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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |Subgroup
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Comma list]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal  
! rowspan="2" | Optimal<br>8ve Stretch (¢)
8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" |Tuning error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3.5
| 2.3.5
|78732/78125, 531441/524288
| 78732/78125, 531441/524288
|{{val|84 133 195}}
| {{val| 84 133 195 }}
|0.498
| +0.498
|0.531
| 0.531
|
| 3.72
|-
|-
|2.3.5.7
| 2.3.5.7
|225/224, 1728/1715, 321489/320000
| 225/224, 1728/1715, 78732/78125
|{{val|84 133 195 236}}
| {{val| 84 133 195 236 }}
|0.141
| +0.141
|0.769
| 0.769
|
| 5.39
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|225/224, 441/440, 1944/1925, 8019/8000
| 225/224, 441/440, 1344/1331, 1728/1715
|{{val|84 133 195 236 291}}
| {{val| 84 133 195 236 291 }} (84)
| -0.225
| -0.225
|1.003
| 1.003
|
| 7.02
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|99/98, 121/120, 1728/1715, 321489/320000
| 99/98, 121/120, 176/175, 78732/78125
|{{val|84 133 195 236 290}} (84e)
| {{val|84 133 195 236 290}} (84e)
|0.601
| +0.601
|1.151
| 1.151
|
| 8.05
|}
|}


=== Rank-2 temperaments by generator ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
!Periods  
! Periods<br>per 8ve
per octave
! Generator<br>(Reduced)
!Generator
! Cents<br>(Reduced)
!Cents
! Associated<br>Ratio
!Associated  
! Temperaments
ratio
!Temperaments
|-
|-
| rowspan="2" |1
| rowspan="2" | 1
| rowspan="2" |[[Wikipedia:Nineteen Eighty-Four|19\84]]
| rowspan="2" | 19\84
| rowspan="2" |271.428
| rowspan="2" | 271.428
| rowspan="2" | 7/6
| rowspan="2" | 7/6
|[[Orwell]] (84e val)
| [[Orwell]] (84e)
|-
|-
|[[Newspeak]] (84p val)
| [[Newspeak]] (84p)
|-
|-
|1
| 1
|27\84
| 27\84
|385.714
| 385.714
|5/4
| 5/4
|[[Mutt]]
| [[Mutt]]
|-
|-
|12
| 12
|27\84
| 27\84<br>(1\84)
(6\84)
| 385.714<br>(14.285)
|385.714
| 5/4<br>(126/125)
(85.714)
| [[Compton]]
|5/4
(20480/19683)
|[[Compton]]
|-
|-
|28
| 28
|49\84
| 49\84<br>(1\84)
(1\84)
| 500.000<br>(14.286)
|500.000
| 4/3<br>(105/104)
(14.286)
| [[Oquatonic]]
|4/3
(105/104)
|[[Oquatonic]]
|}
|}
== Scales ==
== Scales ==
Brightest mode is listed.
Brightest mode is listed.

Revision as of 04:58, 2 October 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 3.72
2.3.5.7 225/224, 1728/1715, 78732/78125 ⟨84 133 195 236] +0.141 0.769 5.39
2.3.5.7.11 225/224, 441/440, 1344/1331, 1728/1715 ⟨84 133 195 236 291] (84) -0.225 1.003 7.02
2.3.5.7.11 99/98, 121/120, 176/175, 78732/78125 ⟨84 133 195 236 290] (84e) +0.601 1.151 8.05

Rank-2 temperaments

Periods
per 8ve 		Generator
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 19\84 271.428 7/6 Orwell (84e)
Newspeak (84p)
1 27\84 385.714 5/4 Mutt
12 27\84
(1\84) 		385.714
(14.285) 		5/4
(126/125) 		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

Retrieved from "https://en.xen.wiki/index.php?title=84edo&oldid=95937"