Xenharmonic Wiki

Orwell: Difference between revisions

← Older edit
VisualWikitext
m Fix confusingly worded sentence in the introduction
m Cleanup on infobox
 
(6 intermediate revisions by 4 users not shown)
Line 10: Line 10:
| Comma basis = [[225/224]], [[1728/1715]] (7-limit); <br> [[99/98]], [[121/120]], [[176/175]] (11-limit)
| Comma basis = [[225/224]], [[1728/1715]] (7-limit); <br> [[99/98]], [[121/120]], [[176/175]] (11-limit)
| Edo join 1 = 22 | Edo join 2 = 31
| Edo join 1 = 22 | Edo join 2 = 31
| Generator = 7/6 | Generator tuning = 271.5 | Optimization method = CTE
| Mapping = 1; 7 -3 8 2
| Generators = 7/6 | Generators tuning = 271.5 | Optimization method = CWE
| MOS scales = [[4L 1s]], [[4L 5s]], [[9L 4s]], [[9L 13s]]
| MOS scales = [[4L 1s]], [[4L 5s]], [[9L 4s]], [[9L 13s]]
| Mapping = 1; 7 -3 8 2
| Pergen = (P8, cP5/7)
| Pergen = (P8, cP5/7)
| Odd limit 1 = 7 | Mistuning 1 = 4.27 | Complexity 1 = 13
| Odd limit 1 = 7 | Mistuning 1 = 4.27 | Complexity 1 = 13
| Odd limit 2 = (L11) 21 | Mistuning 2 = 9.32 | Complexity 2 = 22
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 9.32 | Complexity 2 = 22
}}
}}
[[File:Orwell generator in 31.jpg|thumb|Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.]]
[[File:Orwell generator in 31.jpg|thumb|Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.]]
Line 21: Line 21:
'''Orwell''' – so named because 19 steps of [[84edo]], i.e. 19\84, is a possible generator – is an excellent [[7-limit]] [[regular temperament|temperament]] and an amazing [[11-limit]] temperament because of the simplicity of [[harmonic]] [[11/1|11]].
'''Orwell''' – so named because 19 steps of [[84edo]], i.e. 19\84, is a possible generator – is an excellent [[7-limit]] [[regular temperament|temperament]] and an amazing [[11-limit]] temperament because of the simplicity of [[harmonic]] [[11/1|11]].


In orwell, [[8/5]] is divided into three equal steps, each of which represent [[7/6]], so that [[1728/1715]] ({{S|6/S7}}) is tempered out. Alternatively, the [[5/1|5th harmonic (5/1)]] is divided into 3 equal steps that represent [[~]][[12/7]]. After two 8/5's (six generators), [[9/7]] is found by [[tempering out]] the marvel comma, [[225/224]], and thus the [[3/1|just perfect twelfth (3/1)]] is divided into 7 equal steps.  
In orwell, [[8/5]] is divided into three equal steps, each of which represent [[7/6]], so that [[1728/1715]] ({{S|6/S7}}) is tempered out. This means that the [[5/1|5th harmonic (5/1)]] is divided into three equal steps that represent [[~]][[12/7]]. After two 8/5's (six generators), [[9/7]] is found by [[tempering out]] the marvel comma, [[225/224]], and thus the [[3/1|just perfect twelfth (3/1)]] is divided into 7 equal steps.  


In the 11-limit, two generators are equated to [[15/11]] and [[11/8]] (meaning [[99/98]] and [[121/120]] are tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1–7/6–11/8–8/5, a chord in which every interval is a (tempered) 11-odd-limit consonance. Other such chords in undecimal orwell are the [[keenanismic chords]] and the [[swetismic chords]]. A far more complicated mapping of 11 at 33 generators, tempering out [[441/440]] instead, is also possible and is known as [[newspeak]] temperament.
In the 11-limit, two generators are equated to [[15/11]] and [[11/8]] (meaning [[99/98]] and [[121/120]] are tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1–7/6–11/8–8/5, a chord in which every interval is a (tempered) 11-odd-limit consonance. Other such chords in undecimal orwell are the [[keenanismic chords]] and the [[swetismic chords]]. A far more complicated mapping of 11 at 33 generators, tempering out [[441/440]] instead, is also possible and is known as [[newspeak]] temperament; these two mappings unite on 31edo.


Compatible [[equal temperaments]] include [[22edo]], [[31edo]], [[53edo]], and [[84edo]] (though in 84edo, 11-limit orwell uses the 84e [[val]]). 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.  
Compatible [[equal temperaments]] include [[22edo]], [[31edo]], [[53edo]], and [[84edo]] (though in 84edo, 11-limit orwell uses the 84e [[val]]). 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.  
Line 133: Line 133:


=== Chords and harmony ===
=== Chords and harmony ===
{{Main| Chords of orwell }}
{{See also| Chords of orwell | Functional harmony in rank-2 temperaments }}
{{See also| Functional harmony in rank-2 temperaments }}


The fundamental otonal consonance of orwell, voiced in a roughly {{w|tertian harmony|tertian}} manner, is 4:5:6:7:9:11. In terms of generator steps this is 0–(−3)–7–8–14–2, only available in a 22-tone mos. However, some subsets of this chord are way simpler, such as 8:11:12:14, which is 1–11/8–3/2–7/4 (0–2–7–8).  
The fundamental otonal consonance of orwell, voiced in a roughly {{w|tertian harmony|tertian}} manner, is 4:5:6:7:9:11. In terms of generator steps this is 0–(−3)–7–8–14–2, only available in a 22-tone mos. However, some subsets of this chord are way simpler, such as 8:11:12:14, which is 1–11/8–3/2–7/4 (0–2–7–8).  
Line 527: Line 526:
! 53tet
! 53tet
|-
|-
| [[Marvel family|Marvel]]
| [[Marvel]]
|  
|  
| Negri, septimin, august,<br>amavil, enneaportent
| Negri, septimin, august,<br>amavil, enneaportent
Line 555: Line 554:
|  
|  
|-
|-
| [[Porwell family|Hewuermity]]
| [[Porwell]]
|  
|  
| Triforce, armodue,<br>twothirdtonic
| Triforce, armodue,<br>twothirdtonic
Line 576: Line 575:
| Amity, hemischis
| Amity, hemischis
|-
|-
| [[Orwellismic family|Orwellismic]]
| [[Orwellismic]]
|  
|  
| Beep, secund, infraorwell,<br>niner
| Beep, secund, infraorwell,<br>niner
Line 597: Line 596:
| Quartonic, buzzard
| Quartonic, buzzard
|-
|-
| [[Nuwell family|Nuwell]]
| [[Nuwell]]
|  
|  
| Progression, superpelog
| Progression, superpelog
| Quasisuper, hedgehog
| Quasisuper, hedgehog
| Squares, nusecond
| Squares, nusecond
| Tricot, hamity
| Alphatrimot, hamity
|-
|-
|  
|  
Line 609: Line 608:
| Quasisupra, hedgehog
| Quasisupra, hedgehog
| Squares, nusecond
| Squares, nusecond
| Tricot, hamity
| Alphatrimot, hamity
|-
|-
| [[Horwell family|Horwell]]
| [[Horwell]]
|  
|  
|  
|  
Line 648: Line 647:
; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=zWrOiih7raY ''Orwell Canon 3 in 1 upon a Ground for Baroque Oboe, Viola, Clarinet, and Viola da Gamba''] (2024)
* [https://www.youtube.com/watch?v=zWrOiih7raY ''Orwell Canon 3 in 1 upon a Ground for Baroque Oboe, Viola, Clarinet, and Viola da Gamba''] (2024)
* [https://www.youtube.com/shorts/g7C2OrFd-nk ''Orwell Micro Trio, for Organ (Just: 7 Orwells = 1 Twelfth)''] (2025) &mdash; in open-ended Orwell tuning, but with the generator adjusted to be extremely close to 12\53, at 271.71{{c}}


; [[Herman Miller]]
; [[Herman Miller]]
Line 664: Line 664:


== Keyboards ==
== Keyboards ==
{{See also| Orwell on an isomorphic keyboard }}
{{See also| Orwell on an isomorphic keyboard | Lumatone mapping for orwell }}
{{See also| Lumatone mapping for orwell}}


To play interactive versions of these keyboards, check out [https://github.com/vsicurella/SuperVirtualKeyboard Vito Sicurella's plugin], which works with REAPER:
To play interactive versions of these keyboards, check out [https://github.com/vsicurella/SuperVirtualKeyboard Vito Sicurella's plugin], which works with REAPER:
Retrieved from "https://en.xen.wiki/w/Orwell"