Semicomma family: Difference between revisions

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~~__FORCETOC__~~

The 5-limit parent comma for the '''semicomma family''' is the semicomma, 2109375/2097152 = {{monzo| -21 3 7 }}. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths.

~~=Orson=~~

The 5-limit parent comma for the '''semicomma family''' is the semicomma, 2109375/2097152 = |-21 3 7~~>~~. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths. '''Orson''', the [[~~5-limit|~~5-limit]] temperament tempering it out, has a [[~~generator|~~generator]] of 75/64, which is sharper than 7/6 by 225/224 when untempered, and less sharp than that in any good orson tempering, for example [[~~53edo|~~53edo]] or [[~~84edo|~~84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[~~cent|~~cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.

= Orson =

'''Orson''', the [[5-limit]] temperament tempering out the semicomma, has a [[generator]] of 75/64, which is sharper than [[7/6]] by [[225/224]] when untempered, and less sharp than that in any good orson tempering, for example [[53edo]] or [[84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.

Comma: 2109375/2097152

[[~~Tuning_Ranges_of_Regular_Temperaments~~|valid range]]: [257.143, 276.923] (14b to 13)

[[Tuning Ranges of Regular Temperaments|valid range]]: [257.143, 276.923] (14b to 13)

nice range: [271.229, 271.708]

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strict range: [271.229, 271.708]

[[~~POTE_tuning|~~POTE generator]]: ~75/64 = 271.627

[[POTE generator]]: ~75/64 = 271.627

Map: [<1 0 3|, <0 7 -3|]

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Badness: 0.0408

==Seven limit children==

== Seven limit children ==

The second comma of the [[~~Normal_lists~~|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/~~64625~~ leads to orwell, but we could also add 1029/1024, leading to the 31&159 temperament with wedgie <<21 -9 -7 -63 -70 9||, or 67528125/67108864, giving the 31&243 temperament with wedgie <<28 -12 1 -84 -77 36||, or 4375/4374, giving the 53&243 temperament with wedgie <<7 -3 61 -21 77 150||.

The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/65625 leads to orwell, but we could also add

* 1029/1024, leading to the 31&159 temperament with wedgie <<21 -9 -7 -63 -70 9||, or

* 67528125/67108864, giving the 31&243 temperament with wedgie <<28 -12 1 -84 -77 36||, or

* 4375/4374, giving the 53&243 temperament with wedgie <<7 -3 61 -21 77 150||.

=Orwell=

= Orwell =

~~Main article: [[Orwell~~|Orwell]]

So called because 19\84 (as a [[~~fraction_of_the_octave|~~fraction of the octave]]) is a possible generator of this temperament, orwell divides the interval of a twelfth (a tempered 3/1 frequency ratio) into 7 equal steps. It's compatible with [[22edo|22]], [[31edo|31]], [[53edo|53]] and [[84edo|84]] equal, and may be described as the 22&31 temperament, or <<7 -3 8 -21 -7 27||. It's a good system in the [[~~7-limit|~~7-limit]] and naturally extends into the [[~~11-limit|~~11-limit]]. [[~~84edo|~~84edo]], with the 19\84 generator, provides a good tuning for the 5, 7 and 11 limits, but it does use its second-best 11. However, the 19\84 generator is remarkably close to the 11-limit [[~~POTE_tuning|~~POTE tuning]], as the generator is only 0.0024 cents sharper, and it is a good approximation to the 7-limit POTE generator also; hence 84 may be considered the most recommendable tuning in the 7-limit. [[~~53edo|~~53edo]] might be preferred in the 5-limit because of its nearly pure fifth and in the 11-limit because of it slightly better 11, though most of its 11-limit harmony is actually worse. Aside from the semicomma and 65625/65536, 7-limit orwell tempers out 2430/2401, the nuwell comma, 1728/1715, the orwellisma, 225/224, the septimal kleisma, and 6144/6125, the porwell comma.

So called because 19\84 (as a [[fraction of the octave]]) is a possible generator of this temperament, orwell divides the interval of a twelfth (a tempered 3/1 frequency ratio) into 7 equal steps. It's compatible with [[22edo|22]], [[31edo|31]], [[53edo|53]] and [[84edo|84]] equal, and may be described as the 22&31 temperament, or <<7 -3 8 -21 -7 27||. It's a good system in the [[7-limit]] and naturally extends into the [[11-limit]]. [[84edo]], with the 19\84 generator, provides a good tuning for the 5, 7 and 11 limits, but it does use its second-best 11. However, the 19\84 generator is remarkably close to the 11-limit [[POTE tuning]], as the generator is only 0.0024 cents sharper, and it is a good approximation to the 7-limit POTE generator also; hence 84 may be considered the most recommendable tuning in the 7-limit. [[53edo]] might be preferred in the 5-limit because of its nearly pure fifth and in the 11-limit because of it slightly better 11, though most of its 11-limit harmony is actually worse. Aside from the semicomma and 65625/65536, 7-limit orwell tempers out [[2430/2401]], the nuwell comma, [[1728/1715]], the orwellisma, [[225/224]], the septimal kleisma, and [[6144/6125]], the porwell comma.

The 11-limit version of orwell tempers out 99/98, which means that two of its sharpened 7/6 generators give a flattened 11/8, as well as 121/120, 176/175, 385/384 and 540/539. Despite lowered tuning accuracy, orwell comes into its own in the 11-limit, giving acceptable accuracy and relatively low complexity. Tempering out the orwellisma, 1728/1715, means that orwell interprets three stacked 7/6 generators as an 8/5, and the tempered 1-7/6-11/8-8/5 chord is natural to orwell.

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Orwell has MOS of size 9, 13, 22 and 31. The 9-note MOS is small enough to be retained in the mind as a genuine scale, is pleasing melodically, and has [[Retuning_12edo_to_Orwell9|considerable harmonic resources]] despite its absence of 5-limit triads. The 13 note MOS has those, and of course the 22 and 31 note MOS are very well supplied with everything.

[[Comma~~|Commas~~]]: 225/224, 1728/1715

[[Comma]]s: 225/224, 1728/1715

7-limit

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|27/11 0 3/11 -3/11>, |27/11 0 -8/11 8/11>]

[[~~Fractional_monzos|Eigenmonzos~~]]: 2, 7/5

[[Eigenmonzo]]s: 2, 7/5

9-limit

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|42/17 -6/17 3/17 0>, |41/17 16/17 -8/17 0>]

[[Eigenmonzo~~|Eigenmonzos~~]]: 2, 10/9

[[Eigenmonzo]]s: 2, 10/9

valid range: [266.667, 272.727] (9 to 22)

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strict range: [266.871, 271.708]

[[~~POTE_tuning|~~POTE generator]]: ~7/6 = 271.509

[[POTE generator]]: ~7/6 = 271.509

Algebraic generators: Sabra3, the real root of 12x^3-7x-48.

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Wedgie: <<7 -3 8 -21 -7 27||

EDOs: 22, 31, 53, 84, 137, 221d, 358d

Badness: 0.0207

==11-limit==

[[Comma~~|Commas~~]]: 99/98, 121/120, 176/175

[[Comma]]s: 99/98, 121/120, 176/175

[[~~Minimax_tuning|~~Minimax tuning]]

[[Minimax tuning]]

[|1 0 0 0 0>, |14/11 0 -7/11 7/11 0>, |27/11 0 3/11 -3/11 0>,

|27/11 0 -8/11 8/11 0>, |37/11 0 -2/11 2/11 0>]

[[Eigenmonzo~~|Eigenmonzos~~]]: 2, 7/5

[[Eigenmonzo]]s: 2, 7/5

valid range: [270.968, 272.727] (31 to 22)

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strict range: [270.968, 272.727]

[[~~POTE_tuning|~~POTE generator]]: ~7/6 = 271.426

[[POTE generator]]: ~7/6 = 271.426

Map: [<1 0 3 1 3|, <0 7 -3 8 2|]

~~[[EDO~~|~~Edos]]: [[22edo~~|22]], ~~[[31edo|~~31]], ~~[[53edo|~~53]], ~~[[84edo|~~84e]]

Badness: 0.0152

==13-limit==

=== 13-limit ===

Commas: 99/98, 121/120, 176/175, 275/273

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strict range: [270.968, 271.698]

[[~~POTE_tuning|~~POTE generator]]: ~7/6 = 271.546

[[POTE generator]]: ~7/6 = 271.546

Map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|]

EDOs: 22, 31, 53, 84e, 137e

Badness: 0.0197

[[Orwell#Music|Music in Orwell]]

[[Orwell #Music|Music in Orwell]]

==Blair==

=== Blair ===

Commas: 65/64, 78/77, 91/90, 99/98

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Map: [<1 0 3 1 3 3|, <0 7 -3 8 2 3|]

EDOs: 9, 22, 31f

Badness: 0.0231

==~~Newspeak~~==

=== Winston ===

~~Commas: 225/224, 441/440, 1728/1715~~

~~valid range: [270.968, 271.698] (31 to 53)~~

~~nice range: [266.871, 272.514]~~

~~strict range: [270.968, 271.698]~~

~~POTE tuning: ~7/6 = 271.288~~

~~Map: [<1 0 3 1 -4|, <0 7 -3 8 33|]~~

~~EDOs: 31, 84, 115, 376b, 491bd, 606bde~~

~~Badness: 0.0314~~

~~==Winston~~==

Commas: 66/65, 99/98, 105/104, 121/120

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strict range: [270.968, 272.727]

[[~~POTE_tuning|~~POTE generator]]: ~7/6 = 271.088

[[POTE generator]]: ~7/6 = 271.088

Map: [<1 0 3 1 3 1|, <0 7 -3 8 2 12|]

EDOs: 22f, 31

Badness: 0.0199

=Doublethink=

=== Doublethink ===

Commas: 99/98, 121/120, 169/168, 176/175

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Map: [<1 0 3 1 3 2|, <0 14 -6 16 4 15|]

EDOs: 9, 35, 44, 53, 62, 115ef, 168ef

Badness: 0.0271

=Borwell=

== Newspeak ==

Commas: 225/224, 441/440, 1728/1715

valid range: [270.968, 271.698] (31 to 53)

nice range: [266.871, 272.514]

strict range: [270.968, 271.698]

POTE tuning: ~7/6 = 271.288

Map: [<1 0 3 1 -4|, <0 7 -3 8 33|]

Badness: 0.0314

== Borwell ==

Commas: 225/224, 243/242, 1728/1715

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Map: [<1 7 0 9 17|, <0 -14 6 -16 -35|]

EDOs: 31, 106, 137, 442bd

Badness: 0.0384

=Triwell=

= Triwell =

Commas: 1029/1024, 235298/234375

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Wedgie: <<21 -9 -7 -63 -70 9||

EDOs: 31, 97, 128, 159, 190

Badness: 0.0806

==11-limit==

== 11-limit ==

Commas: 385/384, 441/440, 456533/455625

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Map: [<1 7 0 1 13|, <0 -21 9 7 -37]]

EDOs: 31, 97, 128, 159, 190

Badness: 0.0298

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[[Category:Temperament family]]

[[Category:Semicomma]]

[[Category:Rank 2]]

[[Category:Orwell]]

[[Category:Listen]]

~~[[Category:Orwell]]~~

~~[[Category:Todo:add_definition]]~~

~~[[Category:Todo:intro]]~~

@@ Line 1: / Line 1: @@
-__FORCETOC__
+The 5-limit parent comma for the '''semicomma family''' is the semicomma, 2109375/2097152 = {{monzo| -21 3 7 }}. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths.
-=Orson=
-The 5-limit parent comma for the '''semicomma family''' is the semicomma, 2109375/2097152 = |-21 3 7&gt;. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths. '''Orson''', the [[5-limit|5-limit]] temperament tempering it out, has a [[generator|generator]] of 75/64, which is sharper than 7/6 by 225/224 when untempered, and less sharp than that in any good orson tempering, for example [[53edo|53edo]] or [[84edo|84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[cent|cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.
+= Orson =
+'''Orson''', the [[5-limit]] temperament tempering out the semicomma, has a [[generator]] of 75/64, which is sharper than [[7/6]] by [[225/224]] when untempered, and less sharp than that in any good orson tempering, for example [[53edo]] or [[84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.
 Comma: 2109375/2097152
-[[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [257.143, 276.923] (14b to 13)
+[[Tuning Ranges of Regular Temperaments|valid range]]: [257.143, 276.923] (14b to 13)
 nice range: [271.229, 271.708]
@@ Line 11: / Line 12: @@
 strict range: [271.229, 271.708]
-[[POTE_tuning|POTE generator]]: ~75/64 = 271.627
+[[POTE generator]]: ~75/64 = 271.627
 Map: [&lt;1 0 3|, &lt;0 7 -3|]
@@ Line 19: / Line 20: @@
 Badness: 0.0408
-==Seven limit children==
+== Seven limit children ==
-The second comma of the [[Normal_lists|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/64625 leads to orwell, but we could also add 1029/1024, leading to the 31&amp;159 temperament with wedgie &lt;&lt;21 -9 -7 -63 -70 9||, or 67528125/67108864, giving the 31&amp;243 temperament with wedgie &lt;&lt;28 -12 1 -84 -77 36||, or 4375/4374, giving the 53&amp;243 temperament with wedgie &lt;&lt;7 -3 61 -21 77 150||.
+The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/65625 leads to orwell, but we could also add
+* 1029/1024, leading to the 31&amp;159 temperament with wedgie &lt;&lt;21 -9 -7 -63 -70 9||, or
+* 67528125/67108864, giving the 31&amp;243 temperament with wedgie &lt;&lt;28 -12 1 -84 -77 36||, or
+* 4375/4374, giving the 53&amp;243 temperament with wedgie &lt;&lt;7 -3 61 -21 77 150||.
-=Orwell=
+= Orwell =
-Main article: [[Orwell|Orwell]]
+{{main| Orwell }}
-So called because 19\84 (as a [[fraction_of_the_octave|fraction of the octave]]) is a possible generator of this temperament, orwell divides the interval of a twelfth (a tempered 3/1 frequency ratio) into 7 equal steps. It's compatible with [[22edo|22]], [[31edo|31]], [[53edo|53]] and [[84edo|84]] equal, and may be described as the 22&amp;31 temperament, or &lt;&lt;7 -3 8 -21 -7 27||. It's a good system in the [[7-limit|7-limit]] and naturally extends into the [[11-limit|11-limit]]. [[84edo|84edo]], with the 19\84 generator, provides a good tuning for the 5, 7 and 11 limits, but it does use its second-best 11. However, the 19\84 generator is remarkably close to the 11-limit [[POTE_tuning|POTE tuning]], as the generator is only 0.0024 cents sharper, and it is a good approximation to the 7-limit POTE generator also; hence 84 may be considered the most recommendable tuning in the 7-limit. [[53edo|53edo]] might be preferred in the 5-limit because of its nearly pure fifth and in the 11-limit because of it slightly better 11, though most of its 11-limit harmony is actually worse. Aside from the semicomma and 65625/65536, 7-limit orwell tempers out 2430/2401, the nuwell comma, 1728/1715, the orwellisma, 225/224, the septimal kleisma, and 6144/6125, the porwell comma.
+So called because 19\84 (as a [[fraction of the octave]]) is a possible generator of this temperament, orwell divides the interval of a twelfth (a tempered 3/1 frequency ratio) into 7 equal steps. It's compatible with [[22edo|22]], [[31edo|31]], [[53edo|53]] and [[84edo|84]] equal, and may be described as the 22&amp;31 temperament, or &lt;&lt;7 -3 8 -21 -7 27||. It's a good system in the [[7-limit]] and naturally extends into the [[11-limit]]. [[84edo]], with the 19\84 generator, provides a good tuning for the 5, 7 and 11 limits, but it does use its second-best 11. However, the 19\84 generator is remarkably close to the 11-limit [[POTE tuning]], as the generator is only 0.0024 cents sharper, and it is a good approximation to the 7-limit POTE generator also; hence 84 may be considered the most recommendable tuning in the 7-limit. [[53edo]] might be preferred in the 5-limit because of its nearly pure fifth and in the 11-limit because of it slightly better 11, though most of its 11-limit harmony is actually worse. Aside from the semicomma and 65625/65536, 7-limit orwell tempers out [[2430/2401]], the nuwell comma, [[1728/1715]], the orwellisma, [[225/224]], the septimal kleisma, and [[6144/6125]], the porwell comma.
 The 11-limit version of orwell tempers out 99/98, which means that two of its sharpened 7/6 generators give a flattened 11/8, as well as 121/120, 176/175, 385/384 and 540/539. Despite lowered tuning accuracy, orwell comes into its own in the 11-limit, giving acceptable accuracy and relatively low complexity. Tempering out the orwellisma, 1728/1715, means that orwell interprets three stacked 7/6 generators as an 8/5, and the tempered 1-7/6-11/8-8/5 chord is natural to orwell.
@@ Line 31: / Line 35: @@
 Orwell has MOS of size 9, 13, 22 and 31. The 9-note MOS is small enough to be retained in the mind as a genuine scale, is pleasing melodically, and has [[Retuning_12edo_to_Orwell9|considerable harmonic resources]] despite its absence of 5-limit triads. The 13 note MOS has those, and of course the 22 and 31 note MOS are very well supplied with everything.
-[[Comma|Commas]]: 225/224, 1728/1715
+[[Comma]]s: 225/224, 1728/1715
 -limit
@@ Line 38: / Line 42: @@
 |27/11 0 3/11 -3/11&gt;, |27/11 0 -8/11 8/11&gt;]
-[[Fractional_monzos|Eigenmonzos]]: 2, 7/5
+[[Eigenmonzo]]s: 2, 7/5
 -limit
@@ Line 45: / Line 49: @@
 |42/17 -6/17 3/17 0&gt;, |41/17 16/17 -8/17 0&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 10/9
+[[Eigenmonzo]]s: 2, 10/9
 valid range: [266.667, 272.727] (9 to 22)
@@ Line 53: / Line 57: @@
 strict range: [266.871, 271.708]
-[[POTE_tuning|POTE generator]]: ~7/6 = 271.509
+[[POTE generator]]: ~7/6 = 271.509
 Algebraic generators: Sabra3, the real root of 12x^3-7x-48.
@@ Line 61: / Line 65: @@
 Wedgie: &lt;&lt;7 -3 8 -21 -7 27||
-EDOs: 22, 31, 53, 84, 137, 221d, 358d
+{{EDOs|legend=1| 22, 31, 53, 84, 137, 221d, 358d }}
 Badness: 0.0207
 ==11-limit==
-[[Comma|Commas]]: 99/98, 121/120, 176/175
+[[Comma]]s: 99/98, 121/120, 176/175
-[[Minimax_tuning|Minimax tuning]]
+[[Minimax tuning]]
 [|1 0 0 0 0&gt;, |14/11 0 -7/11 7/11 0&gt;, |27/11 0 3/11 -3/11 0&gt;,
 |27/11 0 -8/11 8/11 0&gt;, |37/11 0 -2/11 2/11 0&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 7/5
+[[Eigenmonzo]]s: 2, 7/5
 valid range: [270.968, 272.727] (31 to 22)
@@ Line 81: / Line 85: @@
 strict range: [270.968, 272.727]
-[[POTE_tuning|POTE generator]]: ~7/6 = 271.426
+[[POTE generator]]: ~7/6 = 271.426
 Map: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]
-[[EDO|Edos]]: [[22edo|22]], [[31edo|31]], [[53edo|53]], [[84edo|84e]]
+{{EDOs|legend=1| 22, 31, 53, 84e }}
 Badness: 0.0152
-==13-limit==
+=== 13-limit ===
 Commas: 99/98, 121/120, 176/175, 275/273
@@ Line 98: / Line 102: @@
 strict range: [270.968, 271.698]
-[[POTE_tuning|POTE generator]]: ~7/6 = 271.546
+[[POTE generator]]: ~7/6 = 271.546
 Map: [&lt;1 0 3 1 3 8|, &lt;0 7 -3 8 2 -19|]
-EDOs: 22, 31, 53, 84e, 137e
+{{EDOs|legend=1| 22, 31, 53, 84e, 137e }}
 Badness: 0.0197
-[[Orwell#Music|Music in Orwell]]
+[[Orwell #Music|Music in Orwell]]
-==Blair==
+=== Blair ===
 Commas: 65/64, 78/77, 91/90, 99/98
@@ Line 121: / Line 125: @@
 Map: [&lt;1 0 3 1 3 3|, &lt;0 7 -3 8 2 3|]
-EDOs: 9, 22, 31f
+{{EDOs|legend=1| 9, 22, 31f }}
 Badness: 0.0231
-==Newspeak==
+=== Winston ===
-Commas: 225/224, 441/440, 1728/1715
-valid range: [270.968, 271.698] (31 to 53)
-nice range: [266.871, 272.514]
-strict range: [270.968, 271.698]
-POTE tuning: ~7/6 = 271.288
-Map: [&lt;1 0 3 1 -4|, &lt;0 7 -3 8 33|]
-EDOs: 31, 84, 115, 376b, 491bd, 606bde
-Badness: 0.0314
-==Winston==
 Commas: 66/65, 99/98, 105/104, 121/120
@@ Line 151: / Line 138: @@
 strict range: [270.968, 272.727]
-[[POTE_tuning|POTE generator]]: ~7/6 = 271.088
+[[POTE generator]]: ~7/6 = 271.088
 Map: [&lt;1 0 3 1 3 1|, &lt;0 7 -3 8 2 12|]
-EDOs: 22f, 31
+{{EDOs|legend=1| 22f, 31 }}
 Badness: 0.0199
-=Doublethink=
+=== Doublethink ===
 Commas: 99/98, 121/120, 169/168, 176/175
@@ Line 172: / Line 159: @@
 Map: [&lt;1 0 3 1 3 2|, &lt;0 14 -6 16 4 15|]
-EDOs: 9, 35, 44, 53, 62, 115ef, 168ef
+{{EDOs|legend=1| 9, 35, 44, 53, 62, 115ef, 168ef }}
 Badness: 0.0271
-=Borwell=
+== Newspeak ==
+Commas: 225/224, 441/440, 1728/1715
+valid range: [270.968, 271.698] (31 to 53)
+nice range: [266.871, 272.514]
+strict range: [270.968, 271.698]
+POTE tuning: ~7/6 = 271.288
+Map: [&lt;1 0 3 1 -4|, &lt;0 7 -3 8 33|]
+{{EDOs|legend=1| 31, 84, 115, 376b, 491bd, 606bde }}
+Badness: 0.0314
+== Borwell ==
 Commas: 225/224, 243/242, 1728/1715
@@ Line 183: / Line 187: @@
 Map: [&lt;1 7 0 9 17|, &lt;0 -14 6 -16 -35|]
-EDOs: 31, 106, 137, 442bd
+{{EDOs|legend=1| 31, 106, 137, 442bd }}
 Badness: 0.0384
-=Triwell=
+= Triwell =
 Commas: 1029/1024, 235298/234375
@@ Line 196: / Line 200: @@
 Wedgie: &lt;&lt;21 -9 -7 -63 -70 9||
-EDOs: 31, 97, 128, 159, 190
+{{EDOs|legend=1| 31, 97, 128, 159, 190 }}
 Badness: 0.0806
-==11-limit==
+== 11-limit ==
 Commas: 385/384, 441/440, 456533/455625
@@ Line 207: / Line 211: @@
 Map: [&lt;1 7 0 1 13|, &lt;0 -21 9 7 -37]]
-EDOs: 31, 97, 128, 159, 190
+{{EDOs|legend=1| 31, 97, 128, 159, 190 }}
 Badness: 0.0298
@@ Line 214: / Line 218: @@
 [[Category:Temperament family]]
 [[Category:Semicomma]]
+[[Category:Rank 2]]
+[[Category:Orwell]]
 [[Category:Listen]]
-[[Category:Orwell]]
-[[Category:Todo:add_definition]]
-[[Category:Todo:intro]]