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 rewrites of sections of the main TAMNAMS page that aren't quite ready to be deployed.

Sandboxed section: Naming mos modes

The easiest way to name the modes of a mos, without having to memorize any names, is to refer to them by their UDP, which refers to how many generators are stacked above and below the tonic to produce a mode of the mos.

This section's running example is 5L 3s, whose brightest mode is LLsLLsLs.

Simplified UDP notation

Normal UDP notation is summarized below:

• For single-period mosses, the UDP is notated as u|d, where u is the number of bright generators stacked above the tonic, d is the number of bright generators stacked below the tonic, and "|" is pronounced as "pipe". The full name of a mos's mode is xL ys u|d.

• For multi-period mosses with p periods, the UDP of is notated as up|dp(p). Since there are generators being stacked above and below every mosperiod - not just the tonic - there are in total u times p and d times p generators being stacked above and below their respective starting pitches. The full name in this case is xL ys up|dp(p).

To make notation easier, TAMNAMS makes the following modifications to UDP notation:

• The UDP for multi-period mosses may be written as u|d(p) rather than up|dp(p). This is because the period already appears in both the quantity of bright (u times p) and dark (d times p) generators, so omitting the p term makes the notation less redundant. In contexts where it doesn't cause confusion, the notation can be simplified further to u|d.

• The UDP for a mode may be shortened to "u|" under the reasoning that omitting the d term, which can be inferred by the u term, makes the notation less redundant. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".
  • The shortened notation of "u|" is sufficient in most cases, but in situations where it makes more sense to think in terms of the dark generator, such as with a mos whose dark generator is the bright generator of a related mos, the notation is instead "|d".

This simplified notation will be used throughout this section, unless otherwise specified. In any case, the name of a mos can be substituted for its xL ys form.

Finding mos modes

Rotating the sequence of steps - that is, moving the step at the beginning to the end - produces a different mode. This can be repeated until the initial mode that was started with is produced.

This rotation process usually returns the modes in rotational order, not by brightness. To get the modes in order by brightness, produce every interval for each mode - starting at the mosunison and ending at the mosoctave - producing an interval matrix. The brightest mode will be the mode that has all of its intervals - excluding the mosunison, mosoctave, and mosperiods if multi-period - in its large size. The 2nd-brightest mode will have one interval in its small size - for multi-period mosses, one interval is in its small size for every instance of the mosperiod - and so on. The darkest mode will have all of its intervals in its small size. A much faster way to do this process is to skip making an interval matrix and sort the modes produced by rotation in alphabetical order, effectively sorting all modes by decreasing brightness. In either case, the UDP for the modes sorted by brightness are (n-1)|0, (n-2)|1, and so on to 0|(n-1), or (n-1)|, (n-2)| to 0|. The table below shows the modes produced rotationally, and can be sorted by UDP.

Modes of 5L 3s, with interval sizes

Mode	Rotational order	UDP	mosunison	1-mosstep	2-mosstep	3-mosstep	4-mosstep	5-mosstep	6-mosstep	7-mosstep	mosoctave
LLsLLsLs	0	7|0	0 (perfect)	L (major)	2L (major)	2L+s (perfect)	3L+s (major)	4L+s (augmented)	4L+2s (major)	5L+2s (major)	5L+3s (perfect)
LsLLsLsL	1	4|3	0 (perfect)	L (major)	L+s (minor)	2L+s (perfect)	3L+s (major)	3L+2s (perfect)	4L+2s (major)	4L+3s (minor)	5L+3s (perfect)
sLLsLsLL	2	1|6	0 (perfect)	s (minor)	L+s (minor)	2L+s (perfect)	2L+2s (minor)	3L+2s (perfect)	3L+3s (minor)	4L+3s (minor)	5L+3s (perfect)
LLsLsLLs	3	6|1	0 (perfect)	L (major)	2L (major)	2L+s (perfect)	3L+s (major)	3L+2s (perfect)	4L+2s (major)	5L+2s (major)	5L+3s (perfect)
LsLsLLsL	4	3|4	0 (perfect)	L (major)	L+s (minor)	2L+s (perfect)	2L+2s (minor)	3L+2s (perfect)	4L+2s (major)	4L+3s (minor)	5L+3s (perfect)
sLsLLsLL	5	0|7	0 (perfect)	s (minor)	L+s (minor)	L+2s (diminished)	2L+2s (minor)	3L+2s (perfect)	3L+3s (minor)	4L+3s (minor)	5L+3s (perfect)
LsLLsLLs	6	5|2	0 (perfect)	L (major)	L+s (minor)	2L+s (perfect)	3L+s (major)	3L+2s (perfect)	4L+2s (major)	5L+2s (major)	5L+3s (perfect)
sLLsLLsL	7	2|5	0 (perfect)	s (minor)	L+s (minor)	2L+s (perfect)	2L+2s (minor)	3L+2s (perfect)	4L+2s (major)	4L+3s (minor)	5L+3s (perfect)

Since multi-period mosses repeats every period rather than at every octave, the number of modes corresponds to the number of pitches in the period. As a result, multi-period mosses always have fewer modes. An example is shown for 3L 6s, with modified UDPs as described in the previous section.

Modes of 3L 6s, with interval sizes

Mode	Mode name	Simplified UDP	Rotational order	mosunison	1-mosstep	2-mosstep	3-mosstep	4-mosstep	5-mosstep	6-mosstep	7-mosstep	8-mosstep	mosoctave
LssLssLss	3L 6s 2|	2|0	0	0 (perfect)	L (augmented)	L+s (perfect)	L+2s (perfect)	2L+2s (augmented)	2L+3s (perfect)	2L+4s (perfect)	3L+4s (augmented)	3L+5s (perfect)	3L+6s (perfect)
sLssLssLs	3L 6s 1|	1|1	2	0 (perfect)	s (perfect)	L+s (perfect)	L+2s (perfect)	L+3s (perfect)	2L+3s (perfect)	2L+4s (perfect)	2L+5s (perfect)	3L+5s (perfect)	3L+6s (perfect)
ssLssLssL	3L 6s 0|	0|2	1	0 (perfect)	s (perfect)	2s (diminished)	L+2s (perfect)	L+3s (perfect)	L+4s (diminished)	2L+4s (perfect)	2L+5s (perfect)	2L+6s (diminished)	3L+6s (perfect)

Alterations to a mode

Alterations to a mode are denoted by listing what 0-indexed mosdegrees are altered by one or more moschromas, using accidentals whose meaning and notation is made clear. As a diatonic example, mixolydian b6 can be written as 5L 2s 5| b6 (where the 6th degree is is a ordinal-indexed 6th, not a 0-indexed mosdegree), but for a non-diatonic example, mode 5| of 5L 3s with a 4-mosdegree lowered by a chroma is written as "5L 3s 5| @4d" (read as "5L 3s 5 pipe at-4-degree", where the "at/@" accidental is from diamond-mos notation).

Named mos modes

Many people, or groups of people, who have described individual mosses have independently came up with names for the mos's modes. The mosses listed below have named mos modes on their respective pages. (todo: add links)

• 5-note mosses: 4L 1s
• 7-note mosses: 1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s, and 6L 1s
• 8-note mosses: 3L 5s, 5L 3s, and 7L 1s
• 9-note mosses: 5L 4s and 7L 2s
• 10-note mosses: 3L 7s

For mossess that no such mode names but a less mathematical name is desired, genchain mode numbering may be used, producing 1st xL ys, 2nd xL ys, and so on.

Sandboxed rewrite: Naming mos intervals and mos degrees

Already deployed on main TAMNAMS page: TAMNAMS#Naming mos intervals

Complements of intervals

The octave complement (or moscomplement, or complement) of a mos interval follows the same logic as the octave complement in regular music theory: in general, for a mos with n pitches, a k-mosstep in its large form has a complement of an (n-k)-mosstep in its small form, and the two intervals are complements of one another. If a mos interval is altered by raising it by some number of chromas, its complement will be lowered by the same number of chromas.

Alternatively, if a specific mos interval is thought of as a quantity of large and small steps, then its complement is the number of steps needed to produce the mos pattern of xL ys itself.

Moscomplements of 3L 4s

Interval		Complement
Name	Size	Name	Size
Perfect 0-mosstep (mosunison)	0	Perfect 7-mosstep (mosoctave)	3L+4s
Major 1-mosstep	L	Minor 6-mosstep	2L+4s
Perfect 2-mosstep	L+s	Diminished 5-mosstep	2L+3s
Major 3-mosstep	2L+s	Minor 4-mosstep	1L+3s
Major 4-mosstep	2L+2s	Minor 3-mosstep	1L+2s
Augmented 5-mosstep	3L+2s	Perfect 2-mosstep	2s
Major 6-mosstep	3L+3s	Minor 1-mosstep	s
Perfect 7-mosstep (mosoctave)	3L+4s	Perfect 0-mosstep (mosunison)	0

Other 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 (pansoft or soft)	1:1 to 3:2 (amphisoft)	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 (panhard or hard)	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 (amphihard)	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

New names for the ranges excluded by hyposoft and hypohard are included: amphisoft and amphihard, named such as they surround the region that hyposoft and hypohard span. The broadest ranges for soft and hard step ratios are called pansoft and panhard, or simply soft and hard.

Extended spectrum

Extended spectrum of step ratios
Central ranges				Extended ranges		Specific step ratios	Notes
						1:1 (equalized)	Trivial/pathological
1:1 to 1:0	1:1 to 2:1 (soft)	1:1 to 3:2 (amphisoft)	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 (hard)	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 (amphihard)	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 (semicollapsed)
				10:1 to 1:0 (pseudocollapsed)
						1:0 (collapsed)	Trivial/pathological

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 (work-in-progress)

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 how mosses can be named any number of generations away from a named mos.

To name mosses that have more than 10 notes, names are based on existing mosses and how they're related to one another, rather than giving each mos a unique name. The easiest and most general way to do this is to refer to such mosses as a mosdescendant. For consistency, mosdescendant names apply to mosses whose child scales exceed 10 notes. Since all mosses ultimately descend from some nL ns mos, every possible mosdescendant (at least up to 5 periods), will be related to some mos that has a TAMNAMS name. These mosses are shown in the table below in bold.

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-)
																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 5s	gramitonic (gram-)
				3L 1s	tetric	4L 3s	smitonic (smi-)
						3L 4s	mosh	7L 3s	dicoid/zaltertic (dico-/zal-)
								3L 7s	sephiroid (seph-)
		2L 1s	trial	3L 2s	antipentic	3L 5s	checkertonic (check-)
						5L 3s	oneirotonic (oneiro-)
				2L 3s	pentic	5L 2s	diatonic (no prefix)
						2L 5s	antidiatonic	7L 2s	superdiatonic (arm-)
								2L 7s	balzano (bal-)
2-period mosses
Mos	Name	Mos	Name	Mos	Name	Mos	Name
2L 2s	biwood	2L 4s	malic	2L 6s	subaric	2L 8s	jaric (jara-)
						8L 2s	taric (tara-)
				6L 2s	ekic (ek-)
		4L 2s	citric	6L 4s	lemon (lem-)
				4L 6s	lime (lime-)
3-period mosses
Mos	Name	Mos	Name
3L 3s	triwood	3L 6s	tcherepnin (cher-)
		6L 3s	hyrulic (hyru-)
4-period mosses
Mos	Name
4L 4s	tetrawood (tetwud-)
5-period mosses
Mos	Name
5L 5s	pentawood (penwud-)

The number of generations a mos is from a named mos can also be specified, so the child mos is a 1st-mosdescendant, its grandchild a 2nd-mosdescendant, its great-grandchild a 3rd-mosdescaendnt, and so on. The algorithm below explains how to find the number of generations two related mosses are, given the mos descends from a named mos whose child mosses already exceed 10 notes.

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.

The prefix of mos- can be replaced with the prefix for the mos itself. As diatonic (5L 2s) doesn't have a prefix, its mosdescendants are called diatonic descendants instead, and mosses that are n generations away from 5L 2s are called nth diatonic descendants.

Names for specific mosdescendants

Child, grandchild, and great-grandchild names can also be referred to as the following:

• A 1st-mosdescendant, or child mos, can be called a moschromatic scale.
• A 2nd-mosdescendant, or grandchild mos, can be called a mosenharmonic scale.
• A 3rd-mosdescendant, or great-grandchild mos, can be called a mossubchromatic scale. (tentative name; open to better suggestions)

As with mosdescendants, the prefix of mos- can be replaced with the prefix of the related mos, and the absence of a prefix refers to the descendants of diatonic (5L 2s).

The designations of moschromatic, mosenharmonic, and mossubchromatic refer to one of 2, 4, and 8 possible mosses respectively. To describe a specific mosdescendant, the name of a step ratio range can be prefixed to the name of the mosdescendant. Specifying the step ratio of these mosdescendants 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.)

Mosdescendant scales sorted by step ratio

Parent scale		Moschromatic (child) scales				Mosenharmonic (grandchild) scales						Mossubchromatic (great-grandchild) scales
Steps	L:s range	Steps	Prefix	Abbrev.	L:s range	Steps	Broad prefixes		Specific prefixes		L:s range	Steps	Broad prefixes		Specific prefixes		L:s range
							Prefix	Abbrev.	Prefix	Abbrev.			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-	amphisoft-	as-	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	hard	h-	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			amphihard-	ah-	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

These prefixes are used for specific mosdescendants, with the notable exception of soft and hard. Those terms may also be used for mosenharmonic and mossubchromatic mosses, producing terminology that is more precise than just mosenharmonic or mossubchromatic but not as specific as their step ratio ranges. To avoid confusion, the specific step ratio prefixes used for mosenharmonic and mossubchromatic scales should not be used for moschromatic scales or each other.

Note: since soft and hard can be used for all three generations, the terms amphisoft and amphihard had to be made since there are no step ratio range names for the ranges outside of hyposoft and hypohard.

Names for mosdescendants with more than 5 periods

TAMNAMS only has names for mosses with up to 10 notes, which covers mosses with up to 5 periods. To name mosses with more than 5 periods, the names for n-wood names for mosses are extended to hexawood, heptawood (or septawood), octawood, nonawood (or enneawood), and decawood. Beyond that, the naming scheme becomes 11-wood, 12-wood, and so on.

Names for n-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

To keep names simple, the names for mosdescendants for mosses with 3 periods or more don't use the names of moschromatic, mosenharmonic, or mossubchromatic, but rather based on the term mosdescendant with the mos's prefix added accordingly, or more generally, written as n-wood descendants. The number of generations from nL ns can also be specified.

Reasoning for names

The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s) - p-chromatic for 5L 7s and m-chromatic for 7L 5s - and was generalized to "moschromatic". The term enharmonic is a term already in use to describe the grandchild mosses of diatonic, and so was generalized to mosenharmonic. 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 mossubchromatic.

Various people have suggested the use of p- and m- as prefixes to refer to specific moschromatic scales, as well as the use of f- and s- for mosenharmonic scales. Generalizing the pattern to 3rd-mosdescendants 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	Child scales			Grandchild scales			Great-grandchild scales
	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.

Other notes

This section was rewritten to heavily simplify mosdescendant naming, and this section contains scattered notes that ultimately justified the rewrite.

• 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 above suggestion which had "prefix-sub-prefix-enharmonic") and "mossubchromatic", possibly shortened to "mossubchromic" (adapted from "subchromatic", as seen in this page).
  • An issue with using letter-based prefixes is that many of them are based on temperaments. A temperament-agnostic interpretation will be needed if these letters are to be generalized outside of the diatonic family.
  • Yet another issue is that the pattern of f-, m-, p-, and s-, all based on temperaments, does not continue with 3rd-generation mosses in that f- and s- are no longer at the extremes and p- is no longer at the midpoint (see table below). Either 3rd-generation mosses need a different set of prefixes, or a different set of prefixes are needed throughout.
  • In the spirit of TAMNAMS being temperament-agnostic, a proper solution may be to not use and shoehorn temperament-suggestive prefixes, but rather use the names for step ratios. This lines up with Frostburn's proposal, but applies to the first three generations, not just the third. (Frostburn's proposed abbreviations may also work.) Under this system, all prefixes can work for all three generations, so soft-chromatic, hyposoft-chromatic, and minisoft-chromatic is allowed, just as soft-subchromatic, hyposoft-subchromatic, and minisoft-subchromatic. The absence of prefixes is also allowed.
    • Hard and soft are preferred over sharp and flat, as those describe accidentals specific to diatonic notation. TAMNAMS generalizes sharps and flats using chromas, realized as amps/ams and ats in diamond-mos notation.

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 name suggestions went through different versions. This section is meant to start a discussion on alternate names should a need come up for it.

Table of proposed name changes

Changes to names to reduce or remove references to temperaments
Mos	Current name			Suggested name(s)			Old suggestions	Reasoning	Possible issues
	Name	Prefix	Abbrev.	Name	Prefix	Abbrev.
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	septonic	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)			Old suggestions	Reasoning	Possible issues
	Name	Prefix	Abbrev.	Name	Prefix	Abbrev.
1L 5s	antimachinoid	amech-	amech	selenite	sel-	sel	selenic	Shorter name. 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	alpine, stelanic	Shorter names. These names follow in the same spirit as "onyx" for 1L 6s in the following ways: "Spinel" contains the word "pine", referencing its sister mos of "pine". Depending on pronunciation, the word "agate" may rhyme with "eight". Depending on pronunciation, the word "olivine" may rhyme with "nine".	Pun. The names suggested don't typically rhyme with the words they're trying to rhyme with or reference, ruining the joke.
1L 8s	antisubneutralic	ablu-	ablu	agate	aga- or agat-	aga	mineric
1L 9s	antisinatonic	asina-	asi	olivine	oliv-	oliv	parivalic, alentic
Changes to names that bear other prefixes
Mos	Current name			Suggested name(s)			Old suggestions	Reasoning	Possible issues
	Name	Prefix	Abbrev.	Name	Prefix	Abbrev.
2L 5s	antidiatonic	pel-	pel	pelotonic	unchagned	unchagned	pelic	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	armic
8L 1s	subneutralic	blu-	blu	azurtonic	azu- or unchanged	azu or unchanged	azuric	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	bara-	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 an abbreviation may be problematic ("bar" may also mean "measure" in sheet music).

Aesthetic rules

These are the rules that attempt to justify the logic behind much of the name suggestions. There are, of course, exceptions to these rules, as some names are arguably too memorable to change.

1. Names for single-period mosses with 5 or fewer notes are the most general names in the sense that they're not limited to an octave period and end with -ic or -al. These should be the only mosses that contain the anti- prefix, shortened to an-. (Exception: monowood is octave-specific and does not end with -ic or -al.)
   1. An extreme alternative to rule 1 is to say that all mosses named under rule 1 should end with -al, but this requires renaming more mosses (antetral, tetral, pental, anpental) for arguably little gain.
2. Names for single-period mosses not of the form 1L ns end with -tonic, suggesting that these are octave-specific and reference a specific interval, a notable pre-TAMNAMS or other temperament-agnostic name, or indirectly reference a temperament if all other options are exhausted. (Exceptions: mosh, semiquartal, zaltertic, balzano, and pine don't end with -tonic.)
3. Names for mosses of the form 1L ns with 6 or more notes are named after gemstones and minerals, following the spirit of 1L 6s being named onyx. These are named differently than those named using the previous rule as these mosses have too broad a tuning range to even suggest a single temperament.
4. Names for multi-period mosses end with -ic and always refer to an octave-equivalent scale. (Execptions: lemon, lime, tcherepnin, and all the -wood scales don't end with -ic.)
5. With the exception of mosses named under rule 1, no mosses should be named in a way that they contain additional prefixes such as anti-, sub-, or super-. (Exception: semiquartal bears the semi- prefix, but its mosprefix is chton-).

Other name changes:

• Antipentic -> anpentic; follows names of other small mosses where an- is used as a shortened form of anti-.

Table of mosses with all proposed name changes (changed names are shown in bold)

Single-period mosses
Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name
1L 1s	trivial monowood	1L 2s	antrial	1L 3s	antetric	1L 4s	pedal	1L 5s	selenite	1L 6s	onyx	1L 7s	spinel	1L 8s	agate	1L 9s	olivine
																9L 1s	sinatonic
														8L 1s	azurtonic
												7L 1s	pine
										6L 1s	arch(a)eotonic
								5L 1s	mechatonic
						4L 1s	manual	5L 4s	semiquartal
								4L 5s	gramitonic
				3L 1s	tetric	4L 3s	smitonic
						3L 4s	mosh	7L 3s	zaltertic
								3L 7s	sephiratonic
		2L 1s	trial	3L 2s	anpentic	3L 5s	checkertonic
						5L 3s	oneirotonic
				2L 3s	pentic	5L 2s	diatonic
						2L 5s	pelotonic	7L 2s	armotonic
								2L 7s	balzano
2-period mosses
Mos	Name	Mos	Name	Mos	Name	Mos	Name
2L 2s	biwood	2L 4s	malic	2L 6s	baric	2L 8s	jaric
						8L 2s	taric
				6L 2s	ekic
		4L 2s	citric	6L 4s	lemon
				4L 6s	lime
3-period mosses
Mos	Name	Mos	Name
3L 3s	triwood	3L 6s	tcherepnin
		6L 3s	hyrulic
4-period mosses
Mos	Name
4L 4s	tetrawood
5-period mosses
Mos	Name
5L 5s	pentawood