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[[Basic]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
[[Basic]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
==Notation==
==Notation==
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sextave (diminished eleventh~tenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sextave (diminished eleventh~tenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
{| class="wikitable"
{| class="wikitable"
Line 43: Line 45:
124.138
124.138
|2\11
|2\11
[[Tel:141.1765|141.1765]]
141.1765
|3\14
|3\14
163.{{Overline|63}}
163.{{Overline|63}}
Line 135: Line 137:
378.947
378.947
|10\21
|10\21
387.0968
387.097
| rowspan="2" |4\8
| rowspan="2" |4\8
400
400
Line 232: Line 234:
| rowspan="2" |12\13
| rowspan="2" |12\13
757.895
757.895
|20\21
| 20\21
774.194
774.194
|8\8
|8\8
Line 728: Line 730:
''666.{{Overline|6}}''
''666.{{Overline|6}}''
|''11\13''
|''11\13''
''676.9231''
''676.923''
|''18\21''
|''18\21''
''685.7143''
''685.714''
|''7\8''
|''7\8''
''700''
''700''
Line 836: Line 838:
''1100''
''1100''
|''27\19''
|''27\19''
''1136.8421''
''1136.842''
|''16\11''
|''16\11''
''1163.{{Overline|63}}''
''1163.{{Overline|63}}''
Line 1,008: Line 1,010:
! colspan="7" |''1600''
! colspan="7" |''1600''
|}
|}


==Intervals==
==Intervals==
Line 1,014: Line 1,017:
!Sextave notation
!Sextave notation
!Interval category name
!Interval category name
!Generators
! Generators
!Notation of sixth inverse
!Notation of sixth inverse
!Interval category name
! Interval category name
|-
|-
| colspan="6" |The 5-note MOS has the following intervals (from some root):
| colspan="6" |The 5-note MOS has the following intervals (from some root):
Line 1,023: Line 1,026:
|La
|La
|sextave (minor sixth)
|sextave (minor sixth)
|0
| 0
|La
|La
|perfect unison
| perfect unison
|-
|-
|1
|1
Line 1,061: Line 1,064:
|augmented unison (chroma)
|augmented unison (chroma)
| -5
| -5
|Lab
| Lab
|diminished sextave
|diminished sextave
|-
|-
|6
|6
|Re#
| Re#
|augmented fourth
|augmented fourth
| -6
| -6
Line 1,126: Line 1,129:
|-
|-
!name
!name
!pattern
! pattern
!notation
!notation
!2nd
!2nd
Line 1,200: Line 1,203:
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{| class="wikitable"
! colspan="3" rowspan="2" |Generator
! colspan="3" |Generator
(bright)
(bright)
! colspan="2" |Normalised
!Normalised
! colspan="2" |''ed8\12 (→ed2\3)''
!''ed8\12 (→ed2\3)''
! rowspan="2" |L
!L
! rowspan="2" |s
!s
! rowspan="2" |L/s
!L/s
! rowspan="2" |Comments
!Comments
|-
!Chroma-positive
!Chroma-negative
!Chroma-positive
!Chroma-negative
|-
|-
|3\5
|3\5
Line 1,218: Line 1,216:
|
|
|514.286
|514.286
|342.857
|''480''
|''480''
|''320''
|1
|1
|1
|1
Line 1,230: Line 1,226:
|
|
|510
|510
|330
|''485.714''
|''485.714''
|''314.286''
|6
|6
|5
|5
|1.200
|1.200
|
|-
|
|48\79
|
|509.7345
|329.2035
|''486.076''
|''313.924''
|17
|14
|1.214
|
|-
|
|31\51
|
|509.589
|328.767
|''486.2745''
|''313.7255''
|11
|9
|1.222
|
|
|-
|-
Line 1,266: Line 1,236:
|
|
|509.{{Overline|09}}
|509.{{Overline|09}}
|327.{{Overline|27}}
|''486.9565''
|''486.9565''
|''313.0435''
|5
|5
|4
|4
|1.250
|1.250
|
|-
|
|39\64
|
|508.966
|326.087
|''487.5''
|''312.5''
|14
|11
|1.273
|
|
|-
|-
Line 1,290: Line 1,246:
|
|
|508.475
|508.475
|325.424
|''487.805''
|''487.805''
|''312.195''
|9
|9
|7
|7
Line 1,302: Line 1,256:
|
|
|508.235
|508.235
|324.706
|''488.136''
|''488.136''
|''311.864''
|13
|13
|10
|10
Line 1,314: Line 1,266:
|
|
|507.692
|507.692
|323.077
|''488.{{Overline|8}}''
|''488.{{Overline|8}}''
|''311.{{Overline|1}}''
|4
|4
|3
|3
|1.333
|1.333
|
|-
|
|63\103
|
|507.383
|322.148
|''489.32''
|''310.68''
|23
|17
|1.353
|
|-
|
|52\85
|
|507.317
|321.951
|''489.412''
|''310.588''
|19
|14
|1.357
|
|-
|
|41\67
|
|507.2165
|321.6495
|''489.552''
|''310.448''
|15
|11
|1.364
|
|
|-
|-
Line 1,362: Line 1,276:
|
|
|507.062
|507.062
|321.127
|''489.796''
|''489.796''
|''310.204''
|11
|11
|8
|8
Line 1,374: Line 1,286:
|
|
|506.{{Overline|6}}
|506.{{Overline|6}}
|320
|''490.323''
|''490.323''
|''309.678''
|7
|7
|5
|5
|1.400
|1.400
|
|-
|
|
|46\75
|506.422
|319.266
|''490.{{Overline|6}}''
|''309.{{Overline|3}}''
|17
|12
|1.417
|
|
|-
|-
Line 1,398: Line 1,296:
|
|
|506.25
|506.25
|318.75
|''490.{{Overline|90}}''
|''490.{{Overline|90}}''
|''309.{{Overline|09}}''
|10
|10
|7
|7
Line 1,410: Line 1,306:
|
|
|506.024
|506.024
|318.072
|''491.228''
|''491.228''
|''308.712''
|13
|13
|9
|9
Line 1,422: Line 1,316:
|
|
|505.882
|505.882
|317.647
|''491.429''
|''491.429''
|''308.571''
|16
|16
|11
|11
Line 1,434: Line 1,326:
|
|
|505.785
|505.785
|317.355
|''491.566''
|''491.566''
|''308.434''
|19
|19
|13
|13
Line 1,446: Line 1,336:
|
|
|505.263
|505.263
|315.79
|''492.308''
|''492.308''
|''307.692''
|3
|3
|2
|2
Line 1,458: Line 1,346:
|
|
|504.673
|504.673
|314.019
|''493.151''
|''493.151''
|''306.849''
|17
|17
|11
|11
Line 1,470: Line 1,356:
|
|
|504.{{Overline|54}}
|504.{{Overline|54}}
|313.{{Overline|63}}
|''493.{{Overline|3}}''
|''493.{{Overline|3}}''
|''306.{{Overline|6}}''
|14
|14
|9
|9
Line 1,482: Line 1,366:
|
|
|504.348
|504.348
|313.043
|''493.617''
|''493.617''
|''306.383''
|11
|11
|7
|7
Line 1,494: Line 1,376:
|
|
|504
|504
|312
|''494.118''
|''494.118''
|''305.882''
|8
|8
|5
|5
|1.600
|1.600
|
|-
|
|
|34\55
|503.{{Overline|703}}
|311.{{Overline|1}}
|''494.{{Overline|54}}''
|''305.{{Overline|45}}''
|13
|8
|1.625
|
|
|-
|-
Line 1,518: Line 1,386:
|47\76
|47\76
|503.571
|503.571
|310.714
|''494.737''
|''494.737''
|''305.263''
|18
|18
|11
|11
Line 1,530: Line 1,396:
|
|
|503.226
|503.226
|309.678
|''495.238''
|''495.238''
|''304.762''
|5
|5
|3
|3
|1.667
|1.667
|
|-
|
|
|31\50
|502.{{Overline|702}}
|308.{{Overline|108}}
|''496''
|''304''
|12
|7
|1.714
|
|
|-
|-
Line 1,554: Line 1,406:
|49\79
|49\79
|502.564
|502.564
|307.692
|''496.2025''
|''496.2025''
|''303.7975''
|19
|19
|11
|11
Line 1,566: Line 1,416:
|
|
|502.326
|502.326
|306.977
|''496.552''
|''496.552''
|''303.448''
|7
|7
|4
|4
Line 1,578: Line 1,426:
|
|
|501.{{Overline|81}}
|501.{{Overline|81}}
|305.{{Overline|45}}
|''497.{{Overline|297}}''
|''497.{{Overline|297}}''
|''302.{{Overline|702}}''
|9
|9
|5
|5
Line 1,590: Line 1,436:
|
|
|501.492
|501.492
|304.478
|''497.{{Overline|7}}''
|''497.{{Overline|7}}''
|''302.{{Overline|2}}''
|11
|11
|6
|6
Line 1,602: Line 1,446:
|
|
|501.265
|501.265
|303.797
|''498.113''
|''498.113''
|''301.887''
|13
|13
|7
|7
Line 1,614: Line 1,456:
|
|
|501.09
|501.09
|303.297
|''498.361''
|''498.361''
|''301.639''
|15
|15
|8
|8
Line 1,626: Line 1,466:
|
|
|500.971
|500.971
|302.913
|''498.551''
|''498.551''
|''301.449''
|17
|17
|9
|9
Line 1,638: Line 1,476:
|
|
|500
|500
|300
|''500''
|''500''
|''300''
|2
|2
|1
|1
Line 1,650: Line 1,486:
|
|
|499.01
|499.01
|297.03
|''501.4925''
|''501.4925''
|''298.5075''
|17
|17
|8
|8
Line 1,662: Line 1,496:
|
|
|498.876
|498.876
|296.629
|''501.695''
|''501.695''
|''298.305''
|15
|15
|7
|7
Line 1,674: Line 1,506:
|
|
|498.701
|498.701
|296.104
|''501.961''
|''501.961''
|''298.039''
|13
|13
|6
|6
Line 1,686: Line 1,516:
|
|
|498.461
|498.461
|295.385
|''502.326''
|''502.326''
|''297.674''
|11
|11
|5
|5
Line 1,698: Line 1,526:
|
|
|498.113
|498.113
|294.34
|''502.857''
|''502.857''
|''297.143''
|9
|9
|4
|4
|2.250
|2.250
|
|-
|
|
|39\62
|497.872
|293.617
|''503.226''
|''296.774''
|16
|7
|2.286
|
|
|-
|-
Line 1,722: Line 1,536:
|
|
|497.561
|497.561
|292.683
|''503.{{Overline|703}}''
|''503.{{Overline|703}}''
|''296.{{Overline|296}}''
|7
|7
|3
|3
|2.333
|2.333
|
|-
|
|
|29\46
|497.143
|291.429
|''504.348''
|''295.652''
|12
|5
|2.400
|
|
|-
|-
Line 1,746: Line 1,546:
|41\65
|41\65
|496.{{Overline|96}}
|496.{{Overline|96}}
|290.{{Overline|90}}
|''504.615''
|''504.615''
|''295.385''
|17
|17
|7
|7
Line 1,758: Line 1,556:
|
|
|496.552
|496.552
|289.655
|''505.263''
|''505.263''
|''294.737''
|5
|5
|2
|2
|2.500
|2.500
|
|-
|
|
|31\49
|496
|288
|''506.122''
|''293.878''
|13
|5
|2.600
|
|-
|
|
|50\79
|495.868
|287.633
|''506.329''
|''293.671''
|21
|8
|2.625
|
|
|-
|-
Line 1,794: Line 1,566:
|
|
|495.652
|495.652
|286.957
|''506.{{Overline|6}}''
|''506.{{Overline|6}}''
|''293.{{Overline|3}}''
|8
|8
|3
|3
Line 1,806: Line 1,576:
|
|
|495.238
|495.238
|285.714
|''507.317''
|''507.317''
|''292.683''
|11
|11
|4
|4
Line 1,818: Line 1,586:
|
|
|495
|495
|285
|''507.692''
|''507.692''
|''292.308''
|14
|14
|5
|5
Line 1,830: Line 1,596:
|
|
|494.536
|494.536
|284.536
|''507.9365''
|''507.9365''
|''292.0635''
|17
|17
|6
|6
Line 1,842: Line 1,606:
|
|
|494.737
|494.737
|284.211
|''508.{{Overline|108}}''
|''508.{{Overline|108}}''
|''291.{{Overline|891}}''
|20
|20
|7
|7
Line 1,854: Line 1,616:
|
|
|494.6565
|494.6565
|283.9695
|''508.235''
|''508.235''
|''291.765''
|23
|23
|8
|8
Line 1,866: Line 1,626:
|
|
|494.{{Overline|594}}
|494.{{Overline|594}}
|283.{{Overline|783}}
|''508.{{Overline|3}}''
|''508.{{Overline|3}}''
|''291.{{Overline|6}}''
|26
|26
|9
|9
Line 1,878: Line 1,636:
|
|
|494.118
|494.118
|282.353
|''509.{{Overline|09}}''
|''509.{{Overline|09}}''
|''290.{{Overline|90}}''
|3
|3
|1
|1
Line 1,890: Line 1,646:
|
|
|493.671
|493.671
|281.013
|''509.804''
|''509.804''
|''290.196''
|28
|28
|9
|9
Line 1,902: Line 1,656:
|
|
|493.617
|493.617
|280.851
|''509.89''
|''509.89''
|''290.11''
|25
|25
|8
|8
Line 1,914: Line 1,666:
|
|
|493.548
|493.548
|280.645
|''510''
|''510''
|''290''
|22
|22
|7
|7
Line 1,926: Line 1,676:
|
|
|493.458
|493.458
|280.374
|''510.145''
|''510.145''
|''289.855''
|19
|19
|6
|6
Line 1,938: Line 1,686:
|
|
|493.{{Overline|3}}
|493.{{Overline|3}}
|280
|''510.345''
|''510.345''
|''289.655''
|16
|16
|5
|5
Line 1,950: Line 1,696:
|
|
|493.151
|493.151
|279.452
|''510.638''
|''510.638''
|''289.362''
|13
|13
|4
|4
Line 1,962: Line 1,706:
|
|
|492.857
|492.857
|278.571
|''511.{{Overline|1}}''
|''511.{{Overline|1}}''
|''288.{{Overline|8}}''
|10
|10
|3
|3
Line 1,974: Line 1,716:
|
|
|492.308
|492.308
|276.923
|''512''
|''512''
|''288''
|7
|7
|2
|2
Line 1,986: Line 1,726:
|
|
|491.803
|491.803
|275.41
|''512.8205''
|''512.8205''
|''287.1795''
|11
|11
|3
|3
Line 1,998: Line 1,736:
|
|
|491.566
|491.566
|274.699
|''513.2075''
|''513.2075''
|''286.7925''
|15
|15
|4
|4
Line 2,010: Line 1,746:
|
|
|491.429
|491.429
|274.286
|''513.433''
|''513.433''
|''286.567''
|19
|19
|5
|5
Line 2,022: Line 1,756:
|
|
|491.339
|491.339
|274.016
|''513.58''
|''513.58''
|''286.42''
|23
|23
|6
|6
Line 2,034: Line 1,766:
|
|
|491.275
|491.275
|273.825
|''513.684''
|''513.684''
|''286.316''
|27
|27
|7
|7
Line 2,046: Line 1,776:
|
|
|490.{{Overline|90}}
|490.{{Overline|90}}
|272.{{Overline|72}}
|''514.286''
|''514.286''
|''285.714''
|4
|4
|1
|1
Line 2,058: Line 1,786:
|
|
|490.435
|490.435
|271.304
|''515.0685''
|''515.0685''
|''284.3315''
|21
|21
|5
|5
Line 2,070: Line 1,796:
|
|
|490.323
|490.323
|270.968
|''515.254''
|''515.254''
|''284.746''
|17
|17
|4
|4
Line 2,082: Line 1,806:
|
|
|490.141
|490.141
|270.422
|''515.{{Overline|5}}''
|''515.{{Overline|5}}''
|''284.{{Overline|4}}''
|13
|13
|3
|3
Line 2,094: Line 1,816:
|
|
|489.795
|489.795
|269.388
|''516.129''
|''516.129''
|''283.871''
|9
|9
|2
|2
Line 2,106: Line 1,826:
|
|
|489.474
|489.474
|268.421
|''516.{{Overline|6}}''
|''516.{{Overline|6}}''
|''283.{{Overline|3}}''
|14
|14
|3
|3
Line 2,118: Line 1,836:
|
|
|489.32
|489.32
|267.961
|''516.923''
|''516.923''
|''283.077''
|19
|19
|4
|4
Line 2,130: Line 1,846:
|
|
|488.{{Overline|8}}
|488.{{Overline|8}}
|266.{{Overline|6}}
|''517.647''
|''517.647''
|''282.353''
|5
|5
|1
|1
Line 2,142: Line 1,856:
|
|
|488.372
|488.372
|265.116
|''518.{{Overline|518}}''
|''518.{{Overline|518}}''
|''281.{{Overline|481}}''
|16
|16
|3
|3
Line 2,154: Line 1,866:
|
|
|488.136
|488.136
|264.407
|''518.{{Overline|918}}''
|''518.{{Overline|918}}''
|''281.{{Overline|081}}''
|11
|11
|2
|2
Line 2,166: Line 1,876:
|
|
|487.912
|487.912
|263.736
|''519.298''
|''519.298''
|''280.702''
|17
|17
|3
|3
Line 2,178: Line 1,886:
|
|
|487.5
|487.5
|262.2
|''520''
|''520''
|''280''
|6
|6
|1
|1
Line 2,190: Line 1,896:
|
|
|480
|480
|240
|''533.{{Overline|3}}''
|''533.{{Overline|3}}''
|''266.{{Overline|6}}''
|1
|1
|0
|0
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