Orwell

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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)

in POTE tuning

in 22edo

in 53edo

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