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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.
Main article: TAMNAMS


== Naming mos descendants ==
This page describes TAMNAMS-like names applied to octave-equivalent mosses with more than 10 notes, as well as non-octave mosses (fifth and tritave equivalent).
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.
 
== Disclaimer ==
The names described in this section may may have limited use. Some of these names may only find usage by a single person or a small group and thus have limited acceptance by the broader xen community. These names may also be subject to change as these names or the scales they refer to gain greater usage by the community, and it may be possible for the same scale to have more than one name.
 
== Relating a mos and its descendants ==
Larger mosses can be described by how they related back to a more familiar mos and vice-versa. In general, all mosses with ''n'' periods relate back to a root mos of ''n''L ''n''s. For TAMNAMS-named mosses, any octave-equivalent mos with more than 10 steps and no more than 5 periods is related to some TAMNAMS-named mos.
 
In either case, any mos can be related to its descendants by treating it as the root of its own scale tree. Particularly in the absence of any names, mosses can be ''described'' as being some descendant of a related ancestor mos ''x''L ''y''s. Such mosses, called ''mos descendants'' – or ''children'', ''grandchildren'', and ''great-grandchildren'', for the first three generations of descendants – contain the following pattern of step counts.
{| class="wikitable"
{| class="wikitable"
! colspan="12" |Base names
! colspan="2" |Parent
|-
! colspan="2" |Child
! colspan="2" |Parent mos
! colspan="2" |Grandchild
! colspan="3" |Child (1st descendant)
! colspan="2" |Great-grandchild
! colspan="3" |Grandchild (2nd descendant)
! colspan="3" |Great-grandchild (3rd descendant)
!''k''th descendant
|-
| colspan="2" |''(mos-name)''
| colspan="3" |''(step-ratio)-''chromatic ''(mos-name)''
''(step-ratio)-(mos-prefix)''enharmonic
| colspan="3" |''(step-ratio)''-enharmonic ''(mos-name)''
''(step-ratio)-(mos-prefix)''enharmonic
| colspan="3" |''(step-ratio)''-subchromatic ''(mos-name)''
''(step-ratio)-(mos-prefix)''subchromatic
|''(k''th'') (mos-name)'' descendant
''(k''th'')-(mos-prefix)''descendant
|-
|-
! colspan="12" |Step ratio prefixes (optional)
!Large steps
!Small steps
!Large steps
!Small steps
!Large steps
!Small steps
!Large steps
!Small steps
|-
|-
! colspan="2" |Parent mos
| rowspan="8" |''x''
! colspan="3" |Child (1st descendant)
| rowspan="8" |''y''
! colspan="3" |Grandchild (2nd descendant)
| rowspan="4" |''x''+''y''
! colspan="3" |Great-grandchild (3rd descendant)
| rowspan="4" |''x''
!''k''th descendant
| rowspan="2" |''x''+''y''
| rowspan="2" |2''x''+''y''
|''x''+''y''
|3''x''+2''y''
|-
|-
!Mos
|3''x''+2''y''
!L:s range
|''x''+''y''
!Mos
!L:s range
!Prefix
!Mos
!L:s range
!Prefix
!Mos
!L:s range
!Prefix
!Prefixes not applicable
|-
|-
| rowspan="8" |xL ys
| rowspan="2" |2''x''+''y''
| rowspan="8" |1:1 to 1:0
| rowspan="2" |''x''+''y''
| rowspan="4" |(x+y)L xs
|3''x''+2''y''
| rowspan="4" |1:1 to 2:1
|2''x''+''y''
(general soft range)
| rowspan="4" |s-
| rowspan="2" |(x+y)L (2x+y)s
| rowspan="2" |1:1 to 3:2
(soft)
| rowspan="2" |s-
|(x+y)L (3x+2y)s
|1:1 to 4:3
(ultrasoft)
|us-
| rowspan="8" |
|-
|-
|(3x+2y)L (x+y)s
|2''x''+''y''
|4:3 to 3:2
|3''x''+2''y''
(parasoft)
|ps-
|-
|-
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="4" |''x''
| rowspan="2" |3:2 to 2:1
| rowspan="4" |''x''+''y''
(hyposoft)
| rowspan="2" |2''x''+''y''
| rowspan="2" |os-
| rowspan="2" |''x''
|(3x+2y)L (2x+y)s
|2''x''+''y''
|3:2 to 5:3
|3''x''+''y''
(quasisoft)
|qs-
|-
|-
|(2x+y)L (3x+2y)s
|3''x''+''y''
|5:3 to 2:1
|2''x''+''y''
(minisoft)
|ms-
|-
|-
| rowspan="4" |xL (x+y)s
| rowspan="2" |''x''
| rowspan="4" |2:1 to 1:0
| rowspan="2" |2''x''+''y''
(general hard range)
|3''x''+''y''
| rowspan="4" |h-
|''x''
| rowspan="2" |(2x+y)L xs
| rowspan="2" |2:1 to 3:1
(hypohard)
| rowspan="2" |oh-
|(2x+y)L (3x+y)s
|2:1 to 5:1
(minihard)
|mh-
|-
|-
|(3x+y)L (2x+y)s
|''x''
|5:2 to 3:1
|3''x''+''y''
(quasihard)
|qh-
|-
| rowspan="2" |xL (2x+y)s
| rowspan="2" |3:1 to 1:0
(hard)
| rowspan="2" |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.
For example, the first three generations of ''diatonic descendants'' can be described as:


The term ''k''th 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:
* ''Children of 5L 2s'': 7L 5s and 5L 7s
#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.
* ''Grandchildren of 5L 2s'': 5L 12s, 12L 5s, 12L 7s, and 7L 12s
#Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
* ''Great-grandchildren of 5L 2s'': 5L 17s, 17L 5s, 17L 12s, 12L 17s, 12L 19s, 19L 12s, 12L 7s, and 7L 19s
#Assign to z the value m2 and w the value m1-m2. Increment n by 1.
 
#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.
=== Finding the ancestor of a descendant mos ''x''L ''y''s ===
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.
For a mos ''x''L ''y''s, perform the following algorithm to find a familiar ancestor with target note count ''n'' or less:
 
#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 ''m<sub>1</sub>'' be assigned the value of max(''z'', ''w'') and ''m<sub>2</sub>'' the value of min(''z'', ''w'').
#Assign to ''z'' the value ''m<sub>2</sub>'' and ''w'' the value ''m<sub>1</sub>''-''m<sub>2</sub>''.
#If ''z''+''w'' is less than or equal to ''n'', then the ancestor mos is ''z''L ''w''s. If not, repeat the process starting at step 2.
 
=== Finding an ancestor's step ratio that produces a descandant mos ''x''L ''y''s ===
For a mos xL ys, perform the following algorithm to find the step ratio for a descendant mos zL ws with target note count n or less:
 
#Let ''z'' and ''w'' be the number of large and small steps of the parent mos to be found. Let ''U'' and ''V'' be two chunks, vectors containing the amounts of L's and s's from xL ys that make up the ancestor mos's large and small steps.
##Assign to ''z'' and ''w'' the values ''x'' and ''y'' respectively.
##Assign to ''U'' the vector { ''u<sub>L</sub>'', ''u<sub>s</sub>'' } = { 1, 0 } and V to the vector { ''v<sub>L</sub>'', ''v<sub>s</sub>'' } = { 0, 1 }.
#Let ''m<sub>1</sub>'' be assigned the value of max(''z'', ''w'') and ''m<sub>2</sub>'' the value of min(''z'', ''w'').
##If w > z, then add ''V'' to ''U''. Otherwise, assign to a temporary vector ''U<sub>temp</sub>'' the value of ''U'', add ''V'' to ''U'', and assign to ''V'' the value of ''U<sub>temp</sub>''.
#Assign to ''z'' the value ''m<sub>2</sub>'' and ''w'' the value ''m<sub>1</sub>''-''m<sub>2</sub>''.
#If ''z''+''w'' is less than or equal to ''n'', then the ancestor mos is ''z''L ''w''s. The step ratio range for the ''z''L ''w''s is (''u<sub>L</sub>''+ ''u<sub>s</sub>''):(''v<sub>L</sub>''+ ''v<sub>Ls</sub>'') to ''u<sub>L</sub>'':''v<sub>s</sub>''. If ''z''+''w'' is not less than or equal to ''n'', repeat the process starting at step 2.
 
== Names for mosses with more than 10 notes ==
 
=== Names for ''n''L ''n''s mosses with more than 5 periods ===
The following names are based on the -wood names, with appropriate Greek numeral prefixes applied.
{| class="wikitable center-all"
{| class="wikitable center-all"
|+Mosses whose children have more than 10 notes (1st and 2nd descendants only)
!Pattern
|-
!Suggested name
! colspan="2" |6-note mosses
! colspan="2" |Chromatic mosses
! colspan="2" |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
|-
! colspan="2" |7-note mosses
! colspan="2" |Chromatic mosses
! colspan="2" |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
|-
! colspan="2" |8-note mosses
! colspan="2" |Chromatic mosses
! colspan="2" |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
|-
! colspan="2" |9-note mosses
! colspan="2" |Chromatic mosses
! colspan="2" |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
|-
! colspan="2" |10-note mosses
! colspan="2" |Chromatic mosses
! colspan="2" |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.
{| class="wikitable"
|+Names for wood scales up to 10 periods
!Mos
!Name
!Prefix
!Prefix
!Abbrev.
!Abbrev.
!Reasoning
|-
|-
|6L 6s
|6L 6s
Line 408: Line 103:
|hexwd-
|hexwd-
|hxw
|hxw
|Greek numeral prefix (hexa-) for six, plus "wood"
|-
|-
|7L 7s
|7L 7s
Line 413: Line 109:
|hepwd-
|hepwd-
|hpw
|hpw
|Greek numeral prefix (hepta-) for seven, plus "wood"
|-
|-
|8L 8s
|8L 8s
Line 418: Line 115:
|octwd-
|octwd-
|ocw
|ocw
|Greek numeral prefix (octo-) for eight, plus "wood"
|-
|-
|9L 9s
|9L 9s
Line 423: Line 121:
|ennwd-
|ennwd-
|enw
|enw
|Greek numeral prefix (ennea-) for nine, plus "wood"
|-
|-
|10L 10s
|10L 10s
|decawood
|decawood
|dekwd-
|decwd-
|dkw
|dkw
|Greek numeral prefix (deca-) for ten, plus "wood"
|-
|-
|11L 11s
|11L 11s
|11-wood
|hendecawood
|11-wud-
|hedwd-
|11wd
|hdw
|Greek numeral prefix (hendeca-) for 11, plus "wood"
|-
|-
|12L 12s
|12L 12s
|12-wood
|dodecawood
|12-wud
|dodwd-
|12wd
|ddw
|Greek numeral prefix (dodeca-) for 12, plus "wood"
|-
|-
|etc...
|13L 13s
|
|13-wood
|
|13wd-
|
|13w
|Number 13 prepended to "wood"
|-
|14L 14s
|14-wood
|14wd-
|14w
|Number 14 prepended to "wood"
|-
|''k''L ''k''s
|''k''-wood
|''k''wd
|''k''w
|General number ''k'' prepended to "wood"
|}
|}
=== Former names worth restoring (proposed) ===
=== Names for mosses with 11 or more notes (excluding ''n''L ''n''s mosses) ===
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).
{| class="wikitable center-all"
{| class="wikitable"
! colspan="4" |11-note mosses
! colspan="3" |11-note mosses
|-
|-
!Mos
!Pattern
!Name
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|2L 9s
|1L 10s
|jonatonic
|tanzanite, tenorite
|Modification of an old name (joanatonic) that applied to its parent scale
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
|More naming puns ('''ten'''zanite or '''ten'''orite).
|-
|-
|4L 7s
|4L 7s
|kleistonic
|kleistonic
|Restoration of an old name
|
|Former TAMNAMS name.
|-
|-
|5L 6s
| rowspan="2" |7L 4s
|xeimtonic
|suprasmitonic
|Restoration of an old name
|
|Former TAMNAMS name.
|-
|-
|7L 4s
|daemotonic
|prasmitonic
|[[User:Eliora|Eliora]]
|Modification of an old name (suprasmitonic)
|Various reasons; see [[7L 4s]].
|-
|-
|8L 3s
| rowspan="2" |9L 2s
|sentonic
|Modification of an old name (sensoid) that applied to its parent scale
|-
|9L 2s
|villatonic
|villatonic
|Indirectly references avila casablanca temperaments
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
|Indirectly references avila and casablanca temperaments.
|-
|-
|10L 1s
|ultradiatonic, superarmotonic
|miratonic
|[[User:CompactStar|CompactStar]]
|Modification of an old name (miraculoid)
|In reference to diatonic and armotonic.
|-
|-
! colspan="3" |12-note mosses
! colspan="4" |12-note mosses
|-
|-
!Mos
!Pattern
!Name
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|1L 11s
|helenite
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
|In reference to the "ele" substring found in the word "eleven".
|-
|-
|5L 7s
|5L 7s
|pychromatic
|p-chromatic
|Modification of an old name (p-chromatic)
|
|-
|Former TAMNAMS name.
|6L 6s
|hexawood
|Extension of -wood scales, already part of other TAMNAMS extension proposals
|-
|-
|7L 5s
|7L 5s
|emchromatic
|m-chromatic
|Modification of an old name (m-chromatic)
|
|Former TAMNAMS name.
|-
|-
|11L 1s
! colspan="4" |13-note mosses
|ripploid
|Restoration of an old name
|-
|-
! colspan="3" |13-note mosses
!Pattern
|-
!Suggested name(s)
!Mos
!Proposed by
!Name
!Reasoning
!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.
{| class="wikitable"
|+
!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
|1L 12s
|zircon
|zircon
|
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
|Zircon is used as a birthstone for December
|Zircon is used as a birthstone for December.
|}
 
=== Other suggestions (proposed) ===
{| class="wikitable"
|-
!Mos(ses)
!Notes
!Name
!Reasoning
!Other names
|-
|7L 6s
|13
|tetarquintal
|"Quarter fifth" scale, referencing temperaments that divide the fifth into four
|
|-
|-
|11L 2s
|11L 2s
|13
|hendecoid
|maioquartal
|[[User:Eliora|Eliora]]
|"Major fourth" scale, as used by Tcherepnin
|From Greek "eleven"; references how "its generator is so close to 11/8 as to be called nothing but that" and that it has 11 large steps.
|hendecoid (proposed by Eliora)
|-
|-
|12L 1s
! colspan="4" |14-note mosses
|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''.
{| class="wikitable"
|+Names of single-period mos linear families (work-in-progress)
! colspan="3" |Trivial families (names not based on "linear")
|-
|-
!Mos
!Pattern
!Name
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|1L (n+1)s
|13L 1s
|monolarge family
|trollic
|Represents an entire family of mosses formerly unnamed by TAMNAMS
|[[User:Godtone|Godtone]]
The name "monolarge" is chosen as it succinctly describes the only possible 1L family
|The name proposed by Godtone refers to 12L 1s, but it refers to 13L 1s as a troll move.
|}
{| class="wikitable center-all"
|-
|-
|2L (2n+1)s
!Note count
|bilarge family
!Pattern
|Named analogously to the monolarge family
!Suggested name(s)
|-
!Proposed by
|3L (3n+1)s
|trilarge family
|Named analogously to the monolarge family
Prevents potential confusion with the name "tetralinear"
|-
! colspan="3" |Families with 3 large steps
|-
!Mos
!Name
!Reasoning
!Reasoning
|-
|-
|3L (3n+2)s
|17
|apentilinear family
|2L 15s
|Named after anpentic
|liesic
|[[User:Frostburn|Frostburn]]
|Frostburn's naming scheme only goes up to 3 generations, so this name is suggested.
|-
|-
! colspan="3" |Families with 4 large steps
| rowspan="2" |19
|3L 16s
|magicaltonic
|[[User:Xenllium|Xenllium]]
|In reference to magic temperament.
|-
|-
!Mos
|16L 3s
!Name
|muggletonic
!Reasoning
|[[User:Xenllium|Xenllium]]
|In reference to muggle temperament.
|-
|-
|4L (4n+1)s
|21
|manulinear family
|10L 11s
|Named after manual
|miracloid
|[[User:Eliora|Eliora]]
|In reference to miracle temperament.
|-
|-
|4L (4n+3)s
| rowspan="3" |22
|smilinear family
|3L 19s
|Named after smitonic
|zheligowskic
|[[User:Frostburn|Frostburn]]
|In reference to Lucjan Żeligowski leading fights against the town of Giedraičiai.
|-
|-
! colspan="3" |Families with 5 large steps
|19L 3s
|giedraitic
|[[User:Frostburn|Frostburn]]
|Named after the basic magic layout of [[Kite Giedraitis]]' [[Kite guitar|guitar]]. Proposed prefix is "kai-".
|-
|-
!Mos
|21L 1s
!Name
|escapist
!Reasoning
|[[User:Eliora|Eliora]]
|References escapade temperament, which is supported by both 21edo and 22edo, covering the entire range.
|-
|-
|5L (5n+1)s
|23
|mechlinear family
|22L 1s
|Named after machinoid (prefix mech-)
|quartismoid
|-
|[[User:Eliora|Eliora]]
|5L (5n+2)s
|Five generators of roughly 33/32 quartertone are equal to 7/6 in the harmonic entropy minimum; also, the extreme ranges of 22edo and 23edo both support this mos.
|p-linear family
|}
|Named after p-chromatic rather than diatonic, which has no prefix
== Names for non-octave mosses ==
|-
 
|5L (5n+3)s
=== 3/1-equivalent mosses ===
|oneirolinear family
{| class="wikitable center-all"
|Named after oneirotonic
! colspan="4" |7-note mosses <3/1>
|-
|5L (5n+4)s
|chtonlinear family
|Named after semiquartal (prefix chton-)
|-
! colspan="3" |Families with 6 large steps
|-
|-
!Mos
!Pattern
!Name
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|6L (6n+1)s
|4L 3s
|archeolinear family
|electric
|Named after archeotonic
|[[User:CompactStar|CompactStar]]
|In reference to electra temperament
|-
|-
|6L (6n+5)s
! colspan="4" |9-note mosses <3/1>
|xeimlinear family
|Named after xeimtonic, a former name for 6L 5s
|-
|-
! colspan="3" |Families with 7 large steps
!Pattern
|-
!Suggested name(s)
!Mos
!Proposed by
!Name
!Reasoning
!Reasoning
|-
|-
|7L (7n+1)s
|4L 5s
|pinelinear family
|lambdatonic
|Named after pine
|n/a
|"Lambda" already refers to 4L 5s
|-
|-
|7L (7n+2)s
! colspan="4" |11-note mosses <3/1>
|armlinear family
|Named after superdiatonic (also called armotonic)
|-
|-
|7L (7n+3)s
!Pattern
|dicolinear or zalinear family
!Suggested name(s)
|Named after dicotonic (also called zaltertic)
!Proposed by
|-
|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
|
|
|-
! colspan="3" |Families with 8 large steps
|-
!Mos
!Name
!Reasoning
!Reasoning
|-
|-
|8L (8n+1)s
|7L 4s
|blulinear family
|superelectric
|Named after subneutralic (prefix blu-)
|[[User:CompactStar|CompactStar]]?
|Expansion of 4L 3s
|-
|-
|8L (8n+3)s
|9L 2s
|
|subarcturus
|
|?
|-
|?
|8L (8n+5)s
|}
|petrlinear family
=== 3/2-equivalent mosses ===
|Named after petroid, a former name for 8L 5s
{| class="wikitable center-all"
! colspan="4" |4-note mosses <3/2>
|-
|-
|8L (8n+7)s
!Pattern
|
!Suggested name(s)
|
!Proposed by
|-
! colspan="3" |Families with 9 large steps
|-
!Mos
!Name
!Reasoning
!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.
{| class="wikitable"
! colspan="6" |2-note mosses (from TAMNAMS)
|-
! colspan="2" |Mos pair
!Single-period?
!Names
!Prefix
!Language
|-
| colspan="2" |1L 1s
|Yes
|trivial
|triv-
|Latin
|-
! colspan="6" |3-note mosses (from TAMNAMS)
|-
! colspan="2" |Mos pair
!Single-period?
!Names
!Prefix
!Language
|-
|1L 2s
|2L 1s
|Yes
|antrial and trial
|(a)tri-
|Greek/Latin
|-
! colspan="6" |4-note mosses (from TAMNAMS)
|-
! colspan="2" |Mos pair
!Single-period?
!Names
!Prefix
!Language
|-
|-
|1L 3s
|1L 3s
|3L 1s
|neptunian
|Yes
|[[User:CompactStar|CompactStar]]
|antetric and tetric
|In reference to "uranian" for 3L 2s<3/2>
|(a)tet-
|Greek
|-
|-
| colspan="2" |2L 2s
! colspan="4" |5-note mosses <3/2>
|No
|2-trivial
|
|
|-
|-
! colspan="6" |5-note mosses (from TAMNAMS)
!Pattern
!Suggested name(s)
!Proposed by
!Reasoning
|-
|-
! colspan="2" |Mos pair
|2L 3s
!Single-period?
|saturnian
!Names
|[[User:CompactStar|CompactStar]]
!Prefix
|In reference to "uranian" for 3L 2s<3/2>
!Language
|-
|-
|1L 4s
|4L 1s
|Yes
|pedal and manual
|ped- and manu-
|Latin
|-
|2L 3s
|3L 2s
|3L 2s
|Yes
|uranian
|antipentic and pentic
|?
|(a)pent-
|?
|Greek
|}
== Names for equave-agnostic mosses ==
Equave-agnostic names (proposed by Ganaram) are an extension to the equave-agnostic names provide by TAMNAMS. They are based on Greek, Latin, and Sanskrit numeral prefixes. Names for multi-period equave-agnostic mosses are not provided, as they would be repetitions of a smaller step pattern.
{| class="wikitable center-all"
|-
|-
! colspan="6" |6-note mosses
! colspan="5" |6-note mosses
|-
|-
! colspan="2" |Mos pair
!Pattern
!Single-period?
!Suggested name
!Names
!Prefix
!Prefix
!Language
!Abbrev.
!Reasoning
|-
|-
|1L 5s
|1L 5s
|anhexic
|ahex-
|ahx
|Greek numeral prefix (hex-) for six, plus "an-"
|-
|5L 1s
|5L 1s
|Yes
|hexic
|anhexic and hexic
|hex-
|(an)hexa-
|hx
|Greek
|Greek numeral prefix "(hex-) for six
|-
|2L 4s
|4L 2s
|No
|2-antrial and 2-trial
|
|
|-
| colspan="2" |3L 3s
|No
|3-trivial
|
|
|-
|-
! colspan="6" |7-note mosses
! colspan="5" |7-note mosses
|-
|-
! colspan="2" |Mos pair
!Pattern
!Single-period?
!Suggested name
!Names
!Prefix
!Prefix
!Language
!Abbrev.
!Reasoning
|-
|-
|1L 6s
|1L 6s
|6L 1s
|ansaptic
|Yes
|ansap-
|ansaptic and saptic
|asp
|(an)sap-
|Sanskrit numeral prefix (sapta-) for seven, plus "an-"
|Sanskrit
|-
|-
|2L 5s
|2L 5s
|5L 2s
|anheptic
|Yes
|anhep-
|anheptic and heptic
|ahp
|(an)hept-
|Greek numeral prefix (hepta-) for seven, plus "an-"
|Greek
|-
|-
|3L 4s
|3L 4s
|anseptenic
|ansep-
|asep
|Latin numeral prefix (septen-) for seven, plus "an-"
|-
|4L 3s
|4L 3s
|Yes
|septenic
|anseptenic and septenic
|sep-
|(an)sept-
|sep
|Latin
|Latin numeral prefix (septen-) for seven
|-
|-
! colspan="6" |8-note mosses
|5L 2s
|heptic
|hep-
|hp
|Greek numeral prefix (hepta-) for seven
|-
|-
! colspan="2" |Mos pair
|6L 1s
!Single-period?
|saptic
!Names
|sap-
|sp
|Sanskrit numeral prefix (sapta-) for seven
|-
! colspan="5" |8-note mosses
|-
!Pattern
!Suggested name
!Prefix
!Prefix
!Language
!Abbrev.
!Reasoning
|-
|-
|1L 7s
|1L 7s
|7L 1s
|anastaic
|Yes
|anast-
|anastaic and astaic
|aast
|(an)asta-
|Sanskrit numeral prefix (aṣṭa-) for eight, plus "an-"
|Sanskrit
|-
|-
|2L 6s
|3L 5s
|6L 2s
|anoctic
|No
|anoct-
|2-antetric and 2-tetric
|aoct
|
|Greek/Latin numeral prefix (octo-) for eight, plus "an-"
|
|-
|-
|3L 5s
|5L 3s
|5L 3s
|Yes
|octic
|anoctic and octic
|oct-
|(an)oct-
|oct
|Greek/Latin
|Greek/Latin numeral prefix (octo-) for eight
|-
|-
| colspan="2" |4L 4s
|7L 1s
|No
|astaic
|
|ast-
|
|ast
|
|Sanskrit numeral prefix (aṣṭa-) for eight
|-
|-
! colspan="6" |9-note mosses
! colspan="5" |9-note mosses
|-
|-
! colspan="2" |Mos pair
!Pattern
!Single-period?
!Suggested name
!Names
!Prefix
!Prefix
!Language
!Abbrev.
!Reasoning
|-
|-
|1L 8s
|1L 8s
|8L 1s
|annavic
|Yes
|annav-
|annavic and navic
|anv
|(an)nav-
|Sanskrit numeral prefix (nava-) for nine, plus "an-"
|Sanskrit
|-
|-
|2L 7s
|2L 7s
|7L 2s
|anennaic
|Yes
|anenn-
|anennaic and ennaic
|aenn
|(an)enna-
|Greek numeral prefix (ennea-) for nine, plus "an-"
|Greek
|-
|-
|3L 6s
|4L 5s
|6L 3s
|annovemic
|No
|annov-
|3-antrial and 3-trial
|anv
|
|Latin numeral prefix (novem-) for nine, plus "an-"
|
|-
|-
|4L 5s
|5L 4s
|5L 4s
|Yes
|novemic
|annovemic and novemic
|nov-
|(an)nov-
|nv
|Latin
|Latin numeral prefix (novem-) for nine
|-
|-
! colspan="6" |10-note mosses
|7L 2s
|ennaic
|enn-
|enn
|Greek numeral prefix (ennea-) for nine
|-
|-
! colspan="2" |Mos pair
|8L 1s
!Single-period?
|navic
!Names
|nav-
|nv
|Sanskrit numeral prefix (nava-) for nine
|-
! colspan="5" |10-note mosses
|-
!Pattern
!Suggested name
!Prefix
!Prefix
!Language
!Abbrev.
!Reasoning
|-
|-
|1L 9s
|1L 9s
|9L 1s
|andashic
|Yes
|andash-
|andashic and dashic
|adsh
|(an)dash-
|Sanskrit numeral prefix (dasha-) for ten, plus "an-"
|Sanskrit
|-
|-
|2L 8s
|3L 7s
|8L 2s
|andeckic
|No
|andeck-
|2-manual and 2-pedal
|adek
|
|Greek/Latin numeral prefix (decem-/deca-) for ten, plus "an-"
|
|-
|-
|3L 7s
|7L 3s
|7L 3s
|Yes
|deckic
|andekic and dekic
|deck-
|(an)dek-
|dek
|Greek
|Greek/Latin numeral prefix (decem-/deca-) for ten
|-
|-
|4L 6s
|9L 1s
|6L 4s
|dashic
|No
|dash-
|2-pentic and 2-anpentic
|dsh
|
|Sanskrit numeral prefix (dasha-) for ten
|
|-
| colspan="2" |5L 5s
|No
|5-trivial
|
|
|}
|}


== Reasoning for names ==
== Appendix ==
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. Various terms have been used to similarly describe child mosses, but not under a temperament-agnostic viewpoint.
The motivation behind these names is from a desire to expand TAMNAMS-like names past the current note limit of 10 steps and, to a lesser extent, preserve former TAMNAMS names given to such mosses.
{| class="wikitable"
 
|-
The names for mos descendants are given the general terms of ''child'', ''grandchild'', ''great-grandchild'', and so on. Formerly, names based on the terms ''chromatic'' and ''enharmonic'' were prescribed, much in the spirit of ''m-chromatic'' and ''p-chromatic''. These terms, accompanied by single-letter prefixes, such as ''m-'' and ''p-'', and others, were used as bases for the descendants of any mos. However, these names were abandoned since the concept of ''chromatic'' did not generalize well outside the context of chromatic pairs, and the single-letter prefixes were considered temperament-suggestive.
!Source of terms
 
!Grandparent (2nd predecessor)
More unique names have been prescribed by others, but have limited use or acceptance by the xen community as a whole.
!Parent (1st predecessor)
!Mos
!Child (1st descendant)
!Grandchild (2nd descendant)
!Great-grandchild (3rd descendant)
!''k''th descendant
|-
|From [[Diatonic, Chromatic, Enharmonic, Subchromatic]]
|n/a
|n/a
|diatonic
|chromatic
|enharmonic
|subchromatic
|n/a
|-
| rowspan="2" |From [[Chromatic pairs]]
| rowspan="2" |sub-haplotonic
(not called this on page)
| rowspan="2" |haplotonic
| rowspan="2" |albitonic
|chromatic
|mega-chromatic
|
| rowspan="2" |n/a
|-
|mega-albitonic
|chromatic
|mega-chromatic
|-
|Terminology used for this page
|n/a
|n/a
|mos
|chromatic mos
|enharmonic mos
|subchromatic mos
|''k''th descendant
|}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.
The names ''m-chromatic'' and ''p-chromatic'', as they apply to 7L 5s and 5L 7s, are left unchanged, but can alternatively be described generally as ''child scales of diatonic'', or specifically, the ''child scale of soft diatonic'' and ''child scale of hard diatonic'' respectively.
{| class="wikitable"
|+Prefixes for diatonic descendants
! rowspan="2" |Diatonic scale
! colspan="3" |Chromatic mosses
! colspan="3" |Enharmonic mosses
! colspan="3" |Subchromatic mosses
|-
!Steps
!Temp-based prefix
!Ratio-based prefix
!Steps
!Temp-based prefix
!Ratio-based prefix
!Steps
!Temp-based prefix
!Ratio-based prefix
|-
| rowspan="8" |[[5L 2s]]
| rowspan="4" |[[7L 5s]]
| rowspan="4" |m- (from meantone)
| rowspan="4" |s-
| rowspan="2" |[[7L 12s]]
| rowspan="2" |f- (from flattone)
| rowspan="2" |s-
|[[7L 19s]]
|t- (from tridecimal)
|us-
|-
|[[19L 7s]]
|f- (from flattone)
|ps-
|-
| rowspan="2" |[[12L 7s]]
| rowspan="2" |m- (from meantone)
| rowspan="2" |os-
|[[19L 12s]]
|m- (from meanpop)
|qs-
|-
|[[12L 19s]]
|h- (from huygens)
|ms-
|-
| rowspan="4" |[[5L 7s]]
| rowspan="4" |p- (from pythagorean)
| rowspan="4" |h-
| rowspan="2" |[[12L 5s]]
| rowspan="2" |p- (from pythagorean)
| rowspan="2" |oh-
|[[12L 17s]]
|p- (from pythagorean)
|mh-
|-
|[[17L 12s]]
|g- (from gentle)
|qh-
|-
| rowspan="2" |[[5L 12s]]
| rowspan="2" |s- (from superpyth)
| rowspan="2" |h-
|[[17L 5s]]
|s- (from superpyth)
|ph-
|-
|[[5L 17s]]
|u- (from ultrapyth)
|uh-
|}

Latest revision as of 19:16, 10 February 2024

Main article: TAMNAMS

This page describes TAMNAMS-like names applied to octave-equivalent mosses with more than 10 notes, as well as non-octave mosses (fifth and tritave equivalent).

Disclaimer

The names described in this section may may have limited use. Some of these names may only find usage by a single person or a small group and thus have limited acceptance by the broader xen community. These names may also be subject to change as these names or the scales they refer to gain greater usage by the community, and it may be possible for the same scale to have more than one name.

Relating a mos and its descendants

Larger mosses can be described by how they related back to a more familiar mos and vice-versa. In general, all mosses with n periods relate back to a root mos of nL ns. For TAMNAMS-named mosses, any octave-equivalent mos with more than 10 steps and no more than 5 periods is related to some TAMNAMS-named mos.

In either case, any mos can be related to its descendants by treating it as the root of its own scale tree. Particularly in the absence of any names, mosses can be described as being some descendant of a related ancestor mos xL ys. Such mosses, called mos descendants – or children, grandchildren, and great-grandchildren, for the first three generations of descendants – contain the following pattern of step counts.

Parent Child Grandchild Great-grandchild
Large steps Small steps Large steps Small steps Large steps Small steps Large steps Small steps
x y x+y x x+y 2x+y x+y 3x+2y
3x+2y x+y
2x+y x+y 3x+2y 2x+y
2x+y 3x+2y
x x+y 2x+y x 2x+y 3x+y
3x+y 2x+y
x 2x+y 3x+y x
x 3x+y

For example, the first three generations of diatonic descendants can be described as:

  • Children of 5L 2s: 7L 5s and 5L 7s
  • Grandchildren of 5L 2s: 5L 12s, 12L 5s, 12L 7s, and 7L 12s
  • Great-grandchildren of 5L 2s: 5L 17s, 17L 5s, 17L 12s, 12L 17s, 12L 19s, 19L 12s, 12L 7s, and 7L 19s

Finding the ancestor of a descendant mos xL ys

For a mos xL ys, perform the following algorithm to find a familiar ancestor with target note count n or less:

  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.
  2. Let m1 be assigned the value of max(z, w) and m2 the value of min(z, w).
  3. Assign to z the value m2 and w the value m1-m2.
  4. If z+w is less than or equal to n, then the ancestor mos is zL ws. If not, repeat the process starting at step 2.

Finding an ancestor's step ratio that produces a descandant mos xL ys

For a mos xL ys, perform the following algorithm to find the step ratio for a descendant mos zL ws with target note count n or less:

  1. Let z and w be the number of large and small steps of the parent mos to be found. Let U and V be two chunks, vectors containing the amounts of L's and s's from xL ys that make up the ancestor mos's large and small steps.
    1. Assign to z and w the values x and y respectively.
    2. Assign to U the vector { uL, us } = { 1, 0 } and V to the vector { vL, vs } = { 0, 1 }.
  2. Let m1 be assigned the value of max(z, w) and m2 the value of min(z, w).
    1. If w > z, then add V to U. Otherwise, assign to a temporary vector Utemp the value of U, add V to U, and assign to V the value of Utemp.
  3. Assign to z the value m2 and w the value m1-m2.
  4. If z+w is less than or equal to n, then the ancestor mos is zL ws. The step ratio range for the zL ws is (uL+ us):(vL+ vLs) to uL:vs. If z+w is not less than or equal to n, repeat the process starting at step 2.

Names for mosses with more than 10 notes

Names for nL ns mosses with more than 5 periods

The following names are based on the -wood names, with appropriate Greek numeral prefixes applied.

Pattern Suggested name Prefix Abbrev. Reasoning
6L 6s hexawood hexwd- hxw Greek numeral prefix (hexa-) for six, plus "wood"
7L 7s heptawood hepwd- hpw Greek numeral prefix (hepta-) for seven, plus "wood"
8L 8s octawood octwd- ocw Greek numeral prefix (octo-) for eight, plus "wood"
9L 9s enneawood ennwd- enw Greek numeral prefix (ennea-) for nine, plus "wood"
10L 10s decawood decwd- dkw Greek numeral prefix (deca-) for ten, plus "wood"
11L 11s hendecawood hedwd- hdw Greek numeral prefix (hendeca-) for 11, plus "wood"
12L 12s dodecawood dodwd- ddw Greek numeral prefix (dodeca-) for 12, plus "wood"
13L 13s 13-wood 13wd- 13w Number 13 prepended to "wood"
14L 14s 14-wood 14wd- 14w Number 14 prepended to "wood"
kL ks k-wood kwd kw General number k prepended to "wood"

Names for mosses with 11 or more notes (excluding nL ns mosses)

11-note mosses
Pattern Suggested name(s) Proposed by Reasoning
1L 10s tanzanite, tenorite Ganaram inukshuk More naming puns (tenzanite or tenorite).
4L 7s kleistonic Former TAMNAMS name.
7L 4s suprasmitonic Former TAMNAMS name.
daemotonic Eliora Various reasons; see 7L 4s.
9L 2s villatonic Ganaram inukshuk Indirectly references avila and casablanca temperaments.
ultradiatonic, superarmotonic CompactStar In reference to diatonic and armotonic.
12-note mosses
Pattern Suggested name(s) Proposed by Reasoning
1L 11s helenite Ganaram inukshuk In reference to the "ele" substring found in the word "eleven".
5L 7s p-chromatic Former TAMNAMS name.
7L 5s m-chromatic Former TAMNAMS name.
13-note mosses
Pattern Suggested name(s) Proposed by Reasoning
1L 12s zircon Ganaram inukshuk Zircon is used as a birthstone for December.
11L 2s hendecoid Eliora From Greek "eleven"; references how "its generator is so close to 11/8 as to be called nothing but that" and that it has 11 large steps.
14-note mosses
Pattern Suggested name(s) Proposed by Reasoning
13L 1s trollic Godtone The name proposed by Godtone refers to 12L 1s, but it refers to 13L 1s as a troll move.
Note count Pattern Suggested name(s) Proposed by Reasoning
17 2L 15s liesic Frostburn Frostburn's naming scheme only goes up to 3 generations, so this name is suggested.
19 3L 16s magicaltonic Xenllium In reference to magic temperament.
16L 3s muggletonic Xenllium In reference to muggle temperament.
21 10L 11s miracloid Eliora In reference to miracle temperament.
22 3L 19s zheligowskic Frostburn In reference to Lucjan Żeligowski leading fights against the town of Giedraičiai.
19L 3s giedraitic Frostburn Named after the basic magic layout of Kite Giedraitis' guitar. Proposed prefix is "kai-".
21L 1s escapist Eliora References escapade temperament, which is supported by both 21edo and 22edo, covering the entire range.
23 22L 1s quartismoid Eliora Five generators of roughly 33/32 quartertone are equal to 7/6 in the harmonic entropy minimum; also, the extreme ranges of 22edo and 23edo both support this mos.

Names for non-octave mosses

3/1-equivalent mosses

7-note mosses <3/1>
Pattern Suggested name(s) Proposed by Reasoning
4L 3s electric CompactStar In reference to electra temperament
9-note mosses <3/1>
Pattern Suggested name(s) Proposed by Reasoning
4L 5s lambdatonic n/a "Lambda" already refers to 4L 5s
11-note mosses <3/1>
Pattern Suggested name(s) Proposed by Reasoning
7L 4s superelectric CompactStar? Expansion of 4L 3s
9L 2s subarcturus ? ?

3/2-equivalent mosses

4-note mosses <3/2>
Pattern Suggested name(s) Proposed by Reasoning
1L 3s neptunian CompactStar In reference to "uranian" for 3L 2s<3/2>
5-note mosses <3/2>
Pattern Suggested name(s) Proposed by Reasoning
2L 3s saturnian CompactStar In reference to "uranian" for 3L 2s<3/2>
3L 2s uranian ? ?

Names for equave-agnostic mosses

Equave-agnostic names (proposed by Ganaram) are an extension to the equave-agnostic names provide by TAMNAMS. They are based on Greek, Latin, and Sanskrit numeral prefixes. Names for multi-period equave-agnostic mosses are not provided, as they would be repetitions of a smaller step pattern.

6-note mosses
Pattern Suggested name Prefix Abbrev. Reasoning
1L 5s anhexic ahex- ahx Greek numeral prefix (hex-) for six, plus "an-"
5L 1s hexic hex- hx Greek numeral prefix "(hex-) for six
7-note mosses
Pattern Suggested name Prefix Abbrev. Reasoning
1L 6s ansaptic ansap- asp Sanskrit numeral prefix (sapta-) for seven, plus "an-"
2L 5s anheptic anhep- ahp Greek numeral prefix (hepta-) for seven, plus "an-"
3L 4s anseptenic ansep- asep Latin numeral prefix (septen-) for seven, plus "an-"
4L 3s septenic sep- sep Latin numeral prefix (septen-) for seven
5L 2s heptic hep- hp Greek numeral prefix (hepta-) for seven
6L 1s saptic sap- sp Sanskrit numeral prefix (sapta-) for seven
8-note mosses
Pattern Suggested name Prefix Abbrev. Reasoning
1L 7s anastaic anast- aast Sanskrit numeral prefix (aṣṭa-) for eight, plus "an-"
3L 5s anoctic anoct- aoct Greek/Latin numeral prefix (octo-) for eight, plus "an-"
5L 3s octic oct- oct Greek/Latin numeral prefix (octo-) for eight
7L 1s astaic ast- ast Sanskrit numeral prefix (aṣṭa-) for eight
9-note mosses
Pattern Suggested name Prefix Abbrev. Reasoning
1L 8s annavic annav- anv Sanskrit numeral prefix (nava-) for nine, plus "an-"
2L 7s anennaic anenn- aenn Greek numeral prefix (ennea-) for nine, plus "an-"
4L 5s annovemic annov- anv Latin numeral prefix (novem-) for nine, plus "an-"
5L 4s novemic nov- nv Latin numeral prefix (novem-) for nine
7L 2s ennaic enn- enn Greek numeral prefix (ennea-) for nine
8L 1s navic nav- nv Sanskrit numeral prefix (nava-) for nine
10-note mosses
Pattern Suggested name Prefix Abbrev. Reasoning
1L 9s andashic andash- adsh Sanskrit numeral prefix (dasha-) for ten, plus "an-"
3L 7s andeckic andeck- adek Greek/Latin numeral prefix (decem-/deca-) for ten, plus "an-"
7L 3s deckic deck- dek Greek/Latin numeral prefix (decem-/deca-) for ten
9L 1s dashic dash- dsh Sanskrit numeral prefix (dasha-) for ten

Appendix

The motivation behind these names is from a desire to expand TAMNAMS-like names past the current note limit of 10 steps and, to a lesser extent, preserve former TAMNAMS names given to such mosses.

The names for mos descendants are given the general terms of child, grandchild, great-grandchild, and so on. Formerly, names based on the terms chromatic and enharmonic were prescribed, much in the spirit of m-chromatic and p-chromatic. These terms, accompanied by single-letter prefixes, such as m- and p-, and others, were used as bases for the descendants of any mos. However, these names were abandoned since the concept of chromatic did not generalize well outside the context of chromatic pairs, and the single-letter prefixes were considered temperament-suggestive.

More unique names have been prescribed by others, but have limited use or acceptance by the xen community as a whole.

The names m-chromatic and p-chromatic, as they apply to 7L 5s and 5L 7s, are left unchanged, but can alternatively be described generally as child scales of diatonic, or specifically, the child scale of soft diatonic and child scale of hard diatonic respectively.

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