TAMNAMS: Difference between revisions

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[[Machine]] is the 5&6 temperament in the 2.9.7.11 subgroup with a comma list of 64/63 and 99/98.

~~Its list of EDO tunings is~~ {{ ~~val list~~ | 5, 6, ~~(5+5=10e,)~~ 11, 12, 16, 17, (5+10e+12=21be,~~) 22, 23, (~~5+5+5+5+6=26qe,~~) 27, 28, 33 }} with non-patent val EDOs in brackets but included~~ for demonstrating virtual completeness of the tuning range and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.

It has {{Optimal ET sequence|legend=1| 5, 6, 11, 12, 16, 17, 22, 23, 27, 28, 33 }} with non-patent val tunings including 5+5=10e, 5+10e+12=21be, 5+5+5+5+6=26qe, which are mentioned here for demonstrating virtual completeness of the tuning range, and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.

==== Onyx (1L 6s) ====

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[[Sephiroth]] is the 3&10 temperament in the 2.5.7.11.13.17.21 subgroup with commas including 65/64, 85/84, 221/220, 105/104, 169/168, 170/169, 221/220, 273/272, 275/273.

~~Its list of patent val EDO tunings is~~ {{ ~~val list~~ | 3, 10, 13, 16, 23, 26 }} with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.

It has {{Optimal ET sequence|legend=1 | 3, 10, 13, 16, 23, 26 }} with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.

* Extreme tunings even occasionally go outside of this range like with 7e, but this would never be considered a good tuning.

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[[Dicot family#Dichotic|Dichotic]] is the 7&10 temerament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63 and is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. To help justify using these temperament for inspiration for the name, note that:

~~Its list of patent val EDO tunings is~~ {{ ~~val list~~ | 7, 10, 17 }} with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).

It has {{Optimal ET sequence|legend=1 | 7, 10, 17 }} with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).

Note there are many more warted tunings than this with even more extreme tunings, which makes it reasonable to loosely associate the exotemperament with the range of vaguely saner tunings.

@@ Line 531: / Line 531: @@
 [[Machine]] is the 5&6 temperament in the 2.9.7.11 subgroup with a comma list of 64/63 and 99/98.
-Its list of EDO tunings is {{ val list | 5, 6, (5+5=10e,) 11, 12, 16, 17, (5+10e+12=21be,) 22, 23, (5+5+5+5+6=26qe,) 27, 28, 33 }} with non-patent val EDOs in brackets but included for demonstrating virtual completeness of the tuning range and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.
+It has {{Optimal ET sequence|legend=1| 5, 6, 11, 12, 16, 17, 22, 23, 27, 28, 33 }} with non-patent val tunings including 5+5=10e, 5+10e+12=21be, 5+5+5+5+6=26qe, which are mentioned here for demonstrating virtual completeness of the tuning range, and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.
 ==== Onyx (1L 6s) ====
@@ Line 546: / Line 546: @@
 [[Sephiroth]] is the 3&10 temperament in the 2.5.7.11.13.17.21 subgroup with commas including 65/64, 85/84, 221/220, 105/104, 169/168, 170/169, 221/220, 273/272, 275/273.
-Its list of patent val EDO tunings is {{ val list | 3, 10, 13, 16, 23, 26 }} with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.
+It has {{Optimal ET sequence|legend=1 | 3, 10, 13, 16, 23, 26 }} with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.
 * Extreme tunings even occasionally go outside of this range like with 7e, but this would never be considered a good tuning.
@@ Line 556: / Line 556: @@
 [[Dicot family#Dichotic|Dichotic]] is the 7&10 temerament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63 and is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. To help justify using these temperament for inspiration for the name, note that:
-Its list of patent val EDO tunings is {{ val list | 7, 10, 17 }} with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).
+It has {{Optimal ET sequence|legend=1 | 7, 10, 17 }} with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).
 Note there are many more warted tunings than this with even more extreme tunings, which makes it reasonable to loosely associate the exotemperament with the range of vaguely saner tunings.