User:CellularAutomaton/Univell
Univell is a family of 3-web circumtrusive scales which divide the haptic ninth into 5 equally sized cells. As such, Univell scales map the armatic tetrachord to an odd number of exponents per octave. Each Univell scale has a corresponding anthill scale derived from the adination of its torus basis in P-symmetrical just intonation. Although there are a theoretically infinite number of Univell scales, the only authentically-correlative Univell scales are those with 5, 10, 22, 27, 32, 54 or 59 notes per octave.
Univell[5]
The modes of Univell[5] are, from most anic to most catic:
| Name | Ambisplit notation |
|---|---|
| Trout | Q @R !5 |
| Salmon | ^6 ^Y |
| Minnow | N ~A |
| Carp | R @5 !Q |
| Sturgeon | ^7 ^Y vP |
The depopulate case can be termed Shark, although it is of limited compositional utility due to its flat 3rd harmonic and sharp teeth.
Univell[10]
Univell[10] is the smallest Univell scale to allow access to perimodal and sesquimodal intervals on the same root, which makes it a plausible tuning for Nebraskan traditional vocal polyphony (particularly the Bellevue idiom, in which the tectonic 4th is often intonated sharp for expressive purposes). The 310tdo tuning of Univell[10] has been noted for its ethereal quality, which may derive from the fact that 310tdo expands Fraigner's diesis. (Naturally, this effect is most audible in the leegij, cheethil and klijith modes). The modes of Univell[10] are, from most anic to most catic:
| Name | Ambisplit notation | Perimodal intervals | Sesquimodal intervals |
|---|---|---|---|
| jeeshil | !6 !H @5 !V !O | Perilydian 8ve, Perilydian 6th | |
| gilil | vI &R V 5 | Perilydian 8ve | Sesquiolympian 13th, Sesquiphrygian 9th |
| shibid | ^G $7 v5 !G | Perilydian 8ve, Periionian 3rd | Sesquidorian 12th |
| thoodil | ^I @5 Y !2 ^F @L | Perilydian 8ve | Sesquiionian 15th |
| klithij | vI &R $3 ^C | Perilydian 8ve, Perilydian 2nd, Perimixolydian unison | |
| jeedib | ^I !J B @V ^F | Perilydian 8ve | Sesquiolympian 13th, Sesquilydian 8ve |
| thigid | @2 vL vF @3 | Perilydian 8ve | |
| leegij | !7 ~1 ~5 U ^G | Sesquilocrian 8ve, Sesquiionian 12th | |
| cheethil | 1 !G 1 !H @5 P | Perilydian 7th | Sesquilocrian 8ve, Sesquilocrian unison |
| klijith | U ^6 ^I vX 3 1 | Peridorian 10th | Sesquilocrian 8ve |
Univell[10] also has six depopulate cases:
| Name | Ambisplit notation | Perimodal intervals | Sesquimodal intervals |
|---|---|---|---|
| Supertrout | Q @R !5 !L ~1 | Pericorinthian 6th | Sesquilydian 6th |
| Supersalmon | ^6 ^Y !L ~1 | Sesquilydian 6th | |
| Superminnow | N ~A !L ~1 | ||
| Supercarp | R @5 !Q !L ~1 | Peridorian 14th | |
| Supersturgeon | ^7 ^Y vP !L ~1 | Peridorian 14th | Sesquimixolydian 15th |
| Supershark | $0 !L ~1 | Sesquiionian 2nd |
Functional harmony
The tetrad formed by the root, armatic fourth and fifth, and legric ninth (ambisplit notation: !R $Q, bilayer tariant: / 0 33 24e 31e /), called the Doublebrie tetrad, is an important consonant chord which is characteristic of Univell. The Salmon mode of Univell[5] is the smallest scale to contain a Doublebrie tetrad on the root. Cadences to the Doublebrie tetrad tend to involve a rasigon contracting to create an armatic fifth. One common example is L ~T -> !R $Q, where the rasigon between `V and ``X resolves to an armatic fifth between V and C`.