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remove key sig section; standardize to "mos-" instead of "oneiro-"
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The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.
The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.


The chain of oneirofourths becomes: ... P@ K@ N@ Q L O J M P K N Q& L& O& ...
The chain of perfect mosfourths becomes: ... P@ K@ N@ Q L O J M P K N Q& L& O& ...


Thus the [[13edo]] gamut is as follows:  
Thus the [[13edo]] gamut is as follows:  
Line 43: Line 43:


== Intervals ==
== Intervals ==
The table of oneirotonic intervals below takes the flat fourth as the generator. Given the size of the subfourth generator ''g'', any oneirotonic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number of generators it takes to reach the interval and reducing mod 1200 if necessary (The % sign can be used for the modulo operation on many search engines). For example, since the major oneirothird is reached by six subfourth generators, [[18edo]]'s major oneirothird is 6*466.67 mod 1200 = 2800 mod 1200 = 400¢, same as the [[12edo]] major third.
The table of oneirotonic intervals below takes the flat fourth as the generator. Given the size of the subfourth generator ''g'', any oneirotonic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number of generators it takes to reach the interval and reducing mod 1200 if necessary (The % sign can be used for the modulo operation on many search engines). For example, since the major mosthird is reached by six subfourth generators, [[18edo]]'s major mosthird is 6*466.67 mod 1200 = 2800 mod 1200 = 400¢, same as the [[12edo]] major third.
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
Line 68: Line 68:
| 1
| 1
| M
| M
| perfect oneirofourth (aka minor fourth, falling fourth)
| perfect mosfourth (aka minor fourth, falling fourth)
| Pon4
| Pmos4
| -1
| -1
| O
| O
| perfect oneirosixth (aka major fifth, rising fifth)
| perfect mossixth (aka major fifth, rising fifth)
| Pon6
| Pmos6
|-
|-
| 2
| 2
| P
| P
| major oneiroseventh
| major mosseventh
| Lon7
| Lmos7
| -2
| -2
| L
| L
| minor oneirothird
| minor mosthird
| son3
| smos3
|-
|-
| 3
| 3
| K
| K
| major oneirosecond
| major mossecond
| Lon2
| Lmos2
| -3
| -3
| Q
| Q
| minor oneiroeighth
| minor moseighth
| son8
| smos8
|-
|-
| 4
| 4
| N
| N
| major oneirofifth (aka minor fifth, falling fifth)
| major mosfifth (aka minor fifth, falling fifth)
| Lon5
| Lmos5
| -4
| -4
| N@
| N@
| minor oneirofifth (aka major fourth, rising fourth)
| minor mosfifth (aka major fourth, rising fourth)
| son4
| smos4
|-
|-
| 5
| 5
| Q&
| Q&
| major oneiroeighth
| major moseighth
| Lon8
| Lmos8
| -5
| -5
| K@
| K@
| minor oneirosecond
| minor mossecond
| son2
| smos2
|-
|-
| 6
| 6
| L&
| L&
| major oneirothird
| major mosthird
| Lon3
| Lmos3
| -6
| -6
| P@
| P@
| minor oneiroseventh
| minor mosseventh
| son7
| smos7
|-
|-
| 7
| 7
| O&
| O&
| augmented oneirosixth
| augmented mossixth
| Aon6
| Amos6
| -7
| -7
| M@
| M@
| diminished oneirofourth
| diminished mosfourth
| d-on4
| d-mos4
|-
|-
| colspan="8" style="text-align:center" | The chromatic 13-note MOS (either [[5L 8s]], [[8L 5s]], or [[13edo]]) also has the following intervals (from some root):
| colspan="8" style="text-align:center" | The chromatic 13-note MOS (either [[5L 8s]], [[8L 5s]], or [[13edo]]) also has the following intervals (from some root):
Line 133: Line 133:
| 8
| 8
| J&
| J&
| augmented oneirounison (aka oneirochroma)
| augmented mosunison (aka oneirochroma)
| Ao1
| Ao1
| -8
| -8
| J@
| J@
| diminished oneirooctave (aka diminished oneironinth)
| diminished mosoctave (aka diminished mosninth)
| d-o9
| d-o9
|-
|-
| 9
| 9
| M&
| M&
| augmented oneirofourth
| augmented mosfourth
| Aon4
| Amos4
| -9
| -9
| O@
| O@
| diminished oneirosixth
| diminished mossixth
| d-on6
| d-mos6
|-
|-
| 10
| 10
| P&
| P&
| augmented oneiroseventh
| augmented mosseventh
| Aon7
| Amos7
| -10
| -10
| L@
| L@
| diminished oneirothird
| diminished mosthird
| d-on3
| d-mos3
|-
|-
| 11
| 11
| K&
| K&
| augmented oneirosecond
| augmented mossecond
| Aon2
| Amos2
| -11
| -11
| Q@
| Q@
| diminished oneiroeighth
| diminished moseighth
| d-on8
| d-mos8
|-
|-
| 12
| 12
| N&
| N&
| augmented oneirofifth
| augmented mosfifth
| Aon5
| Amos5
| -12
| -12
| N@@
| N@@
| diminished oneirofifth
| diminished mosfifth
| d-on5
| d-mos5
|}
|}


Line 240: Line 240:
| 0
| 0
|-
|-
| minor on2nd
| minor mos2nd
| 1\13, 92.31
| 1\13, 92.31
| 1\18, 66.67
| 1\18, 66.67
Line 248: Line 248:
| -5
| -5
|-
|-
| major on2nd
| major mos2nd
| 2\13, 184.62
| 2\13, 184.62
| 3\18, 200.00
| 3\18, 200.00
Line 256: Line 256:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on3rd
| minor mos3rd
| 3\13, 276.92
| 3\13, 276.92
| 4\18, 266.67
| 4\18, 266.67
Line 264: Line 264:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on3rd
| major mos3rd
| 4\13, 369.23
| 4\13, 369.23
| 6\18, 400.00
| 6\18, 400.00
Line 272: Line 272:
| +6
| +6
|-
|-
| dim. on4th
| dim. mos4th
| 4\13, 369.23
| 4\13, 369.23
| 5\18, 333.33
| 5\18, 333.33
Line 280: Line 280:
| -7
| -7
|-
|-
| perf. on4th
| perf. mos4th
| 5\13, 461.54  
| 5\13, 461.54  
| 7\18, 466.67
| 7\18, 466.67
Line 288: Line 288:
| +1
| +1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on5th
| minor mos5th
| 6\13, 553.85
| 6\13, 553.85
| 8\18, 533.33
| 8\18, 533.33
Line 296: Line 296:
| -4
| -4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on5th
| major mos5th
| 7\13, 646.15
| 7\13, 646.15
| 10\18, 666.66
| 10\18, 666.66
Line 304: Line 304:
| +4
| +4
|-
|-
| perf. on6th
| perf. mos6th
| 8\13, 738.46
| 8\13, 738.46
| 11\18, 733.33
| 11\18, 733.33
Line 312: Line 312:
| -1
| -1
|-
|-
| aug. on6th
| aug. mos6th
| 9\13, 830.77
| 9\13, 830.77
| 13\18, 866.66
| 13\18, 866.66
Line 320: Line 320:
| +7
| +7
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on7th
| minor mos7th
| 9\13, 830.77
| 9\13, 830.77
| 12\18, 800.00
| 12\18, 800.00
Line 328: Line 328:
| -6
| -6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on7th
| major mos7th
| 10\13, 923.08
| 10\13, 923.08
| 14\18, 933.33
| 14\18, 933.33
Line 336: Line 336:
| +2
| +2
|-
|-
| minor on8th
| minor mos8th
| 11\13, 1015.39
| 11\13, 1015.39
| 15\18, 1000.00
| 15\18, 1000.00
Line 344: Line 344:
| -3
| -3
|-
|-
| major on8th
| major mos8th
| 12\13, 1107.69
| 12\13, 1107.69
| 17\18, 1133.33
| 17\18, 1133.33
Line 359: Line 359:
* The major mosthird (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342¢) to 4\13 (369¢).
* The major mosthird (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342¢) to 4\13 (369¢).


* [[21edo]]'s P1-Lon2-Lon3-Lon5 approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71¢) and Baroque diatonic semitones (114.29¢, close to quarter-comma meantone's 117.11¢).
* [[21edo]]'s P1-Lmos2-Lmos3-Lmos5 approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71¢) and Baroque diatonic semitones (114.29¢, close to quarter-comma meantone's 117.11¢).
* [[34edo]]'s 9:10:11:13 is even better.
* [[34edo]]'s 9:10:11:13 is even better.


Line 403: Line 403:
| 0
| 0
|-
|-
| minor on2nd
| minor mos2nd
| 2\21, 114.29
| 2\21, 114.29
| 3\34, 105.88
| 3\34, 105.88
Line 410: Line 410:
| -5
| -5
|-
|-
| major on2nd
| major mos2nd
| 3\21, 171.43
| 3\21, 171.43
| 5\34, 176.47
| 5\34, 176.47
Line 417: Line 417:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on3rd
| minor mos3rd
| 5\21, 285.71
| 5\21, 285.71
| 8\34, 282.35
| 8\34, 282.35
Line 424: Line 424:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on3rd
| major mos3rd
| 6\21, 342.86
| 6\21, 342.86
| 10\34, 352.94
| 10\34, 352.94
Line 431: Line 431:
| +6
| +6
|-
|-
| dim. on4th
| dim. mos4th
| 7\21, 400.00
| 7\21, 400.00
| 11\34, 388.24
| 11\34, 388.24
Line 438: Line 438:
| -7
| -7
|-
|-
| perf. on4th
| perf. mos4th
| 7\18, 457.14
| 7\18, 457.14
| 12\31, 458.82
| 12\31, 458.82
Line 445: Line 445:
| +1
| +1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on5th
| minor mos5th
| 10\21, 571.43
| 10\21, 571.43
| 16\34, 564.72
| 16\34, 564.72
Line 452: Line 452:
| -4
| -4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on5th
| major mos5th
| 11\21, 628.57
| 11\21, 628.57
| 18\34, 635.29
| 18\34, 635.29
Line 459: Line 459:
| +4
| +4
|-
|-
| perf. on6th
| perf. mos6th
| 13\21, 742.86
| 13\21, 742.86
| 21\34, 741.18
| 21\34, 741.18
Line 466: Line 466:
| -1
| -1
|-
|-
| aug. on6th
| aug. mos6th
| 14\21, 800.00
| 14\21, 800.00
| 23\34, 811.77
| 23\34, 811.77
Line 473: Line 473:
| +7
| +7
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on7th
| minor mos7th
| 15\21, 857.14
| 15\21, 857.14
| 24\34, 847.06
| 24\34, 847.06
Line 480: Line 480:
| -6
| -6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on7th
| major mos7th
| 16\21, 914.29
| 16\21, 914.29
| 26\34, 917.65
| 26\34, 917.65
Line 487: Line 487:
| +2
| +2
|-
|-
| minor on8th
| minor mos8th
| 18\21, 1028.57
| 18\21, 1028.57
| 29\34, 1023.53
| 29\34, 1023.53
Line 494: Line 494:
| -3
| -3
|-
|-
| major on8th
| major mos8th
| 19\21, 1085.71
| 19\21, 1085.71
| 31\34, 1094.12
| 31\34, 1094.12
Line 546: Line 546:
| +8
| +8
|-
|-
| dim. on2nd
| dim. mos2nd
| 2\29, 82.8
| 2\29, 82.8
| K@@
| K@@
Line 552: Line 552:
| -13
| -13
|-
|-
| minor on2nd
| minor mos2nd
| 3\29, 124.1
| 3\29, 124.1
| K@
| K@
Line 558: Line 558:
| -5
| -5
|-
|-
| major on2nd
| major mos2nd
| 4\29, 165.5
| 4\29, 165.5
| K
| K
Line 564: Line 564:
| +3
| +3
|-
|-
| aug. on2nd
| aug. mos2nd
| 5\29, 206.9
| 5\29, 206.9
| K&
| K&
Line 570: Line 570:
| +11
| +11
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. on3rd
| dim. mos3rd
| 6\29, 248.3
| 6\29, 248.3
| L@
| L@
Line 576: Line 576:
| -10
| -10
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on3rd
| minor mos3rd
| 7\29, 289.7
| 7\29, 289.7
| L
| L
Line 582: Line 582:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on3rd
| major mos3rd
| 8\29, 331.0
| 8\29, 331.0
| L&
| L&
Line 588: Line 588:
| +6
| +6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| aug. on3rd
| aug. mos3rd
| 9\29, 372.4
| 9\29, 372.4
| L&&
| L&&
Line 594: Line 594:
| +14
| +14
|-
|-
| doubly dim. on4th
| doubly dim. mos4th
| 9\29, 372.4
| 9\29, 372.4
| M@@
| M@@
Line 600: Line 600:
| -15
| -15
|-
|-
| dim. on4th
| dim. mos4th
| 10\29, 413.8
| 10\29, 413.8
| M@
| M@
Line 606: Line 606:
| -7
| -7
|-
|-
| perf. on4th
| perf. mos4th
| 11\29, 455.2
| 11\29, 455.2
| M
| M
Line 612: Line 612:
| +1
| +1
|-
|-
| aug. on4th
| aug. mos4th
| 12\29, 496.6
| 12\29, 496.6
| M&
| M&
Line 618: Line 618:
| +9
| +9
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. on5th
| dim. mos5th
| 13\29, 537.9
| 13\29, 537.9
| N@@
| N@@
Line 624: Line 624:
| -12
| -12
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on5th
| minor mos5th
| 14\29, 579.3
| 14\29, 579.3
| N@
| N@
Line 630: Line 630:
| -4
| -4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on5th
| major mos5th
| 15\29 620.7
| 15\29 620.7
| N
| N
Line 636: Line 636:
| +4
| +4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| aug. on5th
| aug. mos5th
| 16\29 662.1
| 16\29 662.1
| N&
| N&
Line 642: Line 642:
| +12
| +12
|-
|-
| dim. on6th
| dim. mos6th
| 17\29, 703.4
| 17\29, 703.4
| O@
| O@
Line 648: Line 648:
| -9
| -9
|-
|-
| perf. on6th
| perf. mos6th
| 18\29, 755.2
| 18\29, 755.2
| O
| O
Line 654: Line 654:
| -1
| -1
|-
|-
| aug. on6th
| aug. mos6th
| 19\29, 786.2
| 19\29, 786.2
| O&
| O&
Line 660: Line 660:
| +7
| +7
|-
|-
| doubly aug. on6th
| doubly aug. mos6th
| 20\29 827.6
| 20\29 827.6
| O&&
| O&&
Line 666: Line 666:
| +15
| +15
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. on7th
| dim. mos7th
| 20\29 827.6
| 20\29 827.6
| P@@
| P@@
Line 672: Line 672:
| -14
| -14
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| minor on7th
| minor mos7th
| 21\29 869.0
| 21\29 869.0
| P@
| P@
Line 678: Line 678:
| -6
| -6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| major on7th
| major mos7th
| 22\29, 910.3
| 22\29, 910.3
| P
| P
Line 684: Line 684:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| aug. on7th
| aug. mos7th
| 23\29, 951.7
| 23\29, 951.7
| P&
| P&
Line 690: Line 690:
| +10
| +10
|-
|-
| dim. on8th
| dim. mos8th
| 24\29, 993.1
| 24\29, 993.1
| Q@
| Q@
Line 696: Line 696:
| -11
| -11
|-
|-
| minor on8th
| minor mos8th
| 25\29, 1034.5
| 25\29, 1034.5
| Q
| Q
Line 702: Line 702:
| -3
| -3
|-
|-
| major on8th
| major mos8th
| 26\29, 1075.9
| 26\29, 1075.9
| Q&
| Q&
Line 708: Line 708:
| +5
| +5
|-
|-
| aug. on8th
| aug. mos8th
| 27\29, 1117.2
| 27\29, 1117.2
| Q&&
| Q&&
Line 845: Line 845:
| 108/55, 160/81
| 108/55, 160/81
| +5
| +5
|}
|}-->
 
== Key signatures ==
Flat keys:
* J@ Oneirominor, L@ Oneiromajor = N@, K@, P@, M@, J@, O@, L@, Q@
* M@ Oneirominor, O@ Oneiromajor = N@, K@, P@, M@, J@, O@, L@
* P@ Oneirominor, J@ Oneiromajor = N@, K@, P@, M@, J@, O@
* K@ Oneirominor, M@ Oneiromajor = N@, K@, P@, M@, J@
* N@ Oneirominor, P@ Oneiromajor = N@, K@, P@, M@
* Q Oneirominor, K@ Oneiromajor = N@, K@, P@
* L Oneirominor, N@ Oneiromajor = N@, K@
* O Oneirominor, Q Oneiromajor = N@
All-natural key signature:
* J Oneirominor, L Oneiromajor = no sharps or flats
Sharp keys:
* M Oneirominor, O Oneiromajor = Q&
* P Oneirominor, J Oneiromajor = Q&, L&
* K Oneirominor, M Oneiromajor = Q&, L&, O&
* N Oneirominor, P Oneiromajor = Q&, L&, O&, J&
* Q& Oneirominor, K Oneiromajor = Q&, L&, O&, J&, M&
** Enharmonic with J@ Oneirominor, L@ Oneiromajor in [[13edo]]
* L& Oneirominor, N Oneiromajor = Q&, L&, O&, J&, M&, P&
** Enharmonic with M@ Oneirominor, O@ Oneiromajor in 13edo
* O& Oneirominor, Q& Oneiromajor = Q&, L&, O&, J&, M&, P&, K&
** Enharmonic with P@ Oneirominor, J@ Oneiromajor in 13edo
* J& Oneirominor, L& Oneiromajor = Q&, L&, O&, J&, M&, P&, K&, N&
** Enharmonic with K@ Oneirominor, M@ Oneiromajor in 13edo
 
-->
== Modes ==
== Modes ==
Oneirotonic modes are named after cities in the Dreamlands.
Oneirotonic modes are named after cities in the Dreamlands.
Retrieved from "https://en.xen.wiki/w/5L_3s"