Notation | |||
! Name | |||
|- | |||
| −12 | |||
| 407.820 | |||
| E | |||
| major third | |||
| 1007.820 | |||
| | |||
| | |||
|- | |||
| −11 | |||
| 573.835 | |||
| | |||
| | |||
| 1173.835 | |||
| | |||
| | |||
|- | |||
| −10 | |||
| 139.850 | |||
| | |||
| | |||
| 739.850 | |||
| | |||
| | |||
|- | |||
| −9 | |||
| 305.865 | |||
| | |||
| | |||
| 905.865 | |||
| A | |||
| major sixth | |||
|- | |||
| −8 | |||
| 471.880 | |||
| | |||
| | |||
| 1071.880 | |||
| | |||
| | |||
|- | |||
| −7 | |||
| 37.895 | |||
| | |||
| | |||
| 637.895 | |||
| | |||
| | |||
|- | |||
| −6 | |||
| 203.910 | |||
| D | |||
| major second | |||
| 803.910 | |||
| | |||
| | |||
|- | |||
| −5 | |||
| 369.925 | |||
| | |||
| | |||
| 969.925 | |||
| | |||
| | |||
|- | |||
| −4 | |||
| 535.940 | |||
| | |||
| | |||
| 1135.940 | |||
| | |||
| | |||
|- | |||
| -3 | |||
| 101.955 | |||
| | |||
| | |||
| 701.955 | |||
| G | |||
| perfect fifth | |||
|- | |||
| −2 | |||
| 267.970 | |||
| | |||
| | |||
| 867.970 | |||
| | |||
| | |||
|- | |||
| −1 | |||
| 433.985 | |||
| | |||
| | |||
| 1033.985 | |||
| | |||
| | |||
|- | |||
| 0 | |||
| 0 | |||
| C | |||
| perfect unison | |||
| 600 | |||
| | |||
| | |||
|- | |||
| 1 | |||
| 166.015 | |||
| | |||
| | |||
| 766.015 | |||
| | |||
| | |||
|- | |||
| 2 | |||
| 332.030 | |||
| | |||
| | |||
| 932.030 | |||
| | |||
| | |||
|- | |||
| 3 | |||
| 498.045 | |||
| F | |||
| perfect fourth | |||
| 1098.045 | |||
| | |||
| | |||
|- | |||
| 4 | |||
| 64.060 | |||
| | |||
| | |||
| 664.060 | |||
| | |||
| | |||
|- | |||
| 5 | |||
| 230.075 | |||
| | |||
| | |||
| 830.075 | |||
| | |||
| | |||
|- | |||
| 6 | |||
| 396.090 | |||
| | |||
| | |||
| 996.090 | |||
| Bb | |||
| minor seventh | |||
|- | |||
| 7 | |||
| 562.105 | |||
| | |||
| | |||
| 1162.105 | |||
| | |||
| | |||
|- | |||
| 8 | |||
| 128.120 | |||
| | |||
| | |||
| 728.120 | |||
| | |||
| | |||
|- | |||
| 9 | |||
| 294.135 | |||
| Eb | |||
| minor third | |||
| 894.135 | |||
| | |||
| | |||
|- | |||
| 10 | |||
| 460.150 | |||
| | |||
| | |||
| 1060.150 | |||
| | |||
| | |||
|- | |||
| 11 | |||
| 26.165 | |||
| | |||
| | |||
| 626.165 | |||
| | |||
| | |||
|- | |||
| 12 | |||
| 192.180 | |||
| | |||
| | |||
| 792.180 | |||
| Ab | |||
| minor sixth | |||
|} | |||
== Temperament interpretations == | == Temperament interpretations == | ||
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The larger generator is equated to [[9/7]] and the smaller one to [[11/10]], treating the period as [[99/70]]. This is also equated to [[17/12]], which leads to the stack of three large generators being [[17/8]]. | The larger generator is equated to [[9/7]] and the smaller one to [[11/10]], treating the period as [[99/70]]. This is also equated to [[17/12]], which leads to the stack of three large generators being [[17/8]]. | ||
[[Category:Ploidacot]] | |||