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{{interwiki
{{interwiki
| en = Orwell
| de = Orwell
| de = Orwell
| en = Orwell
| es =  
| es =  
| ja =  
| ja =  
}}
{{Infobox regtemp
| Title = Orwell
| Subgroups = 2.3.5.7, 2.3.5.7.11
| 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
| 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]]
| Pergen = (P8, cP5/7)
| Odd limit 1 = 7 | Mistuning 1 = 4.27 | Complexity 1 = 13
| 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.]]
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'''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, the [[3/1|just perfect twelfth (3/1)]] is divided into 7 equal steps. One of these steps represents [[7/6]]; three represent [[8/5]]. Alternately, the [[5/1|5th harmonic (5/1)]] divided into 3 equal steps also makes a good orwell generator, being [[~]][[12/7]].
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 [[11/8]] (meaning [[99/98]] is 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 orwell are the [[keenanismic chords]] and the [[swetismic chords]].
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]]. 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 [[Semicomma family #Orwell|tridecimal orwell]], and by adding instead [[66/65]], [[Semicomma family #Winston|winston temperament]]. See [[Orwell extensions]] for details about 13-limit extensions.  
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.  


See [[Semicomma family #Orwell]] for technical details.  
See [[Semicomma family #Orwell]] for technical details. See [[Orwell extensions]] for details about 13-limit extensions.  


== Interval chain ==
== Theory ==
=== Interval chain ===
Odd harmonics 1–21 and their inverses are in '''bold'''.
Odd harmonics 1–21 and their inverses are in '''bold'''.
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
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| 5
| 5
| 157.28
| 157.28
| 12/11, 11/10, 35/32
| 11/10, 12/11, 35/32
|-
|-
| 6
| 6
| 428.73
| 428.73
| 14/11, 9/7, 32/25
| 9/7, 14/11, 32/25
|-
|-
| 7
| 7
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| 9
| 9
| 43.10
| 43.10
| 49/48, 36/35, 33/32
| 33/32, 36/35, 49/48
|-
|-
| 10
| 10
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| 63/32
| 63/32
|}
|}
<nowiki/>* In 11-limit CWE tuning
<nowiki/>* In 11-limit CWE tuning, octave reduced


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


=== Functional harmony ===
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).
{{See also| Functional harmony in rank-2 temperaments }}


The generator, ~7/6, is a septimal interval, so the most basic chords could be 1–7/6–3/2 (0–1–7) and 1–9/7–3/2 (0–6–7), or 1–7/4–3 (0–8–7) and 1–12/7–3 (0–(-1)–7), or tetrads such as 1–7/6–3/2–7/4 (0–1–7–8); this is similar, but also in clear contrast to the 1–5/4–3/2 (0–4–1) and 1–6/5–3/2 (0–(−3)–1) of [[meantone]]. Two approaches to functional harmony thus arise.  
The generator, ~7/6, is a septimal interval, so chords could instead be built around it as 1–7/6–3/2 (0–1–7), 1–7/4–3 (0–8–7), or tetrads such as 1–7/6–3/2–7/4 (0–1–7–8).  


First, we suggest using the septimal chords above as the basis of harmony, but swapping the roles of 3 and 7 according to their temperamental complexities (number of generator steps). Thus a "dominant" chord is either 7/6 or 12/7 over tonic; a "subdominant" chord is either 7/6 or 12/7 under tonic. This leads to an approach closely adherent to mos scales. The 9-tone mos contains a tonic and a "dominant" triad. The 13-tone mos is good for encapsulating tonic, "pre-dominant", and "dominant" functions, triads and tetrads alike.  
To 1–7/6–3/2–7/4 we may add 11/8, or to 1–11/8–3/2–7/4 we may add 7/6, to form an essentially tempered pentad, 1–7/6–11/8–3/2–7/4 (0–1–2–7–8). Its inverse is 1–12/11–9/7–3/2–12/7 (0–5–6–7–(−1)), which can serve as a minor counterpart. This is similar, but also in clear contrast to the 1–5/4–3/2 (0–4–1) and 1–6/5–3/2 (0–(−3)–1) chords of [[meantone]]. Two approaches to functional harmony thus arise.  


Second, we suggest using the same chords as the basis of harmony, and keeping the role of the [[chain of fifths]] as the spine on which the functions are defined. This means dominant is still 3/2 over tonic, for example. A consequence is we must step out of the logic of mos scales, as they are often too restrictive without the many fifths to stack. This is essentially working in JI, but using the commas tempered out in some way to lock into the identity of the temperament.
First, we can treat the septimal chords above as the basis of harmony, but swapping the roles of 3 and 7 according to their temperamental complexities (number of generator steps). Thus a "dominant" chord is either 7/6 or 12/7 over tonic; a "subdominant" chord is either 7/6 or 12/7 under tonic. This leads to an approach closely adherent to mos scales. The 9-tone mos contains a tonic and a "dominant" triad. The 13-tone mos is good for encapsulating tonic, "pre-dominant", and "dominant" functions, triads to pentads alike.
 
Second, we can treat the same chords as the basis of harmony, and keeping the role of the [[chain of fifths]] as the spine on which the functions are defined. This means dominant is still 3/2 over tonic, for example. A consequence is we must step out of the logic of mos scales, as they are often too restrictive without the many fifths to stack. This is essentially working in JI, but using the commas tempered out in some way to lock into the identity of the temperament.


== Scales ==
== Scales ==
=== MOS scales ===
{{Main| Orwell scales }}
 
=== Mos scales ===
* [[Orwell5]]
* [[Orwell5]]


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{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
| Small ("minor") interval
! Small ("minor") interval
| 114.29
| 114.29
| 228.59
| 228.59
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| 1042.87
| 1042.87
|-
|-
| JI intervals represented
! JI intervals represented
| 15/14~16/15
| 15/14~16/15
| 8/7
| 8/7
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| 11/6
| 11/6
|-
|-
| Large ("major") interval
! Large ("major") interval
| 157.13
| 157.13
| 271.43
| 271.43
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| 1085.71
| 1085.71
|-
|-
| JI intervals represented
! JI intervals represented
| 12/11~11/10
| 12/11~11/10
| 7/6
| 7/6
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; 13-tone scales (LsLLsLLLsLLsL, improper)  
; 13-tone scales (LsLLsLLLsLLsL, improper)  
* [[Orwell13]] – 84edo tuning
* [[Orwell13]] – 84edo tuning
* [[Orwellwoo13]] – [6 5/2] eigenmonzo (unchanged-interval) tuning
* [[Orwellwoo13]] – [6 5/2] unchanged-interval (eigenmonzo) tuning


{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
| Small ("minor") interval
! Small ("minor") interval
| 42.84
| 42.84
| 157.13
| 157.13
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| 1085.71
| 1085.71
|-
|-
| JI intervals represented
! JI intervals represented
|  
|  
| 12/11~11/10
| 12/11~11/10
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| 15/8
| 15/8
|-
|-
| Large ("major") interval
! Large ("major") interval
| 114.29
| 114.29
| 228.59
| 228.59
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| 1157.16
| 1157.16
|-
|-
| JI intervals represented
! JI intervals represented
| 15/14~16/15
| 15/14~16/15
| 8/7
| 8/7
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; 22-tone scales
; 22-tone scales
* [[Orwell22]]
* [[Orwell22]]
* [[Orwellwoo22]] – [6 5/2] eigenmonzo (unchanged-interval) tuning
* [[Orwellwoo22]] – [6 5/2] unchanged-interval (eigenmonzo) tuning


=== Transversal scales ===
=== Transversal scales ===
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* [[Orwell-graham]] – 13-tone modmos in 53edo tuning
* [[Orwell-graham]] – 13-tone modmos in 53edo tuning
* [[Orwell13-modmos-containing-minerva12]] – 13-tone modmos in POTE tuning
* [[Orwell13-modmos-containing-minerva12]] – 13-tone modmos in POTE tuning
* [[Minerva12-orwell-tempered]] – minerva[12] tempered to orwell
* [[Minerva12-orwell-tempered]] – Minerva[12] tempered to orwell


== Tunings ==
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! Weight-skew\order !! Euclidean
|-
|-
| Tenney || CTE: ~7/6 = 271.5130¢
! rowspan="2" |  
! colspan="3" | Euclidean
|-
|-
| Weil || CWE: ~7/6 = 271.5097¢
! Constrained
! Constrained & skewed
! Destretched
|-
|-
| Equilateral || CEE: ~7/6 = 271.3553¢
! Equilateral
| CEE: ~7/6 = 271.3553{{c}}
| CSEE: ~7/6 = 271.3339{{c}}
| POEE: ~7/6 = 271.3727{{c}}
|-
|-
| Skewed-equilateral || CSEE: ~7/6 = 271.3339¢
! Tenney
| CTE: ~7/6 = 271.5130{{c}}
| CWE: ~7/6 = 271.5097{{c}}
| POTE: ~7/6 = 271.5087{{c}}
|-
|-
| Benedetti/Wilson || CBE: ~7/6 = 271.5725¢
! Benedetti, <br>Wilson
|-
| CBE: ~7/6 = 271.5725{{c}}
| Skewed-Benedetti/Wilson || CSBE: ~7/6 = 271.5741¢
| CSBE: ~7/6 = 271.5741{{c}}
| POBE: ~7/6 = 271.5576{{c}}
|}
|}


{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
|-
|-
! Weight-skew\order !! Euclidean
! rowspan="2" |
! colspan="3" | Euclidean
|-
|-
| Tenney || CTE: ~7/6 = 271.5597¢
! Constrained
! Constrained & skewed
! Destretched
|-
|-
| Weil || CWE: ~7/6 = 271.4552¢
! Equilateral
| CEE: ~7/6 = 271.4920{{c}}
| CSEE: ~7/6 = 271.3038{{c}}
| POEE: ~7/6 = 271.1665{{c}}
|-
|-
| Equilateral || CEE: ~7/6 = 271.4920¢
! Tenney
| CTE: ~7/6 = 271.5597{{c}}
| CWE: ~7/6 = 271.4552{{c}}
| POTE: ~7/6 = 271.4261{{c}}
|-
|-
| Skewed-equilateral || CSEE: ~7/6 = 271.3038¢
! Benedetti, <br>Wilson
|-
| CBE: ~7/6 = 271.5915{{c}}
| Benedetti/Wilson || CBE: ~7/6 = 271.5915¢
| CSBE: ~7/6 = 271.5302{{c}}
|-
| POBE: ~7/6 = 271.5174{{c}}
| Skewed-Benedetti/Wilson || CSBE: ~7/6 = 271.5302¢
|}
|}


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! Optimized chord !! Generator value !! Polynomial !! Further notes
! Optimized chord !! Generator value !! Polynomial !! Further notes
|-
|-
| 3:4:5 (+1 +1) || ~7/6 = 272.890 || ''f''<sup>10</sup> &minus; 8''f''<sup>3</sup> + 8 = 0 || 1–3–5 equal-beating tuning
| 3:4:5 (+1 +1) || ~7/6 = 272.890{{c}} || ''f''<sup>10</sup> &minus; 8''f''<sup>3</sup> + 8 = 0 || 1–3–5 equal-beating tuning
|-
|-
| 4:5:6 (+1 +1) || ~7/6 = 271.508 || ''f''<sup>10</sup> + 2''f''<sup>3</sup> - 8 = 0 || 1–3–5 equal-beating tuning
| 4:5:6 (+1 +1) || ~7/6 = 271.508{{c}} || ''f''<sup>10</sup> + 2''f''<sup>3</sup> - 8 = 0 || 1–3–5 equal-beating tuning
|}
|}


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|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
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! 53tet
! 53tet
|-
|-
| [[Marvel family|Marvel]]
| [[Marvel]]
|  
|  
| Negri, septimin, august,<br>amavil, enneaportent
| Negri, septimin, august,<br>amavil, enneaportent
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|  
|  
|-
|-
| [[Porwell family|Hewuermity]]
| [[Porwell]]
|  
|  
| Triforce, armodue,<br>twothirdtonic
| Triforce, armodue,<br>twothirdtonic
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| Amity, hemischis
| Amity, hemischis
|-
|-
| [[Orwellismic family|Orwellismic]]
| [[Orwellismic]]
|  
|  
| Beep, secund, infraorwell,<br>niner
| Beep, secund, infraorwell,<br>niner
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| Quartonic, buzzard
| Quartonic, buzzard
|-
|-
| [[Nuwell family|Nuwell]]
| [[Nuwell]]
|  
|  
| Progression, superpelog
| Progression, superpelog
| Quasisuper, hedgehog
| Quasisuper, hedgehog
| Squares, nusecond
| Squares, nusecond
| Tricot, hamity
| Alphatrimot, hamity
|-
|-
|  
|  
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| Quasisupra, hedgehog
| Quasisupra, hedgehog
| Squares, nusecond
| Squares, nusecond
| Tricot, hamity
| Alphatrimot, hamity
|-
|-
| [[Horwell family|Horwell]]
| [[Horwell]]
|  
|  
|  
|  
Line 597: Line 628:
== Music ==
== Music ==
; [[Tarkan Grood]]
; [[Tarkan Grood]]
* ''Mountain Villiage'' (2013) – [https://web.archive.org/web/20201127012514/http://micro.soonlabel.com/gene_ward_smith/Others/Grood/Mountain_Village_TarkanGrood.mp3 play] | [https://soundcloud.com/tarkan-grood/mountain-village-tarkangrood SoundCloud] – Orwell[9]
* ''Mountain Villiage'' (2013) – [https://web.archive.org/web/20201127012514/http://micro.soonlabel.com/gene_ward_smith/Others/Grood/Mountain_Village_TarkanGrood.mp3 play] | [https://soundcloud.com/tarkan-grood/mountain-village-tarkangrood SoundCloud] – in Orwell[9]


; [[Andrew Heathwaite]]
; [[Andrew Heathwaite]]
* ''[[Earwig]]'' (2012) – [https://web.archive.org/web/20201127015238/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/earwig.mp3 play] – in 31edo tuning
* ''[[Earwig]]'' (2012) – [https://web.archive.org/web/20201127015238/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/earwig.mp3 play] – in 31edo tuning
* [[Technical Notes for Newbeams #Elf Dine on Ho Ho|''Elf Dine on Ho Ho'']] (2012) – [https://web.archive.org/web/20201127015137/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3 play] – in 53edo tuning
* [[Technical Notes for Newbeams #Elf Dine on Ho Ho|''Elf Dine on Ho Ho'']] (2012) – [https://web.archive.org/web/20201127015137/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3 play] – in 53edo tuning
* [[Technical Notes for Newbeams #Spun|''Spun'']] (2012) – [https://web.archive.org/web/20201112021340/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3 play] – Orwell[13]
* [[Technical Notes for Newbeams #Spun|''Spun'']] (2012) – [https://web.archive.org/web/20201112021340/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3 play] – in Orwell[13]
* [https://web.archive.org/web/20201127013436/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3 ''one drop of rain'']
* [https://web.archive.org/web/20201127013436/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3 ''one drop of rain'']
* [https://web.archive.org/web/20201127014501/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3 ''i've come with a bucket of roses'']
* [https://web.archive.org/web/20201127014501/http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3 ''i've come with a bucket of roses'']
Line 612: Line 643:
; [[Löis Lancaster]] ([[Roncevaux]])
; [[Löis Lancaster]] ([[Roncevaux]])
* ''Schizo Blue'' – [https://web.archive.org/web/20201127012220/http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/Schizo_Blue__22_EDO_Orwell__first_mix_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 play] | [https://soundcloud.com/lois-lancaster/schizo-blue-22-edo-orwell SoundCloud]{{dead link}}
* ''Schizo Blue'' – [https://web.archive.org/web/20201127012220/http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/Schizo_Blue__22_EDO_Orwell__first_mix_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 play] | [https://soundcloud.com/lois-lancaster/schizo-blue-22-edo-orwell SoundCloud]{{dead link}}
* ''Sejaliscos'' (2013) – [https://web.archive.org/web/20201127012431/http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/Sejaliscos_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 play] | [https://soundcloud.com/lois-lancaster/sejaliscos SoundCloud] – Orwell[9] in 22edo tuning
* ''Sejaliscos'' (2013) – [https://web.archive.org/web/20201127012431/http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/Sejaliscos_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 play] | [https://soundcloud.com/lois-lancaster/sejaliscos SoundCloud] – in Orwell[9], 22edo tuning


; [[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]]
* ''[https://soundcloud.com/morphosyntax-1/a-hidden-world A Hidden World]'' (2022)
* ''[https://soundcloud.com/morphosyntax-1/a-hidden-world A Hidden World]'' (2022) – in Orwell[31]
* ''[https://soundcloud.com/morphosyntax-1/zurg-tuun-vantu-war-is-peace Zurğ tuun vantu]'' (2024)
* ''[https://soundcloud.com/morphosyntax-1/zurg-tuun-vantu-war-is-peace Zurğ tuun vantu]'' (2024) – in Orwell[13], with a generator of 271.5{{c}} and a period of 1199.5{{c}}
 
; [[Sevish]]
* "[[Droplet]]", from ''[[Rhythm and Xen]]'' (2015) – [https://sevish.bandcamp.com/track/droplet Bandcamp] | [https://soundcloud.com/sevish/droplet?in=sevish/sets/rhythm-and-xen SoundCloud] | [https://www.youtube.com/watch?v=xVZy9GUeMqY YouTube] – drum and bass in Orwell[9], 53edo tuning


; [[Gene Ward Smith]]
; [[Gene Ward Smith]]
* ''Trio in Orwell'' – [http://www.archive.org/details/TrioInOrwell details] | [http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play]
* ''Trio in Orwell'' (archived 2010) – [http://www.archive.org/details/TrioInOrwell details] | [http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play] – in Orwell[9], 53edo tuning
* [https://web.archive.org/web/20201112015404/http://micro.soonlabel.com/gene_ward_smith/transformers/swing-orwell9.mp3 ''Swing in Orwell-9'']
* [https://web.archive.org/web/20201112015404/http://micro.soonlabel.com/gene_ward_smith/transformers/swing-orwell9.mp3 ''Swing in Orwell-9'']


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== 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:
Line 640: Line 674:
[[File:orwell13_axis49.png|alt=orwell13_axis49.png|orwell13_axis49.png]]
[[File:orwell13_axis49.png|alt=orwell13_axis49.png|orwell13_axis49.png]]


[[Category:Temperaments]]
[[Category:Orwell| ]] <!-- main article -->
[[Category:Orwell| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Semicomma family]]
[[Category:Semicomma family]]
[[Category:Marvel temperaments]]
[[Category:Marvel temperaments]]
[[Category:Orwellismic temperaments]]
[[Category:Orwellismic temperaments]]
[[Category:Listen]]
[[Category:Listen]]

Latest revision as of 09:33, 9 February 2026

Orwell
Subgroups 2.3.5.7, 2.3.5.7.11
Comma basis 225/224, 1728/1715 (7-limit);
99/98, 121/120, 176/175 (11-limit)
Reduced mapping ⟨1; 7 -3 8 2]
ET join 22 & 31
Generators (CWE) ~7/6 = 271.5 ¢
MOS scales 4L 1s, 4L 5s, 9L 4s, 9L 13s
Ploidacot alpha-heptacot
Pergen (P8, cP5/7)
Minimax error 7-odd-limit: 4.27 ¢;
11-limit 21-odd-limit: 9.32 ¢
Target scale size 7-odd-limit: 13 notes;
11-limit 21-odd-limit: 22 notes
Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.

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.

In orwell, 8/5 is divided into three equal steps, each of which represent 7/6, so that 1728/1715 (S6/S7) is tempered out. This means that the 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 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; 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.

See Semicomma family #Orwell for technical details. See Orwell extensions for details about 13-limit extensions.

Theory

Interval chain

Odd harmonics 1–21 and their inverses are in bold.

# Cents* Approximate ratios
0 0.00 1/1
1 271.46 7/6
2 542.91 11/8, 15/11
3 814.37 8/5
4 1085.82 15/8, 28/15
5 157.28 11/10, 12/11, 35/32
6 428.73 9/7, 14/11, 32/25
7 700.19 3/2
8 971.64 7/4
9 43.10 33/32, 36/35, 49/48
10 314.55 6/5
11 586.01 7/5
12 857.46 18/11
13 1128.92 21/11, 27/14, 48/25
14 200.37 9/8, 28/25
15 471.83 21/16
16 743.28 49/32, 54/35
17 1014.74 9/5
18 86.19 21/20
19 357.65 27/22, 49/40
20 629.10 36/25
21 900.56 27/16, 42/25
22 1172.01 63/32

* In 11-limit CWE tuning, octave reduced

Chords and harmony

See also: Chords of orwell and Functional harmony in rank-2 temperaments

The fundamental otonal consonance of orwell, voiced in a roughly 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 generator, ~7/6, is a septimal interval, so chords could instead be built around it as 1–7/6–3/2 (0–1–7), 1–7/4–3 (0–8–7), or tetrads such as 1–7/6–3/2–7/4 (0–1–7–8).

To 1–7/6–3/2–7/4 we may add 11/8, or to 1–11/8–3/2–7/4 we may add 7/6, to form an essentially tempered pentad, 1–7/6–11/8–3/2–7/4 (0–1–2–7–8). Its inverse is 1–12/11–9/7–3/2–12/7 (0–5–6–7–(−1)), which can serve as a minor counterpart. This is similar, but also in clear contrast to the 1–5/4–3/2 (0–4–1) and 1–6/5–3/2 (0–(−3)–1) chords of meantone. Two approaches to functional harmony thus arise.

First, we can treat the septimal chords above as the basis of harmony, but swapping the roles of 3 and 7 according to their temperamental complexities (number of generator steps). Thus a "dominant" chord is either 7/6 or 12/7 over tonic; a "subdominant" chord is either 7/6 or 12/7 under tonic. This leads to an approach closely adherent to mos scales. The 9-tone mos contains a tonic and a "dominant" triad. The 13-tone mos is good for encapsulating tonic, "pre-dominant", and "dominant" functions, triads to pentads alike.

Second, we can treat the same chords as the basis of harmony, and keeping the role of the chain of fifths as the spine on which the functions are defined. This means dominant is still 3/2 over tonic, for example. A consequence is we must step out of the logic of mos scales, as they are often too restrictive without the many fifths to stack. This is essentially working in JI, but using the commas tempered out in some way to lock into the identity of the temperament.

Scales

Main article: Orwell scales

Mos scales

9-tone scales (sLsLsLsLs, 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-tone scales (LsLLsLLLsLLsL, 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
22-tone scales

Transversal scales

Others

Tunings

7-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Equilateral CEE: ~7/6 = 271.3553 ¢ CSEE: ~7/6 = 271.3339 ¢ POEE: ~7/6 = 271.3727 ¢
Tenney CTE: ~7/6 = 271.5130 ¢ CWE: ~7/6 = 271.5097 ¢ POTE: ~7/6 = 271.5087 ¢
Benedetti,
Wilson 		CBE: ~7/6 = 271.5725 ¢ CSBE: ~7/6 = 271.5741 ¢ POBE: ~7/6 = 271.5576 ¢
11-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Equilateral CEE: ~7/6 = 271.4920 ¢ CSEE: ~7/6 = 271.3038 ¢ POEE: ~7/6 = 271.1665 ¢
Tenney CTE: ~7/6 = 271.5597 ¢ CWE: ~7/6 = 271.4552 ¢ POTE: ~7/6 = 271.4261 ¢
Benedetti,
Wilson 		CBE: ~7/6 = 271.5915 ¢ CSBE: ~7/6 = 271.5302 ¢ POBE: ~7/6 = 271.5174 ¢
DR and equal-beating tunings
Optimized chord Generator value Polynomial Further notes
3:4:5 (+1 +1) ~7/6 = 272.890 ¢ f10 − 8f3 + 8 = 0 1–3–5 equal-beating tuning
4:5:6 (+1 +1) ~7/6 = 271.508 ¢ f10 + 2f3 - 8 = 0 1–3–5 equal-beating tuning

Tuning spectrum

Edo
generator 		Unchanged interval
(eigenmonzo)* 		Generator (¢) Comments
2\9 266.667 Lower bound of 7-odd-limit diamond monotone
7/6 266.871
15/11 268.475
11/7 269.585
11/6 270.127
15/14 270.139
49/48 270.633
21/11 270.728
7\31 270.968 Lower bound of 9- and 11-odd-limit diamond monotone
11/9 271.049
7/4 271.103
7/5 271.137 7- and 11-odd-limit minimax
5/4 271.229
21/20 271.359
21/16 271.385
19\84 271.429 84e val
25/24 271.487
64/63 271.488
5/3 271.564 5-odd-limit minimax
9/5 271.623 9-odd-limit minimax
81/80 271.661
12\53 271.698
3/2 271.708
17\75 272.000
15/8 272.067
36/35 272.086
9/7 272.514
5\22 272.727 Upper bound of 7-, 9- and 11-odd-limit diamond monotone
11/10 273.001
11/8 275.659

* Besides the octave

Non-octave settings

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 would not be one anymore. This temperament could be called watcher, a reference to a class of angels whose very name carries Orwellian connotations. The 12-integer-limit otonality (1::12) and utonality (1/(1::12)) 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 do not perform well past the 10-integer-limit, watcher handles the 12-integer-limit with ease. Straight-fretted watcher guitars could be built as long as the strings were all tuned to period-equivalent notes.

Rank-3 temperaments

Following is a list of rank-3, or planar temperaments that are supported by orwell temperament.

Rank-3 temperament Among others, rank-3 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
Porwell 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 Alphatrimot, hamity
Big brother Progression, superpelog Quasisupra, hedgehog Squares, nusecond Alphatrimot, 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

Tarkan Grood
Andrew Heathwaite
Peter Kosmorsky
Löis Lancaster (Roncevaux)
Claudi Meneghin
Herman Miller
Sevish
Gene Ward Smith
Chris Vaisvil

Keyboards

See also: Orwell on an isomorphic keyboard and Lumatone mapping for orwell

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

Orwell_13.png

Orwell_22.png

orwell13_axis49.png

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