Ploidacot/Pentacot: Difference between revisions
Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=0|Cots=5|Pergen=[P8, P5/5]|Forms=8, 9, 17, 26|Title=Pentacot|Wedgie=5}} '''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Pentacot temperaments typically generate the 8L 1s, 9L 8s, and 17L 9s MOS scales. == Notation == There is no agreed-upon notation for..." Tags: Mobile edit Mobile web edit |
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'''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Pentacot temperaments typically generate the [[8L 1s]], [[9L 8s]], and [[17L 9s]] MOS scales. | '''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Pentacot temperaments typically generate the [[8L 1s]], [[9L 8s]], and [[17L 9s]] MOS scales. | ||
== | == Intervals and notation == | ||
There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather | There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]). | ||
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== Temperament interpretations == | == Temperament interpretations == | ||
An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are | An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are some extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111). | ||
[[Category: | [[Category:Ploidacots|Pentacot]] | ||
Latest revision as of 23:18, 7 January 2026
| Pergen | [P8, P5/5] |
| Numeral form | 5-cot |
| Pure generator size | 140.39 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 8, 9, 17, 26 |
| Characteristic multival entry | 5 |
Pentacot is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Pentacot temperaments typically generate the 8L 1s, 9L 8s, and 17L 9s MOS scales.
Intervals and notation
There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −20 | 792.180 | Ab | minor sixth |
| −19 | 932.571 | ||
| −18 | 1072.962 | ||
| −17 | 13.353 | ||
| −16 | 153.744 | ||
| −15 | 294.135 | Eb | minor third |
| −14 | 434.526 | ||
| −13 | 574.917 | ||
| −12 | 715.308 | ||
| −11 | 845.699 | ||
| −10 | 996.090 | Bb | minor seventh |
| −9 | 1136.481 | ||
| −8 | 76.872 | ||
| −7 | 217.263 | ||
| −6 | 357.654 | ||
| −5 | 498.045 | F | perfect fourth |
| −4 | 638.436 | ||
| −3 | 778.827 | ||
| −2 | 919.218 | ||
| −1 | 1059.609 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 140.391 | ||
| 2 | 280.782 | ||
| 3 | 421.173 | ||
| 4 | 561.564 | ||
| 5 | 701.955 | G | perfect fifth |
| 6 | 842.346 | ||
| 7 | 982.737 | ||
| 8 | 1123.128 | ||
| 9 | 63.519 | ||
| 10 | 203.910 | D | major second |
| 11 | 344.301 | ||
| 12 | 484.692 | ||
| 13 | 625.083 | ||
| 14 | 765.474 | ||
| 15 | 905.865 | A | major sixth |
| 16 | 1046.256 | ||
| 17 | 1186.647 | ||
| 18 | 127.038 | ||
| 19 | 267.429 | ||
| 20 | 407.820 | E | major third |
Temperament interpretations
An obvious interpretation for pentacot is glacier, a 2.3.13 subgroup temperament, where the generator is 13/12 and five of them make a perfect fifth. There are some extensions for full 13-limit: jerome (26 & 43), tsaharuk (77 & 94), and quanic (94 & 111).