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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 for how to name mos descendants. However, this page describes several more systems that apply to non-octave mosses.
Main article: TAMNAMS


The scope of this TAMNAMS extension is as follows:
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).


# Systematically name mosses beyond the named range by how they're related to TAMNAMS-named mosses. The most common way of doing this is by considering what mosses descend from a TAMNAMS-named mos.
== Disclaimer ==
## Secondarily, propose unique names for certain mosses in case they're worth having distinct names. Some of these names are old names that have been around long enough to be memorable.
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.
# Systematically name mosses for non-octave equaves, namely fifth and tritave-equivalent mosses.
# Systematically name mosses regardless of the equave. Such names should be as general as possible.


== Naming mos descendants ==
== Relating a mos and its 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.
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" |Grandchild
! colspan="2" |Great-grandchild
|-
|-
! colspan="2" |Parent mos
!Large steps
! colspan="3" |Child (1st descendant)
!Small steps
! colspan="3" |Grandchild (2nd descendant)
!Large steps
! colspan="3" |Great-grandchild (3rd descendant)
!Small steps
!''k''th descendant
!Large steps
|-
!Small steps
| colspan="2" |''(mos-name)''
!Large steps
| colspan="3" |''(step-ratio)-''chromatic ''(mos-name)''
!Small steps
''(step-ratio)-''chro ''(mos-name)''
 
''(step-ratio)-(mos-prefix)''enharmonic
| colspan="3" |''(step-ratio)''-enharmonic ''(mos-name)''
''(step-ratio)''-enhar ''(mos-name)''
 
''(step-ratio)-(mos-prefix)''enharmonic
| colspan="3" |''(step-ratio)''-subchromatic ''(mos-name)''
''(step-ratio)''-subchro ''(mos-name)''
 
''(step-ratio)-(mos-prefix)''subchromatic
|''(k''th'') (mos-name)'' descendant
''(k''th'')-(mos-prefix)''descendant
|-
! colspan="12" |Step ratio prefixes (optional)
|-
! colspan="2" |Parent mos
! colspan="3" |Child (1st descendant)
! colspan="3" |Grandchild (2nd descendant)
! colspan="3" |Great-grandchild (3rd descendant)
!''k''th descendant
|-
!Mos
!L:s range
!Mos
!L:s range
!Prefix
!Mos
!L:s range
!Prefix
!Mos
!L:s range
!Prefix
!Prefixes not applicable
|-
|-
| rowspan="8" |xL ys
| rowspan="8" |''x''
| rowspan="8" |1:1 to 1:0
| rowspan="8" |''y''
| rowspan="4" |(x+y)L xs
| rowspan="4" |''x''+''y''
| rowspan="4" |1:1 to 2:1
| rowspan="4" |''x''
(general soft range)
| rowspan="2" |''x''+''y''
| rowspan="4" |s-
| rowspan="2" |2''x''+''y''
| rowspan="2" |(x+y)L (2x+y)s
|''x''+''y''
| rowspan="2" |1:1 to 3:2
|3''x''+2''y''
(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
|3''x''+2''y''
|4:3 to 3:2
|''x''+''y''
(parasoft)
|ps-
|-
|-
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="2" |2''x''+''y''
| rowspan="2" |3:2 to 2:1
| rowspan="2" |''x''+''y''
(hyposoft)
|3''x''+2''y''
| rowspan="2" |os-
|2''x''+''y''
|(3x+2y)L (2x+y)s
|3:2 to 5:3
(quasisoft)
|qs-
|-
|-
|(2x+y)L (3x+2y)s
|2''x''+''y''
|5:3 to 2:1
|3''x''+2''y''
(minisoft)
|ms-
|-
|-
| rowspan="4" |xL (x+y)s
| rowspan="4" |''x''
| rowspan="4" |2:1 to 1:0
| rowspan="4" |''x''+''y''
(general hard range)
| rowspan="2" |2''x''+''y''
| rowspan="4" |h-
| rowspan="2" |''x''
| rowspan="2" |(2x+y)L xs
|2''x''+''y''
| rowspan="2" |2:1 to 3:1
|3''x''+''y''
(hypohard)
| rowspan="2" |oh-
|(2x+y)L (3x+y)s
|2:1 to 5:1
(minihard)
|mh-
|-
|-
|(3x+y)L (2x+y)s
|3''x''+''y''
|5:2 to 3:1
|2''x''+''y''
(quasihard)
|qh-
|-
|-
| rowspan="2" |xL (2x+y)s
| rowspan="2" |''x''
| rowspan="2" |3:1 to 1:0
| rowspan="2" |2''x''+''y''
(hard)
|3''x''+''y''
| rowspan="2" |h-
|''x''
|(3x+y)L xs
|3:1 to 4:1
(parahard)
|ph-
|-
|-
|xL (3x+y)s
|''x''
|4:1 to 1:0
|3''x''+''y''
(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.
 
=== Extended ''k''-wood names ===
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 421: Line 103:
|hexwd-
|hexwd-
|hxw
|hxw
|Greek numeral prefix (hexa-) for six, plus "wood"
|-
|-
|7L 7s
|7L 7s
Line 426: Line 109:
|hepwd-
|hepwd-
|hpw
|hpw
|Greek numeral prefix (hepta-) for seven, plus "wood"
|-
|-
|8L 8s
|8L 8s
Line 431: Line 115:
|octwd-
|octwd-
|ocw
|ocw
|Greek numeral prefix (octo-) for eight, plus "wood"
|-
|-
|9L 9s
|9L 9s
Line 436: 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"
|}
|}
=== Specific names for mosses beyond 10 notes (proposed) ===
=== Names for mosses with 11 or more notes (excluding ''n''L ''n''s mosses) ===
These names are intended for notable mosses outside the named range for which its mos descendant name would be insufficient.
{| class="wikitable center-all"
{| class="wikitable"
! colspan="4" |11-note mosses
! colspan="3" |11-note mosses
|-
|-
!Mos
!Pattern
!Suggested name(s)
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|1L 10s
|1L 10s
|tanzanite or tenorite
|tanzanite, tenorite
|More naming puns ('''ten'''zanite or '''ten'''orite)
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
|-
|More naming puns ('''ten'''zanite or '''ten'''orite).
|2L 9s
|joanatonic
|Restoration of an old name that applied to its parent scale
|-
|3L 8s
|
|
|-
|-
|4L 7s
|4L 7s
|kleistonic
|kleistonic
|Restoration of an old name
|-
|5L 6s
|xeimtonic
|Restoration of an old name
|-
|6L 5s
|
|
|
|Former TAMNAMS name.
|-
|-
|7L 4s
| rowspan="2" |7L 4s
|suprasmitonic
|suprasmitonic
|Restoration of an old name
|
|Former TAMNAMS name.
|-
|-
|8L 3s
|daemotonic
|sentonic or sensoid
|[[User:Eliora|Eliora]]
|Modification or restoration of an old name that applied to its parent scale
|Various reasons; see [[7L 4s]].
|-
|-
|9L 2s
| rowspan="2" |9L 2s
|villatonic, ultradiatonic, or superarmotonic
|villatonic
|Indirectly references a'''vila''' and '''casa'''blanca (Spanish for "white house", and a villa is a type of house) temperaments
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
Latter two names are suggested by CompactStar
|Indirectly references avila and casablanca temperaments.
|-
|-
|10L 1s
|ultradiatonic, superarmotonic
|miratonic or miraculoid
|[[User:CompactStar|CompactStar]]
|Modification or restoration of an old name (miraculoid); reference miracle temperament
|In reference to diatonic and armotonic.
|-
|-
! colspan="3" |12-note mosses
! colspan="4" |12-note mosses
|-
|-
!Mos
!Pattern
!Suggested name(s)
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|1L 11s
|1L 11s
|helenite
|helenite
|In reference to the "ele" substring found in the word "eleven"
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
|In reference to the "ele" substring found in the word "eleven".
|-
|-
|2L 10s
|5L 7s
|
|p-chromatic
|
|-
|3L 9s
|
|
|
|-
|Former TAMNAMS name.
|4L 8s
|
|
|-
|5L 7s
|pychromatic or p-chromatic
|Modification or restoration of an old name (p-chromatic)
|-
|6L 6s
|hexawood
|Extension of -wood scales; coincidentally references hexe temperament
|-
|-
|7L 5s
|7L 5s
|emchromatic or m-chromatic
|m-chromatic
|Modification or restoration of an old name (m-chromatic)
|-
|8L 4s
|
|
|
|Former TAMNAMS name.
|-
|-
|9L 3s
! colspan="4" |13-note mosses
|
|
|-
|-
|10L 2s
!Pattern
|
|
|-
|11L 1s
|ripploid
|Restoration of an old name
|-
! colspan="3" |13-note mosses
|-
!Mos
!Suggested name(s)
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|1L 12s
|1L 12s
|zircon
|zircon
|Zircon is used as a birthstone for December
|[[User:Ganaram inukshuk|Ganaram inukshuk]]
|Zircon is used as a birthstone for December.
|-
|-
|2L 11s
|11L 2s
|litonic
|hendecoid
|Portmanteau of liese, triton, and tritonic temperaments
|[[User:Eliora|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.
|-
|-
|3L 10s
! colspan="4" |14-note mosses
|magitonic
|In reference to magic temperament
|-
|-
|4L 9s
!Pattern
|huxloga
!Suggested name(s)
|Portmanteau of huxley, lovecraft, and gariberttet temperaments
!Proposed by
|-
!Reasoning
|5L 8s
|
|
|-
|6L 7s
|
|
|-
|7L 6s
|tetarquintal
|In reference to temperaments that divide the perfect 5th (3/2) into four
|-
|8L 5s
|petroid
|Restoration of an old name
|-
|-
|9L 4s
|13L 1s
|orwelloid
|trollic
|Restoration of an old name that applied to its parent scale
|[[User:Godtone|Godtone]]
|-
|The name proposed by Godtone refers to 12L 1s, but it refers to 13L 1s as a troll move.
|10L 3s
|luachoid
|Already proposed name
|-
|11L 2s
|maioquartal or hendecoid
|In reference to the "major fourths" scale used by Tcherepnin; the latter is proposed by Eliora
|-
|12L 1s
|quasidozenal
|Meant to invoke the phrase "almost twelve"
|}
|}
 
{| class="wikitable center-all"
==== Names for mos linear families (proposed) ====
Rather than name mosses related by the number of large steps they have, where the mosses are of the form xL (nx + y)s and relate back to a mos xL ys (n=0), these mosses can be described as members of a family. 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. By extension, the mos 7L 5s (the sister of 5L 7s) is not seen as a member of this linear family even though it's part of the diatonic family as a whole, but rather as the start of its own linear family; put another way, the mosses 5L 2s, 5L 7s, 5L 12s, 5L 17s, etc are a subfamily within the larger diatonic family.
 
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
!Note count
!Name
!Pattern
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|1L (n+1)s
|17
|monolarge family
|2L 15s
|Represents an entire family of mosses formerly unnamed by TAMNAMS
|liesic
The name "monolarge" is chosen as it succinctly describes the only possible 1L family
|[[User:Frostburn|Frostburn]]
|Frostburn's naming scheme only goes up to 3 generations, so this name is suggested.
|-
|-
|2L (2n+1)s
| rowspan="2" |19
|bilarge family
|3L 16s
|Named analogously to the monolarge family
|magicaltonic
|[[User:Xenllium|Xenllium]]
|In reference to magic temperament.
|-
|-
|3L (3n+1)s
|16L 3s
|trilarge family
|muggletonic
|Named analogously to the monolarge family
|[[User:Xenllium|Xenllium]]
Prevents potential confusion with the name "tetralinear"
|In reference to muggle temperament.
|-
|-
! colspan="3" |Families with 3 large steps
|21
|10L 11s
|miracloid
|[[User:Eliora|Eliora]]
|In reference to miracle temperament.
|-
|-
!Mos
| rowspan="3" |22
!Name
|3L 19s
!Reasoning
|zheligowskic
|[[User:Frostburn|Frostburn]]
|In reference to Lucjan Żeligowski leading fights against the town of Giedraičiai.
|-
|-
|3L (3n+2)s
|19L 3s
|apentilinear family
|giedraitic
|Named after anpentic
|[[User:Frostburn|Frostburn]]
|Named after the basic magic layout of [[Kite Giedraitis]]' [[Kite guitar|guitar]]. Proposed prefix is "kai-".
|-
|-
! colspan="3" |Families with 4 large steps
|21L 1s
|escapist
|[[User:Eliora|Eliora]]
|References escapade temperament, which is supported by both 21edo and 22edo, covering the entire range.
|-
|-
!Mos
|23
!Name
|22L 1s
|quartismoid
|[[User:Eliora|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 ===
{| class="wikitable center-all"
! colspan="4" |7-note mosses <3/1>
|-
!Pattern
!Suggested name(s)
!Proposed by
!Reasoning
!Reasoning
|-
|-
|4L (4n+1)s
|4L 3s
|manulinear family
|electric
|Named after manual
|[[User:CompactStar|CompactStar]]
|In reference to electra temperament
|-
|-
|4L (4n+3)s
! colspan="4" |9-note mosses <3/1>
|smilinear family
|Named after smitonic
|-
|-
! colspan="3" |Families with 5 large steps
!Pattern
|-
!Suggested name(s)
!Mos
!Proposed by
!Name
!Reasoning
!Reasoning
|-
|-
|5L (5n+1)s
|4L 5s
|mechlinear family
|lambdatonic
|Named after machinoid (prefix mech-)
|n/a
|"Lambda" already refers to 4L 5s
|-
|-
|5L (5n+2)s
! colspan="4" |11-note mosses <3/1>
|p-linear family
|Named after p-chromatic rather than diatonic, which has no prefix
|-
|-
|5L (5n+3)s
!Pattern
|oneirolinear family
!Suggested name(s)
|Named after oneirotonic
!Proposed by
|-
|5L (5n+4)s
|chtonlinear family
|Named after semiquartal (prefix chton-)
|-
! colspan="3" |Families with 6 large steps
|-
!Mos
!Name
!Reasoning
!Reasoning
|-
|-
|6L (6n+1)s
|7L 4s
|archeolinear family
|superelectric
|Named after archeotonic
|[[User:CompactStar|CompactStar]]?
|Expansion of 4L 3s
|-
|-
|6L (6n+5)s
|9L 2s
|xeimlinear family
|subarcturus
|Named after xeimtonic, a former name for 6L 5s
|?
|?
|}
=== 3/2-equivalent mosses ===
{| class="wikitable center-all"
! colspan="4" |4-note mosses <3/2>
|-
|-
! colspan="3" |Families with 7 large steps
!Pattern
|-
!Suggested name(s)
!Mos
!Proposed by
!Name
!Reasoning
!Reasoning
|-
|-
|7L (7n+1)s
|1L 3s
|pinelinear family
|neptunian
|Named after pine
|[[User:CompactStar|CompactStar]]
|In reference to "uranian" for 3L 2s<3/2>
|-
|-
|7L (7n+2)s
! colspan="4" |5-note mosses <3/2>
|armlinear family
|Named after superdiatonic (also called armotonic)
|-
|-
|7L (7n+3)s
!Pattern
|dicolinear family
!Suggested name(s)
|Named after dicotonic
!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-chromaticralic (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
|
|
|-
! colspan="3" |Families with 9 large steps
|-
!Mos
!Name
!Reasoning
!Reasoning
|-
|-
|9L (9n+1)s
|2L 3s
|sinalinear family
|saturnian
|Named after sinatonic
|[[User:CompactStar|CompactStar]]
|In reference to "uranian" for 3L 2s<3/2>
|-
|-
|9L (9n+2)s
|3L 2s
|
|uranian
|
|?
|-
|?
|9L (9n+4)s
|
|
|-
|9L (9n+5)s
|
|
|-
|9L (9n+7)s
|
|
|-
|9L (9n+8)s
|
|
|}
|}
 
== Names for equave-agnostic mosses ==
== Non-octave extensions (proposed) ==
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.
Since the perfect 5th and tritave (or perfect 12th) are the two most common non-octave equivalence intervals for which there are scales described, mosses for these two intervals should be the most likely to receive TAMNAMS-like names. For mosses with any other equivalence interval, describing nested mos structures, or in situations where the notion of an equivalence interval is unimportant, equave-agnostic names are proposed.
{| class="wikitable center-all"
 
Names for tritave and fifth-equivalent mosses are assumed to be the same name as their equave-agnostic equivalent, unless a fitting name is already given.
 
=== Equave-agnostic names (proposed) ===
This is a proposed scheme to name mosses regardless of the equivalence interval, These names are meant for nonoctave mosses and nested mos patterns such as with a mos cradle. These names are not final and are open to better suggestions.
{| class="wikitable"
! colspan="5" |4-note mosses (new names only)
|-
!Mos
!Name
!Multi-period?
!Prefix
!Abbrev.
|-
|2L 2s
|double trivial
|Yes (2)
|2triv-
|2trv
|-
|-
! colspan="5" |6-note mosses
! colspan="5" |6-note mosses
|-
|-
!Mos
!Pattern
!Name
!Suggested name
!Multi-period?
!Prefix
!Prefix
!Abbrev.
!Abbrev.
!Reasoning
|-
|-
|1L 5s
|1L 5s
|anhexic
|anhexic
|No
|ahex-
|ahex-
|ahx
|ahx
|-
|Greek numeral prefix (hex-) for six, plus "an-"
|2L 4s
|double antrial
|Yes (2)
|2atri-
|2tri
|-
|3L 3s
|triple trivial
|Yes (3)
|3triv-
|3trv
|-
|4L 2s
|double trial
|Yes (2)
|2tri-
|2tri
|-
|-
|5L 1s
|5L 1s
|hexic
|hexic
|No
|hex-
|hex-
|hx
|hx
|Greek numeral prefix "(hex-) for six
|-
|-
! colspan="5" |7-note mosses
! colspan="5" |7-note mosses
|-
|-
!Mos
!Pattern
!Name
!Suggested name
!Multi-period?
!Prefix
!Prefix
!Abbrev.
!Abbrev.
!Reasoning
|-
|-
|1L 6s
|1L 6s
|ansaptic
|ansaptic
|No
|ansap-
|ansap-
|asp
|asp
|Sanskrit numeral prefix (sapta-) for seven, plus "an-"
|-
|-
|2L 5s
|2L 5s
|anheptic
|anheptic
|No
|anhep-
|anhep-
|ahp
|ahp
|Greek numeral prefix (hepta-) for seven, plus "an-"
|-
|-
|3L 4s
|3L 4s
|anseptenic
|anseptenic
|No
|ansep-
|ansep-
|asep
|asep
|Latin numeral prefix (septen-) for seven, plus "an-"
|-
|-
|4L 3s
|4L 3s
|septenic
|septenic
|No
|sep-
|sep-
|sep
|sep
|Latin numeral prefix (septen-) for seven
|-
|-
|5L 2s
|5L 2s
|heptic
|heptic
|No
|hep-
|hep-
|hp
|hp
|Greek numeral prefix (hepta-) for seven
|-
|-
|6L 1s
|6L 1s
|saptic
|saptic
|No
|sap-
|sap-
|sp
|sp
|Sanskrit numeral prefix (sapta-) for seven
|-
|-
! colspan="5" |8-note mosses
! colspan="5" |8-note mosses
|-
|-
!Mos
!Pattern
!Name
!Suggested name
!Multi-period?
!Prefix
!Prefix
!Abbrev.
!Abbrev.
!Reasoning
|-
|-
|1L 7s
|1L 7s
|anastaic
|anastaic
|No
|anast-
|anast-
|aast
|aast
|-
|Sanskrit numeral prefix (aṣṭa-) for eight, plus "an-"
|2L 6s
|double antetric
|Yes (2)
|2atetra-
|2att
|-
|-
|3L 5s
|3L 5s
|anoctic
|anoctic
|No
|anoct-
|anoct-
|aoct
|aoct
|-
|Greek/Latin numeral prefix (octo-) for eight, plus "an-"
|4L 4s
|quadruple trivial
|Yes (4)
|4triv-
|4trv
|-
|-
|5L 3s
|5L 3s
|octic
|octic
|No
|oct-
|oct-
|oct
|oct
|-
|Greek/Latin numeral prefix (octo-) for eight
|6L 2s
|double tetric
|Yes (2)
|2tetra-
|2tt
|-
|-
|7L 1s
|7L 1s
|astaic
|astaic
|No
|ast-
|ast-
|ast
|ast
|Sanskrit numeral prefix (aṣṭa-) for eight
|-
|-
! colspan="5" |9-note mosses
! colspan="5" |9-note mosses
|-
|-
!Mos
!Pattern
!Name
!Suggested name
!Multi-period?
!Prefix
!Prefix
!Abbrev.
!Abbrev.
!Reasoning
|-
|-
|1L 8s
|1L 8s
|annavic
|annavic
|No
|annav-
|annav-
|anv
|anv
|Sanskrit numeral prefix (nava-) for nine, plus "an-"
|-
|-
|2L 7s
|2L 7s
|anennaic
|anennaic
|No
|anenn-
|anenn-
|aenn
|aenn
|-
|Greek numeral prefix (ennea-) for nine, plus "an-"
|3L 6s
|triple antrial
|Yes (3)
|3atri-
|3atri
|-
|-
|4L 5s
|4L 5s
|annovemic
|annovemic
|No
|annov-
|annov-
|anv
|anv
|Latin numeral prefix (novem-) for nine, plus "an-"
|-
|-
|5L 4s
|5L 4s
|novemic
|novemic
|No
|nov-
|nov-
|nv
|nv
|-
|Latin numeral prefix (novem-) for nine
|6L 3s
|triple trial
|Yes (3)
|3tri-
|3tri
|-
|-
|7L 2s
|7L 2s
|ennaic
|ennaic
|No
|enn-
|enn-
|enn
|enn
|Greek numeral prefix (ennea-) for nine
|-
|-
|8L 1s
|8L 1s
|navic
|navic
|No
|nav-
|nav-
|nv
|nv
|Sanskrit numeral prefix (nava-) for nine
|-
|-
! colspan="5" |10-note mosses
! colspan="5" |10-note mosses
|-
|-
!Mos
!Pattern
!Name
!Suggested name
!Multi-period?
!Prefix
!Prefix
!Abbrev.
!Abbrev.
!Reasoning
|-
|-
|1L 9s
|1L 9s
|andashic
|andashic
|No
|andash-
|andash-
|adsh
|adsh
|-
|Sanskrit numeral prefix (dasha-) for ten, plus "an-"
|2L 8s
|double pedal
|Yes (2)
|2ped-
|2ped
|-
|-
|3L 7s
|3L 7s
|andeckic
|andeckic
|No
|andeck-
|andeck-
|adek
|adek
|-
|Greek/Latin numeral prefix (decem-/deca-) for ten, plus "an-"
|4L 6s
|double pentic
|Yes (2)
|2pent-
|2pt
|-
|5L 5s
|quintuple trivial
|Yes (5)
|5triv-
|5trv
|-
|6L 4s
|double anpentic
|Yes (2)
|2apent-
|2apt
|-
|-
|7L 3s
|7L 3s
|deckic
|deckic
|No
|deck-
|deck-
|dek
|dek
|-
|Greek/Latin numeral prefix (decem-/deca-) for ten
|8L 2s
|double manual
|Yes (2)
|2manu-
|2manu
|-
|-
|9L 1s
|9L 1s
|dashic
|dashic
|No
|dash-
|dash-
|dsh
|dsh
|Sanskrit numeral prefix (dasha-) for ten
|}
|}
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'''.
== 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.


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''.'''''
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.


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).
More unique names have been prescribed by others, but have limited use or acceptance by the xen community as a whole.
 
11-note mosses require naming five pairs, so this naming scheme stops at 10-note mosses.
 
Since the equivalence interval can be anything, names for multi-period mosses are named as a smaller mos repeated (double, triple, quadruple, etc) some number of times. The prefix and abbreviation of the base mos is preceded by the number of duplications. For example, 2L 2s is double trivial, its prefix is 2triv-, and its abbreviation is 2trv.
 
=== Names for 3/2-equivalent mosses (proposed) ===
{| class="wikitable"
! colspan="5" |4-note mosses <3/2>
|-
!Mos
!Name
!Prefix
!Abbrev.
!Reasoning
|-
|1L 3s
|neptunian
|nept-
|nep
|Name proposed by CompactStar, analogous to uranian
|-
! colspan="5" |5-note mosses <3/2>
|-
!Mos
!Name
!Prefix
!Abbrev.
!Reasoning
|-
|3L 2s
|uranian
|ura-
|ura
|Already-existing name
|}


=== Names for 3/1-equivalent mosses (proposed) ===
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"
! colspan="5" |7-note mosses <3/1>
|-
!Mos
!Name
!Prefix
!Abbrev.
!Reasoning
|-
|4L 3s
|electric
|elec-
|ele
|Name proposed by CompactStar
|-
! colspan="5" |9-note mosses <3/1>
|-
!Mos
!Name
!Prefix
!Abbrev.
!Reasoning
|-
|4L 5s
|lambdatonic
|lam-
|lam
|"lambda" already refers to tritave-equivalent 4L 5s
|}
== 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. Various terms have been used to similarly describe child mosses, but not under a temperament-agnostic viewpoint.
{| class="wikitable"
|-
!Source of terms
!Grandparent (2nd predecessor)
!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.
{| 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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