Quintosec family: Difference between revisions

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The '''~~qintosec~~ family''' tempers out the ~~qintosec~~ comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}.

The '''quintosec family''' tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}.

== Quintosec ==

Quintosec is naturally a 2.3.5.11 subgroup temperament. It was documented as ''qintosec'' on the 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 now restored, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.

~~== Qintosec ==~~

[[Subgroup]]: 2.3.5

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: mapping generators: ~524288/455625, ~16384/10125

[[Optimal tuning]] ([[~~POTE~~]]): ~524288/455625 = 1\5, ~16384/10125 = 831.~~105~~ (~16/15 = 111.~~105~~)

[[Optimal tuning]] ([[CTE]]): ~524288/455625 = 1\5, ~16384/10125 = 831.1061 (~16/15 = 111.1061)

{{Optimal ET sequence|legend=1| 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}

{{Optimal ET sequence|legend=1| 10, 45c, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}

[[Badness]]: 0.139191

== ~~Septimal qintosec~~ ==

=== 2.3.5.11 subgroup ===

Qintosec can be described as the 10 & 65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.

Subgroup: 2.3.5.11

Comma list: 5632/5625, 26214400/26198073

Mapping: {{mapping| 5 1 22 45 | 0 2 -3 -8 }}

Optimal tuning (CTE): ~1024/891 = 1\5, ~160/99 = 831.0932 (~16/15 = 111.0932)

{{Optimal ET sequence|legend=1| 10e, 55e, 65, 205, 270, 335, 605, 940, 1545c }}

Badness: 0.0195

== Qintosec ==

Qintosec can be described as the 10 & 65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.

[[Subgroup]]: 2.3.5.7

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[[Category:Temperament families]]

[[Category:~~Qintosec~~ family| ]]

[[Category:Quintosec family| ]]

[[Category:Quintosec| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
-The '''qintosec family''' tempers out the qintosec comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}.
+The '''quintosec family''' tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo| 47 -15 -10 }}.
+== Quintosec ==
+Quintosec is naturally a 2.3.5.11 subgroup temperament. It was documented as ''qintosec'' on the 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 now restored, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.
-== Qintosec ==
 [[Subgroup]]: 2.3.5
@@ Line 10: / Line 12: @@
 : mapping generators: ~524288/455625, ~16384/10125
-[[Optimal tuning]] ([[POTE]]): ~524288/455625 = 1\5, ~16384/10125 = 831.105 (~16/15 = 111.105)
+[[Optimal tuning]] ([[CTE]]): ~524288/455625 = 1\5, ~16384/10125 = 831.1061 (~16/15 = 111.1061)
-{{Optimal ET sequence|legend=1| 10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}
+{{Optimal ET sequence|legend=1| 10, 45c, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}
 [[Badness]]: 0.139191
-== Septimal qintosec ==
+=== 2.3.5.11 subgroup ===
-Qintosec can be described as the 10 &amp; 65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.
+Subgroup: 2.3.5.11
+Comma list: 5632/5625, 26214400/26198073
+Mapping: {{mapping| 5 1 22 45 | 0 2 -3 -8 }}
+Optimal tuning (CTE): ~1024/891 = 1\5, ~160/99 = 831.0932 (~16/15 = 111.0932)
+{{Optimal ET sequence|legend=1| 10e, 55e, 65, 205, 270, 335, 605, 940, 1545c }}
+Badness: 0.0195
+== Qintosec ==
+Qintosec can be described as the 10 &amp; 65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 148: / Line 163: @@
 [[Category:Temperament families]]
-[[Category:Qintosec family| ]] <!-- main article -->
+[[Category:Quintosec family| ]] <!-- main article -->
+[[Category:Quintosec| ]] <!-- key article -->
 [[Category:Rank 2]]