Xenharmonic Wiki

5L 3s: Difference between revisions

← Older editNewer edit →
VisualWikitext
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,004 edits
mNo edit summary
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,004 edits
m changing the default mode on J to Ultharian for the explained reasons
Line 592: Line 592:


== Notation==
== Notation==
The notation used in this article is J Celephaïsian (LsLLsLLs) = JKLMNOPQJ, with reference pitch J = 180 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".)  
The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch J = 180 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.


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


'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M''' M&/N@ '''N/O@''' '''O/N&''' O&/P@ '''P''' P&/Q@ '''Q/J@''' '''J'''
'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M''' M&/N@ '''N/O@''' '''O/N&''' O&/P@ '''P''' '''Q''' Q&/J@ '''J'''


The [[18edo]] gamut is notated as follows:
The [[18edo]] gamut is notated as follows:


'''J''' Q&/K@ J&/L@ '''K''' '''L''' K&/M@ L& '''M''' N@ M&/O@ '''N''' '''O''' P@ O& '''P''' Q@ P&/J@ '''Q''' '''J'''
'''J''' Q&/K@ J&/L@ '''K''' '''L''' K&/M@ L& '''M''' N@ M&/O@ '''N''' '''O''' P@ O& '''P''' '''Q''' P&/J@ Q@ '''J'''


The [[21edo]] gamut:
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'''
'''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'''


Note: N is close to standard C, since the reference pitch 180 Hz for J was chosen to be nearly a pure 16/11 below standard 12edo C.
Note: N is close to standard C, since the reference pitch 180 Hz for J was chosen to be nearly a pure 16/11 below standard 12edo C.
The oneirotonic scale shown in [[Diamond MOS notation]]. The white boxes show where the small steps are, and the diamonds show the reference pitch and octaves above and below it (the white diamond is the reference pitch).
[[File:Oneiro Diamond MOS Notation.jpg|600px]]


== Intervals ==
== Intervals ==
Line 649: Line 645:
| major mossecond
| major mossecond
| -3
| -3
| Q@
| Q
| minor moseighth
| minor moseighth
|-
|-
Line 660: Line 656:
|-
|-
| 5
| 5
| Q
| Q&
| major moseighth
| major moseighth
| -5
| -5
Line 707: Line 703:
| augmented mossecond
| augmented mossecond
| -11
| -11
| Q@@
| Q@
| diminished moseighth
| diminished moseighth
|-
|-
Line 720: Line 716:
== Key signatures ==
== Key signatures ==
Flat keys:
Flat keys:
* J@ Celephaïsian, L@ Dylathian = Q@, N@, K@, P@, M@, J@, O@, L@
* J@ Ultharian, L@ Illarnekian = Q@, N@, K@, P@, M@, J@, O@, L@
* M@ Celephaïsian, O@ Dylathian = Q@, N@, K@, P@, M@, J@, O@
* M@ Ultharian, O@ Illarnekian = Q@, N@, K@, P@, M@, J@, O@
* P@ Celephaïsian, J@ Dylathian = Q@, N@, K@, P@, M@, J@
* P@ Ultharian, J@ Illarnekian = Q@, N@, K@, P@, M@, J@
* K@ Celephaïsian, M@ Dylathian = Q@, N@, K@, P@, M@
* K@ Ultharian, M@ Illarnekian = Q@, N@, K@, P@, M@
* N@ Celephaïsian, P@ Dylathian = Q@, N@, K@, P@
* N@ Ultharian, P@ Illarnekian = Q@, N@, K@, P@
* Q@ Celephaïsian, K@ Dylathian = Q@, N@, K@
* Q@ Ultharian, K@ Illarnekian = Q@, N@, K@
* L Celephaïsian, N@ Dylathian = Q@, N@
* L Ultharian, N@ Illarnekian = Q@, N@
* O Celephaïsian, Q@ Dylathian = Q@
* O Ultharian, Q@ Illarnekian = Q@
All-natural key signature:
All-natural key signature:
* J Celephaïsian, L Dylathian = no sharps or flats
* J Ultharian, L Illarnekian = no sharps or flats
Sharp keys:
Sharp keys:
* M Celephaïsian, O Dylathian = L&
* M Ultharian, O Illarnekian = L&
* P Celephaïsian, J Dylathian = L&, O&
* P Ultharian, J Illarnekian = L&, O&
* K Celephaïsian, M Dylathian = L&, O&, J&
* K Ultharian, M Illarnekian = L&, O&, J&
* N Celephaïsian, P Dylathian = L&, O&, J&, M&
* N Ultharian, P Illarnekian = L&, O&, J&, M&
* Q Celephaïsian, K Dylathian = L&, O&, J&, M&, P&
* Q Ultharian, K Illarnekian = L&, O&, J&, M&, P&
** Enharmonic with J@ Celeph., L@ Dylath. in [[13edo]]
** Enharmonic with J@ Ulthar., L@ Illar. in [[13edo]]
* L& Celephaïsian, N Dylathian = L&, O&, J&, M&, P&, K&
* L& Ultharian, N Illarnekian = L&, O&, J&, M&, P&, K&
** Enharmonic with M@ Celeph., O@ Dylath. in 13edo
** Enharmonic with M@ Ulthar., O@ Illar. in 13edo
* O& Celephaïsian, Q Dylathian = L&, O&, J&, M&, P&, K&, N&
* O& Ultharian, Q Illarnekian = L&, O&, J&, M&, P&, K&, N&
** Enharmonic with P@ Celeph., J@ Dylath. in 13edo
** Enharmonic with P@ Ulthar., J@ Illar. in 13edo
* J& Celephaïsian, L& Dylathian = L&, O&, J&, M&, P&, K&, N&, Q&
* J& Ultharian, L& Illarnekian = L&, O&, J&, M&, P&, K&, N&, Q&
** Enharmonic with K@ Celeph., M@ Dylath. in 13edo
** Enharmonic with K@ Ulthar., M@ Illar. in 13edo


== Modes ==
== Modes ==
Line 757: Line 753:


The modes on the white keys JKLMNOPQJ are:
The modes on the white keys JKLMNOPQJ are:
* J Celephaïsian
* J Ultharian
* K Kadathian
* K Hlanithian
* L Dylathian
* L Illarnekian
* M Ultharian
* M Mnarian
* N Hlanithian
* N Sarnathian
* O Illarnekian
* O Celephaïsian
* P Mnarian
* P Kadathian
* Q Sarnathian
* Q Dylathian


{| class="wikitable"
{| class="wikitable"
Line 781: Line 777:
! (9)
! (9)
|-
|-
| III. Dylathian
| Dylathian
| J
| J
| K
| K
Line 789: Line 785:
| O&
| O&
| P
| P
| Q
| Q&
| (J)
| (J)
|-
|-
| VI. Illarnekian
| Illarnekian
| J
| J
| K
| K
Line 800: Line 796:
| O
| O
| P
| P
| Q
| Q&
| (J)
| (J)
|-
|-
| I. Celephaïsian
| Celephaïsian
| J
| J
| K
| K
Line 811: Line 807:
| O
| O
| P
| P
| Q
| Q&
| (J)
| (J)
|-
|-
| IV. Ultharian
| Ultharian
| J
| J
| K
| K
Line 822: Line 818:
| O
| O
| P
| P
| Q@
| Q
| (J)
| (J)
|-
|-
| VII. Mnarian
| Mnarian
| J
| J
| K
| K
Line 833: Line 829:
| O
| O
| P
| P
| Q@
| Q
| (J)
| (J)
|-
|-
| II. Kadathian
| Kadathian
| J
| J
| K@
| K@
Line 844: Line 840:
| O
| O
| P
| P
| Q@
| Q
| (J)
| (J)
|-
|-
| V. Hlanithian
| Hlanithian
| J
| J
| K@
| K@
Line 855: Line 851:
| O
| O
| P@
| P@
| Q@
| Q
| (J)
| (J)
|-
|-
| VIII. Sarnathian
| Sarnathian
| J
| J
| K@
| K@
Line 866: Line 862:
| O
| O
| P@
| P@
| Q@
| Q
| (J)
| (J)
|}
|}
Line 1,182: Line 1,178:
! Size in 37edo
! Size in 37edo
! Size in POTE tuning
! Size in POTE tuning
! Note name on L
! Note name on Q
! class="unsortable"| Approximate ratios
! class="unsortable"| Approximate ratios
! #Gens up
! #Gens up
Line 1,191: Line 1,187:
| 0\37, 0.00
| 0\37, 0.00
| 0.00
| 0.00
| L
| Q
| 1/1
| 1/1
| 0
| 0
Line 1,200: Line 1,196:
| 5\37, 163.16
| 5\37, 163.16
| 165.65
| 165.65
| M
| J
| 11/10, 10/9
| 11/10, 10/9
| +3
| +3
Line 1,209: Line 1,205:
| 10\37, 324.32
| 10\37, 324.32
| 331.31
| 331.31
| N
| K
| 11/9, 6/5
| 11/9, 6/5
| +6
| +6
Line 1,218: Line 1,214:
| 14\37, 454.05
| 14\37, 454.05
| 455.17
| 455.17
| O
| L
| 13/10, 9/7
| 13/10, 9/7
| +1
| +1
Line 1,227: Line 1,223:
| 19\37, 616.22
| 19\37, 616.22
| 620.87
| 620.87
| P
| M
| 13/9, 10/7
| 13/9, 10/7
| +4
| +4
Line 1,236: Line 1,232:
| 23\37, 778.38
| 23\37, 778.38
| 786.52
| 786.52
| Q
| N
| 11/7
| 11/7
| +7
| +7
Line 1,245: Line 1,241:
| 28\37, 908.11
| 28\37, 908.11
| 910.44
| 910.44
| J
| O
| 22/13
| 22/13
| +2
| +2
Line 1,254: Line 1,250:
| 33\37, 1070.27
| 33\37, 1070.27
| 1076.09
| 1076.09
| K
| P
| 13/7, 28/15
| 13/7, 28/15
| +5
| +5
Line 1,290: Line 1,286:
! Size in 34edo
! Size in 34edo
! Size in POTE tuning
! Size in POTE tuning
! Note name on L
! Note name on Q
! class="unsortable"| Approximate ratios
! class="unsortable"| Approximate ratios
! #Gens up
! #Gens up
Line 1,299: Line 1,295:
| 0\34, 0.00
| 0\34, 0.00
| 0.00
| 0.00
| L
| Q
| 1/1
| 1/1
| 0
| 0
Line 1,308: Line 1,304:
| 5\34, 176.47
| 5\34, 176.47
| 177.45
| 177.45
| M
| J
| 10/9, 11/10
| 10/9, 11/10
| +3
| +3
Line 1,317: Line 1,313:
| 10\34, 352.94
| 10\34, 352.94
| 354.90
| 354.90
| N
| K
| 11/9, 16/13
| 11/9, 16/13
| +6
| +6
Line 1,326: Line 1,322:
| 13\34, 458.82
| 13\34, 458.82
| 459.15
| 459.15
| O
| L
| 13/10, 17/13, 22/17
| 13/10, 17/13, 22/17
| +1
| +1
Line 1,335: Line 1,331:
| 18\34, 635.294  
| 18\34, 635.294  
| 636.60
| 636.60
| P
| M
| 13/9, 16/11
| 13/9, 16/11
| +4
| +4
Line 1,344: Line 1,340:
| 23\34, 811.77
| 23\34, 811.77
| 814.05
| 814.05
| Q
| N
| 8/5
| 8/5
| +7
| +7
Line 1,353: Line 1,349:
| 26\34, 917.65
| 26\34, 917.65
| 918.30
| 918.30
| J
| O
| 17/10
| 17/10
| +2
| +2
Line 1,362: Line 1,358:
| 31\34, 1094.12
| 31\34, 1094.12
| 1095.75
| 1095.75
| K
| P
| 17/9, 32/17
| 17/9, 32/17
| +5
| +5
Line 1,398: Line 1,394:
! Size in 18edo
! Size in 18edo
! Size in 31edo
! Size in 31edo
! Note name on L
! Note name on Q
! 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 1,406: Line 1,402:
| 0\18, 0.00
| 0\18, 0.00
| 0\31, 0.00
| 0\31, 0.00
| L
| Q
| 1/1
| 1/1
| 0
| 0
Line 1,414: Line 1,410:
| 3\18, 200.00
| 3\18, 200.00
| 5\31, 193.55
| 5\31, 193.55
| M
| J
| 9/8, 10/9
| 9/8, 10/9
| +3
| +3
Line 1,422: Line 1,418:
| 6\18, 400.00
| 6\18, 400.00
| 10\31, 387.10
| 10\31, 387.10
| N
| K
| 5/4
| 5/4
| +6
| +6
Line 1,430: Line 1,426:
| 7\18, 466.67
| 7\18, 466.67
| 12\31, 464.52
| 12\31, 464.52
| O
| L
| 21/16, ''13/10''
| 21/16, ''13/10''
| +1
| +1
Line 1,438: Line 1,434:
| 10\18, 666.66
| 10\18, 666.66
| 17\31, 658.06
| 17\31, 658.06
| P
| M
| ''13/9'', ''16/11''
| ''13/9'', ''16/11''
| +4
| +4
Line 1,446: Line 1,442:
| 13\18, 866.66
| 13\18, 866.66
| 22\31, 851.61
| 22\31, 851.61
| Q
| N
| ''13/8'', ''18/11''
| ''13/8'', ''18/11''
| +7
| +7
Line 1,454: Line 1,450:
| 14\18, 933.33
| 14\18, 933.33
| 24\31, 929.03
| 24\31, 929.03
| J
| O
| 12/7
| 12/7
| +2
| +2
Line 1,462: Line 1,458:
| 17\18, 1133.33
| 17\18, 1133.33
| 29\31, 1122.58  
| 29\31, 1122.58  
| K
| P
|  
|  
| +5
| +5
Line 1,504: Line 1,500:
! Size in 63edo
! Size in 63edo
! Size in POTE tuning
! Size in POTE tuning
! Note name on L
! Note name on Q
! class="unsortable"| Approximate ratios
! class="unsortable"| Approximate ratios
! #Gens up
! #Gens up
Line 1,513: Line 1,509:
| 0\63, 0.00
| 0\63, 0.00
| 0.00
| 0.00
| L
| Q
| 1/1
| 1/1
| 0
| 0
Line 1,522: Line 1,518:
| 12\63, 228.57
| 12\63, 228.57
| 227.07
| 227.07
| M
| J
| 8/7
| 8/7
| +3
| +3
Line 1,531: Line 1,527:
| 24\63, 457.14
| 24\63, 457.14
| 453.81
| 453.81
| N
| K
| 13/10, 9/7
| 13/10, 9/7
| +6
| +6
Line 1,540: Line 1,536:
| 25\63, 476.19
| 25\63, 476.19
| 475.63
| 475.63
| O
| L
| 21/16
| 21/16
| +1
| +1
Line 1,549: Line 1,545:
| 37\63, 704.76
| 37\63, 704.76
| 702.54
| 702.54
| P
| M
| 3/2
| 3/2
| +4
| +4
Line 1,558: Line 1,554:
| 49\63, 933.33
| 49\63, 933.33
| 929.45
| 929.45
| Q
| N
| 12/7, 22/13
| 12/7, 22/13
| +7
| +7
Line 1,567: Line 1,563:
| 50\63, 952.38
| 50\63, 952.38
| 951.27
| 951.27
| J
| O
| 26/15
| 26/15
| +2
| +2
Line 1,576: Line 1,572:
| 62\63, 1180.95
| 62\63, 1180.95
| 1178.18
| 1178.18
| K
| P
| 108/55, 160/81
| 108/55, 160/81
| +5
| +5
Retrieved from "https://en.xen.wiki/w/5L_3s"