1171edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,170 edits
hyphenate and link comma-basis
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"
 
(19 intermediate revisions by 8 users not shown)
Line 1: Line 1:
The 1171 equal division divides the octave into 1171 parts of size 1.0248 cents each. It is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]. It has a 5-limit [[comma-basis]] consisting of the monzisma, |54 -37 2> and whoosh, |37 25 -33>. While not a strong higher-limit system, it is uniquely consistent through the 27-limit, and is very strong on the 2.3.5.11 subgroup. We might also note that 1171 is a prime number.
{{Infobox ET}}
{{ED intro}}
 
== Theory ==
1171edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is [[consistency|distinctly consistent]] through the [[27-odd-limit]], and is very strong on the 2.3.5.11 [[subgroup]].
 
=== Prime harmonics ===
{{Harmonics in equal|1171}}
 
=== Subsets and supersets ===
1171edo is the 193rd [[prime edo]]. [[2342edo]] which doubles it, corrects its [[harmonic]] [[7/1|7]] to a near-just quality.
 
== Regular temperament properties ==
=== 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
| 129\1171
| 132.195
| {{Monzo| -38 5 13 }}
| [[Astro]]
|-
| 1
| 243\1171
| 249.018
| {{Monzo| -26 18 -1 }}
| [[Monzismic]]
|-
| 1
| 315\1171
| 322.801
| {{Monzo| -6 23 -13 }}
| [[Senior]]
|-
| 1
| 335\1171
| 343.296
| 8000/6561
| [[Raider]]
|-
| 1
| 547\1171
| 560.547
| 864/625
| [[Whoosh]]
|}
<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]]
* "Right On Friendly Lovers" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/208kkCqXksQWhT0zdxFXYm Spotify] | [https://francium223.bandcamp.com/track/right-on-friendly-lovers Bandcamp] | [https://www.youtube.com/watch?v=_qqisIAkVRc YouTube] − in Friesachic, 1171edo tuning
* "Apply to a Print" from ''I Want To'' (2025) – [https://open.spotify.com/track/5botrdPX1YdFmk2mP6kbOr Spotify] | [https://francium223.bandcamp.com/track/apply-to-a-print Bandcamp] | [https://www.youtube.com/watch?v=ui-ORXPgqaE YouTube] – in Viljevic, 1171edo tuning

Latest revision as of 13:32, 13 March 2026

← 1170edo 1171edo 1172edo →
Prime factorization 1171 (prime)
Step size 1.02477 ¢ 
Fifth 685\1171 (701.964 ¢)
Semitones (A1:m2) 111:88 (113.7 ¢ : 90.18 ¢)
Consistency limit 27
Distinct consistency limit 27

1171 equal divisions of the octave (abbreviated 1171edo or 1171ed2), also called 1171-tone equal temperament (1171tet) or 1171 equal temperament (1171et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1171 equal parts of about 1.02 ¢ each. Each step represents a frequency ratio of 21/1171, or the 1171st root of 2.

Theory

1171edo is a very strong 5-limit division, being the first one past 612 with a lower 5-limit relative error. It has a 5-limit comma basis consisting of the monzisma, [54 -37 2⟩ and whoosh, [37 25 -33⟩. While not a strong higher-limit system, it is distinctly consistent through the 27-odd-limit, and is very strong on the 2.3.5.11 subgroup.

Prime harmonics

Approximation of prime harmonics in 1171edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.009 +0.023 -0.423 +0.006 -0.220 -0.429 -0.331 -0.093 +0.312 -0.373
Relative (%) +0.0 +0.9 +2.2 -41.3 +0.6 -21.5 -41.9 -32.3 -9.1 +30.4 -36.4
Steps
(reduced) 		1171
(0) 		1856
(685) 		2719
(377) 		3287
(945) 		4051
(538) 		4333
(820) 		4786
(102) 		4974
(290) 		5297
(613) 		5689
(1005) 		5801
(1117)

Subsets and supersets

1171edo is the 193rd prime edo. 2342edo which doubles it, corrects its harmonic 7 to a near-just quality.

Regular temperament properties

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 129\1171 132.195 [-38 5 13⟩ Astro
1 243\1171 249.018 [-26 18 -1⟩ Monzismic
1 315\1171 322.801 [-6 23 -13⟩ Senior
1 335\1171 343.296 8000/6561 Raider
1 547\1171 560.547 864/625 Whoosh

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

Music

Francium
  • "Right On Friendly Lovers" from Naughty Girl Era (2024) – Spotify | Bandcamp | YouTube − in Friesachic, 1171edo tuning
  • "Apply to a Print" from I Want To (2025) – Spotify | Bandcamp | YouTube – in Viljevic, 1171edo tuning
Retrieved from "https://en.xen.wiki/index.php?title=1171edo&oldid=225835"