Ploidacot/Tetracot: Difference between revisions
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{{Infobox ploidacot|Ploids=1|Shears=0|Cots=4|Pergen=[P8, P5/4]|Forms=6, 7, 13|Title=Tetracot}} | {{Infobox ploidacot|Ploids=1|Shears=0|Cots=4|Pergen=[P8, P5/4]|Forms=6, 7, 13, 20|Title=Tetracot|Wedgie=4}} | ||
'''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot|dicot]] intervals. | '''Tetracot''' is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tetracot temperaments typically generate the [[1L 5s]] and [[6L 1s]] MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals and containing all [[Ploidacot/Dicot|dicot]] intervals. | ||
Tetracot temperaments often generate [[7L 6s]] and [[7L 13s]] as chromatic scales, and for particularly sharp tunings [[13L 7s]]. More info may be found at [[Ploidacot/Tetracot/Generator tunings]]. | |||
== Intervals and notation == | == Intervals and notation == | ||
While there is no agreed-upon notation system for tetracot, the notation provided here is based on interpreting the generator as a submajor second, and produced by extending dicot notation, allowing for an ^ or v to stand for a quarter of a chromatic semitone, so {{nowrap| | While there is no agreed-upon notation system for tetracot, the notation provided here is based on interpreting the generator as a submajor second, and produced by extending dicot notation, allowing for an ^ or v to stand for a quarter of a chromatic semitone, so {{nowrap|^^Eb {{=}} vvE {{=}} Ed}}. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 13: | Line 15: | ||
! Notation | ! Notation | ||
! Name | ! Name | ||
|- | |||
| −13 | |||
| 118.65 | |||
| ^Db | |||
| supraminor second | |||
|- | |||
| −12 | |||
| 294.13 | |||
| Eb | |||
| minor third | |||
|- | |||
| −11 | |||
| 469.62 | |||
| vF | |||
| subfourth | |||
|- | |||
| −10 | |||
| 645.11 | |||
| Gd | |||
| semidiminished fifth | |||
|- | |- | ||
| −9 | | −9 | ||
| Line 25: | Line 47: | ||
|- | |- | ||
| −7 | | −7 | ||
| | | 1171.58 | ||
| vC | | vC | ||
| suboctave | | suboctave | ||
| Line 40: | Line 62: | ||
|- | |- | ||
| −4 | | −4 | ||
| 498. | | 498.04 | ||
| F | | F | ||
| perfect fourth | | perfect fourth | ||
| Line 55: | Line 77: | ||
|- | |- | ||
| −1 | | −1 | ||
| | | 1024.51 | ||
| ^Bb | | ^Bb | ||
| supraminor seventh | | supraminor seventh | ||
| Line 62: | Line 84: | ||
| 0.00 | | 0.00 | ||
| C | | C | ||
| perfect unison | | perfect unison | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 90: | Line 112: | ||
|- | |- | ||
| 6 | | 6 | ||
| | | 1052.93 | ||
| Bd | | Bd | ||
| neutral seventh | | neutral seventh | ||
| Line 108: | Line 130: | ||
| vE | | vE | ||
| submajor third | | submajor third | ||
|- | |||
| 10 | |||
| 554.89 | |||
| Ft | |||
| semiaugmented fourth | |||
|- | |||
| 11 | |||
| 730.38 | |||
| ^G | |||
| superfifth | |||
|- | |||
| 12 | |||
| 905.87 | |||
| A | |||
| major sixth | |||
|- | |||
| 13 | |||
| 1081.35 | |||
| vB | |||
| submajor seventh | |||
|} | |} | ||