Sensamagic family: Difference between revisions

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== Sensamagic ==

Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]].

A notable tuning of sensamagic is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 703.7424{{c}}, 440.9020{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.

[[Subgroup]]: 2.3.5.7

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* [[7-odd-limit]]

: {{monzo list| 1 0 0 0 | 0 0 1/5 2/5 | 0 0 1 0 | 0 0 0 1 }}

: [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7

: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7

* [[9-odd-limit]]

: {{monzo list| 1 0 0 0 | 0 1 0 0 | 0 5/3 2/3 -2/3 | 0 5/3 -1/3 1/3 }}

: [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

{{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}

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== Undecimal sensamagic ==

Undecimal sensamagic tempers out not only [[385/384]], but [[896/891]], making itself a [[strong extension]] of [[parapyth]].

[[Subgroup]]: 2.3.5.7.11

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: [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}

: error map: {{val| 0.000 +1.840 -0.683 -2.~~1554~~ +0.175 }}

: error map: {{val| 0.000 +1.840 -0.683 -2.154 +0.175 }}

[[Minimax tuning]]:

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== Octarod ==

Octarod tempers out 100/99 and the interval class of [[11/1|11]] is found as a stack of four ~9/7's. The name ''octarod'' presumably comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.

[[Subgroup]]: 2.3.5.7.11

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 == Sensamagic ==
 {{Main| Sensamagic }}
+Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]].
+A notable tuning of sensamagic is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 703.7424{{c}}, 440.9020{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.
 [[Subgroup]]: 2.3.5.7
@@ Line 29: / Line 33: @@
 * [[7-odd-limit]]
 : {{monzo list| 1 0 0 0 | 0 0 1/5 2/5 | 0 0 1 0 | 0 0 0 1 }}
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
 * [[9-odd-limit]]
 : {{monzo list| 1 0 0 0 | 0 1 0 0 | 0 5/3 2/3 -2/3 | 0 5/3 -1/3 1/3 }}
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5
 {{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}
@@ Line 54: / Line 58: @@
 == Undecimal sensamagic ==
 {{Main| Sensamagic }}
+Undecimal sensamagic tempers out not only [[385/384]], but [[896/891]], making itself a [[strong extension]] of [[parapyth]].
 [[Subgroup]]: 2.3.5.7.11
@@ Line 65: / Line 71: @@
 : [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }}
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}
-: error map: {{val| 0.000 +1.840 -0.683 -2.1554 +0.175 }}
+: error map: {{val| 0.000 +1.840 -0.683 -2.154 +0.175 }}
 [[Minimax tuning]]:
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 == Octarod ==
+Octarod tempers out 100/99 and the interval class of [[11/1|11]] is found as a stack of four ~9/7's. The name ''octarod'' presumably comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.
 [[Subgroup]]: 2.3.5.7.11