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Properties | Interval chain | Spectrum of Orwell Tunings by Eigenmonzos | MOSes | Planar temperaments | Chords of orwell | MOS transversals | Music | Keyboards |

Properties

Orwell — so named because 19 steps of 84edo, or 19\84, is a possible generator — is an excellent 7-limit temperament and an amazing (because of the low complexity of 11) 11-limit temperament. The "perfect twelfth" 3/1 is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. It's a member of the Semicomma family. Alternately, the "fifth harmonic" 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7.

In the 11 limit, two generators are equated to 11/8 (meaning 99/98 is tempered out). This means that three stacked generators makes the orwell tetrad 1/1-7/6-11/8-8/5, a chord in which every interval is a (tempered) 11-limit consonance. Other such chords in orwell are the keenanismic tetrads and the swetismic chords.

Compatible equal temperaments include 22edo, 31edo, 53edo, and 84edo. Orwell is in better tune in lower limits than higher ones; the optimal patent val is 296edo in the 5-limit, 137edo in the 7-limit, and 53edo in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the semicomma family. In the 7-limit it tempers out 225/224, 1728/1715, 2430/2401 and 6144/6125 in the 7-limit, and 99/98, 121/120, 176/175, 385/384 and 540/539 in the 11-limit. By adding 275/273 to the list of commas it can be extended to the 13-limit as tridecimal orwell, and by adding instead 66/65, winston temperament.

Watcher


By switching the roles of the period and generator, we end up with a nonoctave temperament that is to orwell what angel and devadoot are to meantone and magic, respectively. There is an interesting MOS with 7 notes per period; if this is derived as a subset of 84edt (which has 12 notes per period, and is almost identical to 53edo), the resulting MOS has the same structure as the 12edo diatonic scale, only compressed so that the period is ~272 cents rather than an octave! Thus, a piano keyboard for this MOS would look exactly the same as a typical keyboard, only what looks like an octave wouldn't be one anymore. This temperament could be called watcher, a reference to a class of angels whose very name carries Orwellian connotations. The 12-limit otonality (1:2:3:4:5:6:7:8:9:10:11:12) and utonality both have complexity 4. If we consider these to be the fundamental consonances, then using the 7-note-per period MOS, there are exactly 3 of each type per period, which again is analogous to the diatonic scale. While angel and devadoot don't perform well past the 10-limit, watcher handles the 12-limit with ease. Straight-fretted watcher guitars could be built as long as the strings were all tuned to period-equivalent notes.

Interval chain

Generators
Cents*
11-limit ratios
(orwell mapping)
13-limit ratios
(orwell mapping)
13-limit ratios
(winston mapping)
13-limit ratios
(blair mapping)
0
0.00
1/1



1
271.43
7/6


13/11, 15/13
2
542.85
11/8, 15/11

18/13
35/26, 39/28
3
814.28
8/5

21/13, 52/33
13/8
4
1085.71
15/8, 28/15

13/7
24/13
5
157.13
12/11, 11/10, 35/32

13/12
14/13
6
428.56
14/11, 9/7, 32/25


13/10, 33/26
7
699.98
3/2

52/35

8
971.41
7/4

26/15

9
42.84
49/48, 36/35, 33/32
40/39
27/26
26/25
10
314.26
6/5

13/11
39/32
11
585.69
7/5

39/28
18/13
12
857.12
18/11
64/39
13/8
21/13
13
1128.54
21/11, 27/14, 48/25
25/13

39/20
14
199.97
9/8, 28/25



15
471.40
21/16

13/10

16
742.82
49/32, 54/35
20/13


17
1014.25
9/5



18
85.67
21/20

26/25
27/26
19
357.10
27/22, 49/40
16/13
39/32

20
628.52
36/25
56/39


21
899.95
27/16, 42/25
22/13


22
1171.38
63/32

39/20

*in 11-limit POTE tuning

Spectrum of Orwell Tunings by Eigenmonzos

Eigenmonzo
Subminor Third
7/6
266.871
14/11
269.585
12/11
270.127
11/9
271.049
8/7
271.103
7/5
271.137 (7 and 11 limit minimx)
5/4
271.229
6/5
271.564 (5 limit minimax)
10/9
271.623 (9 limit minimax)
4/3
271.708
9/7
272.514
11/10
273.001
11/8
275.659
[6 5/2] eigenmonzos: orwellwoo13 orwellwoo22

MOSes

9-note (LsLsLsLss, proper)

Small ("minor") interval
114.29
228.59
385.72
500.02
657.15
771.44
928.57
1042.87
JI intervals represented
15/14~16/15
8/7
5/4
4/3
16/11
14/9~11/7
12/7
11/6
Large ("major") interval
157.13
271.43
428.56
542.85
699.98
814.28
971.41
1085.71
JI intervals represented
12/11~11/10
7/6
14/11~9/7
11/8
3/2
8/5
7/4
15/8

13-note (LLLsLLsLLsLLs, improper)

Small ("minor") interval
42.84
157.13
271.43
314.26
428.56
542.85
585.69
699.98
814.28
857
971.41
1085.71
JI intervals represented

12/11~11/10
7/6
6/5
14/11~9/7
11/8
7/5
3/2
8/5
18/11
7/4
15/8
Large ("major") interval
114.29
228.59
342.88
385.72
500.02
614.31
657.15
771.44
885.74
928.57
1042.87
1157.16
JI intervals represented
15/14~16/15
8/7
11/9
5/4
4/3
10/7
16/11
14/9~11/7
5/3
12/7
11/6


Planar temperaments

Following is a list of rank three, or planar temperaments that are supported by orwell temperament.
Planar temperament
Among others, planar temperament is also supported by...
7-limit
11-limit
extension
9tet
22tet
31tet
53tet
marvel

negri, septimin, august,
amavil, enneaportent
magic, pajara, wizard, porky
meantone, miracle, tritonic,
slender, würschmidt
garibaldi, catakleismic

marvel
negri, septimin, enneaportent
magic, pajarous, wizard
meanpop, miracle, tritoni, slender
garibaldi, catakleismic

minerva
negric, august, amavil
telepathy, pajara
meantone, revelation, würschmidt
cataclysmic

artemis*
wilsec
divination, hemipaj, porky
migration, oracle, tritonic

hewuermity

triforce, armodue,
twothirdtonic
porcupine, astrology, shrutar,
hendecatonic, septisuperfourth
hemiwürschmidt, valentine,
mohajira, grendel
amity, hemischis,
hemikleismic

zeus
triforce, armodue,
twothirdtonic
porcupine, astrology, shrutar,
hendecatonic
hemiwur, valentine, mohajira
hitchcock,
hemikleismic

jupiter

septisuperfourth
hemiwürschmidt, grendel
amity, hemischis
orwellian

beep, secund, infraorwell,
niner
superpyth, doublewide,
echidna
myna, mothra, sentinel,
semisept
quartonic, buzzard

orwellian
pentoid, secund
suprapyth, doublewide
myno, mothra, sentinel


guanyin
infraorwell, niner
superpyth, fleetwood, echidna
myna, mosura, semisept
quartonic, buzzard
nuwell

progression, superpelog
quasisuper, hedgehog
squares, nusecond
tricot, hamity

big brother
progression, superpelog
quasisupra, hedgehog
squares, nusecond
tricot, hamity
horwell


bisupermajor, escaped,
fifthplus
hemithirds, worschmidt,
tertiaseptal
countercata, pontiac

zelda

bisupermajor, sensa
hemithirds, worschmidt, tertia
countercata
*weak extension (one or more generators from the parent temperament are split)

Chords of orwell


MOS transversals

orwell13trans
orwell22trans
orwell31trans
orwell13trans57
orwell22trans57
orwell31trans57


Music

Trio in Orwell play by Gene Ward Smith
earwig, play,
Elf Dine on Ho Ho, play,
Spun, play,
one drop of rain, play,
i've come with a bucket of roses and my own house by Andrew Heathwaite
Orwellian Cameras by Chris Vaisvil
Tunicata and Fugue by Peter Kosmorsky
Mountain Villiage play by Tarkan Grood
Swing in Orwell-9
Schizo Blue by Roncevaux (Löis Lancaster)
Sejaliscos by Roncevaux

Keyboards

If only there were a way to make these interactive, that would be pretty nifty.
Orwell_13.png

Orwell_22.png

orwell13_axis49.png
See: Orwell on an Isomorphic Keyboard