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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 ==
== Theory ==
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=== 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 3, 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.
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== 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|867 -547}}
! rowspan="2" | [[Comma list]]
|{{mapping|547 867}}
! rowspan="2" | [[Mapping]]
| -0.0177
! 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
| 0.0177
| 0.81
| 0.81
|-
|-
|2.3.5
| 2.3.5
|{{monzo|39 -29 3}}, {{monzo|-29 -11 20}}
| {{Monzo| 39 -29 3 }}, {{monzo| -29 -11 20 }}
|{{mapping|547 867 1270}}
| {{Mapping| 547 867 1270 }}
| +0.0180
| +0.0180
| 0.0525
| 0.0525
| 2.39
| 2.39
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 4096000/4084101, 23066015625/23018340352
| 4375/4374, 4096000/4084101, 23066015625/23018340352
|{{mapping|547 867 1270 1536}}
| {{Mapping| 547 867 1270 1536 }}
| -0.0601
| −0.0601
| 0.1428
| 0.1428
| 6.51
| 6.51
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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
|16\547
| 16\547
|35.10
| 35.10
|1990656/1953125
| 1990656/1953125
|[[Gammic]]
| [[Gammic]]
|-
|-
|1
| 1
|51\547
| 51\547
|111.88
| 111.88
|16/15
| 16/15
|[[Vavoom]]
| [[Vavoom]]
|-
|-
|1
| 1
|101\547
| 101\547
|221.57
| 221.57
|8388608/7381125
| 8388608/7381125
|[[Fortune]]
| [[Fortune]]
|-
|-
|1
| 1
|105\547
| 105\547
|230.35
| 230.35
|8/7
| 8/7
|[[Gamera]]
| [[Gamera]]
|-
|-
|1
| 1
|258\547
| 258\547
|566.00
| 566.00
|104/75
| 104/75
|[[Tricot]]
| [[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]


<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]]

Latest revision as of 13:31, 13 March 2026

← 546edo 547edo 548edo →
Prime factorization 547 (prime)
Step size 2.19378 ¢ 
Fifth 320\547 (702.011 ¢)
Semitones (A1:m2) 52:41 (114.1 ¢ : 89.95 ¢)
Consistency limit 9
Distinct consistency limit 9

547 equal divisions of the octave (abbreviated 547edo or 547ed2), also called 547-tone equal temperament (547tet) or 547 equal temperament (547et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 547 equal parts of about 2.19 ¢ each. Each step represents a frequency ratio of 21/547, or the 547th root of 2.

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.

Prime harmonics

Approximation of prime harmonics in 547edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.056 -0.208 +0.827 -0.678 -0.308 +0.346 +0.842 -0.852 -0.692 +0.120
Relative (%) +0.0 +2.6 -9.5 +37.7 -30.9 -14.1 +15.8 +38.4 -38.8 -31.6 +5.5
Steps
(reduced) 		547
(0) 		867
(320) 		1270
(176) 		1536
(442) 		1892
(251) 		2024
(383) 		2236
(48) 		2324
(136) 		2474
(286) 		2657
(469) 		2710
(522)

Subsets and supersets

547edo is the 101st prime edo. 1641edo, which divides edostep in 3, corrects the mapping for the 11-limit.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [867 -547⟩ [⟨547 867]] −0.0177 0.0177 0.81
2.3.5 [39 -29 3⟩, [-29 -11 20⟩ [⟨547 867 1270]] +0.0180 0.0525 2.39
2.3.5.7 4375/4374, 4096000/4084101, 23066015625/23018340352 [⟨547 867 1270 1536]] −0.0601 0.1428 6.51

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
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

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Music

Francium
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