User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions
→Naming mosdescendant scales beyond 3 generations: Clarifying what sections are proposals; some errors corrected; added section for naming linearly growing mosdescendants (wip) |
→Naming mosdescendant scales where successive generations of scales grow linearly: Table catastrophically broke, fixed; added rule for naming edge-case mosdescendants |
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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. | ||
Note: Some names with this system are not finalized, particularly mosschismic and some of the single-letter prefixes. | Note: Some names with this system are not finalized, particularly the term "mosschismic" and some of the single-letter prefixes. | ||
=== Naming | === Naming mosdescendants up to 3 generations === | ||
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: | 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: | ||
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|} | |} | ||
=== Naming | === 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. | 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. | ||
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*# 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. | *# 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 | === Naming mosdescendants for linearly growing scales (work-in-progress) === | ||
In cases where the number of notes with each successive mosdescendant grows linearly, these mosses may be assigned a letter to refer to a specific mosdescendant. | In cases where the number of notes with each successive mosdescendant grows linearly, these mosses may be assigned a letter to refer to a specific mosdescendant. Currently, this applies to mosdescendants whose parent mos has a step ratio that is along the extreme edges of the step ratio spectrum, around pseudoequalized and pseudocollapsed. | ||
{| class="wikitable" | {| class="wikitable" | ||
!Parent scale | !Parent scale | ||
! colspan="2" |Moschromatic ( | ! colspan="2" |Moschromatic scales | ||
! colspan="2" |Mosenharmonic ( | (1st mosdescendants) | ||
! colspan="2" |Mosschismic ( | ! colspan="2" |Mosenharmonic scales | ||
(2nd mosdescendants) | |||
! colspan="2" |Mosschismic scales | |||
(3rd mosdescendants) | |||
! colspan="3" |nth-mosdescendant scales | |||
|- | |- | ||
! | !Steps | ||
! | !Steps | ||
! | !Specific name | ||
! | !Steps | ||
! | !Specific name | ||
! | !Steps | ||
! | !Specific name | ||
!Steps | |||
!Specific name | |||
!Step ratio of parent | |||
|- | |- | ||
| rowspan="10" |xL ys | |||
| rowspan="5" |(x+y)L xs | |||
| rowspan="5" |m-moschromatic | |||
| rowspan="3" |(x+y)L (2x+y)s | |||
| rowspan="3" |f-mosenharmonic | |||
| rowspan="2" |(x+y)L (3x+2y)s | |||
| rowspan="2" |f-mosschismic | |||
|(x+y)L (nx+(n-1)y)s | |||
|nth f-mosdescendant | |||
|Softer than 5:4 | |||
|- | |- | ||
| rowspan="8" | | | rowspan="8" | | ||
| rowspan=" | | rowspan="8" | | ||
| rowspan=" | | rowspan="8" | | ||
| | |||
|- | |- | ||
|(3x+2y)L (x+y)s | |(3x+2y)L (x+y)s | ||
|a-mosschismic | |a-mosschismic | ||
|- | |- | ||
| rowspan="2" |(2x+y)L (x+y)s | | rowspan="2" |(2x+y)L (x+y)s | ||
| Line 1,140: | Line 1,149: | ||
|(3x+2y)L (2x+y)s | |(3x+2y)L (2x+y)s | ||
|u-mosschismic | |u-mosschismic | ||
|- | |- | ||
|(2x+y)L (3x+2y)s | |(2x+y)L (3x+2y)s | ||
|m-mosschismic | |m-mosschismic | ||
|- | |- | ||
| rowspan=" | | rowspan="5" |xL (x+y)s | ||
| rowspan=" | | rowspan="5" |p-moschromatic | ||
| rowspan="2" |(2x+y)L xs | | rowspan="2" |(2x+y)L xs | ||
| rowspan="2" |p-mosenharmonic | | rowspan="2" |p-mosenharmonic | ||
|(2x+y)L (3x+y)s | |(2x+y)L (3x+y)s | ||
|p-mosschismic | |p-mosschismic | ||
|- | |- | ||
|(3x+y)L (2x+y)s | |(3x+y)L (2x+y)s | ||
|q-mosschismic | |q-mosschismic | ||
|- | |- | ||
| rowspan=" | | rowspan="3" |xL (2x+y)s | ||
| rowspan=" | | rowspan="3" |s-mosenharmonic | ||
|(3x+y)L xs | |(3x+y)L xs | ||
|r-mosschismic | |r-mosschismic | ||
|- | |- | ||
|xL (3x+y)s | | rowspan="2" |xL (3x+y)s | ||
|s-mosschismic | | rowspan="2" |s-mosschismic | ||
| | |- | ||
|xL (nx+y)s | |||
|nth s-mosdescendant | |||
|Harder than 5:1 | |||
|} | |} | ||