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