No-threes subgroup temperaments: Difference between revisions
mNo edit summary |
decided to upclean a tiny bit |
||
| Line 14: | Line 14: | ||
Temperaments discussed elsewhere include | Temperaments discussed elsewhere include | ||
* Jubilic → [[Jubilismic clan #Jubilic]] | * Jubilic → [[Jubilismic clan #Jubilic]] | ||
* Didacus → [[Hemimean clan #Didacus]] | |||
* Llywelyn a.k.a. shoe → [[Llywelynsmic clan #Llywelyn a.k.a. shoe]] | |||
* Jacobin superfamily → [[The Jacobins]] | |||
== 2.5.7 temperaments == | == 2.5.7 temperaments == | ||
=== Rainy === | === Rainy === | ||
Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]] (and [[valentine]]). Rainy is notable theoretically as it equates ([[2/1]])/([[5/4]])<sup>3</sup> (128/125, the lesser diesis) with ([[2/1]])/([[8/7]])<sup>5</sup> (the 2.7-subgroup [[cloudy comma]], which is similar to the 2.5-subgroup lesser diesis in that tempering it out tunes the 8/7 about 8.8{{cent}} sharp, while tempering out 128/125 similarly sharpens the 5/4 by about 13.7{{cent}}). By tempering out their difference, stacked 5s and stacked 7s become easier to navigate, using the general-purpose diesis to simplify clusters. (Note that this analysis assumes a [[lattice]]-based conceptualization of [[JI]] which is often called "stacking-based"; see [[taxonomies of xen approaches]].) | Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]] (and [[valentine]]). Rainy is notable theoretically as it equates ([[2/1]])/([[5/4]])<sup>3</sup> (128/125, the lesser diesis) with ([[2/1]])/([[8/7]])<sup>5</sup> (the 2.7-subgroup [[cloudy comma]], which is similar to the 2.5-subgroup lesser diesis in that tempering it out tunes the 8/7 about 8.8{{cent}} sharp, while tempering out 128/125 similarly sharpens the 5/4 by about 13.7{{cent}}). By tempering out their difference, stacked 5s and stacked 7s become easier to navigate, using the general-purpose diesis to simplify clusters. (Note that this analysis assumes a [[lattice]]-based conceptualization of [[JI]] which is often called "stacking-based"; see [[taxonomies of xen approaches]].) | ||
| Line 82: | Line 82: | ||
{{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }} | {{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }} | ||
=== French decimal === | === French decimal === | ||
| Line 359: | Line 356: | ||
* Orgone → [[Orgonia #Orgone]] | * Orgone → [[Orgonia #Orgone]] | ||
* Berylic → [[4th-octave temperaments #Berylic]] | * Berylic → [[4th-octave temperaments #Berylic]] | ||
* [[21st-octave temperaments #21-23-commatic]] | * 21-23-commatic → [[21st-octave temperaments #21-23-commatic]] | ||
* [[31st-octave temperaments #31-17/13-commatic]] | * 31-17/13-commatic → [[31st-octave temperaments #31-17/13-commatic]] | ||
* [[37th-octave temperaments #37-11-commatic (rank-1)]] | * 37-11-commatic (rank-1) → [[37th-octave temperaments #37-11-commatic (rank-1)]] | ||
* etc. | * etc. | ||