Orwellismic temperaments: Difference between revisions
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* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]] | * ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]] | ||
* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]] | * ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]] | ||
* [[Buzzard]] (+5120/5103) → [[ | * [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard|Buzzardsmic clan]] | ||
* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]] | * ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]] | ||
* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]] | * ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]] | ||
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== Sentinel == | == Sentinel == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #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 | [[Subgroup]]: 2.3.5.7 | ||
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Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1201.0893{{c}}, ~ | * WE: ~2 = 1201.0893{{c}}, ~11/7 = 775.1534{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4564{{c}} | ||
{{Optimal ET sequence|legend=0| 14, 17, 31, 79, 110e, 141e }} | {{Optimal ET sequence|legend=0| 14, 17, 31, 79, 110e, 141e }} | ||
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Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1200.4045{{c}}, ~ | * WE: ~2 = 1200.4045{{c}}, ~11/7 = 774.7596{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.5000{{c}} | ||
{{Optimal ET sequence|legend=0| 14, 17, 31 }} | {{Optimal ET sequence|legend=0| 14, 17, 31 }} | ||
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== Secant == | == 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 | [[Subgroup]]: 2.3.5.7 | ||
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== Diesic == | == Diesic == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #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 | [[Subgroup]]: 2.3.5.7 | ||
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== Infraorwell == | == 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 | [[Subgroup]]: 2.3.5.7 | ||
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: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Counterpental]].'' | : ''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 | [[Subgroup]]: 2.3.5.7 | ||
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== Triskaidekic == | == Triskaidekic == | ||
: ''For the 5-limit version, see [[ | : ''For the 5-limit version, see [[13th-octave temperaments #Triskaidekic]].'' | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Orwellismic temperaments| ]] <!-- main article --> | [[Category:Orwellismic temperaments| ]] <!-- main article --> | ||
[[Category:Orwellismic| ]] <!-- key article --> | [[Category:Orwellismic| ]] <!-- key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||