User:Ganaram inukshuk/Notes/TAMNAMS

This is a subpage for TAMNAMS-related notes.

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.

Extended mos pattern names (greater 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, though this is focused on naming single-period mosses up to three generations after a parent scale.

Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, a general description can still be made without establishing concrete names, while using names for already named scales. The rules are described as such:

• If the scale is the child of the parent scale, then the scale is moschromatic.
• If the scale is the grandchild of the parent scale, then the scale is mosenharmonic.
• If the scale is the great-grandchild of the 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 the parent scale, or if referring to a scale regardless of number of generations from the parent, then the scale is a mosdescendent 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 oneirodescendents.

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

In the general case, 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. Specific scales can be referred to by adding an additional prefix; the table below shows those prefixes and the step ratios (of the parent mos) for which they apply. Note that the table shows all possible mosdescendent scales up to three generations, across the entire spectrum of step ratios; specifying a step ratio to any one mos will "lock" the chain of descendents to a single line.

Mosdescendent scales sorted by step ratio

Parent scale			Moschromatic scales				Mosenharmonic scales				Mosschismic scales (names not finalized)
Steps	Step ratio of parent (self)		Steps	Specific name (with prefix)	Step ratio of parent		Steps	Specific name (with prefix)	Step ratio of parent		Steps	Specific name (with prefix)	Step ratio of parent
	General range (softest to hardest)	Specific ratio (given L:s = 2:1 for mos)			General range (softest to hardest)	Specific ratio (given L:s = 2:1 for mos)			General range (softest to hardest)	Specific ratio (given L:s = 2:1 for mos)			General range (softest to hardest)	Specific ratio (given L:s = 2:1 for mos)
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
											(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 (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
											(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 (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
					(3x+y)L xs	r-mosschismic
			(2x+y)L xs	p-mosenharmonic	(2x+y)L (3x+y)s	p-mosschismic
					(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
					(3x+2y)L (x+y)s	a-mosschismic
			(2x+y)L (x+y)s	m-mosenharmonic	(2x+y)L (3x+2y)s	m-mosschismic
					(3x+2y)L (2x+y)s	u-mosschismic

Reasoning for names (and example for 5L 2s)

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", with the prefixes p- and m- 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" with the prefixes s-, p-, f-, and m- for specificity.

This proposal initially considered grandchild scales of a mos, and the recent addition of great-grandchild scales was done for completeness. The use of "schismic" to refer to great-grandchild scales is subject to change (I'm open to better suggestions). The prefixes for mosschismic scales borrow those used for mosenharmonic scales (which itself borrows those used for moschromatic scales) and adds four additional prefixes: q- (quasihard), r- (parahard), a- (parasoft), and u- (quasisoft) (also subject to change).

Names for descendent scales of 5L 2s, sorted by step ratio (softest to hardest)

Diatonic scale		Chromatic scales		Enharmonic scales		Schismic scales
Steps	Name	Steps	Name	Steps	Name	Steps	Name
5L 2s	diatonic	7L 5s	m-chromatic	7L 12s	f-enharmonic	7L 19s	f-schismic
						19L 7s	a-schismic
				12L 7s	m-enharmonic	19L 12s	u-schismic
						12L 19s	m-schismic
		5L 7s	p-chromatic	12L 5s	p-enharmonic	12L 17s	p-schismic
						17L 12s	q-schismic
				5L 12s	s-enharmonic	17L 5s	r-schismic
						5L 17s	s-schismic

Suggested changes for mos pattern names

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

• 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 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.
• Some names are too long (in my opinion).

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

Mos	Current name			Suggested name(s)			Reasoning	Possible issues
	Name	Prefix	Abbrev.	Name	Prefix	Abbrev.
1L 5s	antimachinoid	amech-	amech	selenic	sel-	sel	An indirect reference to luna temperament; "selene" is Greek for "moon". This drops the anti- prefix.
5L 1s	machinoid	mech-	mech	mechatonic	unchagned	unchagned	A more indirect reference to machine temperament.	Still references machine temperament.
2L 5s	antidiatonic	pel-	pel	pelic or pelotonic	unchagned	unchagned	From "pelog" and "armodue". The proposed names are to make both scales more distinct from diatonic. This drops the anti- and super- prefixes.	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	armic or armotonic	unchagned	unchagned
1L 7s	antipine	apine-	apine	astelic, astelanic, or stelanic	stel-	stel	A reference to how 1L 7s is "somewhat of a wasteland as far as low-harmonic-entropy scales are concerned". This drops the anti- prefix.	"Astelic" is coincidentally the name of a YouTuber. The other names avoid this issue.
				conic	con-	con	A pun on pinecones (porcupine and pinecone). This drops the anti- prefix.	Pun.
1L 8s	antisubneutralic	ablu-	ablu	mineric /mɪnˈeɹɪk/	mine- (with a silent e)	minc	A portmanteau of miracle and negri temperaments. Shorter name. This drops the anti- prefix.
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. 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.
1L 9s	antisinatonic	asina-	asi	alentic	alen-	alen	An indirect reference to valentine temperament. This drops the anti- prefix.	Coincidentally the name of a company.
				lupercalic	luper-	lup	In reference to Lupercalia, a Roman fertility festival observed on February 15th, compared to Valentine's day, which is February 14th.	How common is this knowledge?
				pydecic	pyde-	pyd	An indirect reference to "happy decatonic", a name from Graham Breed's naming system. This drops the anti- prefix	The "py" may falsely suggest a connection with Pythagorean tuning.
3L 7s	sephiroid	seph-	seph	septonic	sept- or unchanged	sept or unchanged	The reference to sephiroth is made even more indirect. As a bonus, "sept" (meaning seven) may also refer to the 7 small steps of the mos pattern.	May falsely suggest the scale is 7 notes, when it's actually 10 notes.
				terseptonic			Like "septonic", but with "ter-" added (meaning 3) to reinforce the step pattern of 3L 7s.	Somewhat more complicated than "sephiroid".
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.

Other name changes

These are additional changes that I feel are less likely to be implemented, but made to convey additional meaning through a name's suffixes; if anything, these changes are merely for the aesthetic. These changes are built upon proposed name changes from the previous section.

Rules for mos names (single-period only)

Rule	Names affected	Exceptions
All mosses with 5 steps or fewer end with -al.	anpentic -> anpental pentic -> pental antetric -> antetral tetric -> tetral	any n-wood scales that fall within this range (monowood and biwood)
All other 1L ns mosses end with -ic.	antimachinoid -> selenic antipne -> stelanic antisubneutralic -> mineric antisinatonic -> alentic	onyx (almost sounds like on-ic)
All other mosses end with -toinc.	machinoid -> mechatonic antidiatonic and superdiatonic -> pelotonic and armotonic sephiroid -> septonic subneutralic -> azurtonic	mosh, semiquartal, zaltertic, balzano, pine (they're memorable on their own)

Table of (single-period) mosses with all proposed namechanges

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	antetral	1L 4s	pedal	1L 5s	selenic	1L 6s	onyx	1L 7s	stelanic	1L 8s	mineric	1L 9s	alentic
																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	tetral	4L 3s	smitonic
						3L 4s	mosh	7L 3s	zaltertic
								3L 7s	septonic
		2L 1s	trial	3L 2s	anpental	3L 5s	checkertonic
						5L 3s	oneirotonic
				2L 3s	pental	5L 2s	diatonic
						2L 5s	pelotonic	7L 2s	armotonic
								2L 7s	balzano