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367edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|367}} == Theory == 367et is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit: * {{val|367 582 852 1030}} (paten..."
 
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|367}}
{{ED intro}}


== Theory ==
== Theory ==
367et is only consistent to the [[5-odd-limit]], with three mappings possible for the 7-limit:
367et is only [[consistent]] to the [[5-odd-limit]], with three mappings possible for the 7-limit:
* {{val|367 582 852 1030}} (patent val)
* {{val| 367 582 852 1030 }} (patent val)
* {{val|367 582 852 '''1031'''}} (367d val)
* {{val| 367 582 852 '''1031''' }} (367d val)
* {{val|367 582 '''853''' '''1031'''}} (367cd val)
* {{val| 367 582 '''853''' '''1031''' }} (367cd val)


Using the patent val, it tempers out [[15625/15552]] and {{monzo|102 -57 -5}} in the 5-limit; [[5120/5103]], 15625/15552 and 40353607/39858075 in the 7-limit, supporting [[protolangwidge]].
Using the patent val, it tempers out [[15625/15552]] and {{monzo| 102 -57 -5 }} in the 5-limit; [[5120/5103]] and 40353607/39858075 in the 7-limit.  


Using the 367d val, it tempers out 15625/15552 and {{monzo|102 -57 -5}} in the 5-limit; 15625/15552, 2460375/2458624 and [[2097152/2083725]] in the 7-limit.
Using the 367d val, it tempers out 15625/15552 and {{monzo| 102 -57 -5 }} in the 5-limit; 2460375/2458624 and [[2097152/2083725]] in the 7-limit.


Using the 367cd val, it tempers out 268435456/263671875 and {{monzo|33 -34 9}} in the 5-limit; 5120/5103, 7558272/7503125 and 235298/234375 in the 7-limit.
Using the 367cd val, it tempers out 268435456/263671875 and {{monzo| 33 -34 9 }} in the 5-limit; 5120/5103, 7558272/7503125 and 235298/234375 in the 7-limit.


=== Odd harmonics ===
=== Odd harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
367edo is the 73rd [[prime EDO]]. [[1101edo]], which triples it, gives a good correction to the harmonic 7.
367edo is the 73rd [[prime edo]]. [[1101edo]], which triples it, gives a good correction to the harmonic 7.


== 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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|582 -367}}
! rowspan="2" | [[Comma list]]
|{{mapping|367 582}}
! rowspan="2" | [[Mapping]]
| -0.3288
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 582 -367 }}
| {{mapping| 367 582 }}
| −0.3288
| 0.3287
| 0.3287
| 10.05
| 10.05
|-
|-
|2.3.5
| 2.3.5
|15625/15552, {{monzo|102 -57 -5}}
| 15625/15552, {{monzo| 102 -57 -5 }}
|{{mapping|367 582 852}}
| {{mapping| 367 582 852 }}
| -0.1500
| −0.1500
| 0.3688
| 0.3688
| 11.28
| 11.28
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per 8ve
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|28\367
| 28\367
|91.55
| 91.55
|{{monzo|46 -7 -15}}
| {{monzo| 46 -7 -15 }}
|[[Gross]]
| [[Gross]]
|-
|-
|1
| 1
|97\367
| 97\367
|317.17
| 317.17
|6/5
| 6/5
|[[Hanson]]
| [[Hanson]]
|}
|}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
== Music ==
; [[Francium]]
* "Loss" from ''End Of Sartorius Membranes'' (2024) &ndash; [https://open.spotify.com/track/0fZfyXdtSonjGHoTSQu5O5 Spotify] | [https://francium223.bandcamp.com/track/loss Bandcamp] | [https://www.youtube.com/watch?v=5UmRUMSzoHM YouTube]


<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
[[Category:Listen]]
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