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== Intervals ==
== Intervals ==
The following table of intervals uses both the 7-note 6L 1s [[MOS scale]] of Nelindic for the naturals (simple A-G notation and standard sharps/flats for the [[chroma]]) and the 7-note 3L 4s scale (standard A-G notation using the typical [[Genchain mode numbering|genchain]] from [[mosh]]) for Tetrarchy. The 6L 1s scale can be extended to the 13-note (7L 6s) scale, these would include all of the sharps except for F#. Due to the L/s ratio of 3:1, in the 13-note case, most former diminished intervals become minor, most former minor intervals become augmented, and most former augmented intervals become major. Similarly, the 3L 4s scale can be extended to a 7L 3s scale, by dividing the long intervals into sets of 3 and 2 mossteps.
The following table of intervals uses both the 7-note 6L 1s [[MOS scale]] of Nelindic for the naturals (simple A-G notation and standard sharps/flats for the [[chroma]]) and the 7-note 3L 4s scale (standard A-G notation using the typical [[Genchain mode numbering|genchain]] from [[mosh]]) for Tetrarchy. The 6L 1s scale can be extended to the 13-note (7L 6s) scale, these would include all of the sharps except for F#. Due to the L/s ratio of 3:1, in the 13-note case, most former diminished intervals become minor, most former minor intervals become augmented, and most former augmented intervals become major. Similarly, the 3L 4s scale can be extended to a [[7L 3s (4/1-equivalent)|7L 3s]] scale, by dividing the long intervals into sets of 3 and 2 mossteps. These extended scales will usually be melodically preferable over the 6-note and 7-note scales, which have extremely wide melodic spacing comparable to 3edo.


{| class="wikitable center-all left-2 left-4"
{| class="wikitable center-all left-2 left-4"
Line 34: Line 34:
| aug unison
| aug unison
|Abb
|Abb
|dim mos2nd
|dim 1-mosstep
|88.89
|88.89
| 21/20
| 21/20
Line 40: Line 40:
| 2
| 2
| Bbb
| Bbb
| ddim mos2nd
| ddim 1-mosstep
|G#
|G#
|aug unison
|aug unison
Line 48: Line 48:
| 3
| 3
| Bb
| Bb
| dim mos2nd
| dim 1-mosstep
|Ab
|Ab
|min mos2nd
|min 1-mosstep
|266.67
|266.67
| 7/6
| 7/6
Line 56: Line 56:
| '''4'''
| '''4'''
| '''B'''
| '''B'''
| '''perf mos2nd'''
| '''perf 1-mosstep'''
|Bbb
|Bbb
|ddim mos3rd
|ddim 2-mosstep
|'''355.56'''
|'''355.56'''
| '''16/13'''
| '''16/13'''
Line 64: Line 64:
| 5
| 5
| B#
| B#
| aug mos2nd
| aug 1-mosstep
|A
|A
|maj mos2nd
|maj 1-mosstep
|444.44
|444.44
| 9/7, 13/10
| 9/7, 13/10
Line 72: Line 72:
| 6
| 6
| Cbb
| Cbb
| dim mos3rd
| dim 2-mosstep
|Bb
|Bb
|dim mos3rd
|dim 2-mosstep
|533.33
|533.33
| 27/20, 19/14
| 27/20, 19/14
Line 80: Line 80:
| 7
| 7
| Cb
| Cb
| min mos3rd
| min 2-mosstep
|A#
|A#
|aug mos2nd
|aug 2-mosstep
|622.22
|622.22
| 10/7, 13/9
| 10/7, 13/9
Line 88: Line 88:
| '''8'''
| '''8'''
| C
| C
| maj mos3rd
| maj 2-mosstep
|'''B'''
|'''B'''
|'''perf mos3rd'''
|'''perf 2-mosstep'''
|'''711.11'''
|'''711.11'''
| '''3/2'''
| '''3/2'''
Line 96: Line 96:
| 9
| 9
| C#
| C#
| aug mos3rd
| aug 2-mosstep
|Cbb
|Cbb
|dim mos4th
|dim 3-mosstep
|800.00
|800.00
| 8/5
| 8/5
Line 104: Line 104:
| 10
| 10
| Dbb
| Dbb
| dim mos4th
| dim 3-mosstep
|B#
|B#
|aug mos3rd
|aug 2-mosstep
|888.89
|888.89
| 5/3
| 5/3
Line 112: Line 112:
| 11
| 11
| Db
| Db
| min mos4th
| min 3-mosstep
|Cb
|Cb
|min mos4th
|min 3-mosstep
|977.78
|977.78
| 7/4
| 7/4
Line 120: Line 120:
| 12
| 12
| D
| D
| maj mos4th
| maj 3-mosstep
|Dbb
|Dbb
|ddim mos5th
|ddim 4-mosstep
|1066.67
|1066.67
| 13/7
| 13/7
Line 128: Line 128:
| 13
| 13
| D#
| D#
| aug mos4th
| aug 3-mosstep
|C
|C
|maj mos4th
|maj 3-mosstep
|1155.56
|1155.56
| 39/20, 35/18
| 39/20, 35/18
Line 136: Line 136:
| 14
| 14
| Ebb
| Ebb
| dim mos5th
| dim 4-mosstep
|Db
|Db
|min mos5th
|min 4-mosstep
|1244.44
|1244.44
| 80/39, 72/35
| 80/39, 72/35
Line 144: Line 144:
| 15
| 15
| Eb
| Eb
| min mos5th
| min 4-mosstep
|C#
|C#
|aug mos4th
|aug 3-mosstep
|1333.33
|1333.33
| 28/13
| 28/13
Line 152: Line 152:
| 16
| 16
| E
| E
| maj mos5th
| maj 4-mosstep
|D
|D
|maj mos5th
|maj 4-mosstep
|1422.22
|1422.22
| 16/7
| 16/7
Line 160: Line 160:
| 17
| 17
| E#
| E#
| aug mos5th
| aug 4-mosstep
|Eb
|Eb
|dim mos6th
|dim 5-mosstep
|1511.11
|1511.11
| 12/5
| 12/5
Line 168: Line 168:
| 18
| 18
| Fbb
| Fbb
| dim mos6th
| dim 5-mosstep
|D#
|D#
|aug mos5th
|aug 4-mosstep
|1600.00
|1600.00
| 5/2
| 5/2
Line 176: Line 176:
| '''19'''
| '''19'''
| Fb
| Fb
| min mos6th
| min 5-mosstep
|'''E'''
|'''E'''
|'''perf mos6th'''
|'''perf 5-mosstep'''
|'''1688.89'''
|'''1688.89'''
| '''8/3'''
| '''8/3'''
Line 184: Line 184:
| 20
| 20
| F
| F
| maj mos6th
| maj 5-mosstep
|Fbb
|Fbb
|dim mos7th
|dim 6-mosstep
|1777.78
|1777.78
| 14/5, 36/13
| 14/5, 36/13
Line 192: Line 192:
| 21
| 21
| F#
| F#
| aug mos6th
| aug 5-mosstep
|E#
|E#
|aug mos6th
|aug 5-mosstep
|1866.67
|1866.67
| 80/27, 38/13
| 80/27, 38/13
Line 200: Line 200:
| 22
| 22
| Gb
| Gb
| dim mos7th
| dim 6-mosstep
|Fb
|Fb
|min mos7th
|min 6-mosstep
|1955.56
|1955.56
| 28/9, 40/13
| 28/9, 40/13
Line 208: Line 208:
| '''23'''
| '''23'''
| '''G'''
| '''G'''
| '''perf mos7th'''
| '''perf 6-mosstep'''
|Gbb
|Gbb
|ddim tetratave
|ddim tetratave
Line 216: Line 216:
| 24
| 24
| G#
| G#
| aug mos7th
| aug 6-mosstep
|F
|F
|maj mos7th
|maj 6-mosstep
|2133.33
|2133.33
| 24/7
| 24/7
Line 234: Line 234:
| dim tetratave
| dim tetratave
|F#
|F#
|aug mos7th
|aug 6-mosstep
|2311.11
|2311.11
| 80/21
| 80/21
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