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User:Ganaram inukshuk/Methodologies: Difference between revisions

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X-pattern with the default modes. Also added other possible "default modes".
Ganaram inukshuk (talk | contribs)
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Added a section for 7L 5s and 12L 7s
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Teasing out the properties of the diatonic minor scale is admittedly harder to justify. The current assumption is that the leading tone is lost, but the interval between the first and second degrees is still in its large form as seen diatonic major. This property only works for mosses that have more L's than s's, hence the amended definition described above. This currently remains untested.
Teasing out the properties of the diatonic minor scale is admittedly harder to justify. The current assumption is that the leading tone is lost, but the interval between the first and second degrees is still in its large form as seen diatonic major. This property only works for mosses that have more L's than s's, hence the amended definition described above. This currently remains untested.


===== Other possible answers =====
==== Other possible answers ====
It's also possible to default to a mos's brightest mode, or its middle mode (such as the dorian mode for diatonic). This doesn't work with mosses with an even number of steps, since there will be two middle modes.
It's also possible to default to a mos's brightest mode, or its middle mode (such as the dorian mode for diatonic). This doesn't work with mosses with an even number of steps, since there will be two middle modes.


==== Comparison with other methods ====
==== Comparison with other methods ====
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 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.
{| class="wikitable"
!
! colspan="13" |Bright generator: 13/31
! colspan="18" |Dark generator: 18/31
! rowspan="2" |UDP
! colspan="2" |M-chromatic modes
|-
!C
!Dbb
!C#
!Db
!C##
!D
!Ebb
!D#
!Eb
!D##
!E
!Fb
!E#
!F
!Gbb
!F#
!Gb
!F##
!G
!Abb
!G#
!Ab
!G##
!A
!Bbb
!A#
!Bb
!A##
!B
!Cb
!B#
!C
!Mode (CS)
!Mode (SC)
|-
! rowspan="12" |
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
|<nowiki>0|11</nowiki>
|CS Lydian
|
|-
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
|<nowiki>1|10</nowiki>
|CS Ionian
|
|-
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
|<nowiki>2|9</nowiki>
|CS Mixolydian
|
|-
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
|<nowiki>3|8</nowiki>
|CS Dorian
|
|-
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
|<nowiki>4|7</nowiki>
|CS Aeolian
|
|-
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
|<nowiki>5|6</nowiki>
|CS Phrygian
|SC Lydian
|-
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
|<nowiki>6|5</nowiki>
|CS Locrian
|SC Ionian
|-
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
|<nowiki>7|4</nowiki>
|
|SC Mixolydian
|-
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
|<nowiki>8|3</nowiki>
|
|SC Dorian
|-
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
|<nowiki>9|2</nowiki>
|
|SC Aeolian
|-
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
|<nowiki>10|1</nowiki>
|
|SC Phrygian
|-
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
|<nowiki>11|0</nowiki>
|
|SC Locrian
|}
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"
!
! colspan="18" |Bright generator: 18/31
! colspan="13" |Dark generator: 13/31
! rowspan="2" |UDP
! colspan="3" |M-enharmonic modes
|-
!C
!Dbb
!C#
!Db
!C##
!D
!Ebb
!D#
!Eb
!D##
!E
!Fb
!E#
!F
!Gbb
!F#
!Gb
!F##
!G
!Abb
!G#
!Ab
!G##
!A
!Bbb
!A#
!Bb
!A##
!B
!Cb
!B#
!C
!Mode (CCD)
!Mode (CDC)
!Mode (DCC)
|-
! rowspan="19" |
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
|<nowiki>18|0</nowiki>
|CCD Lydian
|
|
|-
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
|<nowiki>17|1</nowiki>
|CCD Ionian
|
|
|-
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
|<nowiki>16|2</nowiki>
|CCD Mixolydian
|
|
|-
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
|<nowiki>15|3</nowiki>
|CCD Dorian
|
|
|-
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
|<nowiki>14|4</nowiki>
|CCD Aeolian
|
|
|-
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
|<nowiki>13|5</nowiki>
|CCD Phrygian
|CDC Lydian
|
|-
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
|<nowiki>12|6</nowiki>
|CCD Locrian
|CDC Ionian
|
|-
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|<nowiki>11|7</nowiki>
|
|CDC Mixolydian
|
|-
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|<nowiki>10|8</nowiki>
|
|CDC Dorian
|
|-
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|<nowiki>9|9</nowiki>
|
|CDC Aeolian
|
|-
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|<nowiki>8|10</nowiki>
|
|CDC Phrygian
|
|-
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|<nowiki>7|11</nowiki>
|
|CDC Locrian
|
|-
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|<nowiki>6|12</nowiki>
|
|
|DCC Lydian
|-
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|<nowiki>5|13</nowiki>
|
|
|DCC Ionian
|-
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|<nowiki>4|14</nowiki>
|
|
|DCC Mixolydian
|-
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|<nowiki>3|15</nowiki>
|
|
|DCC Dorian
|-
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|<nowiki>2|16</nowiki>
|
|
|DCC Aeolian
|-
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|<nowiki>1|17</nowiki>
|
|
|DCC Phrygian
|-
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|<nowiki>0|18</nowiki>
|
|
|DCC Locrian
|}
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