19th-octave temperaments: Difference between revisions

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[[19edo]] has excellent [[5-limit]] accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with [[harmonic]]s [[7/1|7]], [[11/1|11]], and [[13/1|13]] mapped to an independent generator. Undevigintone has the same [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] mapping as 19et with harmonic 11 mapped to an independent generator.

[[19edo]] has excellent [[5-limit]] accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.

~~See also~~ [[~~enneadecal]] and [[superenneadecal~~]].

* Graywood has the same 3-limit mapping as 19et, but harmonic [[5/1|5]] is mapped to an independent generator.

* Meanmag has the same 5-limit mapping as 19et, but harmonic 7 is mapped to an independent generator.

* Undevigintone has the same 7-limit mapping as 19et, but harmonic 11 is mapped to an independent generator.

For graywood, see [[Syntonic–kleismic equivalence continuum#Graywood]].

For graywood, see [[Syntonic–kleismic equivalence continuum #Graywood]].

See also [[ragismic microtemperaments #Enneadecal|enneadecal]] and [[sensamagic clan #Superenneadecal|superenneadecal]].

== Meanmag ==

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Comma list: 81/80, 385/384, 625/616

~~Mapping:~~ {{~~mapping~~| 19 30 44 0 119 | 0 0 0 1 -1 }}

Optimal tunings:

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Comma list: 81/80, 105/104, 144/143, 625/616

~~Mapping:~~ {{~~mapping~~| 19 30 44 0 119 17 | 0 0 0 1 -1 1 }}

Optimal tunings:

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Comma list: 49/48, 65/64, 81/80, 126/125

~~Mapping:~~ {{~~mapping~~| 19 30 44 53 0 70 | 0 0 0 0 1 0 }}

Optimal tunings:

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+{{Technical data page}}
 {{Infobox fractional-octave|19}}
-[[19edo]] has excellent [[5-limit]] accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with [[harmonic]]s [[7/1|7]], [[11/1|11]], and [[13/1|13]] mapped to an independent generator. Undevigintone has the same [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] mapping as 19et with harmonic 11 mapped to an independent generator.
+[[19edo]] has excellent [[5-limit]] accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.
-See also [[enneadecal]] and [[superenneadecal]].
+* Graywood has the same 3-limit mapping as 19et, but harmonic [[5/1|5]] is mapped to an independent generator.
+* Meanmag has the same 5-limit mapping as 19et, but harmonic 7 is mapped to an independent generator.
+* Undevigintone has the same 7-limit mapping as 19et, but harmonic 11 is mapped to an independent generator.
-For graywood, see [[Syntonic–kleismic equivalence continuum#Graywood]].
+For graywood, see [[Syntonic–kleismic equivalence continuum #Graywood]].
+See also [[ragismic microtemperaments #Enneadecal|enneadecal]] and [[sensamagic clan #Superenneadecal|superenneadecal]].
 == Meanmag ==
@@ Line 29: / Line 34: @@
 Comma list: 81/80, 385/384, 625/616
-Mapping: {{mapping| 19 30 44 0 119 | 0 0 0 1 -1 }}
+{{Mapping|legend=0| 19 30 44 0 119 | 0 0 0 1 -1 }}
 Optimal tunings:
@@ Line 44: / Line 49: @@
 Comma list: 81/80, 105/104, 144/143, 625/616
-Mapping: {{mapping| 19 30 44 0 119 17 | 0 0 0 1 -1 1 }}
+{{Mapping|legend=0| 19 30 44 0 119 17 | 0 0 0 1 -1 1 }}
 Optimal tunings:
@@ Line 75: / Line 80: @@
 Comma list: 49/48, 65/64, 81/80, 126/125
-Mapping: {{mapping| 19 30 44 53 0 70 | 0 0 0 0 1 0 }}
+{{Mapping|legend=0| 19 30 44 53 0 70 | 0 0 0 0 1 0 }}
 Optimal tunings: