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== Relating a mos and its descendants ==
== Relating a mos and its descendants ==
In the absence of any names, mosses can be instead described by how it relates back to a more familiar mos. In general, all mosses with ''n'' periods relate back to a root mos of ''n''L ''n''s. As it pertains to 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.
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. For a mos of the form ''x''L ''y''s, its descendants (children, grandchildren, great-grandchildren, etc) contain the following pattern of step counts.
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="2" |Parent
! colspan="2" |Parent
Line 25: Line 25:
!Small steps
!Small steps
|-
|-
| rowspan="8" |x
| rowspan="8" |''x''
| rowspan="8" |y
| rowspan="8" |''y''
| rowspan="4" |x+y
| rowspan="4" |''x''+''y''
| rowspan="4" |x
| rowspan="4" |''x''
| rowspan="2" |x+y
| rowspan="2" |''x''+''y''
| rowspan="2" |2x+y
| rowspan="2" |2''x''+''y''
|x+y
|''x''+''y''
|3x+2y
|3''x''+2''y''
|-
|-
|3x+2y
|3''x''+2''y''
|x+y
|''x''+''y''
|-
|-
| rowspan="2" |2x+y
| rowspan="2" |2''x''+''y''
| rowspan="2" |x+y
| rowspan="2" |''x''+''y''
|3x+2y
|3''x''+2''y''
|2x+y
|2''x''+''y''
|-
|-
|2x+y
|2''x''+''y''
|3x+2y
|3''x''+2''y''
|-
|-
| rowspan="4" |x
| rowspan="4" |''x''
| rowspan="4" |x+y
| rowspan="4" |''x''+''y''
| rowspan="2" |2x+y
| rowspan="2" |2''x''+''y''
| rowspan="2" |x
| rowspan="2" |''x''
|2x+y
|2''x''+''y''
|3x+y
|3''x''+''y''
|-
|-
|3x+y
|3''x''+''y''
|2x+y
|2''x''+''y''
|-
|-
| rowspan="2" |x
| rowspan="2" |''x''
| rowspan="2" |2x+y
| rowspan="2" |2''x''+''y''
|3x+y
|3''x''+''y''
|x
|''x''
|-
|-
|x
|''x''
|3x+y
|3''x''+''y''
|}
|}
For example, the first three generations of ''diatonic descendants'' can be described as:


=== Finding a named ancestor for a descendant mos ===
* ''Children of 5L 2s'': 7L 5s and 5L 7s
For a mos ''x''L ''y''s, perform the following algorithm to find a familiar descendant with target note count ''n'' or less:
* ''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 ''x''L ''y''s ===
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 ''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 ''m1'' be assigned the value of max(''z'', ''w'') and ''m2'' the value of min(''z'', ''w'').
#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 ''m2'' and ''w'' the value ''m1''-''m2''.
#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 parent mos is ''z''L ''w''s. If not, repeat the process starting at step 2.
#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 mosses with more than 10 notes ==


=== Names for ''n''L ''n''s mosses with more than 5 periods ===
=== Names for ''n''L ''n''s mosses with more than 5 periods ===
The following names are based on the -wood names, with appropriate numeric prefixes applied.
The following names are based on the -wood names, with appropriate Greek numeral prefixes applied.
{| class="wikitable center-all"
{| class="wikitable center-all"
!Pattern
!Pattern
!Name
!Suggested name
!Prefix
!Prefix
!Abbrev.
!Abbrev.
!Reasoning
|-
|-
|6L 6s
|6L 6s
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|hexwd-
|hexwd-
|hxw
|hxw
|Greek numeral prefix (hexa-) for six, plus "wood"
|-
|-
|7L 7s
|7L 7s
Line 91: Line 109:
|hepwd-
|hepwd-
|hpw
|hpw
|Greek numeral prefix (hepta-) for seven, plus "wood"
|-
|-
|8L 8s
|8L 8s
Line 96: Line 115:
|octwd-
|octwd-
|ocw
|ocw
|Greek numeral prefix (octo-) for eight, plus "wood"
|-
|-
|9L 9s
|9L 9s
Line 101: Line 121:
|ennwd-
|ennwd-
|enw
|enw
|Greek numeral prefix (ennea-) for nine, plus "wood"
|-
|-
|10L 10s
|10L 10s
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|decwd-
|decwd-
|dkw
|dkw
|Greek numeral prefix (deca-) for ten, plus "wood"
|-
|-
|11L 11s
|11L 11s
Line 111: Line 133:
|hedwd-
|hedwd-
|hdw
|hdw
|Greek numeral prefix (hendeca-) for 11, plus "wood"
|-
|-
|12L 12s
|12L 12s
Line 116: Line 139:
|dodwd-
|dodwd-
|ddw
|ddw
|Greek numeral prefix (dodeca-) for 12, plus "wood"
|-
|-
|13L 13s
|13L 13s
Line 121: Line 145:
|13wd-
|13wd-
|13w
|13w
|Number 13 prepended to "wood"
|-
|-
|14L 14s
|14L 14s
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|14wd-
|14wd-
|14w
|14w
|Number 14 prepended to "wood"
|-
|-
|''k''L ''k''s
|''k''L ''k''s
Line 131: Line 157:
|''k''wd
|''k''wd
|''k''w
|''k''w
|General number ''k'' prepended to "wood"
|}
|}
=== Names for mosses with 11 or more notes ===
=== Names for mosses with 11 or more notes (excluding ''n''L ''n''s mosses) ===
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="4" |11-note mosses
! colspan="4" |11-note mosses
Line 185: Line 212:
|
|
|Former TAMNAMS name.
|Former TAMNAMS name.
|-
|6L 6s
|hexawood
|
|Extension of ''k''-wood scales; coincidentally references hexe temperament.
|-
|-
|7L 5s
|7L 5s
Line 219: Line 241:
!Proposed by
!Proposed by
!Reasoning
!Reasoning
|-
|7L 7s
|heptawood
|
|Extension of ''k''-wood scales.
|-
|-
|13L 1s
|13L 1s
Line 348: Line 365:
!Proposed by
!Proposed by
!Reasoning
!Reasoning
|-
|2L 3s
|saturnian
|[[User:CompactStar|CompactStar]]
|In reference to "uranian" for 3L 2s<3/2>
|-
|-
|3L 2s
|3L 2s
Line 355: Line 377:
|}
|}
== Names for equave-agnostic mosses ==
== 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"
{| class="wikitable center-all"
! colspan="5" |TAMNAMS-named mosses
|-
!Mos
!Name
!Prefix
!Abbrev.
!Reasoning
|-
|1L 1s
|trivial
|triv
|trv
|Trivial mos pattern, simplest possible mos pattern
|-
|1L 2s
|antrial
|
|
|
|-
|2L 1s
|trial
|
|
|
|-
|1L 3s
|antetric
|
|
|
|-
|3L 1s
|tetric
|
|
|
|-
|1L 4s
|pedal
|
|
|
|-
|2L 3s
|pentic
|
|
|
|-
|3L 2s
|anpentic
|
|
|
|-
|4L 1s
|manual
|
|
|
|-
|-
! colspan="5" |6-note mosses
! colspan="5" |6-note mosses
Line 430: Line 392:
|ahex-
|ahex-
|ahx
|ahx
|
|Greek numeral prefix (hex-) for six, plus "an-"
|-
|-
|5L 1s
|5L 1s
Line 436: Line 398:
|hex-
|hex-
|hx
|hx
|
|Greek numeral prefix "(hex-) for six
|-
|-
! colspan="5" |7-note mosses
! colspan="5" |7-note mosses
Line 450: Line 412:
|ansap-
|ansap-
|asp
|asp
|
|Sanskrit numeral prefix (sapta-) for seven, plus "an-"
|-
|-
|2L 5s
|2L 5s
Line 456: Line 418:
|anhep-
|anhep-
|ahp
|ahp
|
|Greek numeral prefix (hepta-) for seven, plus "an-"
|-
|-
|3L 4s
|3L 4s
Line 462: Line 424:
|ansep-
|ansep-
|asep
|asep
|
|Latin numeral prefix (septen-) for seven, plus "an-"
|-
|-
|4L 3s
|4L 3s
Line 468: Line 430:
|sep-
|sep-
|sep
|sep
|
|Latin numeral prefix (septen-) for seven
|-
|-
|5L 2s
|5L 2s
Line 474: Line 436:
|hep-
|hep-
|hp
|hp
|
|Greek numeral prefix (hepta-) for seven
|-
|-
|6L 1s
|6L 1s
Line 480: Line 442:
|sap-
|sap-
|sp
|sp
|
|Sanskrit numeral prefix (sapta-) for seven
|-
|-
! colspan="5" |8-note mosses
! colspan="5" |8-note mosses
Line 494: Line 456:
|anast-
|anast-
|aast
|aast
|
|Sanskrit numeral prefix (aṣṭa-) for eight, plus "an-"
|-
|-
|3L 5s
|3L 5s
Line 500: Line 462:
|anoct-
|anoct-
|aoct
|aoct
|
|Greek/Latin numeral prefix (octo-) for eight, plus "an-"
|-
|-
|5L 3s
|5L 3s
Line 506: Line 468:
|oct-
|oct-
|oct
|oct
|
|Greek/Latin numeral prefix (octo-) for eight
|-
|-
|7L 1s
|7L 1s
Line 512: Line 474:
|ast-
|ast-
|ast
|ast
|
|Sanskrit numeral prefix (aṣṭa-) for eight
|-
|-
! colspan="5" |9-note mosses
! colspan="5" |9-note mosses
Line 526: Line 488:
|annav-
|annav-
|anv
|anv
|
|Sanskrit numeral prefix (nava-) for nine, plus "an-"
|-
|-
|2L 7s
|2L 7s
Line 532: Line 494:
|anenn-
|anenn-
|aenn
|aenn
|
|Greek numeral prefix (ennea-) for nine, plus "an-"
|-
|-
|4L 5s
|4L 5s
Line 538: Line 500:
|annov-
|annov-
|anv
|anv
|
|Latin numeral prefix (novem-) for nine, plus "an-"
|-
|-
|5L 4s
|5L 4s
Line 544: Line 506:
|nov-
|nov-
|nv
|nv
|
|Latin numeral prefix (novem-) for nine
|-
|-
|7L 2s
|7L 2s
Line 550: Line 512:
|enn-
|enn-
|enn
|enn
|
|Greek numeral prefix (ennea-) for nine
|-
|-
|8L 1s
|8L 1s
Line 556: Line 518:
|nav-
|nav-
|nv
|nv
|
|Sanskrit numeral prefix (nava-) for nine
|-
|-
! colspan="5" |10-note mosses
! colspan="5" |10-note mosses
Line 570: Line 532:
|andash-
|andash-
|adsh
|adsh
|
|Sanskrit numeral prefix (dasha-) for ten, plus "an-"
|-
|-
|3L 7s
|3L 7s
Line 576: Line 538:
|andeck-
|andeck-
|adek
|adek
|
|Greek/Latin numeral prefix (decem-/deca-) for ten, plus "an-"
|-
|-
|7L 3s
|7L 3s
Line 582: Line 544:
|deck-
|deck-
|dek
|dek
|
|Greek/Latin numeral prefix (decem-/deca-) for ten
|-
|-
|9L 1s
|9L 1s
Line 588: Line 550:
|dash-
|dash-
|dsh
|dsh
|
|Sanskrit numeral prefix (dasha-) for ten
|}
|}


== Appendix ==
== 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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