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→Proposal: Naming mosses with more than 10 steps (work-in-progress): Reworded mosdescendant naming so that nth-mosdescendants is first, wip
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== Proposal: Naming mosses with more than 10 steps (work-in-progress) ==
== Proposal: Naming mosses with more than 10 steps (work-in-progress) ==
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, with the main difference here being that mosses are technically not limited to being only three generations away.
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, with the main difference here being that mosses are technically not limited to being only three generations away.
=== Naming mosdescendants ===
The easiest and most general way to refer to a mos that descends from another, TAMNAMS-named mos is to refer to it as a ''mosdescendant'', where the prefix of mos- is substituted for the prefix for the mos itself. For consistency, mosdescendant names apply to named TAMNAMS mosses whose child scales exceed 10 notes, shown in the table below in '''bold'''.
{| class="wikitable"
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
|-
| rowspan="16" |1L 1s
| rowspan="16" |trivial
| rowspan="11" |1L 2s
| rowspan="11" |antrial
| rowspan="8" |1L 3s
| rowspan="8" |antetric
| rowspan="6" |1L 4s
| rowspan="6" |pedal
| rowspan="5" |1L 5s
| rowspan="5" |antimachinoid
| rowspan="4" |1L 6s
| rowspan="4" |onyx
| rowspan="3" |1L 7s
| rowspan="3" |antipine
| rowspan="2" |1L 8s
| rowspan="2" |antisubneutralic
|1L 9s
|'''antisinatonic (asina-)'''
|-
|9L 1s
|'''sinatonic (sina-)'''
|-
|8L 1s
|'''subneutralic (blu-)'''
| colspan="2" rowspan="14" |
|-
|7L 1s
|'''pine (pine-)'''
| colspan="2" rowspan="13" |
|-
|6L 1s
|'''arch(a)eotonic (arch-)'''
| colspan="2" rowspan="12" |
|-
|5L 1s
|'''machinoid (mech-)'''
| colspan="2" rowspan="11" |
|-
| rowspan="2" |4L 1s
| rowspan="2" |manual
|5L 4s
|'''semiquartal (chton-)'''
|-
|4L 5s
|'''gramitonic (gram-)'''
|-
| rowspan="3" |3L 1s
| rowspan="3" |tetric
|4L 3s
|'''smitonic (smi-)'''
| colspan="2" |
|-
| rowspan="2" |3L 4s
| rowspan="2" |mosh
|7L 3s
|'''dicoid/zaltertic (dico-/zal-)'''
|-
|3L 7s
|'''sephiroid (seph-)'''
|-
| rowspan="5" |2L 1s
| rowspan="5" |trial
| rowspan="2" |3L 2s
| rowspan="2" |antipentic
|3L 5s
|'''checkertonic (check-)'''
| colspan="2" rowspan="3" |
|-
|5L 3s
|'''oneirotonic (oneiro-)'''
|-
| rowspan="3" |2L 3s
| rowspan="3" |pentic
|5L 2s
|'''diatonic ''(no prefix)'''''
|-
| rowspan="2" |2L 5s
| rowspan="2" |antidiatonic
|7L 2s
|'''superdiatonic (arm-)'''
|-
|2L 7s
|'''balzano (bal-)'''
|-
! colspan="18" |2-period mosses
|-
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
| colspan="10" rowspan="6" |
|-
| rowspan="5" |2L 2s
| rowspan="5" |biwood
| rowspan="3" |2L 4s
| rowspan="3" |malic
| rowspan="2" |2L 6s
| rowspan="2" |subaric
|2L 8s
|'''jaric (jara-)'''
|-
|8L 2s
|'''taric (tara-)'''
|-
|6L 2s
|'''ekic (ek-)'''
| colspan="2" rowspan="3" |
|-
| rowspan="2" |4L 2s
| rowspan="2" |citric
|6L 4s
|'''lemon (lem-)'''
|-
|4L 6s
|'''lime (lime-)'''
|-
! colspan="18" |3-period mosses
|-
!Mos
!Name
!Mos
!Name
| colspan="14" rowspan="3" |
|-
| rowspan="2" |3L 3s
| rowspan="2" |triwood
|3L 6s
|'''tcherepnin (cher-)'''
|-
|6L 3s
|'''hyrulic (hyru-)'''
|-
! colspan="18" |4-period mosses
|-
!Mos
!Name
| colspan="16" rowspan="2" |
|-
|4L 4s
|'''tetrawood (tetwud-)'''
|-
! colspan="18" |5-period mosses
|-
!Mos
!Name
| colspan="16" rowspan="2" |
|-
|5L 5s
|'''pentawood (penwud-)'''
|}The number of generations a mos is from a named mos can also be specified, so the child mos is a ''1st-mosdescendant'', its grandchild a ''2nd-mosdescendant'', its great-grandchild a ''3rd-mosdescaendnt'', and so on. The algorithm below explains how to find the number of generations two related mosses are, given the mos descends from a named mos whose child mosses already exceed 10 notes:
* Finding a parent mos zL ws for the mosdescendant xL ys, where x, y, z, and w share a greatest common factor that is no greater than 5:
*# 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 no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.
Since diatonic doesn't have a mos prefix, the phrase ''diatonic descendant'' is used to refer to its mosdescendants.


=== Naming mosdescendants up to 3 generations ===
=== Naming mosdescendants up to 3 generations ===
Line 1,410: Line 1,595:
|n-pentic
|n-pentic
|}
|}
=== Naming mosdescendants 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 may 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 mosses with up to 3 periods: finding a parent mos zL ws for the mosdescendant xL ys, where x, y, z, and w share a greatest common factor that is no greater than 3:
*# 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 no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.
* For mosses with 4 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a greatest common factor of n that is 4 or greater:
*# 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.


=== Naming mosdescendants for linearly growing scales (work-in-progress) ===
=== Naming mosdescendants for linearly growing scales (work-in-progress) ===
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