Ploidacot/Omega-tricot: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 1: | Line 1: | ||
{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15|Title=Omega-tricot}}'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts. | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15|Title=Omega-tricot}} | ||
'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts. | |||
== Notation == | == Notation == | ||
While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic. | While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! # | |||
! Cents | |||
! Notation | |||
! Name | |||
|- | |- | ||
| | | −9 | ||
| | | 905.865 | ||
| | | A | ||
| | | major sixth | ||
|- | |- | ||
| | | −8 | ||
| | | 1071.88 | ||
| | | vB | ||
| | | submajor seventh | ||
|- | |- | ||
| | | −7 | ||
| | | 37.895 | ||
| | | ^C | ||
| | | superunison | ||
|- | |- | ||
| | | −6 | ||
| | | 203.91 | ||
| | | D | ||
| | | major second | ||
|- | |- | ||
| | | −5 | ||
| | | 369.925 | ||
| | | vE | ||
| | | submajor third | ||
|- | |- | ||
| | | −4 | ||
| | | 535.94 | ||
| | | ^F | ||
| | | superfourth | ||
|- | |- | ||
| | | −3 | ||
| | | 701.955 | ||
| | | G | ||
| | | perfect fifth | ||
|- | |- | ||
| | | −2 | ||
| | | 867.97 | ||
| | | vA | ||
| | | submajor sixth | ||
|- | |- | ||
| | | −1 | ||
| | | 1033.985 | ||
| | | ^Bb | ||
| | | supraminor seventh | ||
|- | |- | ||
| | | 0 | ||
| | | 0 | ||
| | | C | ||
| | | perfect unison / perfect octave | ||
|- | |- | ||
| | | 1 | ||
| | | 166.015 | ||
| | | vD | ||
| | | submajor second | ||
|- | |- | ||
| | | 2 | ||
| | | 332.03 | ||
| | | ^Eb | ||
| | | supraminor third | ||
|- | |- | ||
| | | 3 | ||
| | | 498.045 | ||
| | | F | ||
| | | perfect fourth | ||
|- | |- | ||
| | | 4 | ||
| | | 664.06 | ||
| | | vG | ||
| | | subfifth | ||
|- | |- | ||
| | | 5 | ||
| | | 830.075 | ||
| | | ^Ab | ||
| | | supraminor sixth | ||
|- | |- | ||
| | | 6 | ||
| | | 996.09 | ||
| | | Bb | ||
| | | minor seventh | ||
|- | |- | ||
| | | 7 | ||
| | | 1162.105 | ||
| | | vC | ||
| | | suboctave | ||
|- | |- | ||
|9 | | 8 | ||
|294.135 | | 128.12 | ||
|Eb | | ^Db | ||
|minor third | | supraminor second | ||
|- | |||
| 9 | |||
| 294.135 | |||
| Eb | |||
| minor third | |||
|} | |} | ||
== Temperament interpretations == | == Temperament interpretations == | ||
=== Porcupine === | === Porcupine === | ||
In [[porcupine]], the generator is [[11/10]], two generators make [[6/5]], and three make 4/3. This is tuned best with a considerably flat generator of about 162 | In [[porcupine]], the generator is [[11/10]], two generators make [[6/5]], and three make 4/3. This is tuned best with a considerably flat generator of about 162{{c}} or so, and naturally extends to the full 11-limit as in [[superpyth]], so the minor seventh is [[7/4]]. | ||
=== Superpine === | === Superpine === | ||
In [[superpine]], the subminor seventh ( | In [[superpine]], the subminor seventh (C–vBb, 13 generators up) is mapped to 7/4, and the mappings for 3 and 5 are as in meantone, so −3 generators is [[3/2]] and −12 generators is [[5/4]]. It is best tuned with a slightly sharp generator of about 168{{c}}. | ||
{{Todo| unify precision }} | {{Todo| unify precision }} | ||
Revision as of 16:01, 9 September 2025
| Pergen | [P8, P4/3] |
| Numeral form | 2-sheared 3-cot |
| Pure generator size | 166.01 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 7, 8, 15 |
| Characteristic multival entry | TBD |
Omega-tricot is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of 4/3, and the period is a 2/1 octave. Omega-tricot temperaments usually generate the 1L 6s and 7L 1s MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.
Notation
While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic.
| # | Cents | Notation | Name |
|---|---|---|---|
| −9 | 905.865 | A | major sixth |
| −8 | 1071.88 | vB | submajor seventh |
| −7 | 37.895 | ^C | superunison |
| −6 | 203.91 | D | major second |
| −5 | 369.925 | vE | submajor third |
| −4 | 535.94 | ^F | superfourth |
| −3 | 701.955 | G | perfect fifth |
| −2 | 867.97 | vA | submajor sixth |
| −1 | 1033.985 | ^Bb | supraminor seventh |
| 0 | 0 | C | perfect unison / perfect octave |
| 1 | 166.015 | vD | submajor second |
| 2 | 332.03 | ^Eb | supraminor third |
| 3 | 498.045 | F | perfect fourth |
| 4 | 664.06 | vG | subfifth |
| 5 | 830.075 | ^Ab | supraminor sixth |
| 6 | 996.09 | Bb | minor seventh |
| 7 | 1162.105 | vC | suboctave |
| 8 | 128.12 | ^Db | supraminor second |
| 9 | 294.135 | Eb | minor third |
Temperament interpretations
Porcupine
In porcupine, the generator is 11/10, two generators make 6/5, and three make 4/3. This is tuned best with a considerably flat generator of about 162 ¢ or so, and naturally extends to the full 11-limit as in superpyth, so the minor seventh is 7/4.
Superpine
In superpine, the subminor seventh (C–vBb, 13 generators up) is mapped to 7/4, and the mappings for 3 and 5 are as in meantone, so −3 generators is 3/2 and −12 generators is 5/4. It is best tuned with a slightly sharp generator of about 168 ¢.