User:Ganaram inukshuk/TAMNAMS Extension

Main article: TAMNAMS

This page describes TAMNAMS-like names applied to octave-equivalent mosses with more than 10 notes, as well as non-octave mosses (fifth and tritave equivalent).

Disclaimer

The names described in this section may may have limited use. Some of these names may only find usage by a single person or a small group and thus have limited acceptance by the broader xen community. These names may also be subject to change as these names or the scales they refer to gain greater usage by the community, and it may be possible for the same scale to have more than one name.

Relating a mos and its descendants

Larger mosses can be described by how they related back to a more familiar mos and vice-versa. In general, all mosses with n periods relate back to a root mos of nL ns. For TAMNAMS-named mosses, any octave-equivalent mos with more than 10 steps and no more than 5 periods is related to some TAMNAMS-named mos.

In either case, any mos can be related to its descendants by treating it as the root of its own scale tree. Particularly in the absence of any names, mosses can be described as being some descendant of a related ancestor mos xL ys. Such mosses, called mos descendants – or children, grandchildren, and great-grandchildren, for the first three generations of descendants – contain the following pattern of step counts.

Parent		Child		Grandchild		Great-grandchild
Large steps	Small steps	Large steps	Small steps	Large steps	Small steps	Large steps	Small steps
x	y	x+y	x	x+y	2x+y	x+y	3x+2y
						3x+2y	x+y
				2x+y	x+y	3x+2y	2x+y
						2x+y	3x+2y
		x	x+y	2x+y	x	2x+y	3x+y
						3x+y	2x+y
				x	2x+y	3x+y	x
						x	3x+y

For example, the first three generations of diatonic descendants can be described as:

• Children of 5L 2s: 7L 5s and 5L 7s
• Grandchildren of 5L 2s: 5L 12s, 12L 5s, 12L 7s, and 7L 12s
• Great-grandchildren of 5L 2s: 5L 17s, 17L 5s, 17L 12s, 12L 17s, 12L 19s, 19L 12s, 12L 7s, and 7L 19s

Finding the ancestor of a descendant mos xL ys

For a mos xL ys, perform the following algorithm to find a familiar ancestor with target note count n or less:

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.
2. Let m₁ be assigned the value of max(z, w) and m₂ the value of min(z, w).
3. Assign to z the value m₂ and w the value m₁-m₂.
4. If z+w is less than or equal to n, then the ancestor mos is zL ws. If not, repeat the process starting at step 2.

Finding an ancestor's step ratio that produces a descandant mos xL ys

For a mos xL ys, perform the following algorithm to find the step ratio for a descendant mos zL ws with target note count n or less:

1. Let z and w be the number of large and small steps of the parent mos to be found. Let U and V be two chunks, vectors containing the amounts of L's and s's from xL ys that make up the ancestor mos's large and small steps.
   1. Assign to z and w the values x and y respectively.
   2. Assign to U the vector { u_L, u_s } = { 1, 0 } and V to the vector { v_L, v_s } = { 0, 1 }.
2. Let m₁ be assigned the value of max(z, w) and m₂ the value of min(z, w).
   1. If w > z, then add V to U. Otherwise, assign to a temporary vector U_temp the value of U, add V to U, and assign to V the value of U_temp.
3. Assign to z the value m₂ and w the value m₁-m₂.
4. If z+w is less than or equal to n, then the ancestor mos is zL ws. The step ratio range for the zL ws is (u_L+ u_s):(v_L+ v_Ls) to u_L:v_s. If z+w is not less than or equal to n, repeat the process starting at step 2.

Names for mosses with more than 10 notes

Names for nL ns mosses with more than 5 periods

The following names are based on the -wood names, with appropriate Greek numeral prefixes applied.

Pattern	Suggested name	Prefix	Abbrev.	Reasoning
6L 6s	hexawood	hexwd-	hxw	Greek numeral prefix (hexa-) for six, plus "wood"
7L 7s	heptawood	hepwd-	hpw	Greek numeral prefix (hepta-) for seven, plus "wood"
8L 8s	octawood	octwd-	ocw	Greek numeral prefix (octo-) for eight, plus "wood"
9L 9s	enneawood	ennwd-	enw	Greek numeral prefix (ennea-) for nine, plus "wood"
10L 10s	decawood	decwd-	dkw	Greek numeral prefix (deca-) for ten, plus "wood"
11L 11s	hendecawood	hedwd-	hdw	Greek numeral prefix (hendeca-) for 11, plus "wood"
12L 12s	dodecawood	dodwd-	ddw	Greek numeral prefix (dodeca-) for 12, plus "wood"
13L 13s	13-wood	13wd-	13w	Number 13 prepended to "wood"
14L 14s	14-wood	14wd-	14w	Number 14 prepended to "wood"
kL ks	k-wood	kwd	kw	General number k prepended to "wood"

Names for mosses with 11 or more notes (excluding nL ns mosses)

11-note mosses
Pattern	Suggested name(s)	Proposed by	Reasoning
1L 10s	tanzanite, tenorite	Ganaram inukshuk	More naming puns (tenzanite or tenorite).
4L 7s	kleistonic		Former TAMNAMS name.
7L 4s	suprasmitonic		Former TAMNAMS name.
	daemotonic	Eliora	Various reasons; see 7L 4s.
9L 2s	villatonic	Ganaram inukshuk	Indirectly references avila and casablanca temperaments.
	ultradiatonic, superarmotonic	CompactStar	In reference to diatonic and armotonic.
12-note mosses
Pattern	Suggested name(s)	Proposed by	Reasoning
1L 11s	helenite	Ganaram inukshuk	In reference to the "ele" substring found in the word "eleven".
5L 7s	p-chromatic		Former TAMNAMS name.
7L 5s	m-chromatic		Former TAMNAMS name.
13-note mosses
Pattern	Suggested name(s)	Proposed by	Reasoning
1L 12s	zircon	Ganaram inukshuk	Zircon is used as a birthstone for December.
11L 2s	hendecoid	Eliora	From Greek "eleven"; references how "its generator is so close to 11/8 as to be called nothing but that" and that it has 11 large steps.
14-note mosses
Pattern	Suggested name(s)	Proposed by	Reasoning
13L 1s	trollic	Godtone	The name proposed by Godtone refers to 12L 1s, but it refers to 13L 1s as a troll move.

Note count	Pattern	Suggested name(s)	Proposed by	Reasoning
17	2L 15s	liesic	Frostburn	Frostburn's naming scheme only goes up to 3 generations, so this name is suggested.
19	3L 16s	magicaltonic	Xenllium	In reference to magic temperament.
	16L 3s	muggletonic	Xenllium	In reference to muggle temperament.
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. Proposed prefix is "kai-".
	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.

Names for non-octave mosses

3/1-equivalent mosses

7-note mosses <3/1>
Pattern	Suggested name(s)	Proposed by	Reasoning
4L 3s	electric	CompactStar	In reference to electra temperament
9-note mosses <3/1>
Pattern	Suggested name(s)	Proposed by	Reasoning
4L 5s	lambdatonic	n/a	"Lambda" already refers to 4L 5s
11-note mosses <3/1>
Pattern	Suggested name(s)	Proposed by	Reasoning
7L 4s	superelectric	CompactStar?	Expansion of 4L 3s
9L 2s	subarcturus	?	?

3/2-equivalent mosses

4-note mosses <3/2>
Pattern	Suggested name(s)	Proposed by	Reasoning
1L 3s	neptunian	CompactStar	In reference to "uranian" for 3L 2s<3/2>
5-note mosses <3/2>
Pattern	Suggested name(s)	Proposed by	Reasoning
2L 3s	saturnian	CompactStar	In reference to "uranian" for 3L 2s<3/2>
3L 2s	uranian	?	?

Names for equave-agnostic mosses

Equave-agnostic names (proposed by Ganaram) are an extension to the equave-agnostic names provide by TAMNAMS. They are based on Greek, Latin, and Sanskrit numeral prefixes. Names for multi-period equave-agnostic mosses are not provided, as they would be repetitions of a smaller step pattern.

6-note mosses
Pattern	Suggested name	Prefix	Abbrev.	Reasoning
1L 5s	anhexic	ahex-	ahx	Greek numeral prefix (hex-) for six, plus "an-"
5L 1s	hexic	hex-	hx	Greek numeral prefix "(hex-) for six
7-note mosses
Pattern	Suggested name	Prefix	Abbrev.	Reasoning
1L 6s	ansaptic	ansap-	asp	Sanskrit numeral prefix (sapta-) for seven, plus "an-"
2L 5s	anheptic	anhep-	ahp	Greek numeral prefix (hepta-) for seven, plus "an-"
3L 4s	anseptenic	ansep-	asep	Latin numeral prefix (septen-) for seven, plus "an-"
4L 3s	septenic	sep-	sep	Latin numeral prefix (septen-) for seven
5L 2s	heptic	hep-	hp	Greek numeral prefix (hepta-) for seven
6L 1s	saptic	sap-	sp	Sanskrit numeral prefix (sapta-) for seven
8-note mosses
Pattern	Suggested name	Prefix	Abbrev.	Reasoning
1L 7s	anastaic	anast-	aast	Sanskrit numeral prefix (aṣṭa-) for eight, plus "an-"
3L 5s	anoctic	anoct-	aoct	Greek/Latin numeral prefix (octo-) for eight, plus "an-"
5L 3s	octic	oct-	oct	Greek/Latin numeral prefix (octo-) for eight
7L 1s	astaic	ast-	ast	Sanskrit numeral prefix (aṣṭa-) for eight
9-note mosses
Pattern	Suggested name	Prefix	Abbrev.	Reasoning
1L 8s	annavic	annav-	anv	Sanskrit numeral prefix (nava-) for nine, plus "an-"
2L 7s	anennaic	anenn-	aenn	Greek numeral prefix (ennea-) for nine, plus "an-"
4L 5s	annovemic	annov-	anv	Latin numeral prefix (novem-) for nine, plus "an-"
5L 4s	novemic	nov-	nv	Latin numeral prefix (novem-) for nine
7L 2s	ennaic	enn-	enn	Greek numeral prefix (ennea-) for nine
8L 1s	navic	nav-	nv	Sanskrit numeral prefix (nava-) for nine
10-note mosses
Pattern	Suggested name	Prefix	Abbrev.	Reasoning
1L 9s	andashic	andash-	adsh	Sanskrit numeral prefix (dasha-) for ten, plus "an-"
3L 7s	andeckic	andeck-	adek	Greek/Latin numeral prefix (decem-/deca-) for ten, plus "an-"
7L 3s	deckic	deck-	dek	Greek/Latin numeral prefix (decem-/deca-) for ten
9L 1s	dashic	dash-	dsh	Sanskrit numeral prefix (dasha-) for ten

Appendix

The motivation behind these names is from a desire to expand TAMNAMS-like names past the current note limit of 10 steps and, to a lesser extent, preserve former TAMNAMS names given to such mosses.

The names for mos descendants are given the general terms of child, grandchild, great-grandchild, and so on. Formerly, names based on the terms chromatic and enharmonic were prescribed, much in the spirit of m-chromatic and p-chromatic. These terms, accompanied by single-letter prefixes, such as m- and p-, and others, were used as bases for the descendants of any mos. However, these names were abandoned since the concept of chromatic did not generalize well outside the context of chromatic pairs, and the single-letter prefixes were considered temperament-suggestive.

More unique names have been prescribed by others, but have limited use or acceptance by the xen community as a whole.

The names m-chromatic and p-chromatic, as they apply to 7L 5s and 5L 7s, are left unchanged, but can alternatively be described generally as child scales of diatonic, or specifically, the child scale of soft diatonic and child scale of hard diatonic respectively.