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 for how to name mos descendants. However, this page describes several more systems that apply to non-octave mosses.

The schemes proposed here are not meant to be a definitive naming scheme. Rather, it's meant to be a starting point for a naming scheme discussion. Some parts of this page also serves as a sandbox.

The scope of this TAMNAMS extension is as follows:

1. Systematically name mosses beyond the named range by how they're related to TAMNAMS-named mosses. The most common way of doing this is by considering what mosses descend from a TAMNAMS-named mos.
   1. Secondarily, propose unique names, or provide suggestions for possible names, for certain mosses in case they're worth having distinct names. Some of these names are old names that have been around long enough to be memorable.
      1. Catalog any names that had already existed or have been proposed elsewhere on the wiki.
2. Systematically name mosses regardless of the equave. Such names should be as general as possible. Names for mosses with no more than 10 notes are prioritized.
3. Propose names for 3/2 (fifth) and 3/1 (tritave) equivalent mosses, or provide suggestions for possible name ideas. Names for mosses with no more than 10 notes are prioritized.

There are two types of names described in this section:

• Systematic names, which use an exiting TAMNAMS name and a step ratio range as a base. This has two subtypes:
  • Descriptive names, a multi-word name that describes the mos itself.
  • Shortened names, a shortened form of a descriptive name.
• Specific names, unique names to be used to make a mos distinct from its parent or ancestor mos.

Mosses for which extension names apply

These names are recommended for mosses whose child mosses exceed 10 notes.

	Eligible parent mosses		Child mosses
	Pattern	Name	Patterns	Note counts
6-note mosses	5L 1s	machinoid	5L 6s, 6L 5s	11
7-note mosses	4L 3s	smitonic	4L 7s, 7L 4s	11
	5L 2s	diatonic	5L 7s, 7L 5s	12
	6L 1s	arch(a)eotonic	6L 7s, 7L 6s	13
8-note mosses	3L 5s	checkertonic	3L 8s, 8L 3s	11
	4L 4s	tetrawood; diminished	4L 8s, 8L 4s	12
	5L 3s	oneirotonic	5L 8s, 8L 5s	13
	6L 2s	ekic	6L 8s, 8L 6s	14
	7L 1s	pine	7L 8s, 8L 7s	15
9-note mosses	2L 7s	balzano	2L 9s, 9L 2s	11
	3L 6s	tcherepnin	3L 9s, 9L 3s	12
	4L 5s	gramitonic	4L 9s, 9L 4s	13
	5L 4s	semiquartal	5L 9s, 9L 5s	14
	6L 3s	hyrulic	6L 9s, 9L 6s	15
	7L 2s	superdiatonic	7L 9s, 9L 7s	16
	8L 1s	subneutralic	8L 9s, 9L 8s	17
10-note mosses	1L 9s	antisinatonic	1L 10s, 10L 1s	11
	2L 8s	jaric	2L 10s, 10L 2s	12
	3L 7s	sephiroid	3L 10s, 10L 3s	13
	4L 6s	lime	4L 10s, 10L 4s	14
	5L 5s	pentawood	5L 10s, 10L 5s	15
	6L 4s	lemon	6L 10s, 10L 6s	16
	7L 3s	dicoid	7L 10s, 10L 7s	17
	8L 2s	taric	8L 10s, 10L 8s	18
	9L 1s	sinatonic	9L 10s, 10L 9s	19

Systematic names for mos descendants

Base names

To name mosses that have more than 10 notes, names 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.

Base systematic names

Name type	Parent mos	Child (1st descendant)	Grandchild (2nd descendant)	Great-grandchild (3rd descendant)	kth descendant
Descriptive name	(mos-name)	chromatic (mos-name)	enharmonic (mos-name)	subchromatic (mos-name)	(kth) (mos-name) descendant
Shortened name	(mos-name)	(mos-prefix)enharmonic	(mos-prefix)enharmonic	(mos-prefix)subchromatic	(mos-prefix)descendant

The term kth descendant or (mos-prefix)descendant is used to refer to descendants more than 3 generations away, but can be used generally for any number of generations. To find the number of generations k separating the two mosses, use the following algorithm:

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.

Hardness modifiers

Optionally, a hardness modifier, which describes a parent mos's step ratio range, can be added before a systematic name to make mosses of the same generation more distinct from one another. Hardness modifiers can be added as a range name or a prefix to either the descriptive name or shortened name; however, to make a descriptive name more clear, it's recommended to use a range name rather than a prefix. Mos descendants farther than 3 generations away from a parent mos do not have hardness modifiers.

Hardness modifiers

Parent mos		Child (1st descendant)				Grandchild (2nd descendant)				Great-grandchild (3rd descendant)
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	os-	(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	oh-	(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 usage (using smitonic)

• Describing the child mosses of smitonic generally: chromatic smitonic
• Describing the child mosses of smitonic based on the parent's step ratio: hard-of-basic chromatic smitonic and soft-of-basic chromatic smitonic
• When context is established that hardness prefixes can be used: h-chromatic smitonic and s-chromatic smitonic

Specific names for mosses beyond 10 notes

This section outlines proposed names and naming suggestions for mosses beyond 10 notes.

Extended k-wood names

To name mos descendants with more than 5 periods, the names for wood mosses are extended to hexawood, heptawood, octawood, enneawood, and decawood. (This is not too different from Frostburn's proposal.) Names for descendants for these scales follow the same scheme as with other TAMNAMS-named mosses.

Names for wood scales up to 10 periods

Mos	Name	Prefix	Abbrev.
6L 6s	hexawood	hexwd-	hxw
7L 7s	heptawood	hepwd-	hpw
8L 8s	octawood	octwd-	ocw
9L 9s	enneawood	ennwd-	enw
10L 10s	decawood	dekwd-	dkw
11L 11s	11-wood	11-wud-	11wd
12L 12s	12-wood	12-wud	12wd
etc...

Specific names for mosses beyond 10 notes (proposed)

Specific names are intended for notable mosses outside the named range for which its mos descendant name would be insufficient. Names suggested by other users are included here for comparison.

Specific names for mosses with 11 to 13 notes

11-note mosses
Mos	Suggested name(s)	Proposed by	Reasoning
1L 10s	tanzanite or tenorite	Ganaram inukshuk	More naming puns (tenzanite or tenorite)
2L 9s
3L 8s
4L 7s	kleistonic		Former TAMNAMS name
5L 6s
6L 5s
7L 4s	suprasmitonic		Former TAMNAMS name
	daemotonic	Ganaram inukshuk, Eliora	Described as being "furthest removed from typical xen approaches of RTT or JI."
9L 2s	villatonic	Ganaram inukshuk	Indirectly references avila and casablanca (houses) temperaments
	ultradiatonic, superarmotonic	CompactStar	In reference to diatonic and armotonic
10L 1s	miratonic or miraculoid	Ganaram inukshuk	Modification or restoration of an old name (miraculoid); reference miracle temperament
12-note mosses
Mos	Suggested name(s)	Proposed by	Reasoning
1L 11s	helenite	Ganaram inukshuk	In reference to the "ele" substring found in the word "eleven"
2L 10s
3L 9s
4L 8s
5L 7s	p-chromatic		Former TAMNAMS name
6L 6s	hexawood		Extension of -wood scales; coincidentally references hexe temperament
7L 5s	m-chromatic		Former TAMNAMS name
8L 4s
9L 3s
10L 2s
11L 1s
13-note mosses
Mos	Suggested name(s)	Proposed by	Reasoning
1L 12s	zircon	Ganaram inukshuk	Zircon is used as a birthstone for December
2L 11s
3L 10s
4L 9s
5L 8s
6L 7s
7L 6s	tetarquintal	Ganaram inukshuk	Indirect reference to tetracot temperament, which divides the perfect 5th (3/2) into four
8L 5s
9L 4s
10L 3s	luachoid		Already proposed name
11L 2s	maioquartal	Ganaram inukshuk	In reference to the "major fourths" scale used by Tcherepnin
	hendecoid	Eliora	From Greek "eleven", references how "its generator is so close to 11/8 as to be called nothing but that".
12L 1s	quasidozenal	Ganaram inukshuk	Meant to invoke the phrase "almost twelve"
14-note mosses
Mos	Suggested name(s)	Proposed by	Reasoning
11L 3s	ketradektriatoh	Osmiorisbendi‎	Already established name
13L 1s	trollic	Godtone	Refers to 12L 1s, but refers to 13L 1s as a troll move
15-note mosses
Mos	Suggested name(s)	Proposed by	Reasoning
14L 1s	sextiliquartal	Eliora	Already proposed name, references temperaments that divide 4/3 into 6 pieces

Other higher note count mosses

Note count	Mos	Suggested name(s)	Proposed by	Reasoning
17	2L 15s	liesic	Frostburn	Frostburn's extension scheme stops here, so this name is suggested
21	10L 11s	miracloid	Eliora	In reference to miracle temperament
22	3L 19s	zheligowskic	Frostburn	In reference to Lucjan Żeligowski leading fights against the town of Giedraičiai.
	19L 3s	giedraitic	Frostburn	Named after the basic magic layout of Kite Giedraitis' guitar.
	21L 1s	escapist	Eliora	References escapade temperament, which is supported by both 21edo and 22edo, covering the entire range.
23	22L 1s	quartismoid	Eliora	Five generators of roughly 33/32 quartertone are equal to 7/6 in the harmonic entropy minimum; also, the extreme ranges of 22edo and 23edo both support this mos.
25	4L 21s	moulinoid	Eliora	In reference to moulin temperament

Non-octave extensions (proposed)

Since the perfect 5th and tritave (or perfect 12th) are the two most common non-octave equivalence intervals for which there are scales described, mosses for these two intervals should be the most likely to receive TAMNAMS-like names. For mosses with any other equivalence interval, describing nested mos structures, or in situations where the notion of an equivalence interval is unimportant, equave-agnostic names are proposed.

Equave-agnostic names (proposed)

This is a proposed scheme to name mosses regardless of the equivalence interval, These names are meant for nonoctave mosses and nested mos patterns such as with a mos cradle. These names are not final and are open to better suggestions.

4-note mosses (new names only)
Mos	Name	Multi-period?	Prefix	Abbrev.
2L 2s	double trivial	Yes (2)	2triv-	2trv
6-note mosses
Mos	Name	Multi-period?	Prefix	Abbrev.
1L 5s	anhexic	No	ahex-	ahx
2L 4s	double antrial	Yes (2)	2atri-	2tri
3L 3s	triple trivial	Yes (3)	3triv-	3trv
4L 2s	double trial	Yes (2)	2tri-	2tri
5L 1s	hexic	No	hex-	hx
7-note mosses
Mos	Name	Multi-period?	Prefix	Abbrev.
1L 6s	ansaptic	No	ansap-	asp
2L 5s	anheptic	No	anhep-	ahp
3L 4s	anseptenic	No	ansep-	asep
4L 3s	septenic	No	sep-	sep
5L 2s	heptic	No	hep-	hp
6L 1s	saptic	No	sap-	sp
8-note mosses
Mos	Name	Multi-period?	Prefix	Abbrev.
1L 7s	anastaic	No	anast-	aast
2L 6s	double antetric	Yes (2)	2atetra-	2att
3L 5s	anoctic	No	anoct-	aoct
4L 4s	quadruple trivial	Yes (4)	4triv-	4trv
5L 3s	octic	No	oct-	oct
6L 2s	double tetric	Yes (2)	2tetra-	2tt
7L 1s	astaic	No	ast-	ast
9-note mosses
Mos	Name	Multi-period?	Prefix	Abbrev.
1L 8s	annavic	No	annav-	anv
2L 7s	anennaic	No	anenn-	aenn
3L 6s	triple antrial	Yes (3)	3atri-	3atri
4L 5s	annovemic	No	annov-	anv
5L 4s	novemic	No	nov-	nv
6L 3s	triple trial	Yes (3)	3tri-	3tri
7L 2s	ennaic	No	enn-	enn
8L 1s	navic	No	nav-	nv
10-note mosses
Mos	Name	Multi-period?	Prefix	Abbrev.
1L 9s	andashic	No	andash-	adsh
2L 8s	double pedal	Yes (2)	2ped-	2ped
3L 7s	andeckic	No	andeck-	adek
4L 6s	double pentic	Yes (2)	2pent-	2pt
5L 5s	quintuple trivial	Yes (5)	5triv-	5trv
6L 4s	double anpentic	Yes (2)	2apent-	2apt
7L 3s	deckic	No	deck-	dek
8L 2s	double manual	Yes (2)	2manu-	2manu
9L 1s	dashic	No	dash-	dsh

Names for these mosses are meant to be as general as possible, starting with established names that are already equave-agnostic: trivial, (an)trial, (an)tetric, (an)pentic, and pedal/manual. Mosses are named in pairs of xL ys and yL xs, where the mos with more small steps than large steps is given the an- prefix, short for anti-; this rule doesn't apply to pentic (2L 3s) and anpentic (3L 2s), where the former is the familiar pentatonic scale.

As there is only one pair of 6-note single-period mosses, 5L 1s and 1L 5s, the pair is named hexic.

With 7-note mosses, there are three pairs of mosses, whose names are based on three languages: Greek, Latin, and Sanskrit. The pair 5L 2s and 2L 5s are given the Greek-based name of heptic, as 5L 2s is the familiar diatonic scale. The next pair, 3L 4s and 4L 3s, are given the Latin-based name of septenic. The last pair, 1L 6s and 6L 1s, are given the Sanskrit-based name of saptic.

This pattern is continued for all successive sequences of mosses for each successive note count: 1L ns and nL 1s are given a Sanskrit-based name, the next single-period pair after that are given a Greek-based name, and the next single-period pair after that are given a Latin-based name. The two 8-note pairs are named astaic (7L 1s and 1L 7s) and octic (5L 3s and 3L 5s) respectively. The three 9-note pairs are named navic (8L 1s and 1L 8s), ennaic (7L 2s and 2L 7s), and novemic (4L 5s and 5L 4s). Finally the two 10-note pairs are named dashic (9L 1s and 1L 9s) and dekic (7L 3s and 3L 7s).

11-note mosses require naming five pairs, so this naming scheme stops at 10-note mosses.

Since the equivalence interval can be anything, names for multi-period mosses are named as a smaller mos repeated (double, triple, quadruple, etc) some number of times. The prefix and abbreviation of the base mos is preceded by the number of duplications. For example, 2L 2s is double trivial, its prefix is 2triv-, and its abbreviation is 2trv.

Names for 3/2-equivalent mosses

Names are based on information that is available on their respective pages. Otherwise, possible ideas are given. Only mosses with 10 or fewer notes are prioritized for names.

4-note mosses <3/2>
Mos	Name (if given)	Prefix	Abbrev.	Reasoning or ideas
1L 3s	neptunian	nept-	nep	Name proposed by CompactStar, analogous to uranian
5-note mosses <3/2>
Mos	Name (if given)	Prefix	Abbrev.	Reasoning or ideas
3L 2s	uranian	ura-	ura	Already-existing name

Names for 3/1-equivalent mosses

Names are based on information that is is available on their respective pages. Otherwise, possible ideas are given. Only mosses with 10 or fewer notes are prioritized for names.

7-note mosses <3/1>
Mos	Name (if given)	Prefix	Abbrev.	Reasoning or ideas
3L 4s				In reference to electromagnetism, 3L 4s <3/1> could be named "magnetic"
4L 3s	electric	elec-	ele	Name proposed by CompactStar
9-note mosses <3/1>
Mos	Name (if given)	Prefix	Abbrev.	Reasoning or ideas
4L 5s	lambdatonic	lam-	lam	"Lambda" already refers to tritave-equivalent 4L 5s

Reasoning for names

The overall motivation for these names is to give names to closely related mosses and refer to individual mosses as some member of a broader family, rather than name individual mosses.

Various terms have been used to similarly describe child mosses, notably the terms haplotonic, albitonic, and chromatic. However, the terms chosen are chromatic, enharmonic, and subchromatic, as they are the closest to being generalizable.

Source of terms	Grandparent (2nd predecessor)	Parent (1st predecessor)	Mos	Child (1st descendant)	Grandchild (2nd descendant)	Great-grandchild (3rd descendant)	kth descendant
From Diatonic, Chromatic, Enharmonic, Subchromatic	n/a	n/a	diatonic	chromatic	enharmonic	subchromatic	n/a
From Chromatic pairs	n/a	haplotonic	albitonic	chromatic	mega-chromatic		n/a
				mega-albitonic	chromatic	mega-chromatic	n/a
Temperament-based prefixes (see diatonic descendants table)	n/a	n/a	mos	prefixed with m- or p-	prefixed with f-, m-, p-, or s-	prefixed with t-, f-, m-, h-, p-, g-, s-, or u-	n/a
Terminology used for this page	n/a	n/a	mos	chromatic mos	enharmonic mos	subchromatic mos	kth descendant

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, has been suggested by various users, but gneralizing the pattern to 3rd mos descendants shows the letters diverging from one another, notably where m- is no longer next to p- and f- and s- are no longer along the extremes. Rather than using these letters, as well as being temperament-agnostic, prefixes based on step ratios are used instead. However, temperament-based prefixes may be used specifically for diatonic descendants as alternatives to the prefixes based on step ratios. For this reason, the former TAMNAMS names m- and p-chromatic are included as specific names.

Prefixes for diatonic descendants

Diatonic scale	Chromatic mosses			Enharmonic mosses			Subchromatic mosses
	Steps	Temp-based prefix	Ratio-based prefix	Steps	Temp-based prefix	Ratio-based prefix	Steps	Temp-based prefix	Ratio-based prefix
5L 2s	7L 5s	m- (from meantone)	s-	7L 12s	f- (from flattone)	s-	7L 19s	t- (from tridecimal)	us-
							19L 7s	f- (from flattone)	ps-
				12L 7s	m- (from meantone)	os-	19L 12s	m- (from meanpop)	qs-
							12L 19s	h- (from huygens)	ms-
	5L 7s	p- (from pythagorean)	h-	12L 5s	p- (from pythagorean)	oh-	12L 17s	p- (from pythagorean)	mh-
							17L 12s	g- (from gentle)	qh-
				5L 12s	s- (from superpyth)	h-	17L 5s	s- (from superpyth)	ph-
							5L 17s	u- (from ultrapyth)	uh-