Xenharmonic Wiki

84edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Expand on theory
Relegate 4L 5s notation to the new notation section
Line 15: Line 15:


== Intervals ==
== Intervals ==
For this table, the notation of Orwell[9] from the [[4L 5s]] page is taken. Notes are denoted as LsLsLsLss = JKLMNOPQRJ, and raising and lowering by a chroma (L − s), 3 steps in this instance, is denoted by & "amp" and a "at" (the symbol "@" unlike in the 4L 5s page cannot be used because of technical details).
{| class="wikitable"
{| class="wikitable"
|+Table of 84edo intervals
|+Table of 84edo intervals
Line 22: Line 21:
! Approximate Ratios*
! Approximate Ratios*
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[4L 5s|4L 5s Notation]]
|-
|-
| 0
| 0
Line 30: Line 28:
| P1
| P1
| D
| D
| Perfect 1sn
| P1
| J
|-
|-
| 1
| 1
Line 40: Line 35:
| ^1
| ^1
| ^D
| ^D
| Up 1sn
| ^1
| J^
|-
|-
| 2
| 2
Line 50: Line 42:
| ^^1
| ^^1
| ^^D
| ^^D
| Downaug 1sn
| vA1
| Jv&
|-
|-
| 3
| 3
Line 60: Line 49:
| ^^^1
| ^^^1
| ^^^D
| ^^^D
| Aug 1sn
| A1
| J&
|-
|-
| 4
| 4
Line 70: Line 56:
| vvvm2
| vvvm2
| vvvEb
| vvvEb
| Upaug 1sn, Downdim 2nd
| ^A1, vd2
| J^&, Kvaa
|-
|-
| 5
| 5
Line 80: Line 63:
| vvm2
| vvm2
| vvEb
| vvEb
| Dim 2nd
| d2
| Kaa
|-
|-
| 6
| 6
Line 90: Line 70:
| vm2
| vm2
| vEb
| vEb
| Updim 2nd
| ^d2
| K^aa
|-
|-
| 7
| 7
Line 100: Line 77:
| m2
| m2
| Eb
| Eb
| Downminor 2nd
| vm2
| Kva
|-
|-
| 8
| 8
Line 110: Line 84:
| ^m2
| ^m2
| ^Eb
| ^Eb
| Minor 2nd
| m2
| Ka
|-
|-
| 9
| 9
Line 120: Line 91:
| ^^m2
| ^^m2
| ^^Eb
| ^^Eb
| Upminor 2nd
| ^m2
| K^a
|-
|-
| 10
| 10
Line 130: Line 98:
| ^^^m2
| ^^^m2
| ^^^Eb
| ^^^Eb
| Downmajor 2nd
| vM2
| Kv
|-
|-
| 11
| 11
Line 140: Line 105:
| vvvM2
| vvvM2
| vvvE
| vvvE
| Major 2nd
| M2
| K
|-
|-
| 12
| 12
Line 150: Line 112:
| vvM2
| vvM2
| vvE
| vvE
| Upmajor 2nd
| ^M2
| K^
|-
|-
| 13
| 13
Line 160: Line 119:
| vM2
| vM2
| vE
| vE
| Downaug 2nd
| vA2
| Kv&
|-
|-
| 14
| 14
Line 170: Line 126:
| M2
| M2
| E
| E
| Aug 2nd
| A2
| K&
|-
|-
| 15
| 15
Line 180: Line 133:
| ^M2
| ^M2
| ^E
| ^E
| Upaug 2nd, Downdim 3rd
| ^A2, vd3
| K^&, Lva
|-
|-
| 16
| 16
Line 190: Line 140:
| ^^M2
| ^^M2
| ^^E
| ^^E
| Dim 3rd
| d3
| La
|-
|-
| 17
| 17
Line 200: Line 147:
| ^^^M2
| ^^^M2
| ^^^E
| ^^^E
| Updim 3rd
| ^d3
| L^a
|-
|-
| 18
| 18
Line 210: Line 154:
| vvvm3
| vvvm3
| vvvF
| vvvF
| Down 3rd
| v3
| Lv
|-
|-
| 19
| 19
Line 220: Line 161:
| vvm2
| vvm2
| vvF
| vvF
| Perfect 3rd
| P3
| L
|-
|-
| 20
| 20
Line 230: Line 168:
| vm3
| vm3
| vF
| vF
| Up 3rd
| ^3
| L^
|-
|-
| 21
| 21
Line 240: Line 175:
| m3
| m3
| F
| F
| Downaug 3rd
| vA3
| Lv&
|-
|-
| 22
| 22
Line 250: Line 182:
| ^m3
| ^m3
| ^F
| ^F
| Aug 3rd
| A3
| L&
|-
|-
| 23
| 23
Line 260: Line 189:
| ^^m3
| ^^m3
| ^^F
| ^^F
| Upaug 3rd, Downdim 4th
| ^A3, vd4
| L^&, Mvaa
|-
|-
| 24
| 24
Line 270: Line 196:
| ^^^m3
| ^^^m3
| ^^^F
| ^^^F
| Dim 4th
| d4
| Maa
|-
|-
| 25
| 25
Line 280: Line 203:
| vvvM3
| vvvM3
| vvvF#
| vvvF#
| Updim 4th
| ^d4
| M^aa
|-
|-
| 26
| 26
Line 290: Line 210:
| vvM3
| vvM3
| vvF#
| vvF#
| Downminor 4th
| vm4
| Mva
|-
|-
| 27
| 27
Line 300: Line 217:
| vM3
| vM3
| vF#
| vF#
| Minor 4th
| m4
| Ma
|-
|-
| 28
| 28
Line 310: Line 224:
| M3
| M3
| F#
| F#
| Upminor 4th
| ^m4
| M^a
|-
|-
| 29
| 29
Line 320: Line 231:
| ^M3
| ^M3
| ^F#
| ^F#
| Downmajor 4th
| vM4
| Mv
|-
|-
| 30
| 30
Line 330: Line 238:
| ^^M3
| ^^M3
| ^^F#
| ^^F#
| Major 4th
| M4
| M
|-
|-
| 31
| 31
Line 340: Line 245:
| ^^^M3
| ^^^M3
| ^^^F#
| ^^^F#
| Upmajor 4th
| ^M4
| M^
|-
|-
| 32
| 32
Line 350: Line 252:
| vvv4
| vvv4
| vvvG
| vvvG
| Downaug 4th
| vA4
| Mv&
|-
|-
| 33
| 33
Line 360: Line 259:
| vv4
| vv4
| vvG
| vvG
| Aug 4th
| A4
| M&
|-
|-
| 34
| 34
Line 370: Line 266:
| v4
| v4
| vG
| vG
| Downminor 5th
| vm5
| Nva
|-
|-
| 35
| 35
Line 380: Line 273:
| P4
| P4
| G
| G
| Minor 5th
| m5
| Na
|-
|-
| 36
| 36
Line 390: Line 280:
| ^4
| ^4
| ^G
| ^G
| Upminor 5th
| ^m5
| N^a
|-
|-
| 37
| 37
Line 400: Line 287:
| ^^4
| ^^4
| ^^G
| ^^G
| Downmajor 5th
| vM5
| Nv
|-
|-
| 38
| 38
Line 410: Line 294:
| ^^^4
| ^^^4
| ^^^G
| ^^^G
| Major 5th
| M5
| N
|-
|-
| 39
| 39
Line 420: Line 301:
| vvvA4
| vvvA4
| vvvG#
| vvvG#
| Upmajor 5th
| ^M5
| N^
|-
|-
| 40
| 40
Line 430: Line 308:
| vvA4
| vvA4
| vvG#
| vvG#
| Downaug 5th
| vA5
| Nv&
|-
|-
| 41
| 41
Line 440: Line 315:
| vA4
| vA4
| vG#
| vG#
| Aug 5th
| A5
| N&
|-
|-
| 42
| 42
Line 450: Line 322:
| A4, d5
| A4, d5
| G#, Ab
| G#, Ab
| Upaug 5th, Downdim 6th
| ^A5, vd6
| N^&, Ovaa
|-
|-
| 43
| 43
Line 460: Line 329:
| ^d5
| ^d5
| ^Ab
| ^Ab
| Dim 6th
| d6
| Oaa
|-
|-
| 44
| 44
Line 470: Line 336:
| ^^d5
| ^^d5
| ^^Ab
| ^^Ab
| Updim 6th
| ^d6
| O^aa
|-
|-
| 45
| 45
Line 480: Line 343:
| ^^^d5
| ^^^d5
| ^^^Ab
| ^^^Ab
| Downminor 6th
| vm6
| Ova
|-
|-
| 46
| 46
Line 490: Line 350:
| vvv5
| vvv5
| vvvA
| vvvA
| Minor 6th
| m6
| Oa
|-
|-
| 47
| 47
Line 500: Line 357:
| vv5
| vv5
| vvA
| vvA
| Upminor 6th
| ^m6
| O^a
|-
|-
| 48
| 48
Line 510: Line 364:
| v5
| v5
| vA
| vA
| Downmajor 6th
| vM6
| Ov
|-
|-
| 49
| 49
Line 520: Line 371:
| P5
| P5
| A
| A
| Major 6th
| M6
| O
|-
|-
| 50
| 50
Line 530: Line 378:
| ^5
| ^5
| ^A
| ^A
| Upmajor 6th
| ^M6
| O^
|-
|-
| 51
| 51
Line 540: Line 385:
| ^^5
| ^^5
| ^^A
| ^^A
| Dim 7th
| d7
| Paa
|-
|-
| 52
| 52
Line 550: Line 392:
| ^^^5
| ^^^5
| ^^^A
| ^^^A
| Aug 6th
| A6
| O&
|-
|-
| 53
| 53
Line 560: Line 399:
| vvvm6
| vvvm6
| vvvBb
| vvvBb
| Downminor 7th
| vm7
| Pva
|-
|-
| 54
| 54
Line 570: Line 406:
| vvm6
| vvm6
| vvBb
| vvBb
| Minor 7th
| m7
| Pa
|-
|-
| 55
| 55
Line 580: Line 413:
| vm6
| vm6
| vBb
| vBb
| Upminor 7th
| ^m7
| P^a
|-
|-
| 56
| 56
Line 590: Line 420:
| m6
| m6
| Bb
| Bb
| Downmajor 7th
| vM7
| Pv
|-
|-
| 57
| 57
Line 600: Line 427:
| ^m6
| ^m6
| ^Bb
| ^Bb
| Major 7th
| M7
| P
|-
|-
| 58
| 58
Line 610: Line 434:
| ^^m6
| ^^m6
| ^^Bb
| ^^Bb
| Upmajor 7th
| ^M7
| P^
|-
|-
| 59
| 59
Line 620: Line 441:
| ^^^m6
| ^^^m6
| ^^^Bb
| ^^^Bb
| Downaug 7th
| vA7
| Pv&
|-
|-
| 60
| 60
Line 630: Line 448:
| vvvM6
| vvvM6
| vvvB
| vvvB
| Aug 7th
| A7
| P&
|-
|-
| 61
| 61
Line 640: Line 455:
| vvM6
| vvM6
| vvB
| vvB
| Upaug 7th, Downdim 8th
| ^A7, vd8
| P^&, Qvaa
|-
|-
| 62
| 62
Line 650: Line 462:
| vM6
| vM6
| vB
| vB
| Dim 8th
| d8
| Qaa
|-
|-
| 63
| 63
Line 660: Line 469:
| M6
| M6
| B
| B
| Updim 8th
| ^d8
| Q^aa
|-
|-
| 64
| 64
Line 670: Line 476:
| ^M6
| ^M6
| ^B
| ^B
| Down 8th
| v8
| Qva
|-
|-
| 65
| 65
Line 680: Line 483:
| ^^M6
| ^^M6
| ^^B
| ^^B
| Perfect 8th
| P8
| Qa
|-
|-
| 66
| 66
Line 690: Line 490:
| ^^^M6
| ^^^M6
| ^^^B
| ^^^B
| Up 8th
| ^8
| Q^a
|-
|-
| 67
| 67
Line 700: Line 497:
| vvvm7
| vvvm7
| vvvC
| vvvC
| Downaug 8th
| vA8
| Qv
|-
|-
| 68
| 68
Line 710: Line 504:
| vvm7
| vvm7
| vvC
| vvC
| Aug 8th
| A8
| Q
|-
|-
| 69
| 69
Line 720: Line 511:
| vm7
| vm7
| vC
| vC
| Upaug 8th, Downdim 9th
| ^A8, vd9
| Q^, Rvaa
|-
|-
| 70
| 70
Line 730: Line 518:
| m7
| m7
| C
| C
| Dim 9th
| d9
| Raa
|-
|-
| 71
| 71
Line 740: Line 525:
| ^m7
| ^m7
| ^C
| ^C
| Updim 9th
| ^d9
| R^aa
|-
|-
| 72
| 72
Line 750: Line 532:
| ^^m7
| ^^m7
| ^^C
| ^^C
| Downminor 9th
| vm9
| Rva
|-
|-
| 73
| 73
Line 760: Line 539:
| ^^^m7
| ^^^m7
| ^^^C
| ^^^C
| Minor 9th
| m9
| Ra
|-
|-
| 74
| 74
Line 770: Line 546:
| vvvM7
| vvvM7
| vvvC#
| vvvC#
| Upminor 9th
| ^m9
| R^a
|-
|-
| 75
| 75
Line 780: Line 553:
| vvM7
| vvM7
| vvC#
| vvC#
| Downmajor 9th
| vM9
| Rv
|-
|-
| 76
| 76
Line 790: Line 560:
| vM7
| vM7
| vC#
| vC#
| Major 9th
| M9
| R
|-
|-
| 77
| 77
Line 800: Line 567:
| M7
| M7
| C#
| C#
| Upmajor 9th
| ^M9
| R^
|-
|-
| 78
| 78
Line 810: Line 574:
| ^M7
| ^M7
| ^C#
| ^C#
| Downaug 9th
| vA9
| Rv&
|-
|-
| 79
| 79
Line 820: Line 581:
| ^^M7
| ^^M7
| ^^C#
| ^^C#
| Aug 9th
| A9
| R&
|-
|-
| 80
| 80
Line 830: Line 588:
| ^^^M7
| ^^^M7
| ^^^C#
| ^^^C#
| Upaug 9th, Downdim 10th
| ^A9, vd10
| R^&, Jva
|-
|-
| 81
| 81
Line 840: Line 595:
| vvv8
| vvv8
| vvvD
| vvvD
| Dim 10th
| d10
| Ja
|-
|-
| 82
| 82
Line 850: Line 602:
| vv8
| vv8
| vvD
| vvD
| Updim 10th
| ^d10
| J^a
|-
|-
| 83
| 83
Line 860: Line 609:
| v8
| v8
| vD
| vD
| Down 10th
| v10
| Jv
|-
|-
| 84
| 84
Line 870: Line 616:
| P8
| P8
| D
| D
| Perfect 10th
|}
| P10
<nowiki>*</nowiki> as a 2.3.5.7.13-subgroup temperament
 
== Notation ==
=== 4L 5s (gramitonic) notation ===
The notation of Orwell[9]. Notes are denoted as LsLsLsLss = JKLMNOPQRJ, and raising and lowering by a chroma (L − s), 3 steps in this instance, is denoted by & "amp" and @ "at".
 
{| class="wikitable center-1 right-2 center-3"
|-
! #
! Cents
! Note
! Name
! Associated Ratio
|-
| 0
| 0.0
| J
| J
| Perfect 0-gramstep
| 1/1
|-
| 8
| 114.3
| K@
| Minor 1-gramstep
| 15/14~16/15
|-
| 11
| 157.1
| K
| Major 1-gramstep
| 11/10~12/11
|-
|-
| 16
| 228.6
| L@
| Diminished 2-gramstep
| 8/7
|-
| 19
| 271.4
| L
| Perfect 2-gramstep
| 7/6
|-
| 27
| 385.7
| M@
| Minor 3-gramstep
| 5/4
|-
| 30
| 428.6
| M
| Major 3-gramstep
| 9/7
|-
| 35
| 500.0
| N@
| Minor 4-gramstep
| 4/3
|-
| 38
| 542.9
| N
| Major 4-gramstep
| 11/8~15/11
|-
| 46
| 657.1
| O@
| Minor 5-gramstep
| 16/11~22/15
|-
| 49
| 700.0
| O
| Major 5-gramstep
| 3/2
|-
| 54
| 771.4
| P@
| Minor 6-gramstep
| 14/9
|-
| 57
| 814.3
| P
| Major 6-gramstep
| 8/5
|-
| 65
| 928.6
| Q@
| Perfect 7-gramstep
| 12/7
|-
| 68
| 971.4
| Q
| Augmented 7-gramstep
| 7/4
|-
| 73
| 1042.9
| R@
| Minor 8-gramstep
| 11/6~20/11
|-
| 76
| 1085.7
| R
| Major 8-gramstep
| 15/8~28/15
|-
| 84
| 1200.0
| J
| Perfect 9-gramstep
| 2/1
|}
|}
<nowiki>*</nowiki> as a 2.3.5.7.13-subgroup temperament


== Regular temperament properties ==
== Regular temperament properties ==
Retrieved from "https://en.xen.wiki/w/84edo"