1794edo: Difference between revisions

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


It's possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val|1794 2834 4160 5037}} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo|-41, 1, 17, 0}}, {{monzo|20, 13, 14, -26}}.  
It is possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val| 1794 2834 4160 5037 }} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo| -41 1 17 0 }}, {{monzo| 20 13 14 -26 }}.  


Nonetheless, 1794edo does offer some simpler interpretations.  
Nonetheless, 1794edo does offer some simpler interpretations.  
Line 13: Line 13:
Remarkably, using the patent val, 1794edo tempers out the [[schisma]].  
Remarkably, using the patent val, 1794edo tempers out the [[schisma]].  


=== Harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|1794}}
{{Harmonics in equal|1794}}
=== Subsets and supersets ===
=== Subsets and supersets ===
 
1794edo has subset edos {{EDOs| 2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.
1794edo has subset edos {{EDOs|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |Subgroup
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Comma list]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal
! rowspan="2" | Optimal<br>8ve stretch (¢)
8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" |Tuning error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|-2843, 1794}}
| {{monzo| -2843 1794 }}
|{{Val|1794 2843}}
| {{mapping| 1794 2843 }}
|0.0892
| 0.0892
|0.0892
| 0.0892
|5.97
| 5.97
|-
|-
|2.11.17.19.29.31.47
| 2.11.17.19.29.31.47
|9251/9248, 347072/346921, 492043/492032, 128116736/128086823,  151329376/151270111, 378544627/378535936
| 9251/9248, 347072/346921, 492043/492032, 128116736/128086823,  151329376/151270111, 378544627/378535936
|{{Val|1794 6206 7333 7621 8715 8888 9965}}
| {{mapping| 1794 6206 7333 7621 8715 8888 9965 }}
| -0.0012
| -0.0012
|0.0259
| 0.0259
|1.74
| 1.74
|}
|}
== Trivia ==
{{Wikipedia| 1794 }}
The number 1794 is known for being the fatal year of the French Revolution.


[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
{{Todo| review }}

Revision as of 14:28, 15 October 2023

← 1793edo 1794edo 1795edo →
Prime factorization 2 × 3 × 13 × 23
Step size 0.668896 ¢ 
Fifth 1049\1794 (701.672 ¢)
Semitones (A1:m2) 167:137 (111.7 ¢ : 91.64 ¢)
Dual sharp fifth 1050\1794 (702.341 ¢) (→ 175\299)
Dual flat fifth 1049\1794 (701.672 ¢)
Dual major 2nd 305\1794 (204.013 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

Theory

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).

It is possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the ⟨1794 2834 4160 5037] val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, [-41 1 17 0⟩, [20 13 14 -26⟩.

Nonetheless, 1794edo does offer some simpler interpretations.

In the 7-limit in the 1794c 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, ⟨1794 2844 4166 5037], it tempers out [21 -8 -6 2⟩, [-7 -15 6 6⟩, [-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 [-67 43 -20⟩ comma. 1794edo tempers out the 2.17.19 [277 -21 -45⟩ and the corresponding temperament is 12 & 891.

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

Odd harmonics

Approximation of odd harmonics in 1794edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.283 +0.308 -0.264 +0.103 -0.147 +0.275 +0.026 +0.061 +0.146 +0.122 -0.181
Relative (%) -42.3 +46.1 -39.5 +15.5 -22.0 +41.1 +3.8 +9.2 +21.8 +18.3 -27.0
Steps
(reduced) 		2843
(1049) 		4166
(578) 		5036
(1448) 		5687
(305) 		6206
(824) 		6639
(1257) 		7009
(1627) 		7333
(157) 		7621
(445) 		7880
(704) 		8115
(939)

Subsets and supersets

1794edo has subset edos 2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [-2843 1794⟩ [⟨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 [⟨1794 6206 7333 7621 8715 8888 9965]] -0.0012 0.0259 1.74
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