User:Ganaram inukshuk/TAMEX
Work-in-progress
- This page assumes the reader is familiar with TAMNAMS mos names, mos prefixes, and step ratios.
TAMEX (from Temperament-Agnostic Moment-of-Symmetry Scale Extension Description System), originally devised by Frostburn and Ganaram inukshuk as two separate naming schemes, is an extension to the mos pattern names provided by TAMNAMS. This scheme is a means of describing how descendant scales (namely, chromatic and enharmonic mosses) with more than 10 steps relate back to smaller mosses and, to a lesser extent, what step ratios of the original mos is needed to produce that descendant mos. Additionally, it is a means of generalizing the notion of a chromatic scale to nondiatonic mosses.
Despite looking like a naming system, what TAMEX provides are descriptions of descendant mosses that relate to a single, TAMNAMS-named mos. Hence, "names" for mosses are meant to be as general as possible and can refer to more than one mos.
Description scheme for TAMNAMS-named mosses
Base descriptions
To describe mosses that have more than 10 notes, descriptions are based on how they're related to another, named mos, based on how many generations apart the two are:
- The immediate child of a mos is a chromatic mos.
- The grandchild scale of a mos is an enharmonic mos.
- The great-grandchild scale of a subchromatic mos.
- In general, a mos that is a kth descendant of a named mos is a kth descendant.
Descriptions can take on one of two forms: a description as two words, or a single word bearing the mos's prefix. Which one to be used is up the user and whichever form is best depending on context. In the case of kth descendants, the ordinal value kth can be omitted to refer to any or all descendant mosses, depending on context.
| Parent mos | Chromatic mosses
(1st descendants) |
Enharmonic mosses
(2nd descendants) |
Subchromatic mosses
(3rd descendants) |
kth descendant mosses |
|---|---|---|---|---|
| mos-name | chromatic mos-name | enharmonic mos-name | subchromatic mos-name | (kth) mos-name descendant |
| mos-name | mosprefix-chromatic | mosprefix-monic | mosprefix-subchromatic | (kth) mosprefix-descendant |
Using 5L 2s (diatonic) as an example, a tree of mosses can be produced as a scale tree.
| Root mos | 1st descendants | 2nd descendants | 3rd descendants | 4th descendants | 5th descendants |
|---|---|---|---|---|---|
| 5L 2s | 7L 5s | 7L 12s | 7L 19s | 7L 26s | 7L 29s |
| 26L 7s | . . . | ||||
| 19L 7s | 26L 19s | ||||
| 19L 26s | |||||
| 12L 7s | 19L 12s | 19L 31s | |||
| 31L 19s | |||||
| 12L 19s | 31L 12s | ||||
| 12L 31s | 12L 43s | ||||
| 5L 7s | 12L 5s | 12L 17s | 12L 29s | 12L 41s | |
| 29L 12s | . . . | ||||
| 17L 12s | 29L 17s | ||||
| 17L 29s | |||||
| 5L 12s | 17L 5s | 17L 22s | |||
| 22L 17s | |||||
| 5L 17s | 22L 5s | ||||
| 5L 22s | 5L 29s |
With 5L 2s as the root mos:
- There are 2 chromatic descendants, or diachromatic scales: 7L 5s and 5L 7s
- There are 4 enharmonic descendants, or diamonic scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s
- There are 8 subchromatic descendants, or diasubchromatic scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.
Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:
- There are 16 4th descendants, or 4th diadescendant scales.
- There are 32 5th descendants, or 5th diadescendant scales.
- There are 2 to the kth power kth descendants, or kth diadescendant scales.
Step ratio descriptions
Optionally, the names for a step ratio range can be added before these descriptions, describing the step ratio of the root mos. Step ratios only apply to the 1st, 2nd, and 3rd descendants.
| Root | Chromatic mosses
(1st descendants) |
Enharmonic mosses
(2nd descendants) |
Subchromatic mosses
(3rd descendants) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mos | L:s range | Mos | L:s range | Range name | Prefix | Mos | L:s range | Range name | Prefix | Mos | L:s range | Range name | Prefix |
| xL ys | 1:1 to 1:0 | (x+y)L xs | 1:1 to 2:1 | soft-of-basic | s- | (x+y)L (2x+y)s | 1:1 to 3:2 | soft | s- | (x+y)L (3x+2y)s | 1:1 to 4:3 | ultrasoft | us- |
| (3x+2y)L (x+y)s | 4:3 to 3:2 | parasoft | ps- | ||||||||||
| (2x+y)L (x+y)s | 3:2 to 2:1 | hyposoft | hs- | (3x+2y)L (2x+y)s | 3:2 to 5:3 | quasisoft | qs- | ||||||
| (2x+y)L (3x+2y)s | 5:3 to 2:1 | minisoft | ms- | ||||||||||
| xL (x+y)s | 2:1 to 1:0 | hard-of-basic | h- | (2x+y)L xs | 2:1 to 3:1 | hypoard | hh- | (2x+y)L (3x+y)s | 2:1 to 5:2 | minihard | mh- | ||
| (3x+y)L (2x+y)s | 5:2 to 3:1 | quasihard | qh- | ||||||||||
| xL (2x+y)s | 3:1 to 1:0 | hard | h- | (3x+y)L xs | 3:1 to 4:1 | parahard | ph- | ||||||
| xL (3x+y)s | 4:1 to 1:0 | ultrahard | uh- | ||||||||||