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Fleshed out rationale for encoding scheme to be used for module:mos. It's all based on vectors of L's and s's.
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=== MOS mode degrees (proposed encoding scheme) ===
=== KB vis ===
{| class="wikitable"
|+Encoding scheme
! rowspan="2" |Value
! colspan="2" |Encoded
! colspan="4" |Decoded
|-
!Intervals with 2 sizes
!Intervals with 1 size
!Nonperfectable intervals
!Bright gen
!Dark gen
!Period intervals
|-
|2
|Large plus 2 chromas
|Perfect plus 2 chromas
|2× Augmented
|2× Augmented
|3× Augmented
|2× Augmented
|-
|1
|Large plus 1 chroma
|Perfect plus 1 chroma
|Augmented
|Augmented
|2× Augmented
|Augmented
|-
|0
|'''Large'''
|'''Perfect'''
|'''Major'''
|'''Perfect'''
|'''Augmented'''
|'''Perfect'''
|-
| -1
|'''Small'''
|Perfect minus 1 chroma
|'''Minor'''
|'''Diminished'''
|'''Perfect'''
|Diminished
|-
| -2
|Small minus 1 chroma
|Perfect minus 2 chromas
|Diminished
|2× Diminished
|Diminished
|2× Diminished
|-
| -3
|Small minus 2 chromas
|Perfect minus 3 chromas
|2× Diminished
|3× Diminished
|2× Diminished
|3× Diminished
|}
Rationale:
 
* Easy to translate values to number of chromas for mos notation. Best done with notation assigned to the brightest mode, but can be adapted for arbitrary notations by adjusting the approprite chroma offsets.
 
Examples of encodings for 5L 2s
{| class="wikitable"
|+Interval encodings for 5L 2s
! rowspan="2" |Interval in mossteps
! colspan="2" |Encoding
! rowspan="2" |Decoding
! rowspan="2" |Standard notation in the key of F
|-
!Mossteps
!Chroma
|-
|0
|0
|0
|Perfect 0-diastep
|F
|-
|s
|1
| -1
|Minor 1-diastep
|Gb
|-
|L
|1
|0
|Major 1-diastep
|G
|-
|L + s
|2
| -1
|Minor 2-diastep
|Ab
|-
|2L
|2
|0
|Major 2-diastep
|A
|-
|2L + s
|3
| -1
|Perfect 3-diastep
|Bb
|-
|3L
|3
|0
|Augmented 3-diastep
|B
|-
|2L + 2s
|4
| -1
|Diminished 4-diastep
|Cb
|-
|3L + s
|4
|0
|Perfect 4-diastep
|C
|-
|3L + 2s
|5
| -1
|Minor 5-diastep
|Db
|-
|4L + s
|5
|0
|Major 5-diastep
|D
|-
|4L + 2s
|6
| -1
|Minor 6-diastep
|Eb
|-
|5L + s
|6
|0
|Major 6-diastep
|E
|-
|5L + 2s
|7
|0
|Perfect 7-diastep
|F
|}
{| class="wikitable sortable"
! colspan="2" |Mode names
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! colspan="8" |Scale degree (encoded)
|-
!Default
!Names
!Bri.
!Rot.
!0
!1
!2
!3
!4
!5
!6
!7
|-
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|1
|1
|LLLsLLs
|0
|1
|1
|1
|1
|1
|1
|0
|-
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
|2
|5
|LLsLLLs
|0
|1
|1
|0
|1
|1
|1
|0
|-
|<nowiki>5L 2s 4|2</nowiki>
|Mixolydian
|3
|2
|LLsLLsL
|0
|1
|1
|0
|1
|1
|0
|0
|-
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|4
|6
|LsLLLsL
|0
|1
|0
|0
|1
|1
|0
|0
|-
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|5
|3
|LsLLsLL
|0
|1
|0
|0
|1
|0
|0
|0
|-
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
|6
|7
|sLLLsLL
|0
|0
|0
|0
|1
|0
|0
|0
|-
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|7
|4
|sLLsLLL
|0
|0
|0
|0
|0
|0
|0
|0
|}
 
===KB vis===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 913: Line 634:


</div>
</div>
== Encoding scheme for module:mos ==
=== Mossteps as a vector of L's and s's ===
For an arbitrary step sequence consisting of L's and s's, the sum of the quantities of L's and s's denotes what mosstep it is. EG, "LLLsL" is a 5-mosstep since it has 5 L's and s's total. This can be expressed as a vector denoting how many L's and s's there are. EG, "LLLsL" becomes { 4, 1 }, denoting 4 large steps and 1 small step.
Alterations by adding a chroma always adds one L and subtracts one s (or subtracts one L and adds one s, if lowering by a chroma), so the sum of L's and s's, even if one of the quantities is negative, will always denote what ''k''-mosstep that interval is. EG, raising "LLLsL" by a chroma produces the vector { 5, 0 }, and raising it by another chroma produces the vector { 6, -1 }.
Through this, the "original size" of the interval can always be deduced.
EG, the vector { 6, -2 } is given, assuming a mos of 5L 2s. Adding 6 and -2 shows that the interval is a 4-mosstep. Taking the brightest mode of 5L 2s (LLLsLLs) and truncating it to the first 4 steps (LLLs), the corresponding vector is { 3, 1 }. This is the vector to compare to. Subtracting the given vector from the comparison vector ( as { 6-3, -2-1 }) produces the vector { 3, -3 }, meaning that { 6, -2 } is the large 4-mosstep raised by 3 chromas. (A shortcut can be employed by simply subtracting only the L-values.) The decoding scheme below shows how the "large 4-mosstep plus 3 chromas" can be decoded into more familiar terms. In this example, since the large 4-mosstep is the perfect bright generator, adding 3 chromas makes it triply augmented.
{| class="wikitable"
|+Encoding scheme
! rowspan="2" |Value
! colspan="2" |Encoded
! colspan="4" |Decoded
|-
!Intervals with 2 sizes
!Intervals with 1 size
!Nonperfectable intervals
!Bright gen
!Dark gen
!Period intervals
|-
|2
|Large plus 2 chromas
|Perfect plus 2 chromas
|2× Augmented
|2× Augmented
|3× Augmented
|2× Augmented
|-
|1
|Large plus 1 chroma
|Perfect plus 1 chroma
|Augmented
|Augmented
|2× Augmented
|Augmented
|-
|0
|'''Large'''
|'''Perfect'''
|'''Major'''
|'''Perfect'''
|'''Augmented'''
|'''Perfect'''
|-
| -1
|'''Small'''
|Perfect minus 1 chroma
|'''Minor'''
|'''Diminished'''
|'''Perfect'''
|Diminished
|-
| -2
|Small minus 1 chroma
|Perfect minus 2 chromas
|Diminished
|2× Diminished
|Diminished
|2× Diminished
|-
| -3
|Small minus 2 chromas
|Perfect minus 3 chromas
|2× Diminished
|3× Diminished
|2× Diminished
|3× Diminished
|}
Rationale:
* Vectors of L's and s's can always be translated back to the original ''k''-mosstep, no matter how many chromas were added. The "unmodified" vector (the large ''k''-mosstep, or perfect ''k''-mosstep for period intervals) can be compared with the mosstep vector to produce the number of chromas.
** Alterations by entire large steps or small steps is considered interval arithmetic.
* Easy to translate values to number of chromas for mos notation. Best done with notation assigned to the brightest mode, but can be adapted for arbitrary notations by adjusting the approprite chroma offsets.
Examples of encodings for 5L 2s
{| class="wikitable"
|+Interval encodings for 5L 2s
! rowspan="2" |Interval in mossteps
! colspan="2" |Encoding
! rowspan="2" |Decoding
! rowspan="2" |Standard notation in the key of F
|-
!Mossteps
!Chroma
|-
|0
|0
|0
|Perfect 0-diastep
|F
|-
|s
|1
| -1
|Minor 1-diastep
|Gb
|-
|L
|1
|0
|Major 1-diastep
|G
|-
|L + s
|2
| -1
|Minor 2-diastep
|Ab
|-
|2L
|2
|0
|Major 2-diastep
|A
|-
|2L + s
|3
| -1
|Perfect 3-diastep
|Bb
|-
|3L
|3
|0
|Augmented 3-diastep
|B
|-
|2L + 2s
|4
| -1
|Diminished 4-diastep
|Cb
|-
|3L + s
|4
|0
|Perfect 4-diastep
|C
|-
|3L + 2s
|5
| -1
|Minor 5-diastep
|Db
|-
|4L + s
|5
|0
|Major 5-diastep
|D
|-
|4L + 2s
|6
| -1
|Minor 6-diastep
|Eb
|-
|5L + s
|6
|0
|Major 6-diastep
|E
|-
|5L + 2s
|7
|0
|Perfect 7-diastep
|F
|}
{| class="wikitable sortable"
! colspan="2" |Mode names
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! colspan="8" |Scale degree (encoded)
|-
!Default
!Names
!Bri.
!Rot.
!0
!1
!2
!3
!4
!5
!6
!7
|-
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|1
|1
|LLLsLLs
|0
|0
|0
|0
|0
|0
|0
|0
|-
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
|2
|5
|LLsLLLs
|0
|0
|0
| -1
|0
|0
|0
|0
|-
|<nowiki>5L 2s 4|2</nowiki>
|Mixolydian
|3
|2
|LLsLLsL
|0
|0
|1
| -1
|0
|0
| -1
|0
|-
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|4
|6
|LsLLLsL
|0
|0
| -1
| -1
|0
|0
| -1
|0
|-
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|5
|3
|LsLLsLL
|0
|0
| -1
| -1
|0
| -1
| -1
|0
|-
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
|6
|7
|sLLLsLL
|0
| -1
| -1
| -1
|0
| -1
| -1
|0
|-
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|7
|4
|sLLsLLL
|0
| -1
| -1
| -1
| -1
| -1
| -1
|0
|}
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