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547edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|547}} 547edo is a strong 5-limit system, tuning fortune, gammic, and vavoom temperaments. Past the 5-limit, good subgroups of choic..."
 
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|547}}
{{ED intro}}


== Theory ==
547edo is a strong [[5-limit]] system, tuning [[fortune]], [[gammic]], and [[vavoom]] temperaments. Past the 5-limit, good subgroups of choice include 2.3.5.13.17.31, or 2.3.5.77.29/23.
547edo is a strong [[5-limit]] system, tuning [[fortune]], [[gammic]], and [[vavoom]] temperaments. Past the 5-limit, good subgroups of choice include 2.3.5.13.17.31, or 2.3.5.77.29/23.


=== Prime harmonics ===
=== Prime harmonics ===
{{harmonics in equal|547}}
{{Harmonics in equal|547}}
 
=== Subsets and supersets ===
=== Subsets and supersets ===
547edo is the 101st [[prime edo]]. 1641edo, which divides edostep in 33, corrects the mapping for the 11-limit.
547edo is the 101st [[prime edo]]. [[1641edo]], which divides edostep in 3, corrects the mapping for the 11-limit.
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 867 -547 }}
| {{Mapping| 547 867 }}
| −0.0177
| 0.0177
| 0.81
|-
| 2.3.5
| {{Monzo| 39 -29 3 }}, {{monzo| -29 -11 20 }}
| {{Mapping| 547 867 1270 }}
| +0.0180
| 0.0525
| 2.39
|-
| 2.3.5.7
| 4375/4374, 4096000/4084101, 23066015625/23018340352
| {{Mapping| 547 867 1270 1536 }}
| −0.0601
| 0.1428
| 6.51
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperaments
|-
| 1
| 16\547
| 35.10
| 1990656/1953125
| [[Gammic]]
|-
| 1
| 51\547
| 111.88
| 16/15
| [[Vavoom]]
|-
| 1
| 101\547
| 221.57
| 8388608/7381125
| [[Fortune]]
|-
| 1
| 105\547
| 230.35
| 8/7
| [[Gamera]]
|-
| 1
| 258\547
| 566.00
| 104/75
| [[Alphatrillium]]
|}
<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]]
* "Activate!" from ''End Of Sartorius Membranes'' (2024) − [https://open.spotify.com/track/2mVV0wyzlDuuk5KZ1YP8QW Spotify] | [https://francium223.bandcamp.com/track/activate Bandcamp] | [https://www.youtube.com/watch?v=-Oxj8OOUW48 YouTube]
* "IT'S A LEG!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/0oRlaPc8uFZz1Nbgtguh8n Spotify] | [https://francium223.bandcamp.com/track/its-a-leg Bandcamp] | [https://www.youtube.com/watch?v=-aQolexQwY4 YouTube] − in Vavoom, 547edo tuning
* from ''Eggs'' (2025)
** "Steam Eggs with Wikipedia" – [https://open.spotify.com/track/5z903cBQkfYCGMZo2YvBP0 Spotify] | [https://francium223.bandcamp.com/track/steam-eggs-with-wikipedia Bandcamp] | [https://www.youtube.com/watch?v=APOWzIFl1Xk YouTube]
** "Her Name Was Egg." – [https://open.spotify.com/track/5IOaQ1cNTUimE9gvui1qlK Spotify] | [https://francium223.bandcamp.com/track/her-name-was-egg Bandcamp] | [https://www.youtube.com/watch?v=ixFhdiEBB_w YouTube]
 
[[Category:Listen]]
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