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→3L 4s (mosh): expanded theory
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Cleanup and slight expansion
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== 3L 4s (mosh) ==
== 3L 4s (mosh) ==
=== Intervals ===
The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.
The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.


{| class="wikitable"
{| class="wikitable"
|+ 24edo mosh
|+ 24edo mosh scale
|-
|-
! Note !! Cents !! Ratio
! Note !! Cents !! Ratio
Line 25: Line 28:
| C || 1200 || 2/1
| C || 1200 || 2/1
|}
|}
In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral chords on C, E, F, G, and A, a 0¢-300¢-650¢ chord on D, and a 0¢-350¢-650¢ chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant. This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in 24edo is 0-200-550-700 cents. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) [[66:72:88:99]], or 0-150-500-700 cents in 24edo. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a 0¢-200¢-500¢-700¢ cent chord on C, and a 0¢-150¢-500¢-650¢ chord on B and D.
 
Just like diatonic, this scale has major and minor intervals, which are found on different notes of the scale. A table of such intervals is below.
 
{| class="wikitable"
|+ Intervals of mosh
|-
! Interval !! Cents !! Ratio !! note on C
|-
| P1 || 0 || 1/1 || C
|-
| A1 || 50 || 33/32 || C#
|-
| m2 || 150 || 12/11 || Db
|-
| M2 || 200 || 9/8 || D
|-
| d3 || 300 || 32/27 || Eb
|-
| P3 || 350 || 11/9 || E
|-
| m4 || 500 || 4/3 || F
|-
| M4 || 550 || 11/8 || F#
|-
| m5 || 650 || 16/11 || Gb
|-
| M5 || 700 || 3/2 || G
|-
| P6 || 850 || 18/11 || A
|-
| A6 || 900 || 27/16 || A#
|-
| m7 || 1000 || 16/9 || Bb
|-
| M7 || 1050 || 11/6 || B
|-
| d8 || 1150 || 64/33 || Cb
|-
| P8 || 1200 || 2/1 || C
|}
 
=== Chords ===
 
In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral (P1-P3-M5) chords on C, E, F, G, and A, a P1-d3-m5 chord on D, and a P1-P3-m5 chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant.
 
This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D.
 
We need names for these chords, and once again we can borrow from diatonic.
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