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TAMNAMS consistency correction
Line 40: Line 40:


== 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 large oneirothird is reached by six subfourth generators, [[18edo]]'s large 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 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.
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! # generators up
! # generators up
! Notation (1/1 = J)
! Notation (1/1 = J)
! Octatonic interval category name
! [[TAMNAMS]] name
! Abbrev.
! Abbrev.
! # generators up
! # generators up
! Notation of 2/1 inverse  
! Notation of 2/1 inverse  
! Octatonic interval category name
! [[TAMNAMS]] name
! Abbrev.
! Abbrev.
|-
|-
Line 66: Line 66:
| M
| M
| perfect oneirofourth (aka minor fourth, falling fourth)
| perfect oneirofourth (aka minor fourth, falling fourth)
| Po4
| Pon4
| -1
| -1
| O
| O
| perfect oneirosixth (aka major fifth, rising fifth)
| perfect oneirosixth (aka major fifth, rising fifth)
| Po6
| Pon6
|-
|-
| 2
| 2
| P
| P
| large oneiroseventh
| major oneiroseventh
| Lo7
| Lon7
| -2
| -2
| L
| L
| small oneirothird
| minor oneirothird
| so3
| son3
|-
|-
| 3
| 3
| K
| K
| large oneirosecond
| major oneirosecond
| Lo2
| Lon2
| -3
| -3
| Q
| Q
| small oneiroeighth
| minor oneiroeighth
| so8
| son8
|-
|-
| 4
| 4
| N
| N
| large oneirofifth (aka minor fifth, falling fifth)
| major oneirofifth (aka minor fifth, falling fifth)
| Lo5
| Lon5
| -4
| -4
| N@
| N@
| small oneirofifth (aka major fourth, rising fourth)
| minor oneirofifth (aka major fourth, rising fourth)
| so4
| son4
|-
|-
| 5
| 5
| Q&
| Q&
| large oneiroeighth
| major oneiroeighth
| Lo8
| Lon8
| -5
| -5
| K@
| K@
| small oneirosecond
| minor oneirosecond
| so2
| son2
|-
|-
| 6
| 6
| L&
| L&
| large oneirothird
| major oneirothird
| Lo3
| Lon3
| -6
| -6
| P@
| P@
| small oneiroseventh
| minor oneiroseventh
| so7
| son7
|-
|-
| 7
| 7
| O&
| O&
| augmented oneirosixth
| augmented oneirosixth
| Ao6
| Aon6
| -7
| -7
| M@
| M@
| diminished oneirofourth
| diminished oneirofourth
| d-o4
| d-on4
|-
|-
| 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 140: Line 140:
| M&
| M&
| augmented oneirofourth
| augmented oneirofourth
| Ao4
| Aon4
| -9
| -9
| O@
| O@
| diminished oneirosixth
| diminished oneirosixth
| d-o6
| d-on6
|-
|-
| 10
| 10
| P&
| P&
| augmented oneiroseventh
| augmented oneiroseventh
| Ao7
| Aon7
| -10
| -10
| L@
| L@
| diminished oneirothird
| diminished oneirothird
| d-o3
| d-on3
|-
|-
| 11
| 11
| K&
| K&
| augmented oneirosecond
| augmented oneirosecond
| Ao2
| Aon2
| -11
| -11
| Q@
| Q@
| diminished oneiroeighth
| diminished oneiroeighth
| d-o8
| d-on8
|-
|-
| 12
| 12
| N&
| N&
| augmented oneirofifth
| augmented oneirofifth
| Ao5
| Aon5
| -12
| -12
| N@@
| N@@
| diminished oneirofifth
| diminished oneirofifth
| d-o5
| d-on5
|}
|}


Line 233: Line 233:
| 0
| 0
|-
|-
| small o2nd
| minor on2nd
| 1\13, 92.31
| 1\13, 92.31
| 1\18, 66.67
| 1\18, 66.67
Line 241: Line 241:
| -5
| -5
|-
|-
| large o2nd
| major on2nd
| 2\13, 184.62
| 2\13, 184.62
| 3\18, 200.00
| 3\18, 200.00
Line 249: Line 249:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o3rd
| minor on3rd
| 3\13, 276.92
| 3\13, 276.92
| 4\18, 266.67
| 4\18, 266.67
Line 257: Line 257:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o3rd
| major on3rd
| 4\13, 369.23
| 4\13, 369.23
| 6\18, 400.00
| 6\18, 400.00
Line 265: Line 265:
| +6
| +6
|-
|-
| dim. o4th
| dim. on4th
| 4\13, 369.23
| 4\13, 369.23
| 5\18, 333.33
| 5\18, 333.33
Line 273: Line 273:
| -7
| -7
|-
|-
| perf. o4th
| perf. on4th
| 5\13, 461.54  
| 5\13, 461.54  
| 7\18, 466.67
| 7\18, 466.67
Line 281: Line 281:
| +1
| +1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o5th
| minor on5th
| 6\13, 553.85
| 6\13, 553.85
| 8\18, 533.33
| 8\18, 533.33
Line 289: Line 289:
| -4
| -4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o5th
| major on5th
| 7\13, 646.15
| 7\13, 646.15
| 10\18, 666.66
| 10\18, 666.66
Line 297: Line 297:
| +4
| +4
|-
|-
| perf. o6th
| perf. on6th
| 8\13, 738.46
| 8\13, 738.46
| 11\18, 733.33
| 11\18, 733.33
Line 305: Line 305:
| -1
| -1
|-
|-
| aug. o6th
| aug. on6th
| 9\13, 830.77
| 9\13, 830.77
| 13\18, 866.66
| 13\18, 866.66
Line 313: Line 313:
| +7
| +7
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o7th
| minor on7th
| 9\13, 830.77
| 9\13, 830.77
| 12\18, 800.00
| 12\18, 800.00
Line 321: Line 321:
| -6
| -6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o7th
| major on7th
| 10\13, 923.08
| 10\13, 923.08
| 14\18, 933.33
| 14\18, 933.33
Line 329: Line 329:
| +2
| +2
|-
|-
| small o8th
| minor on8th
| 11\13, 1015.39
| 11\13, 1015.39
| 15\18, 1000.00
| 15\18, 1000.00
Line 337: Line 337:
| -3
| -3
|-
|-
| large o8th
| major on8th
| 12\13, 1107.69
| 12\13, 1107.69
| 17\18, 1133.33
| 17\18, 1133.33
Line 351: Line 351:
* 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-Lo2-Lo3-Lo5 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-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¢).
* [[34edo]]'s 9:10:11:13 is even better.
* [[34edo]]'s 9:10:11:13 is even better.


Line 393: Line 393:
| 0
| 0
|-
|-
| small o2nd
| minor on2nd
| 2\21, 114.29
| 2\21, 114.29
| 3\34, 105.88
| 3\34, 105.88
Line 400: Line 400:
| -5
| -5
|-
|-
| large o2nd
| major on2nd
| 3\21, 171.43
| 3\21, 171.43
| 5\34, 176.47
| 5\34, 176.47
Line 407: Line 407:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o3rd
| minor on3rd
| 5\21, 285.71
| 5\21, 285.71
| 8\34, 282.35
| 8\34, 282.35
Line 414: Line 414:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o3rd
| major on3rd
| 6\21, 342.86
| 6\21, 342.86
| 10\34, 352.94
| 10\34, 352.94
Line 421: Line 421:
| +6
| +6
|-
|-
| dim. o4th
| dim. on4th
| 7\21, 400.00
| 7\21, 400.00
| 11\34, 388.24
| 11\34, 388.24
Line 428: Line 428:
| -7
| -7
|-
|-
| perf. o4th
| perf. on4th
| 7\18, 457.14
| 7\18, 457.14
| 12\31, 458.82
| 12\31, 458.82
Line 435: Line 435:
| +1
| +1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o5th
| minor on5th
| 10\21, 571.43
| 10\21, 571.43
| 16\34, 564.72
| 16\34, 564.72
Line 442: Line 442:
| -4
| -4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o5th
| major on5th
| 11\21, 628.57
| 11\21, 628.57
| 18\34, 635.29
| 18\34, 635.29
Line 449: Line 449:
| +4
| +4
|-
|-
| perf. o6th
| perf. on6th
| 13\21, 742.86
| 13\21, 742.86
| 21\34, 741.18
| 21\34, 741.18
Line 456: Line 456:
| -1
| -1
|-
|-
| aug. o6th
| aug. on6th
| 14\21, 800.00
| 14\21, 800.00
| 23\34, 811.77
| 23\34, 811.77
Line 463: Line 463:
| +7
| +7
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o7th
| minor on7th
| 15\21, 857.14
| 15\21, 857.14
| 24\34, 847.06
| 24\34, 847.06
Line 470: Line 470:
| -6
| -6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o7th
| major on7th
| 16\21, 914.29
| 16\21, 914.29
| 26\34, 917.65
| 26\34, 917.65
Line 477: Line 477:
| +2
| +2
|-
|-
| small o8th
| minor on8th
| 18\21, 1028.57
| 18\21, 1028.57
| 29\34, 1023.53
| 29\34, 1023.53
Line 484: Line 484:
| -3
| -3
|-
|-
| large o8th
| major on8th
| 19\21, 1085.71
| 19\21, 1085.71
| 31\34, 1094.12
| 31\34, 1094.12
Line 536: Line 536:
| +8
| +8
|-
|-
| dim. o2nd
| dim. on2nd
| 2\29, 82.8
| 2\29, 82.8
| K@@
| K@@
Line 542: Line 542:
| -13
| -13
|-
|-
| small o2nd
| minor on2nd
| 3\29, 124.1
| 3\29, 124.1
| K@
| K@
Line 548: Line 548:
| -5
| -5
|-
|-
| large o2nd
| major on2nd
| 4\29, 165.5
| 4\29, 165.5
| K
| K
Line 554: Line 554:
| +3
| +3
|-
|-
| aug. o2nd
| aug. on2nd
| 5\29, 206.9
| 5\29, 206.9
| K&
| K&
Line 560: Line 560:
| +11
| +11
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. o3rd
| dim. on3rd
| 6\29, 248.3
| 6\29, 248.3
| L@
| L@
Line 566: Line 566:
| -10
| -10
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o3rd
| minor on3rd
| 7\29, 289.7
| 7\29, 289.7
| L
| L
Line 572: Line 572:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o3rd
| major on3rd
| 8\29, 331.0
| 8\29, 331.0
| L&
| L&
Line 578: Line 578:
| +6
| +6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| aug. o3rd
| aug. on3rd
| 9\29, 372.4
| 9\29, 372.4
| L&&
| L&&
Line 584: Line 584:
| +14
| +14
|-
|-
| doubly dim. o4th
| doubly dim. on4th
| 9\29, 372.4
| 9\29, 372.4
| M@@
| M@@
Line 590: Line 590:
| -15
| -15
|-
|-
| dim. o4th
| dim. on4th
| 10\29, 413.8
| 10\29, 413.8
| M@
| M@
Line 596: Line 596:
| -7
| -7
|-
|-
| perf. o4th
| perf. on4th
| 11\29, 455.2
| 11\29, 455.2
| M
| M
Line 602: Line 602:
| +1
| +1
|-
|-
| aug. o4th
| aug. on4th
| 12\29, 496.6
| 12\29, 496.6
| M&
| M&
Line 608: Line 608:
| +9
| +9
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. o5th
| dim. on5th
| 13\29, 537.9
| 13\29, 537.9
| N@@
| N@@
Line 614: Line 614:
| -12
| -12
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o5th
| minor on5th
| 14\29, 579.3
| 14\29, 579.3
| N@
| N@
Line 620: Line 620:
| -4
| -4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o5th
| major on5th
| 15\29 620.7
| 15\29 620.7
| N
| N
Line 626: Line 626:
| +4
| +4
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| aug. o5th
| aug. on5th
| 16\29 662.1
| 16\29 662.1
| N&
| N&
Line 632: Line 632:
| +12
| +12
|-
|-
| dim. o6th
| dim. on6th
| 17\29, 703.4
| 17\29, 703.4
| O@
| O@
Line 638: Line 638:
| -9
| -9
|-
|-
| perf. o6th
| perf. on6th
| 18\29, 755.2
| 18\29, 755.2
| O
| O
Line 644: Line 644:
| -1
| -1
|-
|-
| aug. o6th
| aug. on6th
| 19\29, 786.2
| 19\29, 786.2
| O&
| O&
Line 650: Line 650:
| +7
| +7
|-
|-
| doubly aug. o6th
| doubly aug. on6th
| 20\29 827.6
| 20\29 827.6
| O&&
| O&&
Line 656: Line 656:
| +15
| +15
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. o7th
| dim. on7th
| 20\29 827.6
| 20\29 827.6
| P@@
| P@@
Line 662: Line 662:
| -14
| -14
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small o7th
| minor on7th
| 21\29 869.0
| 21\29 869.0
| P@
| P@
Line 668: Line 668:
| -6
| -6
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large o7th
| major on7th
| 22\29, 910.3
| 22\29, 910.3
| P
| P
Line 674: Line 674:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| aug. o7th
| aug. on7th
| 23\29, 951.7
| 23\29, 951.7
| P&
| P&
Line 680: Line 680:
| +10
| +10
|-
|-
| dim. o8th
| dim. on8th
| 24\29, 993.1
| 24\29, 993.1
| Q@
| Q@
Line 686: Line 686:
| -11
| -11
|-
|-
| small o8th
| minor on8th
| 25\29, 1034.5
| 25\29, 1034.5
| Q
| Q
Line 692: Line 692:
| -3
| -3
|-
|-
| large o8th
| major on8th
| 26\29, 1075.9
| 26\29, 1075.9
| Q&
| Q&
Line 698: Line 698:
| +5
| +5
|-
|-
| aug. o8th
| aug. on8th
| 27\29, 1117.2
| 27\29, 1117.2
| Q&&
| Q&&
Retrieved from "https://en.xen.wiki/w/5L_3s"