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.

Base descriptions

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

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-

Example: descendants of 5L 2s

The descendants of 5L 2s can be organized as a scale tree, as shown.

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.