1794edo: Difference between revisions

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1794edo's divisors are {{EDOs|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.

The best subgroup for 1794 is 2.11.17.19.29.31.47. ~~Nonetheless~~, ~~we will cover some 7-limit interpretations~~.

The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).

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.

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.

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

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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 ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" |Subgroup

! rowspan="2" |[[Comma list]]

! rowspan="2" |[[Mapping]]

! rowspan="2" |Optimal

8ve stretch (¢)

! colspan="2" |Tuning error

|-

![[TE error|Absolute]] (¢)

![[TE simple badness|Relative]] (%)

|-

|2.3

|{{monzo|-2843, 1794}}

|{{Val|1794 2843}}

|0.0892

|5.97

|-

|2.11.17.19.29.31.47

|9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936

|{{Val|1794 6206 7333 7621 8715 8888 9965}}

| -0.0012

|0.0259

|1.74

|}

== Trivia ==

@@ Line 6: / Line 6: @@
 edo's divisors are {{EDOs|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.
-The best subgroup for 1794 is 2.11.17.19.29.31.47. Nonetheless, we will cover some 7-limit interpretations.
+The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).
-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.
+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.
 Remarkably, using the patent val, 1794edo tempers out the schisma.
@@ Line 14: / Line 16: @@
 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 ==
+{| class="wikitable center-4 center-5 center-6"
+! rowspan="2" |Subgroup
+! rowspan="2" |[[Comma list]]
+! rowspan="2" |[[Mapping]]
+! rowspan="2" |Optimal
+ve stretch (¢)
+! colspan="2" |Tuning error
+|-
+![[TE error|Absolute]] (¢)
+![[TE simple badness|Relative]] (%)
+|-
+|2.3
+|{{monzo|-2843, 1794}}
+|{{Val|1794 2843}}
+|0.0892
+|0.0892
+|5.97
+|-
+|2.11.17.19.29.31.47
+|9251/9248, 347072/346921, 492043/492032, 128116736/128086823,  151329376/151270111, 378544627/378535936
+|{{Val|1794 6206 7333 7621 8715 8888 9965}}
+| -0.0012
+|0.0259
+|1.74
+|}
 == Trivia ==
 {{Wikipedia| 1794 }}