User:Ganaram inukshuk/Notes/TAMNAMS

This is a subpage for TAMNAMS-related notes, containing various proposals of varying degrees of usefulness and other useful things. This also contains some rewrites of sections of the main TAMNAMS page that aren't quite ready to be deployed.

Sandboxed rewrites

Reasoning for names

See: TAMNAMS#Reasoning for the names

The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.

Names for small mosses

All names for single-period mosses (mosses of the form xL ys where x and y are coprime) with no more than 5 notes require that some small integer multiple of the period is equal to an octave or a tempered octave, under the reasoning that these mosses are common and broad enough that they may be of interest in non-octave contexts. As such, the names for these mosses are chosen to be extremely general to avoid bias and to avoid being too flavorful, and to allow these names to be reused for such non-octave contexts.

The names of monowood and biwood, for 1L 1s and 2L 2s respectively, requires that an equivalence interval be an octave, whereas the name trivial, also referring to 1L 1s, is equave-agnostic and may be used for non-octave contexts.

Names for multi-period mosses

Multi-period mosses (mosses of the form xL ys where x and y have a greatest common factor of 2 or greater) are given unique names that do not depend on the name of a smaller, octave-specific mos. The inclusion of such mos names was for completeness, which prompted reconsiderations on how these mosses were named. These mosses were formerly named using names that were octave-specific, producing former names such as "antidimanic" and "dipentic".

Names based on a temperament

All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.

Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings didn't cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".

Names for 1L ns mosses

Mosses of the form 1L ns were originally left unnamed as the range for their generator was too broad and such mosses were considered better analyzed as subsets of its (n+1)L 1s mos. An example of this is 1L 6s and 7L 1s, a pair of mosses that are commonly associated with porcupine temperament.

Although the tuning range is very unhelpful for knowing what such mosses will sound like, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name of 1L ns, especially given that in such situations the tuning will likely be specified somewhere already, hence the inclusion of these mos names.

This inclusion also affected the names of multi-period mosses. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (with their parent mos of 4L 2s named citric for consistency).

The anti- prefix vs the an- prefix for naming 1L ns mosses

The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is not as trivial as it may sound.

In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence their original omission), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range.

In the case of mosses with five or fewer notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.

Names for mosses with more than 10 notes

The scope of TAMNAMS name is to give mosses with small note count a notable name. To keep the number of names controlled, only mosses with no more than 10 notes are named. As a result, the names of mosses with 11 and 12 notes were abandoned, notably the names kleistonic, suprasmitonic, m-chromatic, and p-chromatic.

Step ratio spectrum visualization

I wanted to make a table that better visualizes the step ratio ranges as described by TAMNAMS.

Central spectrum

Central spectrum of step ratios
Intermediate ranges				Specific step ratios	Notes
				1:1 (equalized)	Trivial/pathological
1:1 to 1:0	1:1 to 2:1	1:1 to 3:2	1:1 to 4:3 (ultrasoft)		Step ratios especially close to 1:1 may be called pseudoequalized
				4:3 (supersoft)
			4:3 to 3:2 (parasoft)
				3:2 (soft)	Also called monosoft
		3:2 to 2:1 (hyposoft)	3:2 to 5:3 (quasisoft)
				5:3 (semisoft)
			5:3 to 2:1 (minisoft)
				2:1 (basic)	Also called quintessential
	2:1 to 1:0	2:1 to 3:1 (hypohard)	2:1 to 5:2 (minihard)
				5:2 (semihard)
			5:2 to 3:1 (quasihard)
				3:1 (hard)	Also called monohard
		3:1 to 1:0	3:1 to 4:1 (parahard)
				4:1 (superhard)
			4:1 to 1:0 (ultrahard)		Step ratios especially close to 1:0 may be called pseudocollapsed
				1:0 (collapsed)	Trivial/pathological

Extended spectrum

Extended spectrum of step ratios
Central ranges				Extended ranges		Specific step ratios	Notes
						1:1 (equalized)
1:1 to 1:0	1:1 to 2:1	1:1 to 3:2	1:1 to 4:3 (ultrasoft)	1:1 to 6:5 (pseudoequalized)
						6:5 (semiequalized)
				6:5 to 4:3 (ultrasoft)
						4:3 (supersoft)	Nonextreme range, as detailed by central spectrum
			4:3 to 3:2 (parasoft)	4:3 to 3:2 (parasoft)
						3:2 (soft)
		3:2 to 2:1 (hyposoft)	3:2 to 5:3 (quasisoft)	3:2 to 5:3 (quasisoft)
						5:3 (semisoft)
			5:3 to 2:1 (minisoft)	5:3 to 2:1 (minisoft)
						2:1 (basic)
	2:1 to 1:0	2:1 to 3:1 (hypohard)	2:1 to 5:2 (minihard)	2:1 to 5:2 (minihard)
						5:2 (semihard)
			5:2 to 3:1 (quasihard)	5:2 to 3:1 (quasihard)
						3:1 (hard)
		3:1 to 1:0	3:1 to 4:1 (parahard)	3:1 to 4:1 (parahard)
						4:1 (superhard)
			4:1 to 1:0 (ultrahard)	4:1 to 10:1 (ultrahard)	4:1 to 6:1 (hyperhard)
						6:1 (extrahard)
					6:1 to 10:1 (clustered)
						10:1 (pseudocollapsed)
				10:1 to 1:0 (pseudocollapsed)
						1:0 (collapsed)

Original table of extended TAMNAMS names (archived)

This is an attempt to describe various mosses that I feel are worth describing, based on experimenting with these scales or for completion. This contains unofficial scale names that try to be as close to existing names as possible and are not meant to be official or standard. The following table shows single-period mosses sorted by generation rather than note count. As of August 2022, much of this section is rendered unnecessary due to TAMNAMS names being reorganized and many scales being renamed, hence this section is kept for archival purposes.

Extended names are denoted with an asterisk. Named 1L ns (monolarge) scales are denoted using italics and are based on its sister scale with the anti- prefix added.

Mos Family Tree (single-period only), with TAMNAMS Names and extended names
Progenitor scale		1st-order child mosses		2nd-order child mosses		3rd-order child mosses		4th-order child mosses		5th-order child mosses
Steps	Scale name	Steps	Scale name	Steps	Scale name	Steps	Scale name	Steps	Scale name	Steps	Scale name
1L 1s	prototonic* (currently monowood and trivial)	1L 2s	antideuteric* (currently antrial)	1L 3s	antitetric* (currently antetric)	1L 4s	antimanic (currently pedal)	1L 5s	antimachinoid* (currently antimachinoid)	1L 6s	anti-archeotonic (currently onyx)

										6L 1s	archeotonic

								5L 1s	machinoid	5L 6s

										6L 5s

						4L 1s	manual (formerly manic)	4L 5s	gramitonic (formerly orwelloid)	4L 9s

										9L 4s

								5L 4s	semiquartal	5L 9s

										9L 5s

				3L 1s	tetric	3L 4s	mosh	3L 7s	sephiroid	3L 10s

										10L 3s

								7L 3s	dicoid (formerly dicotonic)	7L 10s

										10L 7s

						4L 3s	smitonic	4L 7s	(formerly kleistonic)	4L 11s

										11L 4s

								7L 4s	(formerly suprasmitonic)	7L 11s

										11L 7s

		2L 1s	deuteric* (currently trial)	2L 3s	pentic	2L 5s	antidiatonic	2L 7s	balzano (formerly joanatonic)	2L 9s

										9L 2s

								7L 2s	superdiatonic	7L 9s

										9L 7s

						5L 2s	diatonic	5L 7s	(formerly p-chromatic)	5L 12s	s-enharmonic*

										12L 5s	p-enharmonic*

								7L 5s	(formerly m-chromatic)	7L 12s	f-enharmonic*

										12L 7s	m-enharmonic*

				3L 2s	antipentic	3L 5s	checkertonic (formerly sensoid)	3L 8s		3L 11s

										11L 3s

								8L 3s		8L 11s

										11L 8s

						5L 3s	oneirotonic	5L 8s		5L 13s

										13L 5s

								8L 5s		8L 13s

										13L 8

Extended mos pattern names (fewer than 5 steps, archived)

As of August 14, 2022, all of these scales have been named. These descriptions are kept for archival purposes.

Parent scale				1st-order child scales				2nd-order child scales
Steps	Originally proposed name	Current name	Notes	Steps	Originally proposed name	Current name	Notes	Steps	Originally proposed name	Current name	Notes
1L 1s	prototonic, protic, or monowood	monowood and trivial	The progenitor scale of all single-period mosses. Despite being a monolarge scale, it's also its own sister and is named regardless. The current name "monowood" comes from nL ns scales (such as pentawood for 5L 5s), and is used as a base for such scales. The name trivial comes from the fact that this is a trivial (octave-equivalent) scale, consisting of only its generators.	1L 2s	antideuterotonic or antideuteric	antrial	One of the child scales of 1L 1s. Being a monolarge scale, tetric (3L 1s) may be more worth considering as a parent scale.	1L 3s	antitetric	antetric	Monolarge scale. Similarly to 3L 1s with 1L 2s, 4L 1s may be worth considering as a parent scale.

								3L 1s	tetric	tetric	Parent scale to orwelloid (now gramitonic) and semiquartal, the name tetric is assigned similarly to pentic being the parent of diatonic and antidiatonic.

				2L 1s	deuterotonic or deuteric	trial	One of the child scales of 1L 1s.	2L 3s	-	pentic	Already established name.

								3L 2s	-	antipentic	Already established name.

Proposal: Naming mosses with more than 10 steps

This is a system for describing scales beyond the set of named TAMNAMS scales. Both User:Frostburn (User:Frostburn/TAMNAMS Extension) and I have similar systems, with the main difference here being that mosses are technically not limited to being only three generations away.

Notes:

Interestingly, there is evidence that another Xen Discord user (user:Flirora) suggested the same naming system described here up to 3 generations, with only slight differences with 3rd-generation names. As I was part of a discussion on limiting TAMNAMS names to 10-note mosses, which facilitated naming mosdescendants up to two generations (mosenharmonic scales), rather than this earlier suggestion, it's possible that the same proposal for mosenharmonic scales may have been independently developed twice.
Some names with this system are not finalized, particularly the term "mosschismic" and some of the single-letter prefixes.
- Better names than "mosschismic" include "mossubharmonic" (adapted from the suggestion described above) and "mossubchromatic", possibly shortened to "mossubchromic" (adapted from "subchromatic", as suggested in this page).
- Another issue with the single-letter prefixes described here is that they are technically based off of a temperament. A temperament-agnostic interpretation will be needed if these letters are to be generalized outside of the diatonic family.

Naming mosdescendants up to 3 generations

Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, names for mosses greater than 10 notes can be made systematically using existing names. The rules are described as such:

If the scale is the child of a named parent scale, then the scale is moschromatic.
If the scale is the grandchild of a named parent scale, then the scale is mosenharmonic.
If the scale is the great-grandchild of a named parent scale, then the scale is mosschismic. (tentative name; schismic refers to a family of temperaments; open to better name suggestions)
If the scale is more than 3 generations from a named parent scale, or if referring to a scale regardless of number of generations from the parent, then the scale is a mosdescendant scale.

For describing the scales of a named mos, the prefix of mos- is removed and replaced with the mos's prefix instead. For example, the child, grandchild, and great-grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively, and the entire family of mosses related to oneirotonic are oneirodescendants.

Additionally, the lack of a prefix will specifically describe the descendant scales of 5L 2s: chromatic, enharmonic, and schismic. Descendants of 5L 2s are referred to as "diatonic descendants" rather than "descendants".

Single-letter prefixes for these names are optional, as the single-letter prefixes are meant for specificity. With no prefix specified, moschromatic refers to one of two child scales, mosenharmonic refers to one of four grandchild scales, and mosschismic refers to one of eight great-grandchild scales. The table below shows those prefixes and the mosdescendants for which they apply, as well as the step ratio of the parent mos needed to reach these scales.

Mosdescendant scales sorted by step ratio
Parent scale			Moschromatic (child) scales				Mosenharmonic (grandchild) scales				Mosschismic (great-grandchild) scales
Steps	Step ratio		Steps	Specific name	Step ratio of parent		Steps	Specific name	Step ratio of grandparent		Steps	Specific name	Step ratio of great-grandparent
Steps	General range	Step ratio for 2:1	Steps	Specific name	General range	For L:s = 2:1	Steps	Specific name	General range	For L:s = 2:1	Steps	Specific name	General range	For L:s = 2:1
xL ys	1:1 to 1:0	2:1 (basic)	(x+y)L xs	m-moschromatic	1:1 to 2:1	3:2 (soft)	(x+y)L (2x+y)s	f-mosenharmonic	1:1 to 3:2	4:3 (supersoft)	(x+y)L (3x+2y)s	f-mosschismic	1:1 to 4:3 (ultrasoft)	5:4
							(x+y)L (2x+y)s	f-mosenharmonic	1:1 to 3:2	4:3 (supersoft)	(3x+2y)L (x+y)s	a-mosschismic	4:3 to 3:2 (parasoft)	7:5
							(2x+y)L (x+y)s	m-mosenharmonic	3:2 to 2:1 (hyposoft)	5:3 (semisoft)	(3x+2y)L (2x+y)s	u-mosschismic	3:2 to 5:3 (quasisoft)	8:5
							(2x+y)L (x+y)s	m-mosenharmonic	3:2 to 2:1 (hyposoft)	5:3 (semisoft)	(2x+y)L (3x+2y)s	m-mosschismic	5:3 to 2:1 (minisoft)	7:4
			xL (x+y)s	p-moschromatic	2:1 to 1:0	3:1 (hard)	(2x+y)L xs	p-mosenharmonic	2:1 to 3:1 (hypohard)	5:2 (semihard)	(2x+y)L (3x+y)s	p-mosschismic	2:1 to 5:2 (minihard)	7:3
							(2x+y)L xs	p-mosenharmonic	2:1 to 3:1 (hypohard)	5:2 (semihard)	(3x+y)L (2x+y)s	q-mosschismic	5:2 to 3:1 (quasihard)	8:3
							xL (2x+y)s	s-mosenharmonic	3:1 to 1:0	4:1 (superhard)	(3x+y)L xs	r-mosschismic	3:1 to 4:1 (parahard)	7:2
							xL (2x+y)s	s-mosenharmonic	3:1 to 1:0	4:1 (superhard)	xL (3x+y)s	s-mosschismic	4:1 to 1:0 (ultrahard)	5:1

Simplified table, without step ratios, sorted by position on mos family tree
Parent scale	Moschromatic scales		Mosenharmonic scales		Mosschismic scales
Steps	Steps	Specific name	Steps	Specific name	Steps	Specific name
xL ys	xL (x+y)s	p-moschromatic	xL (2x+y)s	s-mosenharmonic	xL (3x+y)s	s-mosschismic
			xL (2x+y)s	s-mosenharmonic	(3x+y)L xs	r-mosschismic
			(2x+y)L xs	p-mosenharmonic	(2x+y)L (3x+y)s	p-mosschismic
			(2x+y)L xs	p-mosenharmonic	(3x+y)L (2x+y)s	q-mosschismic
	(x+y)L xs	m-moschromatic	(x+y)L (2x+y)s	f-mosenharmonic	(x+y)L (3x+2y)s	f-mosschismic
			(x+y)L (2x+y)s	f-mosenharmonic	(3x+2y)L (x+y)s	a-mosschismic
			(2x+y)L (x+y)s	m-mosenharmonic	(2x+y)L (3x+2y)s	m-mosschismic
			(2x+y)L (x+y)s	m-mosenharmonic	(3x+2y)L (2x+y)s	u-mosschismic

Mosdescendants for single-period mosses

Although it's possible for any mos to have mosdescendants named as described above, for neatness, mosdescendant scale names should apply only to mosses whose immediate child mosses exceed 10 steps. The following tables show which mosses, marked in bold, mosdescendant names can apply.

Single-period mosses for which mosdescendant names apply
Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name
1L 1s	trivial	1L 2s	antrial	1L 3s	antetric	1L 4s	pedal	1L 5s	antimachinoid	1L 6s	onyx	1L 7s	antipine	1L 8s	antisubneutralic	1L 9s	antisinatonic (asina-)
														1L 8s	antisubneutralic	9L 1s	sinatonic (sina-)
														8L 1s	subneutralic (blu-)
												7L 1s	pine (pine-)
										6L 1s	arch(a)eotonic (arch-)
								5L 1s	machinoid (mech-)
						4L 1s	manual	5L 4s	semiquartal (chton-)
						4L 1s	manual	4L 5s	gramitonic (gram-)
				3L 1s	tetric	4L 3s	smitonic (smi-)
						3L 4s	mosh	7L 3s	dicoid/zaltertic (dico-/zal-)
						3L 4s	mosh	3L 7s	sephiroid (seph-)
		2L 1s	trial	3L 2s	antipentic	3L 5s	checkertonic (check-)
				3L 2s	antipentic	5L 3s	oneirotonic (oneiro-)
				2L 3s	pentic	5L 2s	diatonic (no prefix)
						2L 5s	antidiatonic	7L 2s	superdiatonic (arm-)
						2L 5s	antidiatonic	2L 7s	balzano (bal-)

Mosdescendants for multi-period mosses

TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: jaric, taric, ekic, lemon, and lime. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to tcherepnin and hyrulic, the only 3-period mosses named under TAMNAMS, apart from triwood.

2 and 3-period mosses for which mosdescendant names apply
2-period mosses
Mos	Name	Mos	Name	Mos	Name	Mos	Name
2L 2s	biwood	2L 4s	malic	2L 6s	subaric	2L 8s	jaric (jara-)
				2L 6s	subaric	8L 2s	taric (tara-)
				6L 2s	ekic (ek-)
		4L 2s	citric	6L 4s	lemon (lem-)
		4L 2s	citric	4L 6s	lime (lime-)
3-period mosses
Mos	Name	Mos	Name
3L 3s	triwood	3L 6s	tcherepnin (cher-)
3L 3s	triwood	6L 3s	hyrulic (hyru-)

Starting at 4 periods, mosdescendant names apply only to n-wood scales (tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to n-wood descendants.

Since the names for single-period mosses up to 5 notes may also be used for non-octave periods, these names are used for multi-period mosses, producing n-antrial, n-trial, n-antetric, n-tetric, n-antipentic, n-pentic, n-pedal, and n-manual. Note that there are only two named 3rd-generation mosses from nL ns rather than the usual eight; the missing six names (what would be n-smitonic, n-mosh, n-checkertonic, n-oneiorotonic, n-diatonic, and n-antidiatonic) are unsuitable for use for multi-period mos names as these names must refer to an octave period.

The table outlines possible names for n-wood descendants for tetrawood, pentawood, and, in the general case, n-wood. Numeric prefixes may be used for these names, rather than n-.

Possible mosdescendant names for mosses with 4 periods or more
4-period mosses
Mos	Name	Mos	Name	Mos	Name	Mos	Name	Other notes
4L 4s	tetrawood	4L 8s	quadantrial	4L 12s	quadantetric	4L 16s	tetrapedal	Some names have Latin prefixes for ease of spelling.
				4L 12s	quadantetric	16L 4s	tetramanual
				12L 4s	quadtetric
		8L 4s	quadtrial	12L 8s	tetrantipentic
		8L 4s	quadtrial	8L 12s	tetrapentic
5-period mosses
Mos	Name	Mos	Name	Mos	Name	Mos	Name	Other notes
5L 5s	pentawood	5L 10s	quinantrial	5L 15s	quinantetric	5L 20s	pentapedal	Some names have Latin prefixes for ease of spelling.
				5L 15s	quinantetric	20L 5s	pentamanual
				15L 5s	quintetric
		10L 5s	quintrial	15L 10s	quinantipentic
		10L 5s	quintrial	10L 15s	quinpentic
n-period mosses
Mos	Name	Mos	Name	Mos	Name	Mos	Name	Other notes
nL ns	n-wood	nL 2ns	n-antrial	nL 3ns	n-antetric	nL 4ns	n-pedal	A numeric prefix may be used instead, such as hexawood instead of 6-wood. When in doubt, prefix names for n-period mosses with n-.
				nL 3ns	n-antetric	4nL ns	n-manual
				3nL ns	n-tetric
		2nL ns	n-trial	3nL 2ns	n-anpentic
		2nL ns	n-trial	2nL 3ns	n-pentic

Naming mosdescendants beyond 3 generations

Each generation has twice as many mosdescendants as the last, so rather than try to name every possible descendant, mosdescendants more than 3 generations from a given parent mos may be referred to how many generations away it is. Mosschismic scales are 3rd mosdescendants, so after that are 4th-mosdescendants, 5th-mosdescendants, and so on. The algorithms below shows how to find how many generations away a mos xL ys is from another scale.

For mosses with up to 3 periods: finding a parent mos zL ws for the mosdescendant xL ys, where x, y, z, and w share a greatest common factor that is no greater than 3:
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 g = 0, where g 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 g by 1.
4. If the sum of z and w is no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.
For mosses with 4 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a greatest common factor of n that is 4 or greater:
1. Let z and w be assigned the values x and y respectively. Let g = 0, where g is the number of generations away from nL ns.
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 g by 1.
4. If the sum of z and w is exactly 2n, then the mos nL ns is g generations away from xL ys. If not, repeat the process starting at step 2.

Naming mosdescendants for linearly growing scales (work-in-progress)

Some noteworthy mosdescendants may be more than 3 generations away, but may have the same number of large steps as a named parent mos. In such cases, the number of notes with each successive mosdescendant grows linearly, and these mosses may be assigned a letter to refer to a specific mosdescendant. Currently, this applies to mosdescendants whose parent mos has a step ratio that is along the extreme edges of the step ratio spectrum, around pseudoequalized and pseudocollapsed, producing nth s-mosdescendants and nth f-mosdescendants. The mos family tree better shows which mosses grow linearly, shown in bold, as the upper child of each node is always xL (x+y)s, which becomes of xL (nx+y)s over n generations.

Mosdescendants sorted by position on the mos family tree
Parent scale	Moschromatic scales (1st mosdescendants)		Mosenharmonic scales (2nd mosdescendants)		Mosschismic scales (3rd mosdescendants)		4th-mosdescendant scales (selected mosdescendants)		5th-mosdescendant scales (selected mosdescendants)		nth-mosdescendant scales (selected mosdescendants)
Steps	Steps	Specific name	Steps	Specific name	Steps	Specific name	Steps	Specific name	Steps	Specific name	Steps	Specific name
xL ys	xL (x+y)s	p-moschromatic	xL (2x+y)s	s-mosenharmonic	xL (3x+y)s	s-mosschismic	xL (4x+y)s	4th s-mosdescendant	xL (5x+y)s	5th s-mosdescendant	xL (nx+y)s	nth s-mosdescendant
			xL (2x+y)s	s-mosenharmonic	(3x+y)L xs	r-mosschismic
			(2x+y)L xs	p-mosenharmonic	(2x+y)L (3x+y)s	p-mosschismic	(2x+y)L (5x+2y)s	4th p-mosdescendant	(2x+y)L (7x+3y)s	5th p-mosdescendant
			(2x+y)L xs	p-mosenharmonic	(3x+y)L (2x+y)s	q-mosschismic
	(x+y)L xs	m-moschromatic	(x+y)L (2x+y)s	f-mosenharmonic	(x+y)L (3x+2y)s	f-mosschismic	(x+y)L (4x+3y)s	4th f-mosdescendant	(x+y)L (5x+4y)s	5th f-mosdescendant	(x+y)L (nx+(n-1)y)s	nth f-mosdescendant
			(x+y)L (2x+y)s	f-mosenharmonic	(3x+2y)L (x+y)s	a-mosschismic
			(2x+y)L (x+y)s	m-mosenharmonic	(2x+y)L (3x+2y)s	m-mosschismic	(2x+y)L (5x+3y)s	4th m-mosdescendant	(2x+y)L (7x+4y)s	5th m-mosdescendant
			(2x+y)L (x+y)s	m-mosenharmonic	(3x+2y)L (2x+y)s	u-mosschismic

Mosdescendants sorted by step ratio
Parent scale	Moschromatic scales (1st mosdescendants)		Mosenharmonic scales (2nd mosdescendants)		Mosschismic scales (3rd mosdescendants)		nth-mosdescendant scales
Steps	Steps	Specific name	Steps	Specific name	Steps	Specific name	Steps	Specific name	Step ratio of parent
xL ys	(x+y)L xs	m-moschromatic	(x+y)L (2x+y)s	f-mosenharmonic	(x+y)L (3x+2y)s	f-mosschismic	(x+y)L (nx+(n-1)y)s	nth f-mosdescendant	Softer than 5:4
					(x+y)L (3x+2y)s	f-mosschismic
					(3x+2y)L (x+y)s	a-mosschismic
			(2x+y)L (x+y)s	m-mosenharmonic	(3x+2y)L (2x+y)s	u-mosschismic
			(2x+y)L (x+y)s	m-mosenharmonic	(2x+y)L (3x+2y)s	m-mosschismic
	xL (x+y)s	p-moschromatic	(2x+y)L xs	p-mosenharmonic	(2x+y)L (3x+y)s	p-mosschismic
			(2x+y)L xs	p-mosenharmonic	(3x+y)L (2x+y)s	q-mosschismic
			xL (2x+y)s	s-mosenharmonic	(3x+y)L xs	r-mosschismic
					xL (3x+y)s	s-mosschismic
					xL (3x+y)s	s-mosschismic	xL (nx+y)s	nth s-mosdescendant	Harder than 5:1

Reasoning for names

The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s): p-chromatic (5L 7s) and m-chromatic (7L 5s). This was generalized to "chromatic" and "moschromatic", with the prefixes m- and p- for specificity. The names for mosenharmonic scales are based on discussions with xen Discord members for systematically naming the daughter and granddaughter scales of a mos, producing "enharmonic" and "mosenharmonic" with the prefixes f-, m-, p-, and s- for specificity.

Names for mosdescendants are thereby based on replacing the mos- prefix with that for a mos's TAMNAMS name. This effectively brings back the names of m-chromatic and p-chromatic, as TAMNAMS specifically names mosses up to 10 notes. This also names other mosses whose names were lost entirely, mainly kleistonic (4L 7s, now p-smichromatic) and suprasmitonic (7L 4s, now m-smichromatic), two names that were dropped because these mosses had more than 10 notes.

The reason why mosdescendants for mosses with 4 periods or greater are not based on their corresponding n-wood scale is because these mosses do not have any child mosses with 10 notes or fewer, and therefore have no named child mosses from which to build mosdescendant names. Rather, names for these mosdescendants are based on period-agnostic names (antrial, trial, antetric, tetric, etc) to reflect that these are scales based on duplicating a base mos multiple times within an octave.

The addition of mosschismic scales for great-grandchild scales was done for completeness, with the prefixes f-, a-, u-, m-, p- q-, r-, and s- for specificity (names not finalized). Note that mosschismic scales borrows the prefixes as mosenharmonic scales, which itself borrows those for mosenharmonic scales. The table below shows what prefixes are used for which generation of mosdescendants, with an added mnemonic for memorization.

Table of mosdescendent prefixes and meanings
Prefix	For moschromatic scales	For mosenharmonic scales	For mosschismic scales	Mnemonic
f-	n/a	F for flat; f-mosenharmonic scales have a grandparent whose pitches are flatter compared to basic (L:s = 2:1).	F for flat.	FAUM sounds like foam, which sounds soft. F-, a-, u-, and m-mosschismic scales generally have a great-grandparent with a soft step ratio.
a-	n/a	n/a	A from parasoft, as "P" is taken.
u-	n/a	n/a	U from quasisoft, as "Q" is taken.
m-	M for maybe/mellow; based on old name for 7L 5s	M- and p-mosenharmonic scales have a grandparent whose step ratio is close to the "midpoint" of L:s = 2:1.	M and P for midpoint.
p-	P for pure/sharp; based on old name for 5L 7s		M and P for midpoint.	PQRS are four consecutive letters in the alphabet. It's hard to pronounce because there are no vowels. P-, q-, r-, and s-mosschismic scales generally have a great-grandparent with a hard step ratio.
q-	n/a	n/a	Q and R are the only two letters between P and S. Q may stand for quasihard.
r-	n/a	n/a	Q and R are the only two letters between P and S. R may stand for parahard.
s-	n/a	S for sharp; s-mosenharmonic scales have a grandparent whose pitches are sharper compared to basic (L:s = 2:1).	"S" for sharp.

Examples

Names for descendant scales of 5L 2s (diatonic)
Diatonic scale		Chromatic scales		Enharmonic scales		Schismic scales		4th diatonic descendants
Steps	Name	Steps	Name	Steps	Name	Steps	Name	Steps
5L 2s	diatonic	7L 5s	m-chromatic	7L 12s	f-enharmonic	7L 19s	f-schismic	7A 26B
				7L 12s	f-enharmonic	19L 7s	a-schismic	19A 26B
				12L 7s	m-enharmonic	19L 12s	u-schismic	19A 31B
				12L 7s	m-enharmonic	12L 19s	m-schismic	12A 31B
		5L 7s	p-chromatic	12L 5s	p-enharmonic	12L 17s	p-schismic	12A 29B
				12L 5s	p-enharmonic	17L 12s	q-schismic	17A 29B
				5L 12s	s-enharmonic	17L 5s	r-schismic	17A 22B
				5L 12s	s-enharmonic	5L 17s	s-schismic	5A 22B

Names for descendant scales for 5L 3s (oneirotonic)
Oneirotonic scale		Oneirochromatic scales		Oneiroenharmonic scales		Oneiroschismic scales		4th oneirodescendants
Steps	Name	Steps	Name	Steps	Name	Steps	Name	Steps
8L 5s	oneirotonic	8L 5s	m-oneirochromatic	8L 13s	f-oneiroenharmonic	8L 21s	f-oneiroschismic	8A 29B
				8L 13s	f-oneiroenharmonic	21L 8s	a-oneiroschismic	21A 29B
				13L 8s	m-oneiroenharmonic	21L 13s	u-oneiroschismic	21A 34B
				13L 8s	m-oneiroenharmonic	13L 21s	m-oneiroschismic	13A 34B
		5L 8s	p-oneirochromatic	13L 5s	p-oneiroenharmonic	13L 18s	p-oneiroschismic	13A 31B
				13L 5s	p-oneiroenharmonic	18L 13s	q-oneiroschismic	18A 31B
				5L 13s	s-oneiroenharmonic	18L 5s	r-oneiroschismic	18A 23B
				5L 13s	s-oneiroenharmonic	5L 18s	s-oneiroschismic	5A 23B

Proposal: Naming mos modes

Current proposal, with proposed amendment for emphasis on dark generator

There is currently a proposed system for naming mos modes as follows: xL ys u|, where x is the number of large steps, y is the number of small steps, u corresponds to the the mode's UDP (the u in u|d), and | is pronounced as "pipe". As an example, the modes of 4L 1s (manual) can be named as the following:

Modes of manual (4L 1s)
Mode	UDP	TAMNAMS name
LLLLs	4\|0	4L 1s 4\|
LLLsL	3\|1	4L 1s 3\|
LLsLL	2\|2	4L 1s 2\|
LsLLL	1\|3	4L 1s 1\|
sLLLL	0\|4	4L 1s 0\|

In situations where it's more intuitive to think in terms of the dark generator instead of the bright generator, the format is instead xL ys |d, where d corresponds to the mode's UDP (the d in u|d). An example of this can be seen in the classic pentatonic scale (2L 3s), where even though the bright generator corresponds to diatonic's perfect 4th (which is actually diatonic's dark generator), it's common to think of these modes in terms of diatonic's bright generator (even though it's the dark generator of 2L 3s). This is because the bright and dark generators "flip" between 2L 3s to 5L 2s. (In general, generators flip when a mos xL ys has a child of (x+y)L xs, but don't flip if the child is xL (x+y)s, and in general, looking at modes in terms of the dark generator reverses the order of modes compared with the bright generator.)

Modes of pentic (2L 3s)
Mode	UDP	TAMNAMS name
sLsLL	0\|4	2L 3s \|4
sLLsL	1\|3	2L 3s \|3
LsLsL	2\|2	2L 3s \|2
LsLLs	3\|1	2L 3s \|1
LLsLs	4\|0	2L 3s \|0

Mode names based on mosnames

If a more memorable name is desired but there are no assigned names for the mos's modes, interim names can be made using genchain mode numbering on the name of the mos, where the first-brightest mode is called 1st mosname, the second-brightest mode is called 2nd mosname, and so on. Note that these names can only be made if there is a TAMNAMS name for a mos. Excluding current proposals to extend TAMNAMS names beyond the 10-note limit, this means most mos mode names will typically be formatted as xL ys u|.

Modes of pine (7L 1s)
Mode	UDP	Mode name
LLLLLLLs	7\|0	1st pine
LLLLLLsL	6\|1	2nd pine
LLLLLsLL	5\|2	3rd pine
LLLLsLLL	4\|3	4th pine
LLLsLLLL	3\|4	5th pine
LLsLLLLL	2\|5	6th pine
LsLLLLLL	1\|6	7th pine
sLLLLLLL	0\|7	8th pine

Modes of tcherepnin (3L 6s)
Mode	UDP	Mode name
LssLssLss	6\|0(3)	1st tcherepnin
sLssLssLs	3\|3(3)	2nd tcherepnin
ssLssLssL	0\|6(3)	3rd tcherepnin

Suggested changes for mos pattern names (work-in-progress)

This section describes changes to existing TAMNAMS names that I would make. Reasons:

Some names are still based on a temperament (mainly the -oid names), so those are either replaced with a new name or at least altered so the references are more indirect.
There were Discord users with whom I shared a similar sentiment regarding the names of certain scales, mainly the mosses with the anti- prefix and the scales antidiatonic and superdiatonic.
Some names are too long (in my opinion).

The choice of names are not perfect and some may have issues. Some names have multiple suggestions. This section is meant to start a discussion on alternate names.

Table of proposed namechanges
Changes to names to reduce or remove references to temperaments
Mos	Current name			Suggested name(s)			Reasoning	Possible issues
Mos	Name	Prefix	Abbrev.	Name	Prefix	Abbrev.	Reasoning	Possible issues
5L 1s	machinoid	mech-	mech	mechatonic	unchagned	unchagned	A more indirect reference to machine temperament.	Still references machine temperament. May also reference mechanism temperament.
3L 7s	sephiroid	seph-	seph	sephirotonic or sephiratonic	unchagned	unchagned	Rather than alluding to sephiroth temperament, the name should allude to Peter Kosmorsky's Tractatum de Modi Sephiratorum (A Treatise on the Modes of the Sephirates), whose name ultimately comes from the sefirot. The document describes several edos that are said to contain the "modi sephiratorum" (sephirate modes). Therefore, instead of the name "sephiroid", suggesting that the mos pattern resembles the modi sephiratorum, the mos pattern is the modi sephiratorum, hence the mosname "sephirotonic".	May still reference sephiroth temperament. For a more indirect reference, an alternate transliteration of סְפִירוֹת (sefirot) may be used instead. New name is longer than the old name.
7L 3s	dicoid and zaltertic	dico- and zal-	dico and zal	zaltertic	zal-	zal	As of writing, there are two names. I would favor zaltertic over dicoid in that it removes a name that suggests a temperament.	Central zalzalian thirds (another name for neutral thirds) are not the scale's bright generator, but are produced by the scale.
Changes to names that bear the anti- prefix
Mos	Current name			Suggested name(s)			Reasoning	Possible issues
Mos	Name	Prefix	Abbrev.	Name	Prefix	Abbrev.	Reasoning	Possible issues
1L 5s	antimachinoid	amech-	amech	selenic or selenite	sel-	sel	An indirect reference to luna temperament; "selene" is Greek for "moon". The name "selenite" follows the same pattern of 1L 6s being named after a type of gemstone.	Pun.
1L 7s	antipine	apine-	apine	spinel	spin-	spin	Contains the word "pine". A spinel is a type of gemstone, and follows the same pattern as onyx.	Pun. Spinel doesn't rhyme with pine, ruining the joke.
1L 8s	antisubneutralic	ablu-	ablu	agate	aga- or agat-	aga	Shorter name. Depending on one's pronunciation, "agate" rhymes with "eight", similarly with "onyx" and "six".	Pun.
1L 9s	antisinatonic	asina-	asi	olivine	oliv-	oliv	Shorter name. Named in the same spirit as 1L 6s being named "onyx", depending on one's pronunciation of "olivine".	Pun. Olivine is typically pronounced in a way that doesn't rhyme with nine, ruining the joke.
Changes to names that bear other prefixes
Mos	Current name			Suggested name(s)			Reasoning	Possible issues
Mos	Name	Prefix	Abbrev.	Name	Prefix	Abbrev.	Reasoning	Possible issues
2L 5s	antidiatonic	pel-	pel	pelotonic	unchagned	unchagned	From "pelog" and "armodue". The proposed names are to make both scales more distinct from diatonic. These names must be changed together.	The connection to diatonic may be beneficial to some musicians. Additionally, the mode names commonly used for both mosses are those from diatonic (lydian, ionian, etc) with the anti- and super- prefixes added. New names reference pelog tuning and armodue theory.
7L 2s	superdiatonic	arm-	arm	armotonic	unchagned	unchagned
8L 1s	subneutralic	blu-	blu	azurtonic	azu- or unchanged	azu or unchanged	An indirect reference to bleu temperament; azure is a specific shade of blue. Simplified name. Also, the sub- prefix may falsely suggest another scale called "(prefix)neutralic", similar to how subaric (2L 6s) is the parent to both jaric (2L 8s) and taric (8L 2s).	New name is referencing a temperament, albeit indirectly. The sub- prefix reasoning may be a stretch, since subaric, jaric, and taric are the only mosses related this way.
2L 6s	subaric	subar-	subar	baric	bar-	bar	Rhymes perfectly with jaric and taric. May also mean "basic -aric", as this mos with a basic step ratio (L:s=2:1) cannot produce jaric or taric, or rather, produces both but equalized.	Too minor of a modification. The use of "bar" as a prefix or abbreviation may be problematic ("bar" may also mean "measure" in sheet music).

Other name changes:

Antipentic -> anpentic; follows names of other small mosses where an- is shortened to anti-.

Table of (single-period) mosses with all proposed name changes
Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name
1L 1s	trivial	1L 2s	antrial	1L 3s	antetric	1L 4s	pedal	1L 5s	selenite	1L 6s	onyx	1L 7s	spinel	1L 8s	agate	1L 9s	olivine
														1L 8s	agate	9L 1s	sinatonic
														8L 1s	azurtonic
												7L 1s	pine
										6L 1s	arch(a)eotonic
								5L 1s	mechatonic
						4L 1s	manual	5L 4s	semiquartal
						4L 1s	manual	4L 5s	gramitonic
				3L 1s	tetric	4L 3s	smitonic
						3L 4s	mosh	7L 3s	zaltertic
						3L 4s	mosh	3L 7s	sephiratonic
		2L 1s	trial	3L 2s	anpentic	3L 5s	checkertonic
				3L 2s	anpentic	5L 3s	oneirotonic
				2L 3s	pentic	5L 2s	diatonic
						2L 5s	pelotonic	7L 2s	armotonic
						2L 5s	pelotonic	2L 7s	balzano

Mode	UDP	TAMNAMS name
LLLLs	4\|0	4L 1s 4\|
LLLsL	3\|1	4L 1s 3\|
LLsLL	2\|2	4L 1s 2\|
LsLLL	1\|3	4L 1s 1\|
sLLLL	0\|4	4L 1s 0\|

Mode	UDP	TAMNAMS name
sLsLL	0\|4	2L 3s \|4
sLLsL	1\|3	2L 3s \|3
LsLsL	2\|2	2L 3s \|2
LsLLs	3\|1	2L 3s \|1
LLsLs	4\|0	2L 3s \|0