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337edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|337}}
{{ED intro}}
 
== Theory ==
== Theory ==
337et tempers out [[16875/16807]], 1280000000/1275989841, [[14348907/14336000]], 5250987/5242880, 420175/419904 and 201768035/201326592 in the 7-limit. It provides the optimal patent val for the [[kleirtismic]] temperament.
337edo is [[consistent]] to the [[9-odd-limit]], but the error of [[harmonic]] [[5/1|5]] is quite large. If the harmonic is used at all, it tends very flat. The equal temperament [[tempering out|tempers out]] [[16875/16807]], [[420175/419904]], and 5250987/5242880 in the 7-limit. It [[support]]s [[tokko]] and [[sqrtphi]].
 
=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|337}}
{{Harmonics in equal|337}}
=== Subsets and supersets ===
=== Subsets and supersets ===
337edo is the 68th [[prime EDO]].  
337edo is the 68th [[prime edo]].  
 
== 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|-534 337}}
! rowspan="2" | [[Comma list]]
|{{val|337 534}}
! rowspan="2" | [[Mapping]]
| 0.1487
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -534 337 }}
| {{mapping| 337 534 }}
| +0.1487
| 0.1487
| 0.1487
| 4.18
| 4.18
|-
|-
|2.3.5
| 2.3.5
|15625/15552, {{monzo|-88 57 -1}}
| 15625/15552, {{monzo| -88 57 -1 }}
|{{val|337 534 782}}
| {{mapping| 337 534 782 }}
| 0.3495
| +0.3495
| 0.3089
| 0.3089
| 8.67
| 8.67
|-
|-
|2.3.5.7
| 2.3.5.7
|15625/15552, 16875/16807, 7381125/7340032
| 15625/15552, 16875/16807, 7381125/7340032
|{{val|337 534 782 946}}
| {{mapping| 337 534 782 946 }}
| 0.2870
| +0.2870
| 0.2886
| 0.2886
| 8.10
| 8.10
|}
|}
=== 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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|67\337
| 67\337
|238.58
| 238.58
|147/128
| 147/128
|[[Tokko]]
| [[Tokko]]
|-
| 1
| 89\337
| 316.91
| 6/5
| [[Hanson]]
|-
|-
|1
| 1
|89\337
| 117\337
|316.91
| 416.62
|6/5
| 14/11
|[[Hanson]]
| [[Sqrtphi]] (337, 11-limit)
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Music ==
; [[Francium]]
* "The End Of A Good Day" from ''Mysteries'' (2023) &ndash; [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] | [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] | [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/337edo"