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."

~~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 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 ==

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[[Optimal ET sequence]]: {{Optimal ET sequence|7, 14, 27e, 34dh, 41, 89, 130}}

[[Badness]] (Sintel): 0.615

==== Heartsphere ====

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[[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}}

[[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

[[Badness]] (Sintel): 15.766

=== 2.3.7.11.19 subgroup temperaments ===

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[[Optimal ET sequence]]: {{Optimal ET sequence|7, 27deh, 34, 41, 89, 130, 219}}

[[Badness]]: 0.~~010707~~

[[Badness]] (Sintel): 0.529

==== Heartful ====

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[[Optimal ET sequence]]: {{Optimal ET sequence|34dh, 41, 116e, 157e}}

[[Badness]]: 0.~~019908~~

[[Badness]] (Sintel): 0.984

==== Doublehearted ====

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[[Optimal ET sequence]]: {{Optimal ET sequence|14, 27e, 41}}

[[Badness]]: 0.~~011318~~

[[Badness]] (Sintel): 0.560

==== Byhearted ====

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[[Optimal ET sequence]]: {{Optimal ET sequence|14, 34dh, 48, 110e, 158e}}

[[Badness]]: 0.~~018062~~

[[Badness]] (Sintel): 0.893

=== Full 19-limit temperaments ===

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[[Optimal ET sequence]]: {{Optimal ET sequence|14cf, 27effg, 41, 89, 130g}}

[[Badness]] (Sintel): 2.294

==== Monkey ====

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[[Badness]]: 0.016652

==== ~~Byhearted~~ ====

==== Weasel ====

[[Subgroup]]: Full 19-limit

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== See also ==

* [[Rastmic clan]]

* [[Rastmic rank ~~three~~ clan]]

* [[Rastmic rank-3 clan]]

[[Category:Regular temperament theory]]

@@ Line 1: / Line 1: @@
 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."
-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 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 ==
@@ Line 15: / Line 15: @@
 [[Optimal ET sequence]]: {{Optimal ET sequence|7, 14, 27e, 34dh, 41, 89, 130}}
+[[Badness]] (Sintel): 0.615
 ==== Heartsphere ====
@@ Line 21: / Line 23: @@
 [[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}}
+[[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
+[[Badness]] (Sintel): 15.766
 === 2.3.7.11.19 subgroup temperaments ===
@@ Line 39: / Line 43: @@
 [[Optimal ET sequence]]: {{Optimal ET sequence|7, 27deh, 34, 41, 89, 130, 219}}
-[[Badness]]: 0.010707
+[[Badness]] (Sintel): 0.529
 ==== Heartful ====
@@ Line 52: / Line 56: @@
 [[Optimal ET sequence]]: {{Optimal ET sequence|34dh, 41, 116e, 157e}}
-[[Badness]]: 0.019908
+[[Badness]] (Sintel): 0.984
 ==== Doublehearted ====
@@ Line 65: / Line 69: @@
 [[Optimal ET sequence]]: {{Optimal ET sequence|14, 27e, 41}}
-[[Badness]]: 0.011318
+[[Badness]] (Sintel): 0.560
 ==== Byhearted ====
@@ Line 78: / Line 82: @@
 [[Optimal ET sequence]]: {{Optimal ET sequence|14, 34dh, 48, 110e, 158e}}
-[[Badness]]: 0.018062
+[[Badness]] (Sintel): 0.893
 === Full 19-limit temperaments ===
@@ Line 93: / Line 97: @@
 [[Optimal ET sequence]]: {{Optimal ET sequence|14cf, 27effg, 41, 89, 130g}}
+[[Badness]] (Sintel): 2.294
 ==== Monkey ====
@@ Line 184: / Line 190: @@
 [[Badness]]: 0.016652
-==== Byhearted ====
+==== Weasel ====
-{{see also|Tetracot family #Byhearted}}
+{{see also|Tetracot family #Weasel}}
 [[Subgroup]]: Full 19-limit
@@ Line 594: / Line 600: @@
 == See also ==
 * [[Rastmic clan]]
-* [[Rastmic rank three clan]]
+* [[Rastmic rank-3 clan]]
 [[Category:Regular temperament theory]]