Quintosec family: Difference between revisions

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== Quintosec ==

Quintosec has a 1/5-octave period and a generator of around 831 [[cent]]s such that two of them plus a period make the [[3/1|3rd harmonic]]. However, an equivalent generator is the neutral third, in addition to the minimal generator, [[~]][[16/15]]. The [[ploidacot]] of this temperament is pentaploid dicot.

Quintosec is naturally a [[2.3.5.11 subgroup|2.3.5.11-subgroup]] temperament. It was documented as ''qintosec'' on the [https://x31eq.com/temper/ Temperament Finder], which was probably due to a typo<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. The original, intended spelling is restored here, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.

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Optimal tunings:

* WE: ~55/48 = 239.8038{{c}}, ~80/49 = 830.6313{{c}} (~15~~/14~~ = 111.2200{{c}})

* WE: ~55/48 = 239.8038{{c}}, ~80/49 = 830.6313{{c}} (~16/15 = 111.2200{{c}})

* CWE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.2911{{c}} (~15~~/14~~ = 111.2911{{c}})

* CWE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.2911{{c}} (~16/15 = 111.2911{{c}})

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Optimal tunings:

* WE: ~220/189 = 239.9453{{c}}, ~44/27 = 832.2583{{c}} (~15~~/14~~ = 112.4224{{c}})

* WE: ~220/189 = 239.9453{{c}}, ~44/27 = 832.2583{{c}} (~16/15 = 112.4224{{c}})

* CWE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4403{{c}} (~15~~/14~~ = 112.4403{{c}})

* CWE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4403{{c}} (~16/15 = 112.4403{{c}})

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== Sengasec ==

Sengasec can be described as the 10 & 55 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.

Sengasec can be described as the 10 & 65 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit. It was named by [[Xenllium]] in 2021.

[[Subgroup]]: 2.3.5.7

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== Decoid ==

Decoid tempers out 2401/2400, the [[breedsma]], and 67108864/66976875, the [[decovulture comma]], as well as {{monzo| 11 -10 -10 10 }}, the [[linus comma]]. ~~Either~~ ~[[8/7]] or ~[[16/15]] ~~can be used as its generator~~. ~~It may be described as the 130 & 270 temperament, and as one might expect,~~ 181\940 or 233\1210 makes for an excellent tuning choice.

Decoid tempers out 2401/2400, the [[breedsma]], and 67108864/66976875, the [[decovulture comma]], as well as {{monzo| 11 -10 -10 10 }}, the [[linus comma]]. It may be described as the 130 & 270 temperament, and its [[ploidacot]] is decaploid dicot. The hemitwelfth or neutral third can be used as a generator, but also ~[[8/7]], ~[[16/15]], or the [[marvel comma]]. 181\940 or 233\1210 makes for an excellent tuning choice.

[[Subgroup]]: 2.3.5.7

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 == Quintosec ==
+Quintosec has a 1/5-octave period and a generator of around 831 [[cent]]s such that two of them plus a period make the [[3/1|3rd harmonic]]. However, an equivalent generator is the neutral third, in addition to the minimal generator, [[~]][[16/15]]. The [[ploidacot]] of this temperament is pentaploid dicot.
 Quintosec is naturally a [[2.3.5.11 subgroup|2.3.5.11-subgroup]] temperament. It was documented as ''qintosec'' on the [https://x31eq.com/temper/ Temperament Finder], which was probably due to a typo<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. The original, intended spelling is restored here, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.
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 Optimal tunings:
-* WE: ~55/48 = 239.8038{{c}}, ~80/49 = 830.6313{{c}} (~15/14 = 111.2200{{c}})
+* WE: ~55/48 = 239.8038{{c}}, ~80/49 = 830.6313{{c}} (~16/15 = 111.2200{{c}})
-* CWE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.2911{{c}} (~15/14 = 111.2911{{c}})
+* CWE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.2911{{c}} (~16/15 = 111.2911{{c}})
 {{Optimal ET sequence|legend=0| 10, 55d, 65d, 140de }}
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 Optimal tunings:
-* WE: ~220/189 = 239.9453{{c}}, ~44/27 = 832.2583{{c}} (~15/14 = 112.4224{{c}})
+* WE: ~220/189 = 239.9453{{c}}, ~44/27 = 832.2583{{c}} (~16/15 = 112.4224{{c}})
-* CWE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4403{{c}} (~15/14 = 112.4403{{c}})
+* CWE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4403{{c}} (~16/15 = 112.4403{{c}})
 {{Optimal ET sequence|legend=0| 10, 75 }}
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 == Sengasec ==
-Sengasec can be described as the 10 & 55 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.
+Sengasec can be described as the 10 & 65 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit. It was named by [[Xenllium]] in 2021.
 [[Subgroup]]: 2.3.5.7
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 == Decoid ==
-Decoid tempers out 2401/2400, the [[breedsma]], and 67108864/66976875, the [[decovulture comma]], as well as {{monzo| 11 -10 -10 10 }}, the [[linus comma]]. Either ~[[8/7]] or ~[[16/15]] can be used as its generator. It may be described as the 130 & 270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice.
+Decoid tempers out 2401/2400, the [[breedsma]], and 67108864/66976875, the [[decovulture comma]], as well as {{monzo| 11 -10 -10 10 }}, the [[linus comma]]. It may be described as the 130 & 270 temperament, and its [[ploidacot]] is decaploid dicot. The hemitwelfth or neutral third can be used as a generator, but also ~[[8/7]], ~[[16/15]], or the [[marvel comma]]. 181\940 or 233\1210 makes for an excellent tuning choice.
 [[Subgroup]]: 2.3.5.7