971edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Wikispaces>genewardsmith
**Imported revision 556761637 - Original comment: **
Francium (talk | contribs)
+music
 
(10 intermediate revisions by 9 users not shown)
Line 1: Line 1:
<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>2015-08-16 13:17:15 UTC</tt>.<br>
 
: The original revision id was <tt>556761637</tt>.<br>
971edo's fifth is only 0.00174{{c}} sharp of just, as it is the denominator of the first semiconvergent to log<sub>2</sub>(3/2) past 389\665. It is [[consistent]] to the 9-odd-limit, but there is a large relative delta in its approximation to harmonic 5. Skipping the harmonic, it is a good 2.3.7.11.13.17 subgroup system.  
: The revision comment was: <tt></tt><br>
 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
=== Prime harmonics ===
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|971}}
<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 971 equal division has a fifth which is only 0.00174 cents sharp. It is the denominator of the first semiconvergent to log2(3/2) past 389\665.</pre></div>
 
<h4>Original HTML content:</h4>
=== Subsets and supersets ===
<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;971edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 971 equal division has a fifth which is only 0.00174 cents sharp. It is the denominator of the first semiconvergent to log2(3/2) past 389\665.&lt;/body&gt;&lt;/html&gt;</pre></div>
971edo is the 164th [[prime edo]].
 
== Music ==
; [[Francium]]
* "Todd Bonzalez" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/6b3zWRAI12Vn2gwu5kwOML Spotify] | [https://francium223.bandcamp.com/track/todd-bonzalez Bandcamp] | [https://www.youtube.com/watch?v=AfFD4B5LeyM YouTube] − in Alexic, 971edo tuning

Latest revision as of 13:42, 31 March 2025

← 970edo 971edo 972edo →
Prime factorization 971 (prime)
Step size 1.23584 ¢ 
Fifth 568\971 (701.957 ¢)
(semiconvergent)
Semitones (A1:m2) 92:73 (113.7 ¢ : 90.22 ¢)
Consistency limit 9
Distinct consistency limit 9

971 equal divisions of the octave (abbreviated 971edo or 971ed2), also called 971-tone equal temperament (971tet) or 971 equal temperament (971et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 971 equal parts of about 1.24 ¢ each. Each step represents a frequency ratio of 21/971, or the 971st root of 2.

971edo's fifth is only 0.00174 ¢ sharp of just, as it is the denominator of the first semiconvergent to log2(3/2) past 389\665. It is consistent to the 9-odd-limit, but there is a large relative delta in its approximation to harmonic 5. Skipping the harmonic, it is a good 2.3.7.11.13.17 subgroup system.

Prime harmonics

Approximation of prime harmonics in 971edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.002 +0.504 +0.072 -0.134 -0.157 +0.091 +0.324 -0.468 -0.123 +0.587
Relative (%) +0.0 +0.1 +40.8 +5.8 -10.8 -12.7 +7.4 +26.2 -37.9 -10.0 +47.5
Steps
(reduced)
971
(0)
1539
(568)
2255
(313)
2726
(784)
3359
(446)
3593
(680)
3969
(85)
4125
(241)
4392
(508)
4717
(833)
4811
(927)

Subsets and supersets

971edo is the 164th prime edo.

Music

Francium
  • "Todd Bonzalez" from Don't Give Your Kids These Names! (2025) − Spotify | Bandcamp | YouTube − in Alexic, 971edo tuning