Hemimean clan: Difference between revisions
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The '''hemimean clan''' tempers out the no-threes hemimean comma [[3136/3125]]. | The '''hemimean clan''' tempers out the no-threes hemimean comma [[3136/3125]]. | ||
= Didacus = | == Didacus == | ||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
| Line 18: | Line 18: | ||
{{Val list|legend=1| 6, 19, 25, 31, 99, 130, 161, 353, 514c }} | {{Val list|legend=1| 6, 19, 25, 31, 99, 130, 161, 353, 514c }} | ||
== Extensions == | === Extensions === | ||
Full 7-limit [[extension]]s of didacus, in general, split the [[syntonic comma]] into two, each for [[126/125]]~[[225/224]], as 3136/3125 = (126/125)/(225/224). These include hemithirds, misty, semisept, sengagen, subpental, arch, and emka, considered below, as well as [[Meantone family #Septimal meantone|septimal meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], [[Stearnsmic clan #Decistearn|decistearn]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere. | Full 7-limit [[extension]]s of didacus, in general, split the [[syntonic comma]] into two, each for [[126/125]]~[[225/224]], as 3136/3125 = (126/125)/(225/224). These include hemithirds, misty, semisept, sengagen, subpental, arch, and emka, considered below, as well as [[Meantone family #Septimal meantone|septimal meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], [[Stearnsmic clan #Decistearn|decistearn]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere. | ||
A notable subgroup extension of didacus is [[Chromatic pairs #Roulette|roulette]]. | A notable subgroup extension of didacus is [[Chromatic pairs #Roulette|roulette]]. | ||
= Hemithirds = | == Hemithirds == | ||
{{main| Hemithirds }} | {{main| Hemithirds }} | ||
{{see also| Luna family #Hemithirds }} | {{see also| Luna family #Hemithirds }} | ||
| Line 49: | Line 49: | ||
[[Badness]]: 0.044284 | [[Badness]]: 0.044284 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 67: | Line 67: | ||
Badness: 0.019003 | Badness: 0.019003 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 80: | Line 80: | ||
Badness: 0.021738 | Badness: 0.021738 | ||
= Misty = | == Misty == | ||
{{see also| Misty family }} | {{see also| Misty family }} | ||
| Line 97: | Line 97: | ||
[[Badness]]: 0.036802 | [[Badness]]: 0.036802 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 110: | Line 110: | ||
Badness: 0.035932 | Badness: 0.035932 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 123: | Line 123: | ||
Badness: 0.027820 | Badness: 0.027820 | ||
==== 17-limit ==== | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 136: | Line 136: | ||
Badness: 0.023908 | Badness: 0.023908 | ||
==== 19-limit ==== | ===== 19-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 149: | Line 149: | ||
Badness: 0.019878 | Badness: 0.019878 | ||
=== Mystic === | ==== Mystic ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 162: | Line 162: | ||
Badness: 0.036872 | Badness: 0.036872 | ||
== Hemimist == | === Hemimist === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 175: | Line 175: | ||
Badness: 0.047439 | Badness: 0.047439 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 188: | Line 188: | ||
Badness: 0.022923 | Badness: 0.022923 | ||
= Semisept = | == Semisept == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 201: | Line 201: | ||
[[Badness]]: 0.630576 | [[Badness]]: 0.630576 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 216: | Line 216: | ||
[[Badness]]: 0.050472 | [[Badness]]: 0.050472 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 229: | Line 229: | ||
Badness: 0.022476 | Badness: 0.022476 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 242: | Line 242: | ||
Badness: 0.025204 | Badness: 0.025204 | ||
=== 17-limit === | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 255: | Line 255: | ||
Badness: 0.019919 | Badness: 0.019919 | ||
=== 19-limit === | ==== 19-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 268: | Line 268: | ||
Badness: 0.016301 | Badness: 0.016301 | ||
=== 23-limit === | ==== 23-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
| Line 281: | Line 281: | ||
Badness: 0.014957 | Badness: 0.014957 | ||
== Semishly == | === Semishly === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 294: | Line 294: | ||
Badness: 0.028408 | Badness: 0.028408 | ||
= Sengagen = | == Sengagen == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 309: | Line 309: | ||
[[Badness]]: 0.057978 | [[Badness]]: 0.057978 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 322: | Line 322: | ||
Badness: 0.053828 | Badness: 0.053828 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 335: | Line 335: | ||
Badness: 0.053531 | Badness: 0.053531 | ||
== Sengage == | === Sengage === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 348: | Line 348: | ||
Badness: 0.037416 | Badness: 0.037416 | ||
= Subpental = | == Subpental == | ||
{{see also|Sensipent family}} | {{see also|Sensipent family}} | ||
| Line 365: | Line 365: | ||
[[Badness]]: 0.054303 | [[Badness]]: 0.054303 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 378: | Line 378: | ||
Badness: 0.045352 | Badness: 0.045352 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 391: | Line 391: | ||
Badness: 0.023940 | Badness: 0.023940 | ||
= Arch = | == Arch == | ||
{{see also|Escapade family}} | {{see also|Escapade family}} | ||
| Line 408: | Line 408: | ||
[[Badness]]: 0.094345 | [[Badness]]: 0.094345 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 421: | Line 421: | ||
Badness: 0.036541 | Badness: 0.036541 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 434: | Line 434: | ||
Badness: 0.019504 | Badness: 0.019504 | ||
= Emka = | == Emka == | ||
[[Emka]] tempers out {{monzo|-50 -8 27}} in the 5-limit. This temperament can be described as 37&50 temperament, which tempers out the hemimean and 84035/82944 (quinzo-ayo). Alternative extension [[Horwell temperaments #Emkay|emkay]] (87&224) tempers out the same 5-limit comma as the emka, but with the horwell (65625/65536) rather than the hemimean tempered out. | [[Emka]] tempers out {{monzo|-50 -8 27}} in the 5-limit. This temperament can be described as 37&50 temperament, which tempers out the hemimean and 84035/82944 (quinzo-ayo). Alternative extension [[Horwell temperaments #Emkay|emkay]] (87&224) tempers out the same 5-limit comma as the emka, but with the horwell (65625/65536) rather than the hemimean tempered out. | ||
| Line 449: | Line 449: | ||
[[Badness]]: 0.544752 | [[Badness]]: 0.544752 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 464: | Line 464: | ||
[[Badness]]: 0.144338 | [[Badness]]: 0.144338 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 477: | Line 477: | ||
Badness: 0.054744 | Badness: 0.054744 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||