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1171edo: Difference between revisions

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**Imported revision 556692091 - Original comment: **
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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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-14 11:50:51 UTC</tt>.<br>
 
: The original revision id was <tt>556692091</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
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]].
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
=== Prime harmonics ===
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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&gt; and whoosh, |37 25 -33&gt;. 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.</pre></div>
{{Harmonics in equal|1171}}
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;1171edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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 &lt;a class="wiki_link" href="/612edo"&gt;612&lt;/a&gt; with a lower 5-limit &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness"&gt;relative error&lt;/a&gt;. It has a 5-limit comma basis consisting of the monzisma, |54 -37 2&amp;gt; and whoosh, |37 25 -33&amp;gt;. 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.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== 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
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