User:Ganaram inukshuk/TAMEX
This article is a work-in-progress, proposed rewrite of the following page: TAMNAMS Extension and User:Ganaram inukshuk/TAMNAMS Extension
- 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 mosses with more than 10 steps (namely, chromatic and enharmonic mosses) relate to smaller, TAMNAMS-named mosses and, to a lesser extent, what step ratio produces 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 under this system are more general than typical mos names, as these phrases can refer to multiple mosses.
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.
- For great-great-grandchild mosses and beyond, the term descendant is used. Optionally, the number of generations between a named mos and descendant mos can be provided to produce the term kth-order 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.
| Base mos | Chromatic mosses
(1st-order descendants) |
Enharmonic mosses
(2nd-order descendants) |
Subchromatic mosses
(3rd-order descendants) |
kth-order descendant mosses |
|---|---|---|---|---|
| mos-name | chromatic mos-name | enharmonic mos-name | subchromatic mos-name | (kth-order) mos-name descendant |
| mos-name | mosprefix-chromatic | mosprefix-monic | mosprefix-subchromatic | (kth-order) mosprefix-descendant |
Calculating the number of generations for kth-order descendants
For a mos xL ys, where x+y is greater than 10:
- Let z and w be the number of large and small steps of the parent mos to be found. Assign to z and w the values x and y respectively. Let k = 0, where k is the number of generations away from zL ws.
- Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
- Assign the value m2 to z and value m1-m2 to w. Increment n by 1.
- If the sum of z and w is no more than 10, then the parent mos is zL ws, where xL ys is a kth-order descendant of zL ws. If not, repeat the process starting at step 2.
Step ratio descriptions
Optionally, the names for a step ratio range, describing the step ratio of the root mos, can be added before these descriptions, either as a single word or prefix. Any step ratio range can be used for 4th-order descendants and beyond, as context allows.
| Base mos | Chromatic mosses
(1st-order descendants) |
Enharmonic mosses
(2nd-order descendants) |
Subchromatic mosses
(3rd-order 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- | ||||||||||
Examples
Descendants of 5L 2s
The descendants of 5L 2s can be organized as a scale tree, as shown.
| Base mos | 1st-order descendants | 2nd-order descendants | 3rd-order descendants | 4th-order descendants | 5th-order 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 1st-order descendants, chromatic scales, or specifically diachromatic scales: 7L 5s and 5L 7s
- There are 4 2nd-order descendants, enharmonic scales, or specifically diamonic scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s
- There are 8 3rd-order descendants, subchromatic scales, or specifically 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-order descendants, or 4th-order diadescendant scales.
- There are 32 5th-order descendants, or 5th-order diadescendant scales.
- There are 2k (2 to the kth power) kth-order descendants, or kth-order diadescendant scales.
Step ratios ranges can be added to these descriptions, as shown.
| Base mos | 1st-order descendants | 2nd-order descendants | 3rd-order descendants | 4th-order descendants | |||||
|---|---|---|---|---|---|---|---|---|---|
| Mos | Description | Mos | Description | Mos | Description | Mos | Description | Mos | Descriptions |
| 5L 2s | diatonic | 7L 5s | soft diachromatic | 7L 12s | soft diamonic | 7L 19s | ultrasoft diasubchromatic | 7L 26s | ultrasoft 4th-order diadescendants |
| 26L 7s | |||||||||
| 19L 7s | parasoft diasubchromatic | 26L 19s | parasoft 4th-order diadescendants | ||||||
| 19L 26s | |||||||||
| 12L 7s | hyposoft diamonic | 19L 12s | quasisoft diasubchromatic | 19L 31s | quasisoft 4th-order diadescendants | ||||
| 31L 19s | |||||||||
| 12L 19s | minisoft diasubchromatic | 31L 12s | minisoft 4th-order diadescendants | ||||||
| 12L 31s | |||||||||
| 5L 7s | hard diachromatic | 12L 5s | hypohard diamonic | 12L 17s | minihard diasubchromatic | 12L 29s | minihard 4th-order diadescendants | ||
| 29L 12s | |||||||||
| 17L 12s | quasisoft diasubchromatic | 29L 17s | quasihard 4th-order diadescendants | ||||||
| 17L 29s | |||||||||
| 5L 12s | hard diamonic | 17L 5s | parahard diasubchromatic | 17L 22s | parahard4th-order diadescendants | ||||
| 22L 17s | |||||||||
| 5L 17s | ultrahard diasubchromatic | 22L 5s | ultrahard 4th-order diadescendants | ||||||
| 5L 22s | |||||||||