User:Ganaram inukshuk/TAMNAMS Extension

Revision as of 09:02, 24 February 2023 by Ganaram inukshuk (talk | contribs) (Names for mos descendants with more than 5 periods: Reorganized page, moved equave-agnostic names here)

This is a system for describing and naming mos scales beyond the set of named TAMNAMS mosses. 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.

Naming mos descendants

To name mosses that have more than 10 notes, rather than giving mosses unique names, names are based on how they're related to another (named) mos and, optionally, what step ratio is needed for the parent to produce that mos.

Base names
Parent mos Child (1st descendant) Grandchild (2nd descendant) Great-grandchild (3rd descendant) kth descendant
(mos-name) (step-ratio)-chromatic (mos-name)

(step-ratio)-(mos-prefix)enharmonic

(step-ratio)-enharmonic (mos-name)

(step-ratio)-(mos-prefix)enharmonic

(step-ratio)-subchromatic (mos-name)

(step-ratio)-(mos-prefix)subchromatic

(kth) (mos-name) descendant

(kth)-(mos-prefix)descendant

Step ratio prefixes (optional)
Parent mos Child (1st descendant) Grandchild (2nd descendant) Great-grandchild (3rd descendant) kth descendant
Mos L:s range Mos L:s range Prefix Mos L:s range Prefix Mos L:s range Prefix Prefixes not applicable
xL ys 1:1 to 1:0 (x+y)L xs 1:1 to 2:1

(general soft range)

s- (x+y)L (2x+y)s 1:1 to 3:2

(soft)

s- (x+y)L (3x+2y)s 1:1 to 4:3

(ultrasoft)

us-
(3x+2y)L (x+y)s 4:3 to 3:2

(parasoft)

ps-
(2x+y)L (x+y)s 3:2 to 2:1

(hyposoft)

os- (3x+2y)L (2x+y)s 3:2 to 5:3

(quasisoft)

qs-
(2x+y)L (3x+2y)s 5:3 to 2:1

(minisoft)

ms-
xL (x+y)s 2:1 to 1:0

(general hard range)

h- (2x+y)L xs 2:1 to 3:1

(hypohard)

oh- (2x+y)L (3x+y)s 2:1 to 5:1

(minihard)

mh-
(3x+y)L (2x+y)s 5:2 to 3:1

(quasihard)

qh-
xL (2x+y)s 3:1 to 1:0

(hard)

h- (3x+y)L xs 3:1 to 4:1

(parahard)

ph-
xL (3x+y)s 4:1 to 1:0

(ultrahard)

uh-

Mos descendant names have two main forms: a multi-part name, where the base name (chromatic, enharmonic, subchromatic, and descendant) and mos name are separate words, and a one-part name, formed by prefixing the mos's prefix to the base names. The latter is recommended for mosses with no more than three periods, as the only 4 and 5-period mosses named by TAMNAMS are tetrawood and pentawood respectively. If a step ratio is specified for the former, it may be written out fully instead of prefixed to the base word.

The term kth descendant can be used to refer to any mos that descends from another mos, regardless of how many generations apart the two are. To find the number of generations n separating the two mosses, use the following algorithm:

  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 n = 0, where n 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 n by 1.
  4. If the sum of z and w is no more than 10, then the parent mos is zL ws and is n generations from the mos descendant xL ys. If not, repeat the process starting at step 2.

As diatonic (5L 2s) doesn't have a prefix, the terms chromatic, enharmonic, and subchromatic by themselves (and with no other context suggesting a non-diatonic mos) refer to 1st (child), 2nd (grandchild), and 3rd (great-grandchild) diatonic descendants. For consistency, mos descendant names apply to mosses whose child mosses exceed 10 notes. Since all mosses ultimately descend from some nL ns mos, every possible descendant up to 5 periods will be related to a named mos.

Mosses whose children have more than 10 notes (1st and 2nd descendants only)
6-note mosses Chromatic mosses Enharmonic mosses
Pattern Name Patterns Names Patterns Names
1L 5s antimachinoid 1L 6s, 6L 1s n/a 1A 7B, 6A 7B n/a
2L 4s malic 2L 6s, 6L 2s n/a 2A 8B, 6A 8B n/a
3L 3s triwood 3L 6s, 6L 3s n/a 3A 9B, 6A 9B n/a
4L 2s citric 4L 6s, 6L 4s n/a 4A 10B, 6A 10B n/a
5L 1s machinoid 5L 6s, 6L 5s mechromatic 5A 11B, 6A 11B mechenharmonic
7-note mosses Chromatic mosses Enharmonic mosses
Pattern Name Patterns Names Patterns Names
1L 6s onyx 1L 7s, 7L 1s n/a 1A 8B, 7A 8B n/a
2L 5s antidiatonic 2L 7s, 7L 2s n/a 2A 9B, 7A 9B n/a
3L 4s mosh 3L 7s, 7L 3s n/a 3A 10B, 7A 10B n/a
4L 3s smitonic 4L 7s, 7L 4s smichromatic 4A 11B, 7A 11B smienharmonic
5L 2s diatonic 5L 7s, 7L 5s chromatic 5A 12B, 7A 12B enharmonic
6L 1s arch(a)eotonic 6L 7s, 7L 6s archeoromatic 6A 13B, 7A 13B archeoenharmonic
8-note mosses Chromatic mosses Enharmonic mosses
Pattern Name Patterns Names Patterns Names
1L 7s antipine 1L 8s, 8L 1s n/a 1A 9B, 8A 9B n/a
2L 6s subaric 2L 8s, 8L 2s n/a 2A 10B, 8A 10B n/a
3L 5s checkertonic 3L 8s, 8L 3s checkchromatic 3A 11B, 8A 11B checkenharmonic
4L 4s tetrawood; diminished 4L 8s, 8L 4s chromatic tetrawood 4A 12B, 8A 12B enharmonic tetrawood
5L 3s oneirotonic 5L 8s, 8L 5s oneirochromatic 5A 13B, 8A 13B oneiroenharmonic
6L 2s ekic 6L 8s, 8L 6s ekchromatic 6A 14B, 8A 14B ekenharmonic
7L 1s pine 7L 8s, 8L 7s pinechromatic 7A 15B, 8A 15B pinenharmonic
9-note mosses Chromatic mosses Enharmonic mosses
Pattern Name Patterns Names Patterns Names
1L 8s antisubneutralic 1L 9s, 9L 1s n/a 1A 10B, 9A 10B n/a
2L 7s balzano 2L 9s, 9L 2s balchromatic 2A 11B, 9A 11B balenharmonic
3L 6s tcherepnin 3L 9s, 9L 3s cherchromatic 3A 12B, 9A 12B cherenharmonic
4L 5s gramitonic 4L 9s, 9L 4s gramchromatic 4A 13B, 9A 13B gramenharmonic
5L 4s semiquartal 5L 9s, 9L 5s chtonchromatic 5A 14B, 9A 14B chtonenharmonic
6L 3s hyrulic 6L 9s, 9L 6s hyruchromatic 6A 15B, 9A 15B hyrenharmonic
7L 2s superdiatonic 7L 9s, 9L 7s armchromatic 7A 16B, 9A 16B armenharmonic
8L 1s subneutralic 8L 9s, 9L 8s bluchromatic 8A 17B, 9A 17B bluenharmonic
10-note mosses Chromatic mosses Enharmonic mosses
Pattern Name Patterns Names Patterns Names
1L 9s antisinatonic 1L 10s, 10L 1s asinachromatic 1A 11B, 10A 11B asinenharmonic
2L 8s jaric 2L 10s, 10L 2s jarachromatic 2A 12B, 10A 12B jaraenharmonic
3L 7s sephiroid 3L 10s, 10L 3s sephchromatic 3A 13B, 10A 13B sephenharmonic
4L 6s lime 4L 10s, 10L 4s limechromatic 4A 14B, 10A 14B limenharmonic
5L 5s pentawood 5L 10s, 10L 5s chromatic pentawood 5A 15B, 10A 15B enharmonic pentawood
6L 4s lemon 6L 10s, 10L 6s lemchromatic 6A 16B, 10A 16B lemenharmonic
7L 3s dicoid 7L 10s, 10L 7s dicochromatic 7A 17B, 10A 17B dicoenharmonic
8L 2s taric 8L 10s, 10L 8s tarachromatic 8A 18B, 10A 18B tarenharmonic
9L 1s sinatonic 9L 10s, 10L 9s sinachromatic 9A 19B, 10A 19B sinenharmonic

Names for mosses beyond 10 notes

This section outlines proposed names and naming suggestions for mosses beyond 10 notes.

Names for mos descendants with more than 5 periods

To name mos descendants with more than 5 periods, the names for wood mosses are extended to hexawood, heptawood, octawood, enneawood, and decawood. (This is not too different from Frostburn's proposal.) Names for descendants for these scales follow the same scheme as with other TAMNAMS-named mosses.

Names for wood scales up to 10 periods
Mos Name Prefix Abbrev.
6L 6s hexawood hexwd- hxw
7L 7s heptawood hepwd- hpw
8L 8s octawood octwd- ocw
9L 9s enneawood ennwd- enw
10L 10s decawood dekwd- dkw
11L 11s 11-wood 11-wud- 11wd
12L 12s 12-wood 12-wud 12wd
etc...

Former names worth restoring (proposed)

At one point, TAMNAMS had tenuously named mosses up to 12 notes. Following reorganization back in August of 2022, many temperament-suggestive names were replaced, and names for 11 and 12-note mosses were dropped. Of those, these names are (in my opinion) worth restoring, either because these names are noteworthy (eg, m- and p-chromatic) or because these temperament-suggestive names are better suited as names for child mosses (eg, 3L 5s was named sensoid).

11-note mosses
Mos Name Reasoning
2L 9s jonatonic Modification of an old name (joanatonic) that applied to its parent scale
4L 7s kleistonic Restoration of an old name
5L 6s xeimtonic Restoration of an old name
7L 4s prasmitonic Modification of an old name (suprasmitonic)
8L 3s sentonic Modification of an old name (sensoid) that applied to its parent scale
9L 2s villatonic Indirectly references avila casablanca temperaments
10L 1s miratonic Modification of an old name (miraculoid)
12-note mosses
Mos Name Reasoning
5L 7s pychromatic Modification of an old name (p-chromatic)
6L 6s hexawood Extension of -wood scales, already part of other TAMNAMS extension proposals
7L 5s emchromatic Modification of an old name (m-chromatic)
11L 1s ripploid Restoration of an old name
13-note mosses
Mos Name Reasoning
9L 4s orwelloid Restoration of an old name that applied to its parent scale

Names for monolarge mosses (proposed)

These name suggestions are based on a proposal to rename some of the monolarge mosses to be based on gemstones and minerals, following the logic set forth for the name "onyx" for 1L 6s.

Mos Proposed name Current name Reasoning
1L 6s onyx "from a lot of naming puns"
1L 7s spinel antipine Contains the substring "pine"
1L 8s agate antisubneutralic Rhymes with eight
1L 9s olivine antisinatonic Rhymes with nine
1L 10s tanzanite, tenorite "ten"
1L 11s helenite "ele" substring is part of "eleven"
1L 12s zircon Zircon is used as a birthstone for December

Other suggestions (proposed)

Mos(ses) Notes Name Reasoning Other names
7L 6s 13 tetarquintal "Quarter fifth" scale, referencing temperaments that divide the fifth into four
11L 2s 13 maioquartal "Major fourth" scale, as used by Tcherepnin hendecoid (proposed by Eliora)
12L 1s 13 quasidozenal "almost twelve" grumpy tridecatonic (Dwarf Naming Scheme)

Other naming schemes

This section describes additional naming schemes.

Names for mos linear families (proposed)

Mosses with the same number of large steps can be described as its own family, specifically a family of related mosses of the form xL (nx + y)s. This family starts with the mos xL ys, where x < y and n = 0, and continue with mosses with the same number of large steps but a linearly growing quantity of small steps. An example of such a family is the mos sequence 5L 2s, 5L 7s, 5L 12s, 5L 17s, etc, where each successive mos has 5 more small steps than the last.

Mosses in a linear family are based on repeated applications of the replacement ruleset L->Ls and s->s on the initial mos, and reaching the nth member of a linear family requires the initial mos have a hard or pseudocollapsed step ratio. The child mos (x+y)L xs is the start of its own linear family, which relates back to the initial mos xL ys if the initial mos has a step ratio that is soft or pseudoequalized.

Names for these families describe a subset of a mos descendant family, and most mos families go by the name of (mos name) linear family or (mos-prefix)linear family.

Names of single-period mos linear families (work-in-progress)
Trivial families (names not based on "linear")
Mos Name Reasoning
1L (n+1)s monolarge family Represents an entire family of mosses formerly unnamed by TAMNAMS

The name "monolarge" is chosen as it succinctly describes the only possible 1L family

2L (2n+1)s bilarge family Named analogously to the monolarge family
3L (3n+1)s trilarge family Named analogously to the monolarge family

Prevents potential confusion with the name "tetralinear"

Families with 3 large steps
Mos Name Reasoning
3L (3n+2)s apentilinear family Named after anpentic
Families with 4 large steps
Mos Name Reasoning
4L (4n+1)s manulinear family Named after manual
4L (4n+3)s smilinear family Named after smitonic
Families with 5 large steps
Mos Name Reasoning
5L (5n+1)s mechlinear family Named after machinoid (prefix mech-)
5L (5n+2)s p-linear family Named after p-chromatic rather than diatonic, which has no prefix
5L (5n+3)s oneirolinear family Named after oneirotonic
5L (5n+4)s chtonlinear family Named after semiquartal (prefix chton-)
Families with 6 large steps
Mos Name Reasoning
6L (6n+1)s archeolinear family Named after archeotonic
6L (6n+5)s xeimlinear family Named after xeimtonic, a former name for 6L 5s
Families with 7 large steps
Mos Name Reasoning
7L (7n+1)s pinelinear family Named after pine
7L (7n+2)s armlinear family Named after superdiatonic (also called armotonic)
7L (7n+3)s dicolinear or zalinear family Named after dicotonic (also called zaltertic)
7L (7n+4)s prasmilinear family Named after a truncation of a former name for 7L 4s (suprasmitonic)
7L (7n+5)s m-linear family Named after m-chromatic, a former name for 7L 5s, as it's the start of its own linear family
7L (7n+6)s
Families with 8 large steps
Mos Name Reasoning
8L (8n+1)s blulinear family Named after subneutralic (prefix blu-)
8L (8n+3)s
8L (8n+5)s petrlinear family Named after petroid, a former name for 8L 5s
8L (8n+7)s
Families with 9 large steps
Mos Name Reasoning
9L (9n+1)s sinalinear family Named after sinatonic
9L (9n+2)s
9L (9n+4)s
9L (9n+5)s
9L (9n+7)s
9L (9n+8)s

Equave-agnostic names (proposed)

This is a proposed scheme to name mosses regardless of the equivalence interval, either for nonoctave mosses or nested mos patterns such as with a mos cradle. Whether such a proposal is within the scope of TAMNAMS (since it currently concerns octave-equivalent and tempered-octave scales) is not known.

Names for these mosses are meant to be as general as possible, starting with established names that are already equave-agnostic: trivial, (an)trial, (an)tetric, (an)pentic, and pedal/manual. Mosses are named in pairs of xL ys and yL xs, where the mos with more small steps than large steps is given the an- prefix, short for anti-; this rule doesn't apply to pentic (2L 3s) and anpentic (3L 2s), where the former is the familiar pentatonic scale.

As there is only one pair of 6-note single-period mosses, 5L 1s and 1L 5s, the pair is named hexic.

With 7-note mosses, there are three pairs of mosses, whose names are based on three languages: Greek, Latin, and Sanskrit. The pair 5L 2s and 2L 5s are given the Greek-based name of heptic, as 5L 2s is the familiar diatonic scale. The next pair, 3L 4s and 4L 3s, are given the Latin-based name of septenic. The last pair, 1L 6s and 6L 1s, are given the Sanskrit-based name of saptic.

This pattern is continued for all successive sequences of mosses for each successive note count: 1L ns and nL 1s are given a Sanskrit-based name, the next single-period pair after that are given a Greek-based name, and the next single-period pair after that are given a Latin-based name. The two 8-note pairs are named astaic (7L 1s and 1L 7s) and octic (5L 3s and 3L 5s) respectively. The three 9-note pairs are named navic (8L 1s and 1L 8s), ennaic (7L 2s and 2L 7s), and novemic (4L 5s and 5L 4s). Finally the two 10-note pairs are named dashic (9L 1s and 1L 9s) and dekic (7L 3s and 3L 7s).

Only mosses with no more than 10 notes are named this way. Not only does this mirror the current convention of naming mosses up to 10 notes, but because starting at 11 notes, three languages are no longer enough to name these mosses. Multi-period mosses are not given their own names, but are represented as duplications of a smaller mos pattern.

2-note mosses (from TAMNAMS)
Mos pair Single-period? Names Prefix Language
1L 1s Yes trivial triv- Latin
3-note mosses (from TAMNAMS)
Mos pair Single-period? Names Prefix Language
1L 2s 2L 1s Yes antrial and trial (a)tri- Greek/Latin
4-note mosses (from TAMNAMS)
Mos pair Single-period? Names Prefix Language
1L 3s 3L 1s Yes antetric and tetric (a)tet- Greek
2L 2s No 2-trivial
5-note mosses (from TAMNAMS)
Mos pair Single-period? Names Prefix Language
1L 4s 4L 1s Yes pedal and manual ped- and manu- Latin
2L 3s 3L 2s Yes antipentic and pentic (a)pent- Greek
6-note mosses
Mos pair Single-period? Names Prefix Language
1L 5s 5L 1s Yes anhexic and hexic (an)hexa- Greek
2L 4s 4L 2s No 2-antrial and 2-trial
3L 3s No 3-trivial
7-note mosses
Mos pair Single-period? Names Prefix Language
1L 6s 6L 1s Yes ansaptic and saptic (an)sap- Sanskrit
2L 5s 5L 2s Yes anheptic and heptic (an)hept- Greek
3L 4s 4L 3s Yes anseptenic and septenic (an)sept- Latin
8-note mosses
Mos pair Single-period? Names Prefix Language
1L 7s 7L 1s Yes anastaic and astaic (an)asta- Sanskrit
2L 6s 6L 2s No 2-antetric and 2-tetric
3L 5s 5L 3s Yes anoctic and octic (an)oct- Greek/Latin
4L 4s No
9-note mosses
Mos pair Single-period? Names Prefix Language
1L 8s 8L 1s Yes annavic and navic (an)nav- Sanskrit
2L 7s 7L 2s Yes anennaic and ennaic (an)enna- Greek
3L 6s 6L 3s No 3-antrial and 3-trial
4L 5s 5L 4s Yes annovemic and novemic (an)nov- Latin
10-note mosses
Mos pair Single-period? Names Prefix Language
1L 9s 9L 1s Yes andashic and dashic (an)dash- Sanskrit
2L 8s 8L 2s No 2-manual and 2-pedal
3L 7s 7L 3s Yes andekic and dekic (an)dek- Greek
4L 6s 6L 4s No 2-pentic and 2-anpentic
5L 5s No 5-trivial

Reasoning for names

The overall motivation for these names is to give names to closely related mosses and refer to individual mosses as some member of a broader family, rather than name individual mosses.

The names for the first three generations of mosses are based on existing terms. These terms are open to further changes to make pronunciation easier.

  • The phrase chromatic mos is based on former names for the child mosses of diatonic (5L 2s) - p-chromatic for 5L 7s and m-chromatic for 7L 5s - and has seen use on the wiki to refer the children of non-diatonic mosses.
  • The phrase enharmonic mos is based off of Discord discussions on how to name grandchild mosses. This has also seen use on the wiki to refer to the grandchild mosses of 5L 2s.
  • The phrase subchromatic mos is based on a term coined by Mike Battaglia to describe a scale that is more chromatic than either chromatic or enharmonic. These terms also line up with this page, which describes the progression of a diatonic scale's (or mos's) progression of child mosses.

The format of adding a mos's prefix to the terms descendant, chromatic, enharmonic, and subchromatic is best applied to mosses that have no more than three periods. With mosses that descend directly from nL ns mosses especially (4L 4s and above), this is to keep names from being too complicated (eg, chromatic (number)-wood instead of (number)-woodchromatic).

Various people have suggested the use of p- and m- as prefixes to refer to specific chromatic mosses, as well as the use of f- and s- for enharmonic mosses. Generalizing the pattern to 3rd mos descendants shows the letters diverging from one another, notably where m- is no longer next to p- and f- and s- are no longer along the extremes. Rather than using these letters, as well as being temperament-agnostic, prefixes based on step ratios are used instead. However, temperament-based prefixes may be used specifically for diatonic descendants as alternatives to the prefixes based on step ratios.

Prefixes for diatonic descendants
Diatonic scale Chromatic mosses Enharmonic mosses Subchromatic mosses
Steps Temp-based prefix Ratio-based prefix Steps Temp-based prefix Ratio-based prefix Steps Temp-based prefix Ratio-based prefix
5L 2s 7L 5s m- (from meantone) s- 7L 12s f- (from flattone) s- 7L 19s t- (from tridecimal) us-
19L 7s f- (from flattone) ps-
12L 7s m- (from meantone) os- 19L 12s m- (from meanpop) qs-
12L 19s h- (from huygens) ms-
5L 7s p- (from pythagorean) h- 12L 5s p- (from pythagorean) oh- 12L 17s p- (from pythagorean) mh-
17L 12s g- (from gentle) qh-
5L 12s s- (from superpyth) h- 17L 5s s- (from superpyth) ph-
5L 17s u- (from ultrapyth) uh-