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5L 3s: Difference between revisions

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Line 10: Line 10:
== Standing assumptions ==
== Standing assumptions ==
The [[TAMNAMS]] system is used in this article to name 5L 3s intervals and step size ratios and step ratio ranges.
The [[TAMNAMS]] system is used in this article to name 5L 3s intervals and step size ratios and step ratio ranges.
The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, 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".)
The chain of perfect 3-mossteps becomes: ... P@ K@ N@ Q L O J M P K N Q& L& O& ...
Thus the [[13edo]] gamut is as follows:
'''J''' J&/K@ '''K'''/L@ '''L'''/K& L&/M@ '''M''' M&/N@ '''N'''/O@ '''O'''/N& O&/P@ '''P'''/Q@ '''Q'''/P& Q&/J@ '''J'''
The [[18edo]] gamut is notated as follows:
'''J''' K@ J&/L@ '''K''' '''L''' K&/M@ L& '''M''' N@ M&/O@ '''N''' '''O''' N&/P@ O&/Q@ '''P''' '''Q''' P&/J@ Q& '''J'''
The [[21edo]] gamut:
'''J''' J& K@ '''K''' K&/L@ '''L''' L& M@ '''M''' M& N@ '''N''' N&/O@ '''O''' O& P@ '''P''' P&/Q@ '''Q''' Q& J@ '''J'''


== Names ==
== Names ==
Line 39: Line 23:
|-
|-
!  
!  
!Notation (1/1 = J)
![[TAMNAMS]] name
![[TAMNAMS]] name
!In L's and s's
!In L's and s's
!# generators up
!# generators up
!Notation of 2/1 inverse
! [[TAMNAMS]] name
! [[TAMNAMS]] name
!In L's and s's
!In L's and s's
|-
|-
| colspan="8" style="text-align:center" |The 8-note MOS has the following intervals (from some root):
| colspan="6" style="text-align:center" |The 8-note MOS has the following intervals (from some root):
|-
|-
| 0
| 0
| J
| perfect unison
| perfect unison
| 0L + 0s
| 0L + 0s
| 0
| 0
| J
| octave
| octave
| 5L + 3s
| 5L + 3s
|-
|-
| 1
| 1
| M
| perfect 3-step
| perfect 3-step
| 2L + 1s
| 2L + 1s
| -1
| -1
| O
| perfect 5-step
| perfect 5-step
| 3L + 2s
| 3L + 2s
|-
|-
| 2
| 2
| P
| major 6-step
| major 6-step
| 4L + 2s
| 4L + 2s
| -2
| -2
| L
| minor 2-step
| minor 2-step
| 1L + 1s
| 1L + 1s
|-
|-
| 3
| 3
| K
| major (1-)step
| major (1-)step
| 1L + 0s
| 1L + 0s
| -3
| -3
| Q
| minor 7-step
| minor 7-step
| 4L + 3s
| 4L + 3s
|-
|-
| 4
| 4
| N
| major 4-step
| major 4-step
| 3L + 1s
| 3L + 1s
| -4
| -4
| N@
| minor 4-step
| minor 4-step
| 2L + 2s
| 2L + 2s
|-
|-
| 5
| 5
| Q&
| major 7-step
| major 7-step
| 5L + 2s
| 5L + 2s
| -5
| -5
| K@
| minor (1-)step
| minor (1-)step
| 0L + 1s
| 0L + 1s
|-
|-
| 6
| 6
| L&
| major 2-step
| major 2-step
| 2L + 0s
| 2L + 0s
| -6
| -6
| P@
| minor 6-step
| minor 6-step
| 3L + 3s
| 3L + 3s
|-
|-
| 7
| 7
| O&
| augmented 5-step
| augmented 5-step
| 4L + 1s
| 4L + 1s
| -7
| -7
| M@
| diminished 3-step
| diminished 3-step
| 1L + 2s
| 1L + 2s
|-
|-
| 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="6" style="text-align:center" |The chromatic 13-note MOS (either [[5L 8s]], [[8L 5s]], or [[13edo]]) also has the following intervals (from some root):
|-
|-
| 8
| 8
| J&
| augmented 0-step (aka moschroma)
| augmented 0-step (aka moschroma)
| 1L - 1s
| 1L - 1s
| -8
| -8
| J@
| diminished 8-step (aka diminished mosoctave)
| diminished 8-step (aka diminished mosoctave)
| 4L + 4s
| 4L + 4s
|-
|-
| 9
| 9
| M&
| augmented 3-step
| augmented 3-step
| 3L + 0s
| 3L + 0s
| -9
| -9
| O@
| diminished 5-step
| diminished 5-step
| 2L + 3s
| 2L + 3s
|-
|-
| 10
| 10
| P&
| augmented 6-step
| augmented 6-step
| 5L + 1s
| 5L + 1s
| -10
| -10
| L@
| diminished 2-step
| diminished 2-step
| 0L + 2s
| 0L + 2s
|-
|-
| 11
| 11
| K&
| augmented 1-step
| augmented 1-step
| 2L - 1s
| 2L - 1s
| -11
| -11
| Q@
| diminished 7-step
| diminished 7-step
| 3L + 4s
| 3L + 4s
|-
|-
| 12
| 12
| N&
| augmented 4-step
| augmented 4-step
| 4L + 0s
| 4L + 0s
| -12
| -12
| N@@
| diminished 4-step
| diminished 4-step
| 1L + 3s
| 1L + 3s
Line 178: Line 134:
! Size in 18edo (hard)
! Size in 18edo (hard)
! Size in 21edo (soft)
! Size in 21edo (soft)
! class="unsortable" |Note name on J
! #Gens up
! #Gens up
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 185: Line 140:
| 0\18, 0.00
| 0\18, 0.00
| 0\21, 0.00
| 0\21, 0.00
| J
| 0
| 0
|-
|-
Line 192: Line 146:
| 1\18, 66.67
| 1\18, 66.67
| 2\21, 114.29
| 2\21, 114.29
| K@
| -5
| -5
|-
|-
Line 199: Line 152:
| 3\18, 200.00
| 3\18, 200.00
| 3\21, 171.43
| 3\21, 171.43
| K
| +3
| +3
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 206: Line 158:
| 4\18, 266.67
| 4\18, 266.67
| 5\21, 285.71
| 5\21, 285.71
| L
| -2
| -2
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 213: Line 164:
| 6\18, 400.00
| 6\18, 400.00
| 6\21, 342.86
| 6\21, 342.86
| L&
| +6
| +6
|-
|-
Line 220: Line 170:
| 5\18, 333.33
| 5\18, 333.33
| 7\21, 400.00
| 7\21, 400.00
| M@
| -7
| -7
|-
|-
Line 227: Line 176:
| 7\18, 466.67
| 7\18, 466.67
| 8\21, 457.14
| 8\21, 457.14
| M
| +1
| +1
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 234: Line 182:
| 8\18, 533.33
| 8\18, 533.33
| 10\21, 571.43
| 10\21, 571.43
| N@
| -4
| -4
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 241: Line 188:
| 10\18, 666.66
| 10\18, 666.66
| 11\31, 628.57
| 11\31, 628.57
| N
| +4
| +4
|-
|-
Line 248: Line 194:
| 11\18, 733.33
| 11\18, 733.33
| 13\21, 742.86
| 13\21, 742.86
| O
| -1
| -1
|-
|-
Line 255: Line 200:
| 13\18, 866.66
| 13\18, 866.66
| 14\21, 800.00
| 14\21, 800.00
| O&
| +7
| +7
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 262: Line 206:
| 12\18, 800.00
| 12\18, 800.00
| 15\21, 857.14
| 15\21, 857.14
| P@
|  -6
|  -6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 269: Line 212:
| 14\18, 933.33
| 14\18, 933.33
| 16\21, 914.29
| 16\21, 914.29
| P
| +2
| +2
|-
|-
Line 276: Line 218:
| 15\18, 1000.00
| 15\18, 1000.00
| 18\21, 1028.57
| 18\21, 1028.57
| Q
| -3
| -3
|-
|-
Line 283: Line 224:
| 17\18, 1133.33
| 17\18, 1133.33
| 19\21, 1085.71
| 19\21, 1085.71
| Q&
| +5
| +5
|}
|}
Line 337: Line 277:
! Size in 18edo (hard)
! Size in 18edo (hard)
! Size in 31edo (semihard)
! Size in 31edo (semihard)
! class="unsortable" |Note name on J
! class="unsortable" |Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! class="unsortable" |Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! #Gens up
! #Gens up
Line 345: Line 284:
| 0\18, 0.00
| 0\18, 0.00
| 0\31, 0.00
| 0\31, 0.00
| J
| 1/1
| 1/1
| 0
| 0
Line 353: Line 291:
| 1\18, 66.67
| 1\18, 66.67
| 2\31, 77.42
| 2\31, 77.42
| K@
| 21/20, ''22/21''
| 21/20, ''22/21''
| -5
| -5
Line 361: Line 298:
| 3\18, 200.00
| 3\18, 200.00
| 5\31, 193.55
| 5\31, 193.55
| K
| 9/8, 10/9
| 9/8, 10/9
| +3
| +3
Line 369: Line 305:
| 4\18, 266.67
| 4\18, 266.67
| 7\31, 270.97
| 7\31, 270.97
| L
| 7/6
| 7/6
| -2
| -2
Line 377: Line 312:
| 6\18, 400.00
| 6\18, 400.00
| 10\31, 387.10
| 10\31, 387.10
| L&
| 5/4
| 5/4
| +6
| +6
Line 385: Line 319:
| 5\18, 333.33
| 5\18, 333.33
| 9\31, 348.39
| 9\31, 348.39
| M@
| ''16/13, 11/9''
| ''16/13, 11/9''
| -7
| -7
Line 393: Line 326:
| 7\18, 466.67
| 7\18, 466.67
| 12\31, 464.52
| 12\31, 464.52
| M
| 21/16, ''13/10'', 17/13
| 21/16, ''13/10'', 17/13
| +1
| +1
Line 401: Line 333:
| 8\18, 533.33
| 8\18, 533.33
| 14\31, 541.94
| 14\31, 541.94
| N@
| ''11/8''
| ''11/8''
| -4
| -4
Line 409: Line 340:
| 10\18, 666.66
| 10\18, 666.66
| 17\31, 658.06
| 17\31, 658.06
| N
| ''13/9'', ''16/11''
| ''13/9'', ''16/11''
| +4
| +4
Line 417: Line 347:
| 11\18, 733.33
| 11\18, 733.33
| 19\31, 735.48
| 19\31, 735.48
| O
| 26/17
| 26/17
| -1
| -1
Line 425: Line 354:
| 13\18, 866.66
| 13\18, 866.66
| 22\31, 851.61
| 22\31, 851.61
| O&
| ''13/8'', ''18/11''
| ''13/8'', ''18/11''
| +7
| +7
Line 433: Line 361:
| 12\18, 800.00
| 12\18, 800.00
| 21\31, 812.90
| 21\31, 812.90
| P@
| 8/5
| 8/5
| -6
| -6
Line 441: Line 368:
| 14\18, 933.33
| 14\18, 933.33
| 24\31, 929.03
| 24\31, 929.03
| P
| 12/7
| 12/7
| +2
| +2
Line 449: Line 375:
| 15\18, 1000.00
| 15\18, 1000.00
| 26\31, 1006.45
| 26\31, 1006.45
| Q
| 9/5, 16/9
| 9/5, 16/9
| -3
| -3
Line 457: Line 382:
| 17\18, 1133.33
| 17\18, 1133.33
| 29\31, 1122.58
| 29\31, 1122.58
| Q&
|
|
| +5
| +5
Line 501: Line 425:
! Size in 21edo (soft)
! Size in 21edo (soft)
! Size in 34edo (semisoft)
! Size in 34edo (semisoft)
! class="unsortable" |Note name on J
! class="unsortable" |Approximate ratios
! class="unsortable" |Approximate ratios
! #Gens up
! #Gens up
Line 508: Line 431:
| 0\21, 0.00
| 0\21, 0.00
| 0\34, 0.00
| 0\34, 0.00
| J
| 1/1
| 1/1
| 0
| 0
Line 515: Line 437:
| 2\21, 114.29
| 2\21, 114.29
| 3\34, 105.88
| 3\34, 105.88
| K@
| 16/15
| 16/15
| -5
| -5
Line 522: Line 443:
| 3\21, 171.43
| 3\21, 171.43
| 5\34, 176.47
| 5\34, 176.47
| K
| 10/9, 11/10
| 10/9, 11/10
| +3
| +3
Line 529: Line 449:
| 5\21, 285.71
| 5\21, 285.71
| 8\34, 282.35
| 8\34, 282.35
| L
| 13/11, 20/17
| 13/11, 20/17
| -2
| -2
Line 536: Line 455:
| 6\21, 342.86
| 6\21, 342.86
| 10\34, 352.94
| 10\34, 352.94
| L&
| 11/9
| 11/9
| +6
| +6
Line 543: Line 461:
| 7\21, 400.00
| 7\21, 400.00
| 11\34, 388.24
| 11\34, 388.24
| M@
| 5/4
| 5/4
| -7
| -7
Line 550: Line 467:
| 8\21, 457.14
| 8\21, 457.14
| 12\31, 458.82
| 12\31, 458.82
| M
| 13/10
| 13/10
| +1
| +1
Line 557: Line 473:
| 10\21, 571.43
| 10\21, 571.43
| 16\34, 564.72
| 16\34, 564.72
| N@
| 18/13, 32/23
| 18/13, 32/23
| -4
| -4
Line 564: Line 479:
| 11\21, 628.57
| 11\21, 628.57
| 18\34, 635.29
| 18\34, 635.29
| N
| 13/9, 23/16
| 13/9, 23/16
| +4
| +4
Line 571: Line 485:
| 13\21, 742.86
| 13\21, 742.86
| 21\34, 741.18
| 21\34, 741.18
| O
| 20/13
| 20/13
| -1
| -1
Line 578: Line 491:
| 14\21, 800.00
| 14\21, 800.00
| 23\34, 811.77
| 23\34, 811.77
| O&
| 8/5
| 8/5
| +7
| +7
Line 585: Line 497:
| 15\21, 857.14
| 15\21, 857.14
| 24\34, 847.06
| 24\34, 847.06
| P@
| 18/11
| 18/11
| -6
| -6
Line 592: Line 503:
| 16\21, 914.29
| 16\21, 914.29
| 26\34, 917.65
| 26\34, 917.65
| P
| 22/13, 17/10
| 22/13, 17/10
| +2
| +2
Line 599: Line 509:
| 18\21, 1028.57
| 18\21, 1028.57
| 29\34, 1023.53
| 29\34, 1023.53
| Q
| 9/5
| 9/5
| -3
| -3
Line 606: Line 515:
| 19\21, 1085.71
| 19\21, 1085.71
| 31\34, 1094.12
| 31\34, 1094.12
| Q&
| 15/8
| 15/8
| +5
| +5
Line 639: Line 547:
! class="unsortable" |Degree
! class="unsortable" |Degree
! Size in 29edo (supersoft)
! Size in 29edo (supersoft)
! class="unsortable" |Note name on J
! class="unsortable" |Approximate ratios (29edo)
! class="unsortable" |Approximate ratios (29edo)
!#Gens up
!#Gens up
Line 645: Line 552:
| unison
| unison
| 0\29, 0.00
| 0\29, 0.00
| J
| 1/1
| 1/1
| 0
| 0
Line 651: Line 557:
| oneirochroma
| oneirochroma
| 1\29, 41.4
| 1\29, 41.4
| J&
|
|
| +8
| +8
Line 657: Line 562:
| dim. step
| dim. step
| 2\29, 82.8
| 2\29, 82.8
| K@@
|
|
| -13
| -13
Line 663: Line 567:
| minor step
| minor step
| 3\29, 124.1
| 3\29, 124.1
| K@
| 14/13
| 14/13
| -5
| -5
Line 669: Line 572:
| major step
| major step
| 4\29, 165.5
| 4\29, 165.5
| K
| 11/10
| 11/10
| +3
| +3
Line 675: Line 577:
| aug. step
| aug. step
| 5\29, 206.9
| 5\29, 206.9
| K&
| 9/8
| 9/8
| +11
| +11
Line 681: Line 582:
| dim. 2-step
| dim. 2-step
| 6\29, 248.3
| 6\29, 248.3
| L@
| 15/13
| 15/13
| -10
| -10
Line 687: Line 587:
| minor 2-step
| minor 2-step
| 7\29, 289.7
| 7\29, 289.7
| L
| 13/11
| 13/11
| -2
| -2
Line 693: Line 592:
| major 2-step
| major 2-step
| 8\29, 331.0
| 8\29, 331.0
| L&
|
|
| +6
| +6
Line 699: Line 597:
| aug. 2-step
| aug. 2-step
| 9\29, 372.4
| 9\29, 372.4
| L&&
|
|
| +14
| +14
Line 705: Line 602:
| doubly dim. 3-step
| doubly dim. 3-step
| 9\29, 372.4
| 9\29, 372.4
| M@@
|
|
| -15
| -15
Line 711: Line 607:
| dim. 3-step
| dim. 3-step
| 10\29, 413.8
| 10\29, 413.8
| M@
| 14/11
| 14/11
| -7
| -7
Line 717: Line 612:
| perf. 3-step
| perf. 3-step
| 11\29, 455.2
| 11\29, 455.2
| M
| 13/10
| 13/10
| +1
| +1
Line 723: Line 617:
| aug. 3-step
| aug. 3-step
| 12\29, 496.6
| 12\29, 496.6
| M&
| 4/3
| 4/3
| +9
| +9
Line 729: Line 622:
| dim. 4-step
| dim. 4-step
| 13\29, 537.9
| 13\29, 537.9
| N@@
| 15/11
| 15/11
| -12
| -12
Line 735: Line 627:
| minor 4-step
| minor 4-step
| 14\29, 579.3
| 14\29, 579.3
| N@
| 7/5
| 7/5
| -4
| -4
Line 741: Line 632:
| major 4-step
| major 4-step
| 15\29 620.7
| 15\29 620.7
| N
| 10/7
| 10/7
| +4
| +4
Line 747: Line 637:
| aug. 4-step
| aug. 4-step
| 16\29 662.1
| 16\29 662.1
| N&
| 22/15
| 22/15
| +12
| +12
Line 753: Line 642:
| dim. 5-step
| dim. 5-step
| 17\29, 703.4
| 17\29, 703.4
| O@
| 3/2
| 3/2
| -9
| -9
Line 759: Line 647:
| perf. 5-step
| perf. 5-step
| 18\29, 755.2
| 18\29, 755.2
| O
| 20/13
| 20/13
| -1
| -1
Line 765: Line 652:
| aug. 5-step
| aug. 5-step
| 19\29, 786.2
| 19\29, 786.2
| O&
| 11/7
| 11/7
| +7
| +7
Line 771: Line 657:
| doubly aug. 5-step
| doubly aug. 5-step
| 20\29 827.6
| 20\29 827.6
| O&&
|
|
| +15
| +15
Line 777: Line 662:
| dim. 6-step
| dim. 6-step
| 20\29 827.6
| 20\29 827.6
| P@@
|
|
| -14
| -14
Line 783: Line 667:
| minor 6-step
| minor 6-step
| 21\29 869.0
| 21\29 869.0
| P@
|
|
| -6
| -6
Line 789: Line 672:
| major 6-step
| major 6-step
| 22\29, 910.3
| 22\29, 910.3
| P
| 22/13
| 22/13
| +2
| +2
Line 795: Line 677:
| aug. 6-step
| aug. 6-step
| 23\29, 951.7
| 23\29, 951.7
| P&
| 26/15
| 26/15
| +10
| +10
Line 801: Line 682:
| dim. 7-step
| dim. 7-step
| 24\29, 993.1
| 24\29, 993.1
| Q@
| 16/9
| 16/9
| -11
| -11
Line 807: Line 687:
| minor 7-step
| minor 7-step
| 25\29, 1034.5
| 25\29, 1034.5
| Q
| 20/11
| 20/11
| -3
| -3
Line 813: Line 692:
| major 7-step
| major 7-step
| 26\29, 1075.9
| 26\29, 1075.9
| Q&
| 13/7
| 13/7
| +5
| +5
Line 819: Line 697:
| aug. 7-step
| aug. 7-step
| 27\29, 1117.2
| 27\29, 1117.2
| Q&&
|  
|  
| +13
| +13
Line 825: Line 702:
| dim. 8-step
| dim. 8-step
| 28\29, 1158.6
| 28\29, 1158.6
| J@
|
|
| -8
| -8
Line 838: Line 714:
! class="unsortable" |Degree
! class="unsortable" |Degree
! Size in 23edo (superhard)
! Size in 23edo (superhard)
! class="unsortable" |Note name on J
! class="unsortable" |Approximate ratios (23edo)
! class="unsortable" |Approximate ratios (23edo)
! #Gens up
! #Gens up
Line 844: Line 719:
| unison
| unison
| 0\23, 0.0
| 0\23, 0.0
| J
| 1/1
| 1/1
| 0
| 0
Line 850: Line 724:
| oneirochroma
| oneirochroma
| 3\23, 156.5
| 3\23, 156.5
| J&
|
|
| +8
| +8
Line 856: Line 729:
| minor step
| minor step
| 1\23, 52.2
| 1\23, 52.2
| K@
|
|
| -5
| -5
Line 862: Line 734:
| major step
| major step
| 4\23, 208.7
| 4\23, 208.7
| K
|
|
| +3
| +3
Line 868: Line 739:
| aug. step
| aug. step
| 7\23, 365.2
| 7\23, 365.2
| K&
| 21/17, inverse φ
| 21/17, inverse φ
| +11
| +11
Line 874: Line 744:
| dim. 2-step
| dim. 2-step
| 2\23, 104.3
| 2\23, 104.3
| L@
| 17/16
| 17/16
| -10
| -10
Line 880: Line 749:
| minor 2-step
| minor 2-step
| 5\23, 260.9
| 5\23, 260.9
| L
|
|
| -2
| -2
Line 886: Line 754:
| major 2-step
| major 2-step
| 8\23, 417.4
| 8\23, 417.4
| L&
| 14/11
| 14/11
| +6
| +6
Line 892: Line 759:
| dim. 3-step
| dim. 3-step
| 6\23, 313.0
| 6\23, 313.0
| M@
| 6/5
| 6/5
| -7
| -7
Line 898: Line 764:
| perf. 3-step
| perf. 3-step
| 9\23, 469.6
| 9\23, 469.6
| M
| 21/16
| 21/16
| +1
| +1
Line 904: Line 769:
| aug. 3-step
| aug. 3-step
| 12\23, 626.1
| 12\23, 626.1
| M&
|
|
| +9
| +9
Line 910: Line 774:
| dim. 4-step
| dim. 4-step
| 7\23, 365.2
| 7\23, 365.2
| N@@
| 21/17, inverse φ
| 21/17, inverse φ
| -12
| -12
Line 916: Line 779:
| minor 4-step
| minor 4-step
| 10\23, 521.7
| 10\23, 521.7
| N@
|
|
| -4
| -4
Line 922: Line 784:
| major 4-step
| major 4-step
| 13\23, 678.3
| 13\23, 678.3
| N
|
|
| +4
| +4
Line 928: Line 789:
| aug. 4-step
| aug. 4-step
| 16\23, 834.8
| 16\23, 834.8
| N&
| 34/21, φ
| 34/21, φ
| +12
| +12
Line 934: Line 794:
| dim. 5-step
| dim. 5-step
| 11\23, 573.9
| 11\23, 573.9
| O@
|
|
| -9
| -9
Line 940: Line 799:
| perf. 5-step
| perf. 5-step
| 14\23, 730.4
| 14\23, 730.4
| O
| 32/21
| 32/21
| -1
| -1
Line 946: Line 804:
| aug. 5-step
| aug. 5-step
| 17\23, 887.0
| 17\23, 887.0
| O&
| 5/3
| 5/3
| +7
| +7
Line 952: Line 809:
| minor 6-step
| minor 6-step
| 15\23 782.6
| 15\23 782.6
| P@
| 11/7
| 11/7
| -6
| -6
Line 958: Line 814:
| major 6-step
| major 6-step
| 18\23, 939.1
| 18\23, 939.1
| P
|
|
| +2
| +2
Line 964: Line 819:
| aug. 6-step
| aug. 6-step
| 21\23, 1095.7
| 21\23, 1095.7
| P&
| 32/17
| 32/17
| +10
| +10
Line 970: Line 824:
| dim. 7-step
| dim. 7-step
| 16\23, 834.8
| 16\23, 834.8
| Q@
| 34/21, φ
| 34/21, φ
| -11
| -11
Line 976: Line 829:
| minor 7-step
| minor 7-step
| 19\23, 991.3
| 19\23, 991.3
| Q
|
|
| -3
| -3
Line 982: Line 834:
| major 7-step
| major 7-step
| 22\23, 1147.8
| 22\23, 1147.8
| Q&
|
|
| +5
| +5
Line 989: Line 840:
| dim. 8-step
| dim. 8-step
| 20\23, 1043.5
| 20\23, 1043.5
| J@
|
|
| -8
| -8
Line 1,043: Line 893:
! Size in 63edo
! Size in 63edo
! Size in POTE tuning
! Size in POTE tuning
! Note name on Q
! class="unsortable" |Approximate ratios
! class="unsortable" |Approximate ratios
! #Gens up
! #Gens up
Line 1,052: Line 901:
| 0\63, 0.00
| 0\63, 0.00
| 0.00
| 0.00
| Q
| 1/1
| 1/1
| 0
| 0
Line 1,061: Line 909:
| 12\63, 228.57
| 12\63, 228.57
| 227.07
| 227.07
| J
| 8/7
| 8/7
| +3
| +3
Line 1,070: Line 917:
| 24\63, 457.14
| 24\63, 457.14
| 453.81
| 453.81
| K
| 13/10
| 13/10
| +6
| +6
Line 1,079: Line 925:
| 25\63, 476.19
| 25\63, 476.19
| 475.63
| 475.63
| L
| 21/16
| 21/16
| +1
| +1
Line 1,088: Line 933:
| 37\63, 704.76
| 37\63, 704.76
| 702.54
| 702.54
| M
| 3/2
| 3/2
| +4
| +4
Line 1,097: Line 941:
| 49\63, 933.33
| 49\63, 933.33
| 929.45
| 929.45
| N
| 12/7, 22/13
| 12/7, 22/13
| +7
| +7
Line 1,106: Line 949:
| 50\63, 952.38
| 50\63, 952.38
| 951.27
| 951.27
| O
| 26/15
| 26/15
| +2
| +2
Line 1,115: Line 957:
| 62\63, 1180.95
| 62\63, 1180.95
| 1178.18
| 1178.18
| P
| 49/25, 160/81
| 49/25, 160/81
| +5
| +5
Retrieved from "https://en.xen.wiki/w/5L_3s"