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=== Other ===
=== Other ===
84edo is a significantly composite number, with divisors 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Being a small multiple of 12, it tempres out the [[Pythagorean comma]], thus supporting period-12 temperament [[compton]]. Being a small multiple of 28, it tempers out the [[oquatonic comma]], which maps 5/4 to 9\28.{{Primes in edo|84}}
84edo is a significantly composite number, with divisors of 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Being a small multiple of 12, it tempers out the [[Pythagorean comma]], thus supporting period-12 temperament [[compton]]. Being a small multiple of 28, it tempers out the [[Oquatonic|oquatonic comma]], which maps 5/4 to 9\28.{{Primes in edo|84}}


== Table of intervals ==
== Table of intervals ==
Line 22: Line 22:
{| class="wikitable"
{| class="wikitable"
|+Table of 84edo intervals
|+Table of 84edo intervals
!Step
! Degree
!Size (Cents)
! Size (Cents)
!Orwell note
! colspan="3" | [[Ups and Downs Notation]]
(if tonic is J)
! colspan="3" | [[4L 5s|4L 5s Notation]]
!Orwellian Name
! Associated ratio
!Associated ratio
|-
|-
|0
| 0
|0.000
| 0.000
|J
| Perfect 1sn
|unison, prime
| P1
|1/1 exact
| D
| Perfect 1sn
| P1
| J
| 1/1 exact
|-
|-
|3
| 1
|42.857
| 14.286
|J&
| Up 1sn
|
| ^1
|
| ^D
| Up 1sn
| ^1
| J^
|
|-
| 2
| 28.571
| Dup 1sn
| ^^1
| ^^D
| Downaug 1sn
| vA1
| Jv&
|
|-
| 3
| 42.857
| Trup 1sn
| ^^^1
| ^^^D
| Aug 1sn
| A1
| J&
|  
|-
| 4
| 57.143
| Trudminor 2nd
| vvvm2
| vvvEb
| Upaug 1sn, Downdim 2nd
| ^A1, vd2
| J^&, Kv@@
|
|-
| 5
| 71.429
| Dudminor 2nd
| vvm2
| vvEb
| Dim 2nd
| d2
| K@@
|
|-
| 6
| 85.714
| Downminor 2nd
| vm2
| vEb
| Updim 2nd
| ^d2
| K^@@
|
|-
| 7
| 100.000
| Minor 2nd
| m2
| Eb
| Downminor 2nd
| vm2
| Kv@
|
|-
| 8
| 114.286
| Upminor 2nd
| ^m2
| ^Eb
| Minor 2nd
| m2
| K@
|
|-
| 9
| 128.571
| Dupminor 2nd
| ^^m2
| ^^Eb
| Upminor 2nd
| ^m2
| K^@
|
|-
| 10
| 142.857
| Trupminor 2nd
| ^^^m2
| ^^^Eb
| Downmajor 2nd
| vM2
| Kv
|
|-
| 11
| 157.143
| Trudmajor 2nd
| vvvM2
| vvvE
| Major 2nd
| M2
| K
|
|-
| 12
| 171.429
| Dudmajor 2nd
| vvM2
| vvE
| Upmajor 2nd
| ^M2
| K^
|
|-
| 13
| 185.714
| Downmajor 2nd
| vM2
| vE
| Downaug 2nd
| vA2
| Kv&
|
|-
| 14
| 200.000
| Major 2nd
| M2
| E
| Aug 2nd
| A2
| K&
|
|-
| 15
| 214.286
| Upmajor 2nd
| ^M2
| ^E
| Upaug 2nd, Downdim 3rd
| ^A2, vd3
| K^&, Lv@
|
|-
| 16
| 228.571
| Dupmajor 2nd
| ^^M2
| ^^E
| Dim 3rd
| d3
| L@
|
|-
| 17
| 242.857
| Trupmajor 2nd
| ^^^M2
| ^^^E
| Updim 3rd
| ^d3
| L^@
|
|-
| 18
| 257.143
| Trudminor 3rd
| vvvm3
| vvvF
| Down 3rd
| v3
| Lv
|
|-
| 19
| 271.429
| Dudminor 3rd
| vvm2
| vvF
| Perfect 3rd
| P3
| L
| [[7/6]]
|-
| 20
| 285.714
| Downminor 3rd
| vm3
| vF
| Up 3rd
| ^3
| L^
|
|-
| 21
| 300.000
| Minor 3rd
| m3
| F
| Downaug 3rd
| vA3
| Lv&
|
|-
| 22
| 314.286
| Upminor 3rd
| ^m3
| ^F
| Aug 3rd
| A3
| L&
|
|-
| 23
| 328.571
| Dupminor 3rd
| ^^m3
| ^^F
| Upaug 3rd, Downdim 4th
| ^A3, vd4
| L^&, Mv@@
|
|-
| 24
| 342.857
| Trupminor 3rd
| ^^^m3
| ^^^F
| Dim 4th
| d4
| M@@
|
|-
| 25
| 357.143
| Trudmajor 3rd
| vvvM3
| vvvF#
| Updim 4th
| ^d4
| M^@@
|
|-
| 26
| 371.429
| Dudmajor 3rd
| vvM3
| vvF#
| Downminor 4th
| vm4
| Mv@
|
|-
| 27
| 385.714
| Downmajor 3rd
| vM3
| vF#
| Minor 4th
| m4
| M@
|
|-
| 28
| 400.000
| Major 3rd
| M3
| F#
| Upminor 4th
| ^m4
| M^@
|
|-
| 29
| 414.286
| Upmajor 3rd
| ^M3
| ^F#
| Downmajor 4th
| vM4
| Mv
|
|-
| 30
| 428.571
| Dupmajor 3rd
| ^^M3
| ^^F#
| Major 4th
| M4
| M
|
|-
| 31
| 442.857
| Trupmajor 3rd
| ^^^M3
| ^^^F#
| Upmajor 4th
| ^M4
| M^
|
|-
| 32
| 457.143
| Trud 4th
| vvv4
| vvvG
| Downaug 4th
| vA4
| Mv&
|
|-
| 33
| 471.429
| Dud 4th
| vv4
| vvG
| Aug 4th
| A4
| M&
|
|-
| 34
| 485.714
| Down 4th
| v4
| vG
| Downminor 5th
| vm5
| Nv@
|
|-
| 35
| 500.000
| Perfect 4th
| P4
| G
| Minor 5th
| m5
| N@
|
|-
| 36
| 514.286
| Up 4th
| ^4
| ^G
| Upminor 5th
| ^m5
| N^@
|
|-
| 37
| 528.571
| Dup 4th
| ^^4
| ^^G
| Downmajor 5th
| vM5
| Nv
|
|-
| 38
| 542.857
| Trup 4th
| ^^^4
| ^^^G
| Major 5th
| M5
| N
| [[11/8]] in the 84b val
|-
| 39
| 557.143
| Trudaug 4th
| vvvA4
| vvvG#
| Upmajor 5th
| ^M5
| N^
|
|-
| 40
| 571.429
| Dudaug 4th
| vvA4
| vvG#
| Downaug 5th
| vA5
| Nv&
|
|-
| 41
| 585.714
| Downaug 4th
| vA4
| vG#
| Aug 5th
| A5
| N&
|
|-
| 42
| 600.000
| Aug 4th, Dim 5th
| A4, d5
| G#, Ab
| Upaug 5th, Downdim 6th
| ^A5, vd6
| N^&, Ov@@
|
|-
| 43
| 614.286
| Updim 5th
| ^d5
| ^Ab
| Dim 6th
| d6
| O@@
|
|-
| 44
| 628.571
| Dupdim 5th
| ^^d5
| ^^Ab
| Updim 6th
| ^d6
| O^@@
|
|-
| 45
| 642.857
| Trupdim 5th
| ^^^d5
| ^^^Ab
| Downminor 6th
| vm6
| Ov@
|
|-
| 46
| 657.143
| Trud 5th
| vvv5
| vvvA
| Minor 6th
| m6
| O@
|
|-
| 47
| 671.429
| Dud 5th
| vv5
| vvA
| Upminor 6th
| ^m6
| O^@
|
|-
| 48
| 685.714
| Down 5th
| v5
| vA
| Downmajor 6th
| vM6
| Ov
|
|-
| 49
| 700.000
| Perfect 5th
| P5
| A
| Major 6th
| M6
| O
| [[3/2]]
|-
| 50
| 714.286
| Up 5th
| ^5
| ^A
| Upmajor 6th
| ^M6
| O^
|
|-
| 51
| 728.571
| Dup 5th
| ^^5
| ^^A
| Dim 7th
| d7
| P@@
|
|-
| 52
| 742.857
| Trup 5th
| ^^^5
| ^^^A
| Aug 6th
| A6
| O&
|
|-
| 53
| 757.143
| Trudminor 6th
| vvvm6
| vvvBb
| Downminor 7th
| vm7
| Pv@
|
|-
| 54
| 771.429
| Dudminor 6th
| vvm6
| vvBb
| Minor 7th
| m7
| P@
|
|-
| 55
| 785.714
| Downminor 6th
| vm6
| vBb
| Upminor 7th
| ^m7
| P^@
|
|-
| 56
| 800.000
| Minor 6th
| m6
| Bb
| Downmajor 7th
| vM7
| Pv
|
|-
| 57
| 814.286
| Upminor 6th
| ^m6
| ^Bb
| Major 7th
| M7
| P
| [[5/3]]
|-
| 58
| 828.571
| Dupminor 6th
| ^^m6
| ^^Bb
| Upmajor 7th
| ^M7
| P^
|
|-
| 59
| 842.857
| Trupminor 6th
| ^^^m6
| ^^^Bb
| Downaug 7th
| vA7
| Pv&
|
|-
| 60
| 857.143
| Trudmajor 6th
| vvvM6
| vvvB
| Aug 7th
| A7
| P&
| [[105/64]]
|-
| 61
| 871.429
| Dudmajor 6th
| vvM6
| vvB
| Upaug 7th, Downdim 8th
| ^A7, vd8
| P^&, Qv@@
|
|-
| 62
| 885.714
| Downmajor 6th
| vM6
| vB
| Dim 8th
| d8
| Q@@
|
|-
| 63
| 900.000
| Major 6th
| M6
| B
| Updim 8th
| ^d8
| Q^@@
|
|-
| 64
| 914.286
| Upmajor 6th
| ^M6
| ^B
| Down 8th
| v8
| Qv@
|
|-
| 65
| 928.571
| Dupmajor 6th
| ^^M6
| ^^B
| Perfect 8th
| P8
| Q@
|
|-
| 66
| 942.857
| Trupmajor 6th
| ^^^M6
| ^^^B
| Up 8th
| ^8
| Q^@
|
|-
| 67
| 957.143
| Trudminor 7th
| vvvm7
| vvvC
| Downaug 8th
| vA8
| Qv
|
|-
| 68
| 971.429
| Dudminor 7th
| vvm7
| vvC
| Aug 8th
| A8
| Q
|
|-
| 69
| 985.714
| Downminor 7th
| vm7
| vC
| Upaug 8th, Downdim 9th
| ^A8, vd9
| Q^, Rv@@
|
|-
| 70
| 1000.000
| Minor 7th
| m7
| C
| Dim 9th
| d9
| R@@
|
|-
| 71
| 1014.286
| Upminor 7th
| ^m7
| ^C
| Updim 9th
| ^d9
| R^@@
|
|-
| 72
| 1028.571
| Dupminor 7th
| ^^m7
| ^^C
| Downminor 9th
| vm9
| Rv@
|
|-
| 73
| 1042.857
| Trupminor 7th
| ^^^m7
| ^^^C
| Minor 9th
| m9
| R@
|  
|-
|-
|11
| 74
|157.143
| 1057.143
|K
| Trudmajor 7th
|second
| vvvM7
|
| vvvC#
| Upminor 9th
| ^m9
| R^@
|  
|-
|-
|19
| 75
|271.429
| 1071.429
|L
| Dudmajor 7th
|third
| vvM7
|[[7/6]]
| vvC#
| Downmajor 9th
| vM9
| Rv
|  
|-
|-
|22
| 76
|314.286
| 1085.714
|L&
| Downmajor 7th
|major third
| vM7
|
| vC#
| Major 9th
| M9
| R
|  
|-
|-
|30
| 77
|428.571
| 1100.000
|M
| Major 7th
|fourth
| M7
|
| C#
| Upmajor 9th
| ^M9
| R^
|  
|-
|-
|38
|542.857
|N
|fifth
|[[11/8]] in the 84b val
|-
|-
|41
| 78
|585.714
| 1114.286
|N&
| Upmajor 7th
|
| ^M7
|
| ^C#
| Downaug 9th
| vA9
| Rv&
|  
|-
|-
|49
| 79
|700.000
| 1128.571
|O
| Dupmajor 7th
|sixth
| ^^M7
|[[3/2]]
| ^^C#
| Aug 9th
| A9
| R&
|  
|-
|-
|57
| 80
|814.286
| 1142.857
|P
| Trupmajor 7th
|seventh
| ^^^M7
|[[5/3]]
| ^^^C#
| Upaug 9th, Downdim 10th
| ^A9, vd10
| R^&, Jv@
|  
|-
|-
|60
| 81
|857.143
| 1157.143
|P&
| Trud 8ve
|
| vvv8
|[[105/64]]
| vvvD
| Dim 10th
| d10
| J@
|  
|-
|-
|68
| 82
|971.429
| 1171.429
|Q
| Dud 8ve
|eighth
| vv8
|
| vvD
| Updim 10th
| ^d10
| J^@
|  
|-
|-
|76
| 83
|1085.714
| 1185.714
|R
| Down  8ve
|ninth
| v8
|
| vD
| Down 10th
| v10
| Jv
|  
|-
|-
|79
| 84
|1128.571
| 1200.000
|R&
| Perfect 8ve
|
| P8
|
| D
| Perfect 10th
| P10
| J
| [[2/1]] exact
|-
|-
|84
|1200.000
|J (tenth above)
|perfect tenth
|[[2/1]] exact
|}
|}


Line 206: Line 967:
Brightest mode is listed.
Brightest mode is listed.
* Orwell[9], [[4L 5s]] - 11 8 11 8 11 8 11 8 8  
* Orwell[9], [[4L 5s]] - 11 8 11 8 11 8 11 8 8  
* Orwell[13] - [[9L 4s]] - 3883883883888
* Orwell[13] - [[9L 4s]] - 8 8 8 3 8 8 3 8 8 3 8 8 3
* Orwell[22] - [[13L 9s]]
* Orwell[22] - [[13L 9s]]
* Orwell[31] - [[22L 9s]]
* Orwell[31] - [[22L 9s]]

Revision as of 15:21, 30 September 2022

← 83edo 84edo 85edo →
Prime factorization 22 × 3 × 7
Step size 14.2857 ¢ 
Fifth 49\84 (700 ¢) (→ 7\12)
Semitones (A1:m2) 7:7 (100 ¢ : 100 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

In the 13-limit it is the optimal patent val for the rank five temperament tempering out 144/143.

Orwell

84edo is where the orwell temperament takes its name from, since the generator of 7/6 is equal to 19 steps of the EDO, referencing the book 1984.

From a regular temperament perspective, orwell in 84edo comes in two varieties - the 84e val ⟨84 133 195 236 290], supporting the original orwell, and its patent val ⟨84 133 195 236 291] representing newspeak. 84edo orwell offers MOS of size 9, 13, 22, and 31, of which the 31 note scale is the maximum evenness scale.

Other

84edo is a significantly composite number, with divisors of 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Being a small multiple of 12, it tempers out the Pythagorean comma, thus supporting period-12 temperament compton. Being a small multiple of 28, it tempers out the oquatonic comma, which maps 5/4 to 9\28.Script error: No such module "primes_in_edo".

Table of 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 @ "at".

Table of 84edo intervals
Degree Size (Cents) Ups and Downs Notation 4L 5s Notation Associated ratio
0 0.000 Perfect 1sn P1 D Perfect 1sn P1 J 1/1 exact
1 14.286 Up 1sn ^1 ^D Up 1sn ^1 J^
2 28.571 Dup 1sn ^^1 ^^D Downaug 1sn vA1 Jv&
3 42.857 Trup 1sn ^^^1 ^^^D Aug 1sn A1 J&
4 57.143 Trudminor 2nd vvvm2 vvvEb Upaug 1sn, Downdim 2nd ^A1, vd2 J^&, Kv@@
5 71.429 Dudminor 2nd vvm2 vvEb Dim 2nd d2 K@@
6 85.714 Downminor 2nd vm2 vEb Updim 2nd ^d2 K^@@
7 100.000 Minor 2nd m2 Eb Downminor 2nd vm2 Kv@
8 114.286 Upminor 2nd ^m2 ^Eb Minor 2nd m2 K@
9 128.571 Dupminor 2nd ^^m2 ^^Eb Upminor 2nd ^m2 K^@
10 142.857 Trupminor 2nd ^^^m2 ^^^Eb Downmajor 2nd vM2 Kv
11 157.143 Trudmajor 2nd vvvM2 vvvE Major 2nd M2 K
12 171.429 Dudmajor 2nd vvM2 vvE Upmajor 2nd ^M2 K^
13 185.714 Downmajor 2nd vM2 vE Downaug 2nd vA2 Kv&
14 200.000 Major 2nd M2 E Aug 2nd A2 K&
15 214.286 Upmajor 2nd ^M2 ^E Upaug 2nd, Downdim 3rd ^A2, vd3 K^&, Lv@
16 228.571 Dupmajor 2nd ^^M2 ^^E Dim 3rd d3 L@
17 242.857 Trupmajor 2nd ^^^M2 ^^^E Updim 3rd ^d3 L^@
18 257.143 Trudminor 3rd vvvm3 vvvF Down 3rd v3 Lv
19 271.429 Dudminor 3rd vvm2 vvF Perfect 3rd P3 L 7/6
20 285.714 Downminor 3rd vm3 vF Up 3rd ^3 L^
21 300.000 Minor 3rd m3 F Downaug 3rd vA3 Lv&
22 314.286 Upminor 3rd ^m3 ^F Aug 3rd A3 L&
23 328.571 Dupminor 3rd ^^m3 ^^F Upaug 3rd, Downdim 4th ^A3, vd4 L^&, Mv@@
24 342.857 Trupminor 3rd ^^^m3 ^^^F Dim 4th d4 M@@
25 357.143 Trudmajor 3rd vvvM3 vvvF# Updim 4th ^d4 M^@@
26 371.429 Dudmajor 3rd vvM3 vvF# Downminor 4th vm4 Mv@
27 385.714 Downmajor 3rd vM3 vF# Minor 4th m4 M@
28 400.000 Major 3rd M3 F# Upminor 4th ^m4 M^@
29 414.286 Upmajor 3rd ^M3 ^F# Downmajor 4th vM4 Mv
30 428.571 Dupmajor 3rd ^^M3 ^^F# Major 4th M4 M
31 442.857 Trupmajor 3rd ^^^M3 ^^^F# Upmajor 4th ^M4 M^
32 457.143 Trud 4th vvv4 vvvG Downaug 4th vA4 Mv&
33 471.429 Dud 4th vv4 vvG Aug 4th A4 M&
34 485.714 Down 4th v4 vG Downminor 5th vm5 Nv@
35 500.000 Perfect 4th P4 G Minor 5th m5 N@
36 514.286 Up 4th ^4 ^G Upminor 5th ^m5 N^@
37 528.571 Dup 4th ^^4 ^^G Downmajor 5th vM5 Nv
38 542.857 Trup 4th ^^^4 ^^^G Major 5th M5 N 11/8 in the 84b val
39 557.143 Trudaug 4th vvvA4 vvvG# Upmajor 5th ^M5 N^
40 571.429 Dudaug 4th vvA4 vvG# Downaug 5th vA5 Nv&
41 585.714 Downaug 4th vA4 vG# Aug 5th A5 N&
42 600.000 Aug 4th, Dim 5th A4, d5 G#, Ab Upaug 5th, Downdim 6th ^A5, vd6 N^&, Ov@@
43 614.286 Updim 5th ^d5 ^Ab Dim 6th d6 O@@
44 628.571 Dupdim 5th ^^d5 ^^Ab Updim 6th ^d6 O^@@
45 642.857 Trupdim 5th ^^^d5 ^^^Ab Downminor 6th vm6 Ov@
46 657.143 Trud 5th vvv5 vvvA Minor 6th m6 O@
47 671.429 Dud 5th vv5 vvA Upminor 6th ^m6 O^@
48 685.714 Down 5th v5 vA Downmajor 6th vM6 Ov
49 700.000 Perfect 5th P5 A Major 6th M6 O 3/2
50 714.286 Up 5th ^5 ^A Upmajor 6th ^M6 O^
51 728.571 Dup 5th ^^5 ^^A Dim 7th d7 P@@
52 742.857 Trup 5th ^^^5 ^^^A Aug 6th A6 O&
53 757.143 Trudminor 6th vvvm6 vvvBb Downminor 7th vm7 Pv@
54 771.429 Dudminor 6th vvm6 vvBb Minor 7th m7 P@
55 785.714 Downminor 6th vm6 vBb Upminor 7th ^m7 P^@
56 800.000 Minor 6th m6 Bb Downmajor 7th vM7 Pv
57 814.286 Upminor 6th ^m6 ^Bb Major 7th M7 P 5/3
58 828.571 Dupminor 6th ^^m6 ^^Bb Upmajor 7th ^M7 P^
59 842.857 Trupminor 6th ^^^m6 ^^^Bb Downaug 7th vA7 Pv&
60 857.143 Trudmajor 6th vvvM6 vvvB Aug 7th A7 P& 105/64
61 871.429 Dudmajor 6th vvM6 vvB Upaug 7th, Downdim 8th ^A7, vd8 P^&, Qv@@
62 885.714 Downmajor 6th vM6 vB Dim 8th d8 Q@@
63 900.000 Major 6th M6 B Updim 8th ^d8 Q^@@
64 914.286 Upmajor 6th ^M6 ^B Down 8th v8 Qv@
65 928.571 Dupmajor 6th ^^M6 ^^B Perfect 8th P8 Q@
66 942.857 Trupmajor 6th ^^^M6 ^^^B Up 8th ^8 Q^@
67 957.143 Trudminor 7th vvvm7 vvvC Downaug 8th vA8 Qv
68 971.429 Dudminor 7th vvm7 vvC Aug 8th A8 Q
69 985.714 Downminor 7th vm7 vC Upaug 8th, Downdim 9th ^A8, vd9 Q^, Rv@@
70 1000.000 Minor 7th m7 C Dim 9th d9 R@@
71 1014.286 Upminor 7th ^m7 ^C Updim 9th ^d9 R^@@
72 1028.571 Dupminor 7th ^^m7 ^^C Downminor 9th vm9 Rv@
73 1042.857 Trupminor 7th ^^^m7 ^^^C Minor 9th m9 R@
74 1057.143 Trudmajor 7th vvvM7 vvvC# Upminor 9th ^m9 R^@
75 1071.429 Dudmajor 7th vvM7 vvC# Downmajor 9th vM9 Rv
76 1085.714 Downmajor 7th vM7 vC# Major 9th M9 R
77 1100.000 Major 7th M7 C# Upmajor 9th ^M9 R^
78 1114.286 Upmajor 7th ^M7 ^C# Downaug 9th vA9 Rv&
79 1128.571 Dupmajor 7th ^^M7 ^^C# Aug 9th A9 R&
80 1142.857 Trupmajor 7th ^^^M7 ^^^C# Upaug 9th, Downdim 10th ^A9, vd10 R^&, Jv@
81 1157.143 Trud 8ve vvv8 vvvD Dim 10th d10 J@
82 1171.429 Dud 8ve vv8 vvD Updim 10th ^d10 J^@
83 1185.714 Down 8ve v8 vD Down 10th v10 Jv
84 1200.000 Perfect 8ve P8 D Perfect 10th P10 J 2/1 exact

Regular temperament properties

Subgroup Comma list Mapping Optimal

8ve stretch (¢)

Tuning error
Absolute (¢) Relative (%)
2.3.5 78732/78125, 531441/524288 ⟨84 133 195] 0.498 0.531
2.3.5.7 225/224, 1728/1715, 321489/320000 ⟨84 133 195 236] 0.141 0.769
2.3.5.7.11 225/224, 441/440, 1944/1925, 8019/8000 ⟨84 133 195 236 291] -0.225 1.003
2.3.5.7.11 99/98, 121/120, 1728/1715, 321489/320000 ⟨84 133 195 236 290] (84e) 0.601 1.151

Rank-2 temperaments by generator

Periods

per octave

Generator Cents Associated

ratio

Temperaments
1 19\84 271.428 7/6 Orwell (84e val)
Newspeak (84p val)
1 27\84 385.714 5/4 Mutt
12 27\84

(6\84)

385.714

(85.714)

5/4

(20480/19683)

Compton
28 49\84

(1\84)

500.000

(14.286)

4/3

(105/104)

Oquatonic

Scales

Brightest mode is listed.

  • Orwell[9], 4L 5s - 11 8 11 8 11 8 11 8 8
  • Orwell[13] - 9L 4s - 8 8 8 3 8 8 3 8 8 3 8 8 3
  • Orwell[22] - 13L 9s
  • Orwell[31] - 22L 9s

Music

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