Semicomma family: Difference between revisions

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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 ==

'''Orson''', first discovered by [[Erv Wilson]], is the [[5-limit]] temperament tempering out the semicomma. It 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.

'''Orson''', first discovered by [[Erv Wilson]], is the [[5-limit]] temperament tempering out the semicomma. It 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|53EDO]] or [[84edo|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.

Subgroup: 2.3.5

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[[Comma list]]: 2109375/2097152

[[Mapping]]: [{{val| 1 0 3}}, {{val| 0 7 -3}}]

[[Mapping]]: [{{val| 1 0 3 }}, {{val| 0 7 -3 }}]

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

[[Tuning ranges]]:

* [[~~diamond~~ monotone]] range: [257.143, 276.923] (3\14 to 3\13)

* [[Diamond monotone]] range: [257.143, 276.923] (3\14 to 3\13)

* [[~~diamond~~ tradeoff]] range: [271.229, 271.708]

* [[Diamond tradeoff]] range: [271.229, 271.708]

* ~~diamond~~ monotone and tradeoff ~~range~~: [271.229, 271.708]

* Diamond monotone and tradeoff: [271.229, 271.708]

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[[Badness]]: 0.040807

=== Seven limit children ===

The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65625/65536 (or 225/224) leads to orwell, but we could also add

* 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or

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* 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}.

== Orwell ==

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 {{multival| 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.

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 {{multival| 7 -3 8 -21 -7 27 }}. It's a good system in the [[7-limit]] and naturally extends into the [[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]], 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.

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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[[Minimax tuning]]:

* [[7-odd-limit]]

* [[7-odd-limit]]: ~7/6 = {{monzo| 2/11 0 -1/11 1/11 }}

: [{{monzo| 1 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 }}, {{monzo| 27/11 0 3/11 -3/11 }}, {{monzo| 27/11 0 -8/11 8/11 }}]

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

* 9-odd-limit

* 9-odd-limit: ~7/6 = {{monzo| 3/17 2/17 -1/17 }}

: [{{monzo| 1 0 0 0 }}, {{monzo| 21/17 14/17 -7/17 0 }}, {{monzo| 42/17 -6/17 3/17 0 }}, {{monzo| 41/17 16/17 -8/17 0 }}]

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

[[Tuning ranges]]:

* [[~~diamond~~ monotone]] range: [266.667, 272.727] (2\9 to 5\22)

* [[Diamond monotone]] range: [266.667, 272.727] (2\9 to 5\22)

* [[~~diamond~~ tradeoff]] range: [266.871, 271.708]

* [[Diamond tradeoff]] range: [266.871, 271.708]

* ~~diamond~~ monotone and tradeoff ~~range~~: [266.871, 271.708]

* Diamond monotone and tradeoff: [266.871, 271.708]

[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.

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[[Badness]]: 0.020735

=== 11-limit ===

Subgroup: 2.3.5.7.11

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Minimax tuning:

* 11-odd-limit

* 11-odd-limit: ~7/6 = {{monzo| 2/11 0 -1/11 1/11 }}

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 0 }}, {{monzo| 27/11 0 3/11 -3/11 0 }}, {{monzo| 27/11 0 -8/11 8/11 0 }}, {{monzo| 37/11 0 -2/11 2/11 0 }}]

: Eigenmonzos: 2, 7/5

Tuning ranges:

* ~~[[diamond~~ monotone]] range: [270.968, 272.727] (7\31 to 5\22)

* Diamond monotone range: [270.968, 272.727] (7\31 to 5\22)

* ~~[[diamond~~ tradeoff]] range: [266.871, 275.659]

* Diamond tradeoff range: [266.871, 275.659]

* ~~diamond~~ monotone and tradeoff ~~range~~: [270.968, 272.727]

* Diamond monotone and tradeoff: [270.968, 272.727]

Vals: {{Val list| 9, 22, 31, 53, 84e }}

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Badness: 0.015231

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

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Tuning ranges:

* ~~[[diamond~~ monotone]] range: [270.968, 271.698] (7\31 to 12\53)

* Diamond monotone range: [270.968, 271.698] (7\31 to 12\53)

* ~~[[diamond~~ tradeoff]] range: [266.871, 275.659]

* Diamond tradeoff range: [266.871, 275.659]

* ~~diamond~~ monotone and tradeoff ~~range~~: [270.968, 271.698]

* Diamond monotone and tradeoff: [270.968, 271.698]

Vals: {{Val list| 22, 31, 53, 84e, 137e }}

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Badness: 0.019718

==== Blair ====

Subgroup: 2.3.5.7.11.13

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Badness: 0.023086

==== Winston ====

Subgroup: 2.3.5.7.11.13

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Tuning ranges:

* ~~[[diamond~~ monotone]] range: [270.968, 272.727] (7\31 to 5\22)

* Diamond monotone range: [270.968, 272.727] (7\31 to 5\22)

* ~~[[diamond~~ tradeoff]] range: [266.871, 281.691]

* Diamond tradeoff range: [266.871, 281.691]

* ~~diamond~~ monotone and tradeoff ~~range~~: [270.968, 272.727]

* Diamond monotone and tradeoff: [270.968, 272.727]

Vals: {{Val list| 22f, 31 }}

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Badness: 0.019931

==== Doublethink ====

Subgroup: 2.3.5.7.11.13

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Tuning ranges:

* ~~[[diamond~~ monotone]] range: [135.484, 136.364] (7\62 to 5\44)

* Diamond monotone range: [135.484, 136.364] (7\62 to 5\44)

* ~~[[diamond~~ tradeoff]] range: [128.298, 138.573]

* Diamond tradeoff range: [128.298, 138.573]

* ~~diamond~~ monotone and tradeoff ~~range~~: [135.484, 136.364]

* Diamond monotone and tradeoff: [135.484, 136.364]

Vals: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}

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Badness: 0.027120

=== Newspeak ===

Subgroup: 2.3.5.7.11

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Tuning ranges:

* ~~[[diamond~~ monotone]] range: [270.968, 271.698] (7\31 to 12\53)

* Diamond monotone range: [270.968, 271.698] (7\31 to 12\53)

* ~~[[diamond~~ tradeoff]] range: [266.871, 272.514]

* Diamond tradeoff range: [266.871, 272.514]

* ~~diamond~~ monotone and tradeoff ~~range~~: [270.968, 271.698]

* Diamond monotone and tradeoff: [270.968, 271.698]

Vals: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}

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Badness: 0.031438

=== Borwell ===

Subgroup: 2.3.5.7.11

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Badness: 0.038377

== Triwell ==

The triwell temperament (31&159) slices orwell major sixth ~128/75 into three generators, nine of which give the fifth harmonic.

Subgroup: 2.3.5.7

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[[Badness]]: 0.080575

=== 11-limit ===

Subgroup: 2.3.5.7.11

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Badness: 0.029807

== Quadrawell ==

The ''quadrawell'' temperament (31&212~~, named by [[User:Xenllium|Xenllium]]~~) has an [[8/7]] generator of about 232 cents, twelve of which give the fifth harmonic.

The ''quadrawell'' temperament (31&212) has an [[8/7]] generator of about 232 cents, twelve of which give the fifth harmonic.

Subgroup: 2.3.5.7

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[[Badness]]: 0.075754

=== 11-limit ===

Subgroup: 2.3.5.7.11

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Badness: 0.036493

== Sabric ==

The ''sabric'' temperament (53&190~~, named by [[User:Xenllium]]~~) tempers out the [[4375/4374|ragisma]], 4375/4374. It is so named because it is closely related to the '''Sabra2 tuning''' (generator: 271.607278 cents).

The ''sabric'' temperament (53&190) tempers out the [[4375/4374|ragisma]], 4375/4374. It is so named because it is closely related to the '''Sabra2 tuning''' (generator: 271.607278 cents).

Subgroup: 2.3.5.7

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[[Badness]]: 0.088355

== Rainwell ==

The ''rainwell'' temperament (31&265~~, named by [[User:Xenllium]]~~) tempers out the mirkwai comma, 16875/16807 and the [[rainy comma]], 2100875/2097152.

The ''rainwell'' temperament (31&265) tempers out the mirkwai comma, 16875/16807 and the [[rainy comma]], 2100875/2097152.

Subgroup: 2.3.5.7

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Badness: 0.143488

=== 11-limit ===

Subgroup: 2.3.5.7.11

@@ Line 1: / Line 1: @@
 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  ==
+== Orson ==
-'''Orson''', first discovered by [[Erv Wilson]], is the [[5-limit]] temperament tempering out the semicomma. It 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.
+'''Orson''', first discovered by [[Erv Wilson]], is the [[5-limit]] temperament tempering out the semicomma. It 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|53EDO]] or [[84edo|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.
 Subgroup: 2.3.5
@@ Line 8: / Line 8: @@
 [[Comma list]]: 2109375/2097152
-[[Mapping]]: [{{val| 1 0 3}}, {{val| 0 7 -3}}]
+[[Mapping]]: [{{val| 1 0 3 }}, {{val| 0 7 -3 }}]
 [[POTE generator]]: ~75/64 = 271.627
 [[Tuning ranges]]:
-* [[diamond monotone]] range: [257.143, 276.923] (3\14 to 3\13)
+* [[Diamond monotone]] range: [257.143, 276.923] (3\14 to 3\13)
-* [[diamond tradeoff]] range: [271.229, 271.708]
+* [[Diamond tradeoff]] range: [271.229, 271.708]
-* diamond monotone and tradeoff range: [271.229, 271.708]
+* Diamond monotone and tradeoff: [271.229, 271.708]
 {{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
@@ Line 21: / Line 21: @@
 [[Badness]]: 0.040807
-=== Seven limit children  ===
+=== Seven limit children ===
 The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65625/65536 (or 225/224) leads to orwell, but we could also add
 * 1029/1024, leading to the 31&amp;159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or
@@ Line 27: / Line 27: @@
 * 4375/4374, giving the 53&amp;243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}.
-== Orwell  ==
+== Orwell ==
 {{main| Orwell }}
-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 {{multival| 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.
+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 {{multival| 7 -3 8 -21 -7 27 }}. It's a good system in the [[7-limit]] and naturally extends into the [[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]], 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.
 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 47: / Line 47: @@
 [[Minimax tuning]]:
-* [[7-odd-limit]]
+* [[7-odd-limit]]: ~7/6 = {{monzo| 2/11 0 -1/11 1/11 }}
 : [{{monzo| 1 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 }}, {{monzo| 27/11 0 3/11 -3/11 }}, {{monzo| 27/11 0 -8/11 8/11 }}]
 : [[Eigenmonzo]]s: 2, 7/5
-* 9-odd-limit
+* 9-odd-limit: ~7/6 = {{monzo| 3/17 2/17 -1/17 }}
 : [{{monzo| 1 0 0 0 }}, {{monzo| 21/17 14/17 -7/17 0 }}, {{monzo| 42/17 -6/17 3/17 0 }}, {{monzo| 41/17 16/17 -8/17 0 }}]
 : [[Eigenmonzo]]s: 2, 10/9
 [[Tuning ranges]]:
-* [[diamond monotone]] range: [266.667, 272.727] (2\9 to 5\22)
+* [[Diamond monotone]] range: [266.667, 272.727] (2\9 to 5\22)
-* [[diamond tradeoff]] range: [266.871, 271.708]
+* [[Diamond tradeoff]] range: [266.871, 271.708]
-* diamond monotone and tradeoff range: [266.871, 271.708]
+* Diamond monotone and tradeoff: [266.871, 271.708]
 [[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
@@ Line 65: / Line 65: @@
 [[Badness]]: 0.020735
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 75: / Line 75: @@
 Minimax tuning:
-* 11-odd-limit
+* 11-odd-limit: ~7/6 = {{monzo| 2/11 0 -1/11 1/11 }}
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 0 }}, {{monzo| 27/11 0 3/11 -3/11 0 }}, {{monzo| 27/11 0 -8/11 8/11 0 }}, {{monzo| 37/11 0 -2/11 2/11 0 }}]
 : Eigenmonzos: 2, 7/5
 Tuning ranges:
-* [[diamond monotone]] range: [270.968, 272.727] (7\31 to 5\22)
+* Diamond monotone range: [270.968, 272.727] (7\31 to 5\22)
-* [[diamond tradeoff]] range: [266.871, 275.659]
+* Diamond tradeoff range: [266.871, 275.659]
-* diamond monotone and tradeoff range: [270.968, 272.727]
+* Diamond monotone and tradeoff: [270.968, 272.727]
 Vals: {{Val list| 9, 22, 31, 53, 84e }}
@@ Line 88: / Line 88: @@
 Badness: 0.015231
-==== 13-limit  ====
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
@@ Line 98: / Line 98: @@
 Tuning ranges:
-* [[diamond monotone]] range: [270.968, 271.698] (7\31 to 12\53)
+* Diamond monotone range: [270.968, 271.698] (7\31 to 12\53)
-* [[diamond tradeoff]] range: [266.871, 275.659]
+* Diamond tradeoff range: [266.871, 275.659]
-* diamond monotone and tradeoff range: [270.968, 271.698]
+* Diamond monotone and tradeoff: [270.968, 271.698]
 Vals: {{Val list| 22, 31, 53, 84e, 137e }}
@@ Line 106: / Line 106: @@
 Badness: 0.019718
-==== Blair  ====
+==== Blair ====
 Subgroup: 2.3.5.7.11.13
@@ Line 119: / Line 119: @@
 Badness: 0.023086
-==== Winston  ====
+==== Winston ====
 Subgroup: 2.3.5.7.11.13
@@ Line 129: / Line 129: @@
 Tuning ranges:
-* [[diamond monotone]] range: [270.968, 272.727] (7\31 to 5\22)
+* Diamond monotone range: [270.968, 272.727] (7\31 to 5\22)
-* [[diamond tradeoff]] range: [266.871, 281.691]
+* Diamond tradeoff range: [266.871, 281.691]
-* diamond monotone and tradeoff range: [270.968, 272.727]
+* Diamond monotone and tradeoff: [270.968, 272.727]
 Vals: {{Val list| 22f, 31 }}
@@ Line 137: / Line 137: @@
 Badness: 0.019931
-==== Doublethink  ====
+==== Doublethink ====
 Subgroup: 2.3.5.7.11.13
@@ Line 147: / Line 147: @@
 Tuning ranges:
-* [[diamond monotone]] range: [135.484, 136.364] (7\62 to 5\44)
+* Diamond monotone range: [135.484, 136.364] (7\62 to 5\44)
-* [[diamond tradeoff]] range: [128.298, 138.573]
+* Diamond tradeoff range: [128.298, 138.573]
-* diamond monotone and tradeoff range: [135.484, 136.364]
+* Diamond monotone and tradeoff: [135.484, 136.364]
 Vals: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
@@ Line 155: / Line 155: @@
 Badness: 0.027120
-=== Newspeak  ===
+=== Newspeak ===
 Subgroup: 2.3.5.7.11
@@ Line 165: / Line 165: @@
 Tuning ranges:
-* [[diamond monotone]] range: [270.968, 271.698] (7\31 to 12\53)
+* Diamond monotone range: [270.968, 271.698] (7\31 to 12\53)
-* [[diamond tradeoff]] range: [266.871, 272.514]
+* Diamond tradeoff range: [266.871, 272.514]
-* diamond monotone and tradeoff range: [270.968, 271.698]
+* Diamond monotone and tradeoff: [270.968, 271.698]
 Vals: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}
@@ Line 173: / Line 173: @@
 Badness: 0.031438
-=== Borwell  ===
+=== Borwell ===
 Subgroup: 2.3.5.7.11
@@ Line 186: / Line 186: @@
 Badness: 0.038377
-== Triwell  ==
+== Triwell ==
+The triwell temperament (31&amp;159) slices orwell major sixth ~128/75 into three generators, nine of which give the fifth harmonic.
 Subgroup: 2.3.5.7
@@ Line 201: / Line 203: @@
 [[Badness]]: 0.080575
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 214: / Line 216: @@
 Badness: 0.029807
-== Quadrawell  ==
+== Quadrawell ==
-The ''quadrawell'' temperament (31&amp;212, named by [[User:Xenllium|Xenllium]]) has an [[8/7]] generator of about 232 cents, twelve of which give the fifth harmonic.
+The ''quadrawell'' temperament (31&amp;212) has an [[8/7]] generator of about 232 cents, twelve of which give the fifth harmonic.
 Subgroup: 2.3.5.7
@@ Line 231: / Line 233: @@
 [[Badness]]: 0.075754
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 244: / Line 246: @@
 Badness: 0.036493
-== Sabric  ==
+== Sabric ==
-The ''sabric'' temperament (53&amp;190, named by [[User:Xenllium]]) tempers out the [[4375/4374|ragisma]], 4375/4374. It is so named because it is closely related to the '''Sabra2 tuning''' (generator: 271.607278 cents).
+The ''sabric'' temperament (53&amp;190) tempers out the [[4375/4374|ragisma]], 4375/4374. It is so named because it is closely related to the '''Sabra2 tuning''' (generator: 271.607278 cents).
 Subgroup: 2.3.5.7
@@ Line 261: / Line 263: @@
 [[Badness]]: 0.088355
-== Rainwell  ==
+== Rainwell ==
-The ''rainwell'' temperament (31&amp;265, named by [[User:Xenllium]]) tempers out the mirkwai comma, 16875/16807 and the [[rainy comma]], 2100875/2097152.
+The ''rainwell'' temperament (31&amp;265) tempers out the mirkwai comma, 16875/16807 and the [[rainy comma]], 2100875/2097152.
 Subgroup: 2.3.5.7
@@ Line 278: / Line 280: @@
 Badness: 0.143488
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11