1794edo: Difference between revisions

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Nonetheless, 1794edo does offer some simpler interpretations.

In the 7-limit in the 1794c val, {{val| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo| 21 -8 -6 2 }}, {{monzo| -7 -15 6 6 }}, {{monzo| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s.

In the 7-limit in the 1794c val, {{val| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo| 21 -8 -6 2 }}, {{monzo| -7 -15 6 6 }}, {{monzo| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s. In the 2.11.17 realm, 1794edo supports the 148 & 83 temperament, defined by tempering out the 2.11.17 {{monzo| -67 43 -20 }} comma. 1794edo tempers out the 2.17.19 {{monzo| 277 -21 -45 }} and the corresponding temperament is 12 & 891.

Remarkably, using the patent val, 1794edo tempers out the schisma.

In the 2.11.17 realm, 1794edo shares the {{monzo| -67 43 -20 }} comma with EDOs like {{EDOs| 148, 231, and 296 }}. In the 2.17.19 subgroup, 1794edo tempers out the {{monzo| 277 -21 -45 }}. Most notably, shares this property with {{EDOs| 12, 24, 36, 48 }}, as well as {{EDOs| 855, 867, 879 and 891 }}, with 855 being a multiple of 171. This is distantly reminiscent of the technique when 12edo's 1 and 3-step intervals, for example C# and D# counting from C, are assumed to be 17/16 and 19/16.

== Regular temperament properties ==

@@ Line 12: / Line 12: @@
 Nonetheless, 1794edo does offer some simpler interpretations.
-In the 7-limit in the 1794c val, {{val| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo| 21 -8 -6 2 }}, {{monzo| -7 -15 6 6 }}, {{monzo| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s.
+In the 7-limit in the 1794c val, {{val| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo| 21 -8 -6 2 }}, {{monzo| -7 -15 6 6 }}, {{monzo| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s. In the 2.11.17 realm, 1794edo supports the 148 & 83 temperament, defined by tempering out the 2.11.17 {{monzo| -67 43 -20 }} comma. 1794edo tempers out the 2.17.19 {{monzo| 277 -21 -45 }} and the corresponding temperament is 12 & 891.
 Remarkably, using the patent val, 1794edo tempers out the schisma.
-In the 2.11.17 realm, 1794edo shares the {{monzo| -67 43 -20 }} comma with EDOs like {{EDOs| 148, 231, and 296 }}. In the 2.17.19 subgroup, 1794edo tempers out the {{monzo| 277 -21 -45 }}. Most notably, shares this property with {{EDOs| 12, 24, 36, 48 }}, as well as {{EDOs| 855, 867, 879 and 891 }}, with 855 being a multiple of 171. This is distantly reminiscent of the technique when 12edo's 1 and 3-step intervals, for example C# and D# counting from C, are assumed to be 17/16 and 19/16.
 == Regular temperament properties ==