Orwell
Orwell – so named because 19 steps of 84edo, i.e. 19\84, is a possible generator – is an excellent 7-limit temperament and an amazing 11-limit temperament because of the simplicity of harmonic 11.
See Semicomma family #Orwell for technical details.
Properties
In orwell, the just perfect twelfth (3/1) is divided into 7 equal steps. One of these steps represents 7/6; three represent 8/5. 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 chords 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, and in the 11-limit, 99/98, 121/120, 176/175, 385/384 and 540/539. 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
Prime harmonics and their inverses are in bold.
| # | Cents* | 11-limit Ratios (Orwell Mapping) |
13-limit Extension (Orwell Mapping) |
13-limit Extension (Winston Mapping) |
13-limit Extension (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
Chords
- Main article: Chords of orwell
Scales
MOS scales
- 9-tone scales (sLsLsLsLs, proper)
- Orwell9 – 84edo tuning
- Orwell9-12 – 7-limit POTE tuning, mapped to 12-tones
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-tone scales (LsLLsLLLsLLsL, improper)
- Orwell13 – 84edo tuning
- Orwellwoo13 – [6 5/2] eigenmonzo (unchanged-interval) tuning
| 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 |
- 22-tone scales
- Orwell22
- Orwellwoo22 – [6 5/2] eigenmonzo (unchanged-interval) tuning
Transversal scales
Others
- Orwell-graham – 13-tone modmos in 53edo tuning
- Orwell13-modmos-containing-minerva12 – 13-tone modmos in POTE tuning
- Minerva12-orwell-tempered – minerva[12] tempered to orwell
Tuning spectrum
| eigenmonzo (unchanged-interval) |
subminor third (¢) |
comments |
|---|---|---|
| 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-odd-limit minimax |
| 5/4 | 271.229 | |
| 6/5 | 271.564 | 5-odd-limit minimax |
| 10/9 | 271.623 | 9-odd-limit minimax |
| 4/3 | 271.708 | |
| 9/7 | 272.514 | |
| 11/10 | 273.001 | |
| 11/8 | 275.659 |
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 | ||
| Orwellismic | 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)
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
- See also: Orwell on an Isomorphic Keyboard
- See also: Lumatone mapping for orwell
To play interactive versions of these keyboards, check out Vito Sicurella's plugin, which works with REAPER:
https://github.com/vsicurella/SuperVirtualKeyboard/releases/tag/0.021?fbclid=IwAR0ShCAy672Ruaz1VSVaU2beGuX2RI3elIfZOyrn9T9OHOYuQNXTGBCyIgU
