Orwellismic temperaments: Difference between revisions

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Temperaments discussed elsewhere are:

* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]

* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep|Bug family]]

* [[Mothra]] (+81/80) → [[Meantone family #Mothra|Meantone family]]

* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard|Buzzardsmic clan]]

* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]

* ''[[Echidna]]'' (+2048/2025) → [[Stearnsmic clan #Echidna|Stearnsmic clan]]

* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]

* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]

* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]

* [[Mothra]] (+81/80) → [[Meantone family #Mothra|Meantone family]]

* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]

* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]

* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]

* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]

* [[Buzzard]] (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]

* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]

* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]]

Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips.

Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips, in the order of increasing [[badness]].

== Sentinel ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Sentinel]].''

Sentinel tempers out [[3645/3584]] and may be described as the {{nowrap| 14 & 17 }} temperament. It is related to [[squares]], but the mappings differ for the [[5/1|5th harmonic]]. Like squares, it splits the [[6/1|6th harmonic]] into four subminor sixths of 11/7~14/9 (or splits a perfect eleventh into four supermajor thirds of 9/7~14/11), and uses it for a generator; its [[ploidacot]] is beta-tetracot. However, the 5th harmonic is found by -15 generator steps instead of +16 as in squares.

As one might expect, [[31edo]] is a good tuning for this temperament, in which case it is identical to squares. Among the alternatives are [[48edo]] and [[79edo]], both in their [[patent val]]s.

[[Subgroup]]: 2.3.5.7

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Optimal tunings:

* WE: ~2 = 1201.0893{{c}}, ~14/9 = 775.1534{{c}}

* WE: ~2 = 1201.0893{{c}}, ~11/7 = 775.1534{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.4564{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4564{{c}}

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Optimal tunings:

* WE: ~2 = 1200.4045{{c}}, ~14/9 = 774.7596{{c}}

* WE: ~2 = 1200.4045{{c}}, ~11/7 = 774.7596{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.5000{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.5000{{c}}

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== Secant ==

Secant, the {{nowrap| 26 & 58 }} temperament, is generated by a slightly sharp ~10/9, seven of which plus a semi-octave period give the [[3/1|3rd harmonic]]. Its ploidacot is diploid alpha-heptacot. [[58edo]], [[84edo]] and [[142edo]] all make for excellent tunings.

[[Subgroup]]: 2.3.5.7

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== Diesic ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Diesic]].''

Diesic is generated by a diesis-sized interval of ~36/35, hence the name. It may be described as the {{nowrap| 31 & 32c }} temperament. It is related to [[slender]], both sharing the ploidacot of omega-13-cot, but the mappings differ for the [[5/1|5th harmonic]].

[[Subgroup]]: 2.3.5.7

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== Infraorwell ==

Infraorwell may be described as the {{nowrap| 49 & 58 }} temperament. It is generated by a ~7/6, less sharp than the generator of [[orwell]] but still sharp of just, so that three generators make a ~8/5, but seven generators does not give the [[3/1|3rd harmonic]]. Instead, sixteen generators give the [[12/1|12th harmonic]]; the ploidacot for this temperament is therefore gamma-16-cot. [[58edo]] makes for a recommendable tuning, though [[49edo]] and [[67edo]] are among the possibilities.

[[Subgroup]]: 2.3.5.7

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: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Counterpental]].''

Named by [[User:Flirora|+merlan #flirora]] in 2021, pentaorwell tempers out 179200/177147 and is the {{nowrap| 75 & 80 }} temperament.

Named by [[User:Flirora|+merlan #flirora]] in 2021, pentaorwell tempers out 179200/177147 and is the {{nowrap| 75 & 80 }} temperament. Its ploidacot is pentaploid monocot.

[[Subgroup]]: 2.3.5.7

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Badness (Sintel): 3.17

~~[[Category:Temperament collections]]~~

~~[[Category:Pages with mostly numerical content]]~~

[[Category:Orwellismic temperaments| ]]

[[Category:Orwellismic| ]]

[[Category:~~Rank~~ 2]]

[[Category:Temperament collections]]

[[Category:Catalogs of rank-2 temperaments]]

@@ Line 3: / Line 3: @@
 Temperaments discussed elsewhere are:
+* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
 * [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep|Bug family]]
+* [[Mothra]] (+81/80) → [[Meantone family #Mothra|Meantone family]]
+* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard|Buzzardsmic clan]]
+* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
+* ''[[Echidna]]'' (+2048/2025) → [[Stearnsmic clan #Echidna|Stearnsmic clan]]
+* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
 * ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
-* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
-* [[Mothra]] (+81/80) → [[Meantone family #Mothra|Meantone family]]
 * [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
-* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
-* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
 * ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
-* [[Buzzard]] (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
 * ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
 * ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]]
-Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips.
+Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips, in the order of increasing [[badness]].
 == Sentinel ==
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Sentinel]].''
+Sentinel tempers out [[3645/3584]] and may be described as the {{nowrap| 14 & 17 }} temperament. It is related to [[squares]], but the mappings differ for the [[5/1|5th harmonic]]. Like squares, it splits the [[6/1|6th harmonic]] into four subminor sixths of 11/7~14/9 (or splits a perfect eleventh into four supermajor thirds of 9/7~14/11), and uses it for a generator; its [[ploidacot]] is beta-tetracot. However, the 5th harmonic is found by -15 generator steps instead of +16 as in squares.
+As one might expect, [[31edo]] is a good tuning for this temperament, in which case it is identical to squares. Among the alternatives are [[48edo]] and [[79edo]], both in their [[patent val]]s.
 [[Subgroup]]: 2.3.5.7
@@ Line 45: / Line 50: @@
 Optimal tunings:
-* WE: ~2 = 1201.0893{{c}}, ~14/9 = 775.1534{{c}}
+* WE: ~2 = 1201.0893{{c}}, ~11/7 = 775.1534{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.4564{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4564{{c}}
 {{Optimal ET sequence|legend=0| 14, 17, 31, 79, 110e, 141e }}
@@ Line 60: / Line 65: @@
 Optimal tunings:
-* WE: ~2 = 1200.4045{{c}}, ~14/9 = 774.7596{{c}}
+* WE: ~2 = 1200.4045{{c}}, ~11/7 = 774.7596{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.5000{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.5000{{c}}
 {{Optimal ET sequence|legend=0| 14, 17, 31 }}
@@ Line 68: / Line 73: @@
 == Secant ==
+Secant, the {{nowrap| 26 & 58 }} temperament, is generated by a slightly sharp ~10/9, seven of which plus a semi-octave period give the [[3/1|3rd harmonic]]. Its ploidacot is diploid alpha-heptacot. [[58edo]], [[84edo]] and [[142edo]] all make for excellent tunings.
 [[Subgroup]]: 2.3.5.7
@@ Line 147: / Line 154: @@
 == Diesic ==
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Diesic]].''
+Diesic is generated by a diesis-sized interval of ~36/35, hence the name. It may be described as the {{nowrap| 31 & 32c }} temperament. It is related to [[slender]], both sharing the ploidacot of omega-13-cot, but the mappings differ for the [[5/1|5th harmonic]].
 [[Subgroup]]: 2.3.5.7
@@ Line 196: / Line 205: @@
 == Infraorwell ==
+Infraorwell may be described as the {{nowrap| 49 & 58 }} temperament. It is generated by a ~7/6, less sharp than the generator of [[orwell]] but still sharp of just, so that three generators make a ~8/5, but seven generators does not give the [[3/1|3rd harmonic]]. Instead, sixteen generators give the [[12/1|12th harmonic]]; the ploidacot for this temperament is therefore gamma-16-cot. [[58edo]] makes for a recommendable tuning, though [[49edo]] and [[67edo]] are among the possibilities.
 [[Subgroup]]: 2.3.5.7
@@ Line 246: / Line 257: @@
 : ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Counterpental]].''
-Named by [[User:Flirora|+merlan #flirora]] in 2021, pentaorwell tempers out 179200/177147 and is the {{nowrap| 75 & 80 }} temperament.
+Named by [[User:Flirora|+merlan #flirora]] in 2021, pentaorwell tempers out 179200/177147 and is the {{nowrap| 75 & 80 }} temperament. Its ploidacot is pentaploid monocot.
 [[Subgroup]]: 2.3.5.7
@@ Line 379: / Line 390: @@
 Badness (Sintel): 3.17
-[[Category:Temperament collections]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Orwellismic temperaments| ]] <!-- main article -->
 [[Category:Orwellismic| ]] <!-- key article -->
-[[Category:Rank 2]]
+[[Category:Temperament collections]]
+[[Category:Catalogs of rank-2 temperaments]]