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 mine is focused on naming single-period mosses as far as 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 descendent scale is the child of the parent scale, then the scales are collectively referred to as moschromatic scales.
• If the descendent scale is the grandchild of the parent scale, then the scales are collectively referred to as mosenharmonic scales.
• If the descendent scale is the great-grandchild of the parent scale, then the scales are collectively referred to as mosschismic scales. (tentative name; schismic refers to a family of temperaments; open to better name suggestions)

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 descendent scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively. The lack of a prefix will specifically describe the descendent scales of 5L 2s: chromatic, enharmonic, and schismic.

Specific scales can be referred to by adding an additional prefix. The table below shows those prefixes and the step ratios for which they apply.

Moschromatic, mosenharmonic, and mosschismic scales sorted by step ratio

Parent scale			Moschromatic scales				Mosenharmonic scales				Mosschismic scales (names not finalized)
Steps	Step ratio range (hardest to softest)	Basic step ratio	Steps	Specific name (with prefix)	Step ratio range (hardest to softest)	Basic step ratio (relative to parent)	Steps	Specific name (with prefix)	Step ratio range (hardest to softest)	Basic step ratio (relative to parent)	Steps	Specific name (with prefix)	Step ratio range (hardest to softest)	Basic step ratio (relative to parent)
xL ys	1:0 to 1:1	2:1 (basic)	xL (x+y)s	p-moschromatic	1:0 to 2:1 (general hard range)	3:1 (hard)	xL (2x+y)s	s-mosenharmonic	1:0 to 3:1	4:1 (superhard)	xL (3x+y)s	s-mosschismic	1:0 to 4:1 (ultrahard)	5:1
											(3x+y)L xs	r-mosschismic	4:1 to 3:1 (parahard)	7:2
							(2x+y)L xs	p-mosenharmonic	3:1 to 2:1 (hypohard)	5:2 (semihard)	(3x+y)L (2x+y)s	q-mosschismic	3:1 to 5:2 (quasihard)	8:3
											(2x+y)L (3x+y)s	p-mosschismic	5:2 to 2:1 (minihard)	7:3
			(x+y)L xs	m-moschromatic	2:1 to 1:1 (general soft range)	3:2 (soft)	(2x+y)L (x+y)s	m-mosenharmonic	2:1 to 3:2 (hyposoft)	5:3 (semisoft)	(2x+y)L (3x+2y)s	m-mosschismic	2:1 to 5:3 (minisoft)	7:4
											(3x+2y)L (2x+y)s	u-mosschismic	5:3 to 3:2 (quasisoft)	8:5
							(x+y)L (2x+y)s	f-mosenharmonic	3:2 to 1:1	4:3 (supersoft)	(3x+2y)L (x+y)s	a-mosschismic	3:2 to 4:3 (parasoft)	7:5
											(x+y)L (3x+2y)s	f-mosschismic	4:3 to 1:1 (ultrasoft)	5:4

Moschromatic, mosenharmonic, and mosschismic scales as shown in the 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

Example: 5L 2s

Parent scale			1st-order child scales			2nd-order child scales
Steps	Name	Notes	Steps	Name	Notes	Steps	Name	Notes
5L 2s	diatonic	Already established name.	5L 7s	p-chromatic	Names are based on former names of these mosses: p-chromatic and m-chromatic. If the distinction between p- and m- isn't needed, both scales may collectively be referred to as "chromatic".	5L 12s	s-enharmonic	Names are based on discussions with xen discord members on attempting to name daughter and granddaughter scales in a systematic way. If the distinction between s-, p-, f-, and m- isn't needed, all four scales may collectively be referred to as "enharmonic".
						12L 5s	p-enharmonic
			7L 5s	m-chromatic		7L 12s	f-enharmonic
						12L 7s	m-enharmonic

Suggested changes for mos pattern names

This section describes changes to existing TAMNAMS names that I would make. (I made this list because there were Discord users with whom I shared a similar sentiment regarding the names of certain scales, mainly the mosses with the anti- prefix.)

Mos	Current name	Proposed name	Reasoning	Possible issues
1L 5s	antimachinoid	selenic	An indirect reference to luna temperament; "selene" is Greek for "moon". This drops the anti- prefix.
2L 5s	antidiatonic	pelic	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 for both mosses are those from diatonic (lydian, ionian, etc) with the anti- and super- prefixes added.
7L 2s	superdiatonic	armic
1L 7s	antipine	astelic, astelanic, or stelanic	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	A pun on pinecones (porcupine and pinecone). This drops the anti- prefix.	Pun.
1L 8s	antisubneutralic	mineric	A portmanteau of miracle and negri temperaments. Shorter name. This drops the anti- prefix.
1L 9s	antisinatonic	alentic	An indirect reference to valentine temperament. This drops the anti- prefix.	Coincidentally the name of a company.
		pydecic	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.