Ploidacot/Diploid alpha-dicot: Difference between revisions
Found and added correct pergen Tags: Mobile edit Mobile web edit Advanced mobile edit |
m Removing from Category:Ploidacots using Cat-a-lot |
||
| (8 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
{{Breadcrumb}} | {{Breadcrumb}} | ||
{{Infobox ploidacot|Ploids=2|Shears=1|Cots=2|Pergen=[P8/2, M2/4]|Forms= | {{Infobox ploidacot|Ploids=2|Shears=1|Cots=2|Pergen=[P8/2, M2/4]|Forms=18, 20, 22, 24|Title=Diploid alpha-dicot|Wedgie=4}} | ||
'''Diploid alpha-dicot''' is a temperament archetype with a half-octave period, and a generator of a quartertone. In a pure tuning, this is exactly a quarter of [[9/8]]. | '''Diploid alpha-dicot''' is a temperament archetype with a half-octave period, and a generator of a quartertone. In a pure tuning, this is exactly a quarter of [[9/8]]. | ||
| Line 7: | Line 7: | ||
== Intervals and notation == | == Intervals and notation == | ||
Diploid alpha-dicot 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. As such, there is no universally accepted convention. Note and interval names are provided where diploid alpha-dicot intervals align with standard monocot intervals. | |||
{| class="wikitable" | |||
|+ style="font-size: 105%;" | Diploid alpha-dicot intervals (assuming pure fifth and octave) | |||
|- | |||
! rowspan="2" | # | |||
! colspan="3" | Ploid 1 | |||
! colspan="3" | Ploid 2 | |||
|- | |||
! Cents | |||
! Notation | |||
! Name | |||
! Cents | |||
! Notation | |||
! Name | |||
|- | |||
| −6 | |||
| 294.13 | |||
| Eb | |||
| minor third | |||
| 894.13 | |||
| — | |||
| — | |||
|- | |||
| −5 | |||
| 345.11 | |||
| — | |||
| — | |||
| 945.11 | |||
| — | |||
| — | |||
|- | |||
| −4 | |||
| 396.09 | |||
| — | |||
| — | |||
| 996.09 | |||
| Bb | |||
| minor seventh | |||
|- | |||
| −3 | |||
| 447.07 | |||
| — | |||
| — | |||
| 1047.07 | |||
| — | |||
| — | |||
|- | |||
| −2 | |||
| 498.04 | |||
| F | |||
| perfect fourth | |||
| 1098.04 | |||
| — | |||
| — | |||
|- | |||
| −1 | |||
| 549.02 | |||
| — | |||
| — | |||
| 1149.02 | |||
| — | |||
| — | |||
|- | |||
| 0 | |||
| 0 | |||
| C | |||
| unison | |||
| 600 | |||
| — | |||
| — | |||
|- | |||
| 1 | |||
| 50.98 | |||
| — | |||
| — | |||
| 650.98 | |||
| — | |||
| — | |||
|- | |||
| 2 | |||
| 101.96 | |||
| — | |||
| — | |||
| 701.96 | |||
| G | |||
| perfect fifth | |||
|- | |||
| 3 | |||
| 152.93 | |||
| — | |||
| — | |||
| 752.93 | |||
| — | |||
| — | |||
|- | |||
| 4 | |||
| 203.91 | |||
| D | |||
| major second | |||
| 803.91 | |||
| — | |||
| — | |||
|- | |||
| 5 | |||
| 254.89 | |||
| — | |||
| — | |||
| 854.89 | |||
| — | |||
| — | |||
|- | |||
| 6 | |||
| 305.87 | |||
| — | |||
| — | |||
| 905.87 | |||
| A | |||
| major sixth | |||
|} | |||
== Temperament interpretations == | == Temperament interpretations == | ||
Perhaps the most typical interpretation of this ploidacot is [[shrutar]]. The period is [[45/32]][[~]][[64/45]], and the generator is [[33/32]][[~]][[36/35]] | Perhaps the most typical interpretation of this ploidacot is [[shrutar]]. The period is [[45/32]][[~]][[64/45]], and the generator is [[33/32]][[~]][[36/35]], so that [[3/2]] is a period up two generators, [[5/4]] is found at a period down four generators, [[7/4]] at a period up seven generators, and [[11/8]] at a period down one generator. [[17/16]] can represent two generators, and the period can be expressed as [[17/12]][[~]][[24/17]] in the 17-limit. The generator is ideally tuned slightly sharp of pure-3 tuning. | ||
Latest revision as of 06:38, 16 July 2026
| Pergen | [P8/2, M2/4] |
| Numeral form | 2-ploid 1-sheared 2-cot |
| Pure generator size | 50.98 ¢ |
| Pure period size | 600 ¢ |
| Forms | 18, 20, 22, 24 |
| Characteristic multival entry | 4 |
Diploid alpha-dicot is a temperament archetype with a half-octave period, and a generator of a quartertone. In a pure tuning, this is exactly a quarter of 9/8.
Diploid alpha-dicot temperaments usually generate MOS structures with two large steps and many small ones, with reasonable hardness appearing somewhere around 2L 18s. As such, MOS scales can be less than useful in this region.
Intervals and notation
Diploid alpha-dicot 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. As such, there is no universally accepted convention. Note and interval names are provided where diploid alpha-dicot intervals align with standard monocot intervals.
| # | Ploid 1 | Ploid 2 | ||||
|---|---|---|---|---|---|---|
| Cents | Notation | Name | Cents | Notation | Name | |
| −6 | 294.13 | Eb | minor third | 894.13 | — | — |
| −5 | 345.11 | — | — | 945.11 | — | — |
| −4 | 396.09 | — | — | 996.09 | Bb | minor seventh |
| −3 | 447.07 | — | — | 1047.07 | — | — |
| −2 | 498.04 | F | perfect fourth | 1098.04 | — | — |
| −1 | 549.02 | — | — | 1149.02 | — | — |
| 0 | 0 | C | unison | 600 | — | — |
| 1 | 50.98 | — | — | 650.98 | — | — |
| 2 | 101.96 | — | — | 701.96 | G | perfect fifth |
| 3 | 152.93 | — | — | 752.93 | — | — |
| 4 | 203.91 | D | major second | 803.91 | — | — |
| 5 | 254.89 | — | — | 854.89 | — | — |
| 6 | 305.87 | — | — | 905.87 | A | major sixth |
Temperament interpretations
Perhaps the most typical interpretation of this ploidacot is shrutar. The period is 45/32~64/45, and the generator is 33/32~36/35, so that 3/2 is a period up two generators, 5/4 is found at a period down four generators, 7/4 at a period up seven generators, and 11/8 at a period down one generator. 17/16 can represent two generators, and the period can be expressed as 17/12~24/17 in the 17-limit. The generator is ideally tuned slightly sharp of pure-3 tuning.