Heartland: Difference between revisions
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The '''heartland''' is the name given to the collection of temperaments that are children of or related to the '''heartland temperament''', the 2.3.7.11.19 subgroup temperament tempering out both [[243/242]] and [[1083/1078]], and its full 19-limit extension, heartsphere. The term "heartland" loosely means "interior part." | The '''heartland''' is the name given to the collection of temperaments that are children of or related to the '''heartland temperament''', the 2.3.7.11.19 subgroup temperament tempering out both [[243/242]] and [[1083/1078]], and its full 19-limit extension, heartsphere. The term "heartland" loosely means "interior part." | ||
For extending the heartland temperament to the 2.3.5.7.11.19 subgroup, it is natural to temper out 361/360, 441/440 or 540/539, which makes a weak extension of the [[Breed family|jove temperament]]. For extending to the 2.3.5.7.11.13.19 subgroup, tempering out 364/363 gives an excellent tuning. | |||
== Temperament data == | == Temperament data == | ||
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[[Optimal ET sequence]]: {{Optimal ET sequence|7, 14, 27e, 34dh, 41, 89, 130}} | [[Optimal ET sequence]]: {{Optimal ET sequence|7, 14, 27e, 34dh, 41, 89, 130}} | ||
[[Badness]] (Sintel): 0.615 | |||
==== Heartsphere ==== | ==== Heartsphere ==== | ||
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[[Comma list]]: 243/242, 1083/1078 | [[Comma list]]: 243/242, 1083/1078 | ||
[[Mapping]]: | [[Mapping]]: [⟨1 1 0 0 2 0 0 1], ⟨0 4 0 0 10 0 0 3], ⟨0 0 1 0 0 0 0 0], ⟨0 0 0 1 0 0 0 1], ⟨0 0 0 0 0 1 0 0], ⟨0 0 0 0 0 0 1 0]] | ||
[[Optimal tuning]] (POTE): ~2 = 1＼1, ~21/19 = 175.2713, ~5/4 = 386.0840, ~7/4 = 969.3784, ~13/8 = 840.1616, ~17/16 = 104.5510 | [[Optimal tuning]] (POTE): ~2 = 1＼1, ~21/19 = 175.2713, ~5/4 = 386.0840, ~7/4 = 969.3784, ~13/8 = 840.1616, ~17/16 = 104.5510 | ||
[[Badness]] (Sintel): 15.766 | |||
=== 2.3.7.11.19 subgroup temperaments === | === 2.3.7.11.19 subgroup temperaments === | ||
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[[Optimal ET sequence]]: {{Optimal ET sequence|7, 27deh, 34, 41, 89, 130, 219}} | [[Optimal ET sequence]]: {{Optimal ET sequence|7, 27deh, 34, 41, 89, 130, 219}} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.529 | ||
==== Heartful ==== | ==== Heartful ==== | ||
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[[Optimal ET sequence]]: {{Optimal ET sequence|34dh, 41, 116e, 157e}} | [[Optimal ET sequence]]: {{Optimal ET sequence|34dh, 41, 116e, 157e}} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.984 | ||
==== Doublehearted ==== | ==== Doublehearted ==== | ||
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[[Optimal ET sequence]]: {{Optimal ET sequence|14, 27e, 41}} | [[Optimal ET sequence]]: {{Optimal ET sequence|14, 27e, 41}} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.560 | ||
==== Byhearted ==== | ==== Byhearted ==== | ||
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[[Optimal ET sequence]]: {{Optimal ET sequence|14, 34dh, 48, 110e, 158e}} | [[Optimal ET sequence]]: {{Optimal ET sequence|14, 34dh, 48, 110e, 158e}} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.893 | ||
=== Full 19-limit temperaments === | === Full 19-limit temperaments === | ||
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[[Optimal ET sequence]]: {{Optimal ET sequence|14cf, 27effg, 41, 89, 130g}} | [[Optimal ET sequence]]: {{Optimal ET sequence|14cf, 27effg, 41, 89, 130g}} | ||
[[Badness]] (Sintel): 2.294 | |||
==== Monkey ==== | ==== Monkey ==== | ||
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[[Badness]]: 0.016652 | [[Badness]]: 0.016652 | ||
==== | ==== Weasel ==== | ||
{{see also|Tetracot family # | {{see also|Tetracot family #Weasel}} | ||
[[Subgroup]]: Full 19-limit | [[Subgroup]]: Full 19-limit | ||
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== See also == | == See also == | ||
* [[Rastmic clan]] | * [[Rastmic clan]] | ||
* [[Rastmic rank | * [[Rastmic rank-3 clan]] | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||