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Added a section for 7L 5s and 12L 7s
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Interestingly, this definition of a default mode has some overlap with [[Naming Rank-2 Scales|Jake Freivald's method]] of enumerating a mos's modes.
Interestingly, this definition of a default mode has some overlap with [[Naming Rank-2 Scales|Jake Freivald's method]] of enumerating a mos's modes.


== My approach to 7L 5s and 12L 7s ==
== My approach to diatonic descendant mosses ==
My approach at looking at diatonic's mosdescendants of 7L 5s starts at looking at how the modes of 5L 2s can be broken down. Given a chroma is the absolute difference between a large and small step (c = | L - s |), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap.
My current approach to xenharmony, at least as it pertains to being both familiar and different, is to play with the familiar mos pattern of 5L 2s but to add additional notes in between. If restricted to 12edo, this means one of two things to me:
 
* Using the 12-note chromatic scale.
* Using half-sharps and half-flats.
 
For me, this is antithetical to how I explore mosses, as well as being downright boring. Using the idea of mosses, an entire infinite family tree of possible scales can be explored, all containing the familiar 5L 2s as a subset. Some scales are even backwards-compatible with existing notation.
 
The following table is a table of all the mosdescendants of 5L 2s up to 3 generations. (Names are based on my version of TAMNAMS name extension; some names are not finalized). Mosses in bold denote mosses I've played enough with to make a fair amount of notes, at least enough to understand how they relate back to 5L 2s. Also listed are basic edos (the smallest edo needed to realize the given mos) and a few temperaments for reference.
{| class="wikitable"
! colspan="4" |Diatonic scale
! colspan="5" |Chromatic scales
! colspan="5" |Enharmonic scales
! colspan="5" |"Schismic" scales
|-
!Steps
!Bright generator
!Basic edo
!Temperament
!Steps
!Specific name
!Bright generator
(relative to 5L 2s)
!Basic edo
!Temperament
!Steps
!Specific name
!Bright generator
(relative to 5L 2s)
!Basic edo
!Temperament
!Steps
!Specific name
!Bright generator
(relative to 5L 2s)
!Basic edo
!Temperament
|-
| rowspan="8" |[[5L 2s]]
| rowspan="8" |Perfect 5th
| rowspan="8" |[[12edo]]
| rowspan="8" |
| rowspan="4" |[[5L 7s]]
| rowspan="4" |p-moschromatic
| rowspan="4" |Perfect 5th
| rowspan="4" |[[17edo]]
| rowspan="4" |
| rowspan="2" |[[5L 12s]]
| rowspan="2" |s-mosenharmonic
| rowspan="2" |Perfect 5th
| rowspan="2" |[[22edo]]
| rowspan="2" |
|[[5L 17s]]
|s-mosschismic
|Perfect 5th
|[[27edo]]
|
|-
|[[17L 5s]]
|r-mosschismic
|Perfect 4th
|[[39edo]]
|
|-
| rowspan="2" |[[12L 5s]]
| rowspan="2" |p-mosenharmonic
| rowspan="2" |Perfect 4th
| rowspan="2" |[[29edo]]
| rowspan="2" |
|[[12L 17s]]
|p-mosschismic
|Perfect 4th
|[[41edo]]
|
|-
|[[17L 12s]]
|q-mosschismic
|Perfect 5th
|[[46edo]]
|
|-
| rowspan="4" |[[7L 5s|'''7L 5s''']]
| rowspan="4" |'''m-moschromatic'''
| rowspan="4" |Perfect 4th
| rowspan="4" |[[19edo]]
| rowspan="4" |meantone[12]
| rowspan="2" |[[7L 12s]]
| rowspan="2" |f-mosenharmonic
| rowspan="2" |Perfect 4th
| rowspan="2" |[[26edo]]
| rowspan="2" |flattone[19]
|[[7L 19s]]
|f-mosschismic
|Perfect 4th
|[[33edo]]
|
|-
|[[19L 7s]]
|a-mosschismic
|Perfect 5th
|[[45edo]]
|flattone[26]
|-
| rowspan="2" |[[12L 7s|'''12L 7s''']]
| rowspan="2" |'''m-mosenharmonic'''
| rowspan="2" |Perfect 5th
| rowspan="2" |[[31edo]]
| rowspan="2" |meantone[19]
|[[12L 19s]]
|m-mosschismic
|Perfect 5th
|[[43edo]]
|
|-
|[[19L 12s]]
|u-mosschismic
|Perfect 4th
|[[50edo]]
|meantone[31]
|}
The following list is some commentary on some of the basic edos shown in the table:
 
* '''19edo''': I've seen one musician describe it as a baby version of 31edo, and I'm inclined to agree in that it's basically an equalized 12L 7s.
* '''31edo''': This, and 50edo to an extent, is currently my go-to edo for meantone temperament. Generally speaking, I like the mellow sound of meantone, which explains why I do absolutely nothing to date with 17edo and friends. It's also compatible with half-sharp and half-flat notation, so "quartertone" compositions are possible.
 
=== 7L 5s ===
Given a chroma is the absolute difference between a large and small step (c = | L - s |), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap.
{| class="wikitable"
{| class="wikitable"
!
!
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|SC Locrian
|SC Locrian
|}
|}
Basically, a chroma and small step are not the same size, more commonly described with the terms "diatonic and chromatic semitones". This unevenness manifests itself as the m-chromatic scale, a scale I admittedly don't use as often compared to 12L 7s. The mode "CS ionian" is basically an incomplete form of one of my favorite modes in 12L 7s.
=== 12L 7s ===
This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = | L - 2s |. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. The use of "CS/SC" and "CCD/CDC/DCC" is to enforce how these modes are broken down; there are 13 modes of 12L 7s that contain ionian as a subset (UDPs 17|1 to 5|13), so it's confusing to say there are 13 ionian modes.
This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = | L - 2s |. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. The use of "CS/SC" and "CCD/CDC/DCC" is to enforce how these modes are broken down; there are 13 modes of 12L 7s that contain ionian as a subset (UDPs 17|1 to 5|13), so it's confusing to say there are 13 ionian modes.
{| class="wikitable"
{| class="wikitable"
Line 996: Line 1,124:
|DCC Locrian
|DCC Locrian
|}
|}
The resulting mos is dubbed m-enharmonic, or commonly (and simply) 12L 7s. Here, two chromas undershoot a whole tone, and the difference between two chromas and a whole tone is an even smaller interval: the diesis. This coincides with a lot of theory related to meantone, but my favorite use is to use it as a '''"super-leading" tone'''. In the key of C, B is considered the leading tone; in comparison, I define a "super-leading tone" as any note that's a diesis below another note. By that definition, every tone in 5L 2s has a super-leading tone.
CCD ionian is a prime example in that every tone in 5L 2s contains this "super-leading" tone. For example, Cx is the super-leading tone for D. This also works in reverse, as with falling from Dbb to C; a prime example for that is DCC ionian. Alternating between the two can achieve a sense of almost approaching something.
Of course, there is always the option of creating a melody using the "notes between the notes between the notes", creating something that sounds like it should work normally but is extremely constrained.
todo:examples
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