User:Ganaram inukshuk/TAMNAMS Extension

This is a system for describing and naming mos scales beyond the set of named TAMNAMS mosses. Both User:Frostburn (User:Frostburn/TAMNAMS Extension) and I have similar systems, with the main difference here being how mosses can be named any number of generations away from a named mos.

Naming mos descendants

To name mosses that have more than 10 notes, rather than giving mosses unique names, names are based on how they're related to another (named) mos.

• A child mos is a chromatic mos. For the child of a named mos, the name is chromatic (mos name).
• A grandchild mos is an enharmonic mos. For the grandchild of a named mos, the name is enharmonic (mos name).
• A great-grandchild mos is a subchromatic mos. For the great-grandchild of a named mos, the name is subchromatic (mos name).
• A mos that is more than 3 generations away is called a descendant mos. For the descendant of a named mos, the name is (mos name) descendant. This term can also be used to describe any mos descendant any number of generations away from a named mos.

These phrases may also be shortened by adding the mos's prefix to the terms chromatic, enharmonic, subchromatic, or descendant respectively, if the named mos has no more than 3 periods.

Optionally, for the phrase mos descendant, the number of generations away from a named mos can be specified, producing the terms nth mos descendant, nth (mos name) descendant, and nth (mos-prefix)descendant, using the algorithm below to find n:

1. 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 n = 0, where n is the number of generations away from zL ws.
2. Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
3. Assign to z the value m2 and w the value m1-m2. Increment n by 1.
4. If the sum of z and w is no more than 10, then the parent mos is zL ws and is n generations from the mos descendant xL ys. If not, repeat the process starting at step 2.

As diatonic (5L 2s) doesn't have a prefix, the terms chromatic, enharmonic, and subchromatic by themselves (and with no other context suggesting a non-diatonic mos) refer to 1st (child), 2nd (grandchild), and 3rd (great-grandchild) diatonic descendants. For consistency, mos descendant names apply to mosses whose child mosses exceed 10 notes. Since all mosses ultimately descend from some nL ns mos, every possible descendant up to 5 periods will be related to a named mos.

Mosses whose children have more than 10 notes (1st and 2nd descendants only)

6-note mosses		Chromatic mosses		Enharmonic mosses
Pattern	Name	Patterns	Names	Patterns	Names
1L 5s	antimachinoid	1L 6s, 6L 1s	n/a	1A 7B, 6A 7B	n/a
2L 4s	malic	2L 6s, 6L 2s	n/a	2A 8B, 6A 8B	n/a
3L 3s	triwood	3L 6s, 6L 3s	n/a	3A 9B, 6A 9B	n/a
4L 2s	citric	4L 6s, 6L 4s	n/a	4A 10B, 6A 10B	n/a
5L 1s	machinoid	5L 6s, 6L 5s	mechromatic	5A 11B, 6A 11B	mechenharmonic
7-note mosses		Chromatic mosses		Enharmonic mosses
Pattern	Name	Patterns	Names	Patterns	Names
1L 6s	onyx	1L 7s, 7L 1s	n/a	1A 8B, 7A 8B	n/a
2L 5s	antidiatonic	2L 7s, 7L 2s	n/a	2A 9B, 7A 9B	n/a
3L 4s	mosh	3L 7s, 7L 3s	n/a	3A 10B, 7A 10B	n/a
4L 3s	smitonic	4L 7s, 7L 4s	smichromatic	4A 11B, 7A 11B	smienharmonic
5L 2s	diatonic	5L 7s, 7L 5s	chromatic	5A 12B, 7A 12B	enharmonic
6L 1s	arch(a)eotonic	6L 7s, 7L 6s	archeoromatic	6A 13B, 7A 13B	archeoenharmonic
8-note mosses		Chromatic mosses		Enharmonic mosses
Pattern	Name	Patterns	Names	Patterns	Names
1L 7s	antipine	1L 8s, 8L 1s	n/a	1A 9B, 8A 9B	n/a
2L 6s	subaric	2L 8s, 8L 2s	n/a	2A 10B, 8A 10B	n/a
3L 5s	checkertonic	3L 8s, 8L 3s	checkchromatic	3A 11B, 8A 11B	checkenharmonic
4L 4s	tetrawood; diminished	4L 8s, 8L 4s	chromatic tetrawood	4A 12B, 8A 12B	enharmonic tetrawood
5L 3s	oneirotonic	5L 8s, 8L 5s	oneirochromatic	5A 13B, 8A 13B	oneiroenharmonic
6L 2s	ekic	6L 8s, 8L 6s	ekchromatic	6A 14B, 8A 14B	ekenharmonic
7L 1s	pine	7L 8s, 8L 7s	pinechromatic	7A 15B, 8A 15B	pinenharmonic
9-note mosses		Chromatic mosses		Enharmonic mosses
Pattern	Name	Patterns	Names	Patterns	Names
1L 8s	antisubneutralic	1L 9s, 9L 1s	n/a	1A 10B, 9A 10B	n/a
2L 7s	balzano	2L 9s, 9L 2s	balchromatic	2A 11B, 9A 11B	balenharmonic
3L 6s	tcherepnin	3L 9s, 9L 3s	cherchromatic	3A 12B, 9A 12B	cherenharmonic
4L 5s	gramitonic	4L 9s, 9L 4s	gramchromatic	4A 13B, 9A 13B	gramenharmonic
5L 4s	semiquartal	5L 9s, 9L 5s	chtonchromatic	5A 14B, 9A 14B	chtonenharmonic
6L 3s	hyrulic	6L 9s, 9L 6s	hyruchromatic	6A 15B, 9A 15B	hyrenharmonic
7L 2s	superdiatonic	7L 9s, 9L 7s	armchromatic	7A 16B, 9A 16B	armenharmonic
8L 1s	subneutralic	8L 9s, 9L 8s	bluchromatic	8A 17B, 9A 17B	bluenharmonic
10-note mosses		Chromatic mosses		Enharmonic mosses
Pattern	Name	Patterns	Names	Patterns	Names
1L 9s	antisinatonic	1L 10s, 10L 1s	asinachromatic	1A 11B, 10A 11B	asinenharmonic
2L 8s	jaric	2L 10s, 10L 2s	jarachromatic	2A 12B, 10A 12B	jaraenharmonic
3L 7s	sephiroid	3L 10s, 10L 3s	sephchromatic	3A 13B, 10A 13B	sephenharmonic
4L 6s	lime	4L 10s, 10L 4s	limechromatic	4A 14B, 10A 14B	limenharmonic
5L 5s	pentawood	5L 10s, 10L 5s	chromatic pentawood	5A 15B, 10A 15B	enharmonic pentawood
6L 4s	lemon	6L 10s, 10L 6s	lemchromatic	6A 16B, 10A 16B	lemenharmonic
7L 3s	dicoid, zaltertic	7L 10s, 10L 7s	dicochromatic, zalchromatic	7A 17B, 10A 17B	dicoenharmonic, zalenharmonic
8L 2s	taric	8L 10s, 10L 8s	tarachromatic	8A 18B, 10A 18B	tarenharmonic
9L 1s	sinatonic	9L 10s, 10L 9s	sinachromatic	9A 19B, 10A 19B	sinenharmonic

Names for mos descendants by step ratio

The designations of chromatic, enharmonic, and subchromatic by themselves does not describe a specific mos descendant. To do that, the name of a step ratio range can be prefixed to the terms chromatic, enharmonic, and subchromatic (or (mos-prefix)chromatic, (mos-prefix)enharmonic, and (mos-prefix)subchromatic). Specifying the step ratio is optional, and the names for step ratios can be abbreviated into a one or two-letter prefix. (Frostburn's abbreviations can be used here, too.) These prefixes are used for specific descendants, with the notable exception of soft and hard. For enharmonic mosses, these describe mosses with a step ratio outside the hyposoft and hypohard range. For subchromatic mosses, these describe mosses within the entire soft and hard ranges, producing terminology more specific than just subchromatic but not as specific as the specific step ratio ranges. These prefixes must include a hyphen.

Descendant mosses sorted by generation and step ratio

Parent mos		Chromatic mosses				Enharmonic mosses				Subchromatic mosses
Steps	L:s range	Steps	Prefix	Abbrev.	L:s range	Steps	Prefix	Abbrev.	L:s range	Steps	Broad prefixes		Specific prefixes		L:s range
											Prefix	Abbrev.	Prefix	Abbrev.
xL ys	1:1 to 1:0	(x+y)L xs	soft-	s-	1:1 to 2:1	(x+y)L (2x+y)s	soft-	s-	1:1 to 3:2	(x+y)L (3x+2y)s	soft-	s-	ultrasoft-	us-	1:1 to 4:3
										(3x+2y)L (x+y)s			parasoft-	ps-	4:3 to 3:2
						(2x+y)L (x+y)s	hyposoft-	os-	3:2 to 2:1	(3x+2y)L (2x+y)s			quasisoft-	qs-	3:2 to 5:3
										(2x+y)L (3x+2y)s			minisoft-	ms-	5:3 to 2:1
		xL (x+y)s	hard-	h-	2:1 to 1:0	(2x+y)L xs	hypohard-	oh-	2:1 to 3:1	(2x+y)L (3x+y)s	hard-	h-	minihard-	mh-	2:1 to 5:2
										(3x+y)L (2x+y)s			quasihard-	qh-	5:2 to 3:1
						xL (2x+y)s	hard-	h-	3:1 to 1:0	(3x+y)L xs			parahard-	ph-	3:1 to 4:1
										xL (3x+y)s			ultrahard-	uh-	4:1 to 1:0

Example with balzano (2L 7s)

Balzano (parent)		Chromatic balzano		Enharmonic balzano		Subchromatic balzano
Steps	Name	Steps	Name	Steps	Name	Steps	Broad name	Specific name
2L 7s	balzano	9L 2s	s-balchromatic	9L 11s	s-balenharmonic	9L 20s	s-balsubchromatic	us-balsubchromatic
						20L 9s		ps-balsubchromatic
				11L 9s	os-balenharmonic	20L 11s		qs-balsubchromatic
						11L 20s		ms-balsubchromatic
		2L 9s	h-balchromatic	11L 2s	oh-balenharmonic	11L 13s	h-balsubchromatic	mh-balsubchromatic
						13L 11s		qh-balsubchromatic
				2L 11s	h-balenharmonic	13L 2s		ph-balsubchromatic
						2L 13s		uh-balsubchromatic

Other mos names

This section describes additional names for mosses that have more than 10 notes but are worthy of names.

Names for mos descendants with more than 5 periods

To name mos descendants with more than 5 periods, the names for wood mosses are extended to hexawood, heptawood (or septawood), octawood, nonawood (or enneawood), and decawood. (This is not too different from Frostburn's proposal.) Beyond that, the naming scheme becomes 11-wood, 12-wood, and so on, and mosses are referred to chromatic (number)-wood, enharmonic (number)-wood, and subchromatic (number)-wood. The term (number)-wood descendants is also used, and to refer to nth (number)-wood descendants, the algorithm is used below to find the number of generations:

1. 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 n = 0, where n is the number of generations away from zL ws.
2. Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
3. Assign to z the value m2 and w the value m1-m2. Increment n by 1.
4. If both z and w are equal to 1, then the parent mos is nL ns and is n generations from the mos descendant xL ys. If not, repeat the process starting at step 2.

Names for wood scales up to 10 periods

Mos	Name	Prefix	Abbrev.
6L 6s	hexawood	hexwud-	hw
7L 7s	septawood or heptawood	sepwud- or hepwud-	sw or hw
8L 8s	octawood	octwud-	ow
9L 9s	nonawood or enneawood	nonawud- or ennwud-	nw or enw
10L 10s	decawood	dekwud-	dkw
11L 11s	11-wood	11-wud-	11wd
12L 12s	12-wood	12-wud	12wd
etc...

Names for mos linear families

A mos linear family is a family of related mosses of the form xL (nx + y)s. This family starts with the mos xL ys, where x < y and n=0, and continue with mosses with the same number of large steps but a linearly growing quantity of small steps. An example of such a family is the mos sequence 5L 2s, 5L 7s, 5L 12s, 5L 17s, etc, where each successive mos has 5 more small steps than the last.

Mosses in this family relate to one another by repeated application of the replacement ruleset L->Ls and s->s to the initial mos's step pattern. In terms of step ratio, these mosses relate back to the initial mos if the initial mos has a hard or pseudoequalized step ratio. Continuing with the example of 5L 2s, the smallest edo that can reach 5L 7s is 17edo (where L:s = 2:1, therefore 5L+7s = 17), producing a 5L 2s mos with a step ratio of 3:1, whereas reaching the mos 5L 17s requires the initial mos of 5L 2s to have a step ratio of 5:1.

Names of single-period mos linear families (work-in-progress)

Trivial families
Mos	Name	Reasoning
1L ns	monolarge family	Represents an entire family of mosses formerly unnamed by TAMNAMS
2L (2n+1)s	bilarge family	Named analogously to the monolarge family
Families with 3 large steps
Mos	Name	Reasoning
3L (3n+1)s	tetralinear family	Named after tetric, the first mos in this sequence (n=0)
3L (3n+2)s	anpentilinear family	Named after anpentic
Families with 4 large steps
Mos	Name	Reasoning
4L (4n+1)s	manulinear family	Named after manual
4L (4n+3)s	smilinear family	Named after smitonic
Families with 5 large steps
Mos	Name	Reasoning
5L (5n+1)s	mechlinear family	Named after machinoid
5L (5n+2)s	p-linear family	Named after p-chromatic rather than diatonic, which has no prefix
5L (5n+3)s	oneirolinear family	Named after oneirotonic
5L (5n+4)s	chtonlinear family	Named after semiquartal (prefix chton-)
Families with 6 large steps
Mos	Name	Reasoning
6L (6n+1)s	archeolinear family	Named after archeotonic
6L (6n+5)s	xeimlinear family	Named after xeimtonic, a former name for 6L 5s
Families with 7 large steps
Mos	Name	Reasoning
7L (7n+1)s	pinelinear family	Named after pine
7L (7n+2)s	armlinear family	Named after armotonic (also called superdiatonic)
7L (7n+3)s	dicolinear or zalinear family	Named after dicotonic (also called zaltertic)
7L (7n+4)s	prasmilinear family	Named after suprasmitonic, a former name for 7L 4s but with a truncated name
7L (7n+5)s	m-linear family	Named after m-chromatic rather than diatonic
7L (7n+6)s
Families with 8 large steps
Mos	Name	Reasoning
8L (8n+1)s	blulinear family	Named after subneutralic (prefix blu-)
8L (8n+3)s
8L (8n+5)s	petrlinear family	Named after petroid, a former name for 8L 5s
8L (8n+7)s
Families with 9 large steps
Mos	Name	Reasoning
9L (9n+1)s	sinalinear family	Named after sinatonic
9L (9n+2)s
9L (9n+4)s
9L (9n+5)s
9L (9n+7)s
9L (9n+8)s

Reasoning for names

The names for chromatic scales are based on former names for the child mosses of diatonic (5L 2s) - p-chromatic for 5L 7s and m-chromatic for 7L 5s - and was generalized to chromatic mos. The term enharmonic is already in use to describe the grandchild mosses of diatonic, and so was generalized to enharmonic mos. The term subchromatic is a term coined by Mike Battaglia to describe a scale that is more chromatic than either chromatic or enharmonic, and is generalized to subchromatic mos.

The format of adding a mos's prefix to the terms descendant, chromatic, enharmonic, and subchromatic is best applied to mosses that have no more than three periods. With mosses that descend directly from nL ns mosses especially (4L 4s and above), this is to keep names from being too cumbersome (eg, chromatic (number)-wood instead of (number)-woodchromatic).

Various people have suggested the use of p- and m- as prefixes to refer to specific chromatic mosses, as well as the use of f- and s- for enharmonic mosses. Generalizing the pattern to 3rd mos descendants reveals an issue where the letters started to diverge from one another, notably where m- is no longer next to p- and f- and s- are no longer along the extremes. Rather than to use these letters and to maintain temperament agnosticism, prefixes based on step ratios are used instead.

Temperament-based mosdescendant prefixes

Diatonic scale	Chromatic mosses			Enharmonic mosses			Subchromatic mosses
	Steps	Notable temperament	Prefix	Steps	Notable temperament	Prefix	Steps	Notable temperament	Prefix
5L 2s	7L 5s	meantone	m-	7L 12s	flattone	f-	7L 19s	tridecimal	t-
							19L 7s	flattone	f-
				12L 7s	meantone	m-	19L 12s	meanpop	m-
							12L 19s	huygens	h-
	5L 7s	pythagorean	p-	12L 5s	pythagorean	p-	12L 17s	pythagorean	p-
							17L 12s	gentle	g-
				5L 12s	superpyth	s-	17L 5s	superpyth	s-
							5L 17s	ultrapyth	u-

The temperament-based prefixes may be used specifically for diatonic descendants as alternatives to the prefixes based on step ratios, effectively bringing back the names of p-chromatic and m-chromatic.