Trienstonic clan: Difference between revisions
m Consistency and - redundant category |
→Octokaidecal: anti-pajara |
||
| (3 intermediate revisions by 3 users not shown) | |||
| Line 3: | Line 3: | ||
== Trienstonian == | == Trienstonian == | ||
This low-accuracy temperament is generated by a fifth, tuned very sharp such that a stack of three reach a ~7/4. [[5edo]] is the tuning that conflates 7/6~9/8 (+2 generator steps) with ~8/7 (-3 generator steps). If you do not care about the intervals of 9 in this temperament, you can tune the fifth sharper for the [[7-odd-limit]], leading to an [[5L 3s|oneirotonic]] scale or otherwise a [[5L 2s|diatonic]] scale with negative small steps. A tuning that prioritizes the 7-odd-limit also tunes the fifth sharper than the [[pentic]] range, instead generating an [[antipentic]] scale. Trienstonian can be considered the [[2.3.7 subgroup|2.3.7]] analog of [[mavila]] temperament, with extremely sharp fifths rather than extremely flat ones. | This low-accuracy temperament is generated by a fifth, tuned very sharp such that a stack of three reach a ~7/4. [[5edo]] is the tuning that conflates 7/6~9/8 (+2 generator steps) with ~8/7 (-3 generator steps). If you do not care about the intervals of 9 in this temperament, you can tune the fifth sharper for the [[7-odd-limit]], leading to an [[5L 3s|oneirotonic]] scale or otherwise a [[5L 2s|diatonic]] scale with negative small steps. A tuning that prioritizes the 7-odd-limit also tunes the fifth sharper than the [[pentic]] range, instead generating an [[antipentic]] scale. Trienstonian can be considered the [[2.3.7 subgroup|2.3.7]] analog of [[mavila]] temperament, with extremely sharp fifths rather than extremely flat ones, being on the other side of 3\5 from [[archy]] fifths, just like how mavila fifths are on the other side of 4\7 from [[meantone]] fifths. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
| Line 12: | Line 12: | ||
{{Mapping|legend=3| 1 0 0 -2 | 0 1 0 3 }} | {{Mapping|legend=3| 1 0 0 -2 | 0 1 0 3 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 31: | Line 30: | ||
Members of the clan discussed elsewhere are: | Members of the clan discussed elsewhere are: | ||
* | |||
* [[Antonian]] (+10/9 or +15/14) → [[Very low accuracy temperaments #Septimal antonian|Very low accuracy temperaments]] | |||
* [[Father]] (+16/15) → [[Father family #Septimal father|Father family]] | |||
* ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone|Meantone family]] | |||
* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]] | * ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]] | ||
* ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]] | * ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]] | ||
* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]] | |||
* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]] | |||
* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]] | |||
* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]] | * ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]] | ||
Considered below are uncle, octokaidecal, and parakangaroo. | |||
== Uncle == | == Uncle == | ||
| Line 75: | Line 70: | ||
== Octokaidecal == | == Octokaidecal == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Supersharp]].'' | : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Supersharp]].'' | ||
Octokaidecal extends trienstonian by tempering out [[50/49]], thus splitting the octave in half. It generates the [[8L 2s]] (taric) mos scale, with tunings on the other side of [[10edo]] as [[2L 8s]] (jaric). Compared to [[pajara]], decatonic thirds ([[8/7]] and [[7/6]]) and fourths ([[6/5]] and [[5/4]]) have their mappings reversed, meaning octokaidecal can be considered what is to pajara as [[mavila]] is to [[meantone]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||