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|(''k''th) ''mosprefix''-descendant
|(''k''th) ''mosprefix''-descendant
|}
|}
Using [[5L 2s]] (diatonic) as an example, a tree of mosses can be produced as a scale tree.
{| class="wikitable"
!Root mos
!1st descendants
!2nd descendants
!3rd descendants
!4th descendants
!5th descendants
|-
| rowspan="16" |5L 2s
| rowspan="8" |7L 5s
| rowspan="4" |7L 12s
| rowspan="2" |7L 19s
|7L 26s
|7L 29s
|-
|26L 7s
| rowspan="6" |. . .
|-
| rowspan="2" |19L 7s
|26L 19s
|-
|19L 26s
|-
| rowspan="4" |12L 7s
| rowspan="2" |19L 12s
|19L 31s
|-
|31L 19s
|-
| rowspan="2" |12L 19s
|31L 12s
|-
|12L 31s
|12L 43s
|-
| rowspan="8" |5L 7s
| rowspan="4" |12L 5s
| rowspan="2" |12L 17s
|12L 29s
|12L 41s
|-
|29L 12s
| rowspan="6" |. . .
|-
| rowspan="2" |17L 12s
|29L 17s
|-
|17L 29s
|-
| rowspan="4" |5L 12s
| rowspan="2" |17L 5s
|17L 22s
|-
|22L 17s
|-
| rowspan="2" |5L 17s
|22L 5s
|-
|5L 22s
|5L 29s
|}
With 5L 2s as the root mos:
* There are 2 chromatic descendants, or '''diachromatic''' scales: 7L 5s and 5L 7s
* There are 4 enharmonic descendants, or '''diamonic''' scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s
* There are 8 subchromatic descendants, or '''diasubchromatic''' scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.
Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:
* There are 16 4th descendants, or '''4th diadescendant''' scales''.''
* There are 32 5th descendants, or '''5th diadescendant''' scales.
* There are 2 to the ''k''th power ''k''th descendants, or '''''k''th diadescendant''' scales.
=== Step ratio descriptions ===
=== Step ratio descriptions ===
Optionally, the names for a step ratio range can be added before these descriptions, describing the step ratio of the root mos. Step ratios only apply to the 1st, 2nd, and 3rd descendants.
Optionally, the names for a step ratio range can be added before these descriptions, describing the step ratio of the root mos. Step ratios only apply to the 1st, 2nd, and 3rd descendants.
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|uh-
|uh-
|}
|}
=== Example: descendants of 5L 2s ===
The descendants of 5L 2s can be organized as a scale tree, as shown.
{| class="wikitable"
!Root mos
!1st descendants
!2nd descendants
!3rd descendants
!4th descendants
!5th descendants
|-
| rowspan="16" |5L 2s
| rowspan="8" |7L 5s
| rowspan="4" |7L 12s
| rowspan="2" |7L 19s
|7L 26s
|7L 29s
|-
|26L 7s
| rowspan="6" |. . .
|-
| rowspan="2" |19L 7s
|26L 19s
|-
|19L 26s
|-
| rowspan="4" |12L 7s
| rowspan="2" |19L 12s
|19L 31s
|-
|31L 19s
|-
| rowspan="2" |12L 19s
|31L 12s
|-
|12L 31s
|12L 43s
|-
| rowspan="8" |5L 7s
| rowspan="4" |12L 5s
| rowspan="2" |12L 17s
|12L 29s
|12L 41s
|-
|29L 12s
| rowspan="6" |. . .
|-
| rowspan="2" |17L 12s
|29L 17s
|-
|17L 29s
|-
| rowspan="4" |5L 12s
| rowspan="2" |17L 5s
|17L 22s
|-
|22L 17s
|-
| rowspan="2" |5L 17s
|22L 5s
|-
|5L 22s
|5L 29s
|}
With 5L 2s as the root mos:
* There are 2 chromatic descendants, or '''diachromatic''' scales: 7L 5s and 5L 7s
* There are 4 enharmonic descendants, or '''diamonic''' scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s
* There are 8 subchromatic descendants, or '''diasubchromatic''' scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.
Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:
* There are 16 4th descendants, or '''4th diadescendant''' scales''.''
* There are 32 5th descendants, or '''5th diadescendant''' scales.
* There are 2 to the ''k''th power ''k''th descendants, or '''''k''th diadescendant''' scales.
== Naming scheme ==
== Naming scheme ==


== Specific names ==
== Specific names ==