Orwell: Difference between revisions

[[File:Orwell generator in 31.jpg|thumb|Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.]]

[[Semicomma_family#Seven limit children-Orwell|Orwell]] — so named because 19 steps of [[84edo|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|Semicomma family]]. Alternately, the "fifth harmonic" 5/1 divided into 3 equal steps also makes a good orwell generator, being ~12/7.

Compatible equal temperaments include [[22edo|22edo]], [[31edo|31edo]], [[53edo|53edo]], and [[84edo|84edo]]. Orwell is in better tune in lower limits than higher ones; the [[Optimal_patent_val|optimal patent val]] is [[296edo|296edo]] in the 5-limit, [[137edo|137edo]] in the 7-limit, and [[53edo|53edo]] in the 11-limit. It tempers out the semicomma in the 5-limit, and so belongs to the [[Semicomma_family|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 [[Semicomma_family#Orwell-13-limit|tridecimal orwell]], and by adding instead 66/65, [[Semicomma_family#Winston|winston temperament]].

By switching the roles of the period and generator, we end up with a nonoctave temperament that is to orwell what [[Angel|angel]] and [[devadoot|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|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 [https://en.wikipedia.org/wiki/Watcher_(angel) 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.

Prime harmonics and their inverses are in bold.

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*in 11-limit POTE tuning

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[6 5/2] eigenmonzos: [[orwellwoo13|orwellwoo13]] [[orwellwoo22|orwellwoo22]]

[[file:OrwellNonatonicPOTE.mp3]] in POTE tuning

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Following is a list of rank three, or planar temperaments that are supported by orwell temperament.

*weak extension (one or more generators from the parent temperament are split)

[http://www.archive.org/details/TrioInOrwell Trio in Orwell] [http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith]]

[http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/Sejaliscos_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 Sejaliscos] by [https://soundcloud.com/lois-lancaster/sejaliscos Roncevaux]

To play interactive versions of these keyboards, check out Vito Sicurella's plugin, which works with REAPER:

[[File:Orwell_13.png|alt=Orwell_13.png|1023x292px|Orwell_13.png]]

[[File:orwell13_axis49.png|alt=orwell13_axis49.png|orwell13_axis49.png]]

[[Category:84edo]]