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This is a system for describing scales beyond the set of named TAMNAMS scales. Both [[User:Frostburn]] ([[User:Frostburn/TAMNAMS Extension]]) and I have similar systems, though this is focused on naming single-period mosses up to three generations after a parent scale.
This is a system for describing scales beyond the set of named TAMNAMS scales. Both [[User:Frostburn]] ([[User:Frostburn/TAMNAMS Extension]]) and I have similar systems, though this is focused on naming single-period mosses up to three generations after a parent scale.


=== General names for mosdescendant scales ===
=== Naming mosdescendant scales up to 3 generations ===
Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, names based on existing names can be made systematically. The rules are described as such:
Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, names for mosses greater than 10 notes can be made systematically using existing names. The rules are described as such:


* If the scale is the child of a named parent scale, then the scale is '''moschromatic'''.
* If the scale is the child of a named parent scale, then the scale is '''moschromatic'''.
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For describing the scales of a named mos, the prefix of mos- is removed and replaced with the mos's prefix instead. For example, the child, grandchild, and great-grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively, and the entire family of mosses related to oneirotonic are oneirodescendants.
For describing the scales of a named mos, the prefix of mos- is removed and replaced with the mos's prefix instead. For example, the child, grandchild, and great-grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively, and the entire family of mosses related to oneirotonic are oneirodescendants.


Additionally, the lack of a prefix will specifically describe the descendent scales of 5L 2s: chromatic, enharmonic, and schismic. Descendents of 5L 2s are referred to as "diatonic descendants" rather than "descendants".
Additionally, the lack of a prefix will specifically describe the descendant scales of 5L 2s: chromatic, enharmonic, and schismic. Descendants of 5L 2s are referred to as "diatonic descendants" rather than "descendants".


In the general case, moschromatic refers to one of two child scales, mosenharmonic refers to one of four grandchild scales, and mosschismic refers to one of eight great-grandchild scales. Specific scales can be referred to by adding an additional prefix; the table below shows those prefixes and the step ratios (of the parent mos) for which they apply. Note that the table shows all possible mosdescendant scales up to three generations, across the entire spectrum of step ratios; specifying a step ratio to any one mos will "lock" the chain of descendants to a single line.
In the general case, moschromatic refers to one of two child scales, mosenharmonic refers to one of four grandchild scales, and mosschismic refers to one of eight great-grandchild scales. Specific scales can be referred to by adding an additional prefix; the table below shows those prefixes and the step ratios (of the parent mos) for which they apply. Note that the table shows all possible mosdescendant scales up to three generations, across the entire spectrum of step ratios; specifying a step ratio to any one mos will "lock" the chain of descendants to a single line.
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! colspan="4" |Mosenharmonic (grandchild) scales
! colspan="4" |Mosenharmonic (grandchild) scales
! colspan="4" |Mosschismic (great-grandchild) scales
! colspan="4" |Mosschismic (great-grandchild) scales
(names not finalized)
|-
|-
! rowspan="2" |Steps
! rowspan="2" |Steps
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!Step ratio for 2:1
!Step ratio for 2:1
!General range
!General range
!For step ratio of 2:1
!For L:s = 2:1
!General range
!General range
!For step ratio of 2:1
!For L:s = 2:1
!General range
!General range
!For step ratio of 2:1
!For L:s = 2:1
|-
|-
| rowspan="8" |xL ys
| rowspan="8" |xL ys
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=== Mosdescendants for multi-period mosses ===
=== Mosdescendants for multi-period mosses ===
TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: jaric, taric, ekic, lemon, and lime. Starting at 3 periods, mosdescendant names apply only to the corresponding n-wood scale (triwood, tetrawood, pentawood, etc), where the names of descendants are based on names for single-period mosses up to 5 notes, with any descendants after that being referred to '''n-wood descendants'''. Currently, tetrawood and pentawood (4L 4s and 5L 5s) only have pages for their immediate children (2L 4s and 8L 4s, and 5L 10s and 10L 5s respectively), so although it may make more sense to limit mosdescendant names for n-wood scales to the immediate children, names for n-wood scales up to 5n notes are shown anyway for completeness.
TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: jaric, taric, ekic, lemon, and lime.
{| class="wikitable"
{| class="wikitable"
|+2-period mosses for which mosdescendant names apply
|+2-period mosses for which mosdescendant names apply
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|'''lime'''
|'''lime'''
|}
|}
Starting at 3 periods, mosdescendant names apply only to the corresponding n-wood scale (triwood, tetrawood, pentawood, etc), where the names of descendants are based on names for single-period mosses up to 5 notes and thereby limited to mosses with 5n notes; any descendants after that are referred as to '''n-wood descendants'''. Note that this means there are only two named 3rd-generation mosses from nL ns, rather than the usual eight. The cap of 5n notes mirrors that of TAMNAMS; currently, the names for single-period mosses up to 5 notes may also refer to non-octave periods and therefore (for our purposes) multi-period octave scales.
Currently, tetrawood and pentawood (4L 4s and 5L 5s) only have pages for their immediate children (2L 4s and 8L 4s, and 5L 10s and 10L 5s respectively), so although it may make more sense to limit mosdescendant names for n-wood scales to the immediate children (nL 2ns and 2nL ns), names for n-wood scales up to 5n notes are shown anyway for completeness.
{| class="wikitable"
{| class="wikitable"
|+Possible mosdescendant names for mosses with 3 periods or more
|+Possible mosdescendant names for mosses with 3 periods or more
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|nL 4ns
|nL 4ns
|n-pedal
|n-pedal
| rowspan="5" |A numeric prefix, such as hexawood instead of 6-wood, may be used instead.
| rowspan="5" |A numeric prefix may be used instead, such as hexawood instead of 6-wood.
When in doubt, prefix names with n-.
|-
|-
|4nL ns
|4nL ns
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|n-pentic
|n-pentic
|}
|}
=== Reasoning for names (and example for 5L 2s) ===
The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s): p-chromatic (5L 7s) and m-chromatic (7L 5s). This was generalized to "chromatic", with the prefixes p- and m- for specificity. The names for mosenharmonic scales are based on discussions with xen Discord members for systematically naming the daughter and granddaughter scales of a mos, producing "enharmonic" with the prefixes s-, p-, f-, and m- for specificity.


This proposal initially considered grandchild scales of a mos, and the recent addition of great-grandchild scales was done for completeness. The use of "schismic" to refer to great-grandchild scales is subject to change (I'm open to better suggestions). The prefixes for mosschismic scales borrow those used for mosenharmonic scales (which itself borrows those used for moschromatic scales) and adds four additional prefixes: q- (quasihard), r- (parahard), a- (parasoft), and u- (quasisoft) (also subject to change).
=== Naming mosdescendant scales beyond 3 generations ===
Each generation has twice as many mosdescendants as the last, so rather than try to name every possible descendant, mosdescendants more than 3 generations from a given parent mos can be referred to how many generations away it is. Mosschismic scales are 3rd mosdescendants, so after that are 4th-mosdescendants, 5th-mosdescendants, and so on. The algorithms below shows how to find how many generations away a mos xL ys is from another scale.
 
* For single-period and 2-period scales: finding a parent mos zL ws for the mosdescendant xL ys, where x and y are either coprime (have a common factor of 1) or have a common factor of 2:
*# 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 g = 0, where g is the number of generations away from zL ws.
*# Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
*# Assign to z the value m2 and w the value m1-m2. Increment g by 1.
*# If the sum of z and w is less than or equal to 10, then the mos name is that assigned to the mos zL ws, which is g generations away from xL ys. If not, repeat the process starting at step 2.
* For scales with 3 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a common factor of n, where n > 2:
*# Let z and w be assigned the values x and y respectively. Let g = 0, where g is the number of generations away from nL ns.
*# Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
*# Assign to z the value m2 and w the value m1-m2. Increment g by 1.
*# If the sum of z and w is exactly 2n, then the mos nL ns is g generations away from xL ys. If not, repeat the process starting at step 2.
 
=== Reasoning for names ===
The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s): p-chromatic (5L 7s) and m-chromatic (7L 5s). This was generalized to "chromatic" and "moschromatic", with the prefixes m- and p- for specificity. The names for mosenharmonic scales are based on discussions with xen Discord members for systematically naming the daughter and granddaughter scales of a mos, producing "enharmonic" and "mosenharmonic" with the prefixes f-, m-, p-, and s- for specificity.
 
This proposal initially considered grandchild scales of a mos, and the recent addition of great-grandchild scales was done for completeness. The use of "schismic" to refer to great-grandchild scales is subject to change (I'm open to better suggestions), with the prefixes f-, a-, u-, m-, p- q-, r-, and s- for specificity. Note that mosschismic scales borrows the prefixes as mosenharmonic scales, which itself borrows those for mosenharmonic scales. The table below shows what prefixes are used for which generation of mosdescendants, with an added mnemonic for memorization.
{| class="wikitable"
{| class="wikitable"
|+Table of mosdescendent prefixes and meanings
|+Table of mosdescendent prefixes and meanings
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|}
|}
{| class="wikitable"
{| class="wikitable"
|+Names for descendent scales of 5L 2s, sorted by step ratio (softest to hardest)
|+Names for descendant scales of 5L 2s
! colspan="2" |Diatonic scale
! colspan="2" |Diatonic scale
! colspan="2" |Chromatic scales
! colspan="2" |Chromatic scales
! colspan="2" |Enharmonic scales
! colspan="2" |Enharmonic scales
! colspan="2" |Schismic scales
! colspan="2" |Schismic scales
!4th diatonic descendants
|-
|-
!Steps
!Steps
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!Steps
!Steps
!Name
!Name
!Steps
|-
|-
| rowspan="8" |[[5L 2s]]
| rowspan="8" |[[5L 2s]]
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|[[7L 19s]]
|[[7L 19s]]
|f-schismic
|f-schismic
|7A 26B
|-
|-
|[[19L 7s]]
|[[19L 7s]]
|a-schismic
|a-schismic
|19A 26B
|-
|-
| rowspan="2" |[[12L 7s]]
| rowspan="2" |[[12L 7s]]
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|[[19L 12s]]
|[[19L 12s]]
|u-schismic
|u-schismic
|19A 31B
|-
|-
|[[12L 19s]]
|[[12L 19s]]
|m-schismic
|m-schismic
|12A 31B
|-
|-
| rowspan="4" |[[5L 7s]]
| rowspan="4" |[[5L 7s]]
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|[[12L 17s]]
|[[12L 17s]]
|p-schismic
|p-schismic
|12A 29B
|-
|-
|[[17L 12s]]
|[[17L 12s]]
|q-schismic
|q-schismic
|17A 29B
|-
|-
| rowspan="2" |[[5L 12s]]
| rowspan="2" |[[5L 12s]]
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|[[17L 5s]]
|[[17L 5s]]
|r-schismic
|r-schismic
|17A 22B
|-
|-
|[[5L 17s]]
|[[5L 17s]]
|s-schismic
|s-schismic
|5A 22B
|}
|}


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