Ploidacot/Omega-tricot: Difference between revisions
No edit summary |
m Removing from Category:Ploidacots using Cat-a-lot |
||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15|Title=Omega-tricot|Wedgie=3}} | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15, 22|Title=Omega-tricot (beta-tricot)|Wedgie=3}} | ||
'''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. | '''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. | ||
== | == Intervals and notation == | ||
While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second | While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^C and vC# are enharmonic. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Omega-tricot intervals (assuming pure fifth and octave) | |||
|- | |- | ||
! # | ! # | ||
| Line 60: | Line 61: | ||
| 0 | | 0 | ||
| C | | C | ||
| perfect unison | | perfect unison | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 114: | Line 115: | ||
=== Superpine === | === Superpine === | ||
In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}. | In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}. | ||
Latest revision as of 06:38, 16 July 2026
| Pergen | [P8, P4/3] |
| Numeral form | 2-sheared 3-cot |
| Pure generator size | 166.01 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 7, 8, 15, 22 |
| Characteristic multival entry | 3 |
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.
Intervals and notation
While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^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 |
| 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 generator is again mapped to 11/10, and the mapping for 5 is as in meantone, so 5/4 is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to 39/32 (so that 5 generators span 13/8). The canonical mapping of 7 places 7/2 at 13 generators, equating the generator to 35/32. It is best tuned with a slightly sharp generator of about 168 ¢.