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89edo: Difference between revisions

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→Music: Add Bryan Deister's ''microtonal improvisation in 89edo'' (2025)
 
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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:hstraub|hstraub]] and made on <tt>2011-06-22 07:27:36 UTC</tt>.<br>
: The original revision id was <tt>238144841</tt>.<br>
: 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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">89edo divides the octave into 89 steps of size 13.48 cents each, and tempers out the commas 126/125, 1728/1715, 32805/32768, 2401/2400, 176/175, 243/242, 441/440 and 540/539. It is an especially good tuning for [[Starling temperaments|myna temperament]], both in the 7-limit, tempering out 126/126 and 1728/1715, and in the 11-limit, where 176/175 is tempered out also. It is likewise a good tuning for the rank three temperament thrush, tempering out 126/125 and 176/175.


89 has a fifth less than a cent flat and a major third less than five cents sharp, with a 7 two cents sharp and an 11 1.5 cents sharp. It thus delivers reasonably good 11-limit harmony and very good no-fives harmony along with the very useful approximations represented by its commas.
== Theory ==
89edo has a [[3/1|harmonic 3]] less than a cent flat and a [[5/1|harmonic 5]] less than five cents sharp, with a [[7/1|7]] two cents sharp and an [[11/1|11]] 1.5 cents sharp. It thus delivers reasonably good 11-limit harmony and very good no-fives harmony along with the very useful approximations represented by its commas. On a related note, a notable characteristic of this edo is that it is the lowest in a series of four consecutive edos to temper out [[quartisma]].


=Scales=
It [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; [[126/125]], [[1728/1715]], and [[2401/2400]] in the 7-limit; and [[176/175]], [[243/242]], [[441/440]] and [[540/539]] in the 11-limit. It is an especially good tuning for the [[myna]] temperament, both in the [[7-limit]], tempering out 126/125 and 1728/1715, and in the [[11-limit]], where 176/175 is tempered out also. It is likewise a good tuning for the rank-3 temperament [[thrush]], tempering out 126/125 and 176/175.
[[myna7]]
[[myna11]]
[[myna15]]


=Music=
The [[13-limit]] is a little tricky as [[13/1|13]] is tuned distinctly flat, tempering out [[169/168]], [[364/363]], [[729/728]], [[832/825]], and [[1287/1280]]. [[13/10]] and [[15/13]] are particularly out of tune in this system, each being about 9 cents off. The alternative 89f val fixes that but tunes [[13/8]] much sharper, conflating it with [[18/11]]. It tempers out [[144/143]], [[196/195]], [[351/350]], and [[352/351]] instead, and [[support]]s 13-limit myna and thrush. However, [[58edo]] is a better tuning for those purposes.
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3|Myna Music]] by [[Igliashon Jones]]</pre></div>
 
<h4>Original HTML content:</h4>
The [[17/1|17]] and [[19/1|19]] are tuned fairly well, making it [[consistent]] to the no-13 [[21-odd-limit]]. The equal temperament tempers out [[256/255]] and [[561/560]] in the 17-limit; and [[171/170]], [[361/360]], [[513/512]], and [[1216/1215]] in the 19-limit.  
<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;89edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;89edo divides the octave into 89 steps of size 13.48 cents each, and tempers out the commas 126/125, 1728/1715, 32805/32768, 2401/2400, 176/175, 243/242, 441/440 and 540/539. It is an especially good tuning for &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;myna temperament&lt;/a&gt;, both in the 7-limit, tempering out 126/126 and 1728/1715, and in the 11-limit, where 176/175 is tempered out also. It is likewise a good tuning for the rank three temperament thrush, tempering out 126/125 and 176/175.&lt;br /&gt;
 
&lt;br /&gt;
89edo is the 11th in the {{w|Fibonacci sequence}}, which means its 55th step approximates logarithmic φ (i.e. 1200{{nowrap|(φ − 1)}}{{c}} within a fraction of a cent.
89 has a fifth less than a cent flat and a major third less than five cents sharp, with a 7 two cents sharp and an 11 1.5 cents sharp. It thus delivers reasonably good 11-limit harmony and very good no-fives harmony along with the very useful approximations represented by its commas.&lt;br /&gt;
 
&lt;br /&gt;
=== Prime harmonics ===
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Scales&lt;/h1&gt;
{{Harmonics in equal|89}}
&lt;a class="wiki_link" href="/myna7"&gt;myna7&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/myna11"&gt;myna11&lt;/a&gt;&lt;br /&gt;
=== Subsets and supersets ===
&lt;a class="wiki_link" href="/myna15"&gt;myna15&lt;/a&gt;&lt;br /&gt;
89edo is the 24th [[prime edo]], following [[83edo]] and before [[97edo]].
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Music&lt;/h1&gt;
== Intervals ==
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3" rel="nofollow"&gt;Myna Music&lt;/a&gt; by &lt;a class="wiki_link" href="/Igliashon%20Jones"&gt;Igliashon Jones&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Interval table}}
 
== Notation ==
=== Ups and downs notation ===
89edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals:
 
{{Sharpness-sharp8}}
 
== Approximation to JI ==
=== Zeta peak index ===
{{ZPI
| zpi = 497
| steps = 89.0229355804124
| step size = 13.4796723133902
| tempered height = 7.567368
| pure height = 7.158697
| integral = 1.124501
| gap = 16.042570
| octave = 1199.69083589172
| consistent = 12
| distinct = 12
}}
 
== 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| -141 89 }}
| {{mapping| 89 141 }}
| +0.262
| 0.262
| 1.95
|-
| 2.3.5
| 32805/32768, 10077696/9765625
| {{mapping| 89 141 207 }}
| −0.500
| 1.098
| 8.15
|-
| 2.3.5.7
| 126/125, 1728/1715, 32805/32768
| {{mapping| 89 141 207 250 }}
| −0.550
| 0.955
| 7.08
|-
| 2.3.5.7.11
| 126/125, 176/175, 243/242, 16384/16335
| {{mapping| 89 141 207 250 308 }}
| −0.526
| 0.855
| 6.35
|}
 
=== 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
| 13\89
| 175.28
| 72/65
| [[Sesquiquartififths]] / [[sesquart]]
|-
| 1
| 21\89
| 283.15
| 13/11
| [[Neominor]]
|-
| 1
| 23\89
| 310.11
| 6/5
| [[Myna]]
|-
| 1
| 29\89
| 391.01
| 5/4
| [[Amigo]]
|-
| 1
| 37\89
| 498.87
| 4/3
| [[Grackle]]
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Scales ==
* [[Myna7]]
* [[Myna11]]
* [[Myna15]]
 
== Instruments ==
; Lumatone
''See [[Lumatone mapping for 89edo]].''
 
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=2JNIeqvXKlM ''microtonal improvisation in 89edo''] (2025)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=5Du9RfDUqCs ''Singing Golden Myna''] (2022) – myna[11] in 89edo
 
[[Category:Listen]]
[[Category:Myna]]
[[Category:Thrush]]
Retrieved from "https://en.xen.wiki/w/89edo"