Ploidacot/Beta-pentacot: Difference between revisions
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Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=2|Cots=5|Pergen=[P8, ccP4/5]|Forms=25, 27, 29, 31|Title=Beta-pentacot|Wedgie=5}} '''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make 6/1 (sixth harmonic, two octaves above a perfect fifth 3/2), and the period is a 2/1 octave. Beta-pentacot temperaments typically generate the 2L 19s, 2L 21s, 2L 23s, and 2L 25..." Tags: Mobile edit Mobile web edit |
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{{Infobox ploidacot|Ploids=1|Shears=2|Cots=5|Pergen=[P8, ccP4/5]|Forms=25, 27, 29 | {{Infobox ploidacot|Ploids=1|Shears=2|Cots=5|Pergen=[P8, ccP4/5]|Forms=23, 25, 27, 29|Title=Beta-pentacot|Wedgie=5}} | ||
'''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth [[3/2]]), and the period is a [[2/1]] octave. Beta-pentacot temperaments typically generate the [[2L 19s]], [[2L 21s]], [[2L 23s]], and [[2L 25s]] MOS scales, and either [[2L 27s]] (and thus [[29L 2s]]) or [[27L 2s]] as children. | '''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth [[3/2]]), and the period is a [[2/1]] octave. Beta-pentacot temperaments typically generate the [[2L 19s]], [[2L 21s]], [[2L 23s]], and [[2L 25s]] MOS scales, and either [[2L 27s]] (and thus [[29L 2s]]) or [[27L 2s]] as children. | ||
== | == Intervals and notation == | ||
There is no agreed-upon notation for beta-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 their sum. Note and interval names are provided where beta-pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]). | There is no agreed-upon notation for beta-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 their sum. Note and interval names are provided where beta-pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]). | ||
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An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of [[trimyna]], where the generator is [[10/7]], three of them stack to make [[22/15]], and five of them stack to make [[3/2]]. Immediately it extends to full 11-limit [[tritonic]] (29 & 31). | An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of [[trimyna]], where the generator is [[10/7]], three of them stack to make [[22/15]], and five of them stack to make [[3/2]]. Immediately it extends to full 11-limit [[tritonic]] (29 & 31). | ||
[[Category: | [[Category:Ploidacots|Beta-pentacot]] | ||
Latest revision as of 23:21, 7 January 2026
| Pergen | [P8, ccP4/5] |
| Numeral form | 2-sheared 5-cot |
| Pure generator size | 579.61 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 23, 25, 27, 29 |
| Characteristic multival entry | 5 |
Beta-pentacot is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make 6/1 (sixth harmonic, two octaves above a perfect fifth 3/2), and the period is a 2/1 octave. Beta-pentacot temperaments typically generate the 2L 19s, 2L 21s, 2L 23s, and 2L 25s MOS scales, and either 2L 27s (and thus 29L 2s) or 27L 2s as children.
Intervals and notation
There is no agreed-upon notation for beta-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 their sum. Note and interval names are provided where beta-pentacot intervals align with standard monocot intervals (which use chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −15 | 294.135 | Eb | minor third |
| −14 | 914.526 | ||
| −13 | 334.917 | ||
| −12 | 955.308 | ||
| −11 | 375.699 | ||
| −10 | 996.090 | Bb | minor seventh |
| −9 | 416.481 | ||
| −8 | 1036.872 | ||
| −7 | 457.263 | ||
| −6 | 1077.654 | ||
| −5 | 498.045 | F | perfect fourth |
| −4 | 1118.436 | ||
| −3 | 538.827 | ||
| −2 | 1159.218 | ||
| −1 | 579.609 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 620.391 | ||
| 2 | 40.782 | ||
| 3 | 661.173 | ||
| 4 | 81.564 | ||
| 5 | 701.955 | G | perfect fifth |
| 6 | 122.346 | ||
| 7 | 742.737 | ||
| 8 | 163.128 | ||
| 9 | 783.519 | ||
| 10 | 203.910 | D | major second |
| 11 | 824.301 | ||
| 12 | 244.692 | ||
| 13 | 865.083 | ||
| 14 | 285.474 | ||
| 15 | 905.865 | A | major sixth |
Temperament interpretations
An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of trimyna, where the generator is 10/7, three of them stack to make 22/15, and five of them stack to make 3/2. Immediately it extends to full 11-limit tritonic (29 & 31).