Xenharmonic Wiki

1889edo: Difference between revisions

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**Imported revision 556811887 - 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>2015-08-17 12:15:54 UTC</tt>.<br>
== Theory ==
: The original revision id was <tt>556811887</tt>.<br>
1889edo is strong in the [[23-limit]], though [[1578edo|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament.  
: 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|1889|columns=9}}
<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 1889 division divides the octave into 1889 equal parts of 0.6353 cents each. It is strong in the 23-limit, though [[1578edo|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]], rather puts it in the shade. It is distinctly consistent through the 27-limit, but not, unlike 1578, to the 29-limit.</pre></div>
{{Harmonics in equal|1889|columns=9|start=10|title=Approximation of prime harmonics in 1889edo (continued)}}
<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;1889edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 1889 division divides the octave into 1889 equal parts of 0.6353 cents each. It is strong in the 23-limit, though &lt;a class="wiki_link" href="/1578edo"&gt;1578&lt;/a&gt;, which among other things has a lower 23-limit  &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness"&gt;relative error&lt;/a&gt;, rather puts it in the shade. It is distinctly consistent through the 27-limit, but not, unlike 1578, to the 29-limit.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Subsets and supersets ===
1889edo is the 290th [[prime edo]].
 
== Intervals ==
{{Main|Table of 1889edo intervals}}
 
== 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| 2994 -1889 }}
| {{Mapping| 1889 2994 }}
| −0.0012
| 0.0012
| 0.19
|-
| 2.3.5
| {{Monzo| 54 -37 2 }}, {{monzo| -66 -36 53 }}
| {{Mapping| 1889 2994 4386 }}
| +0.0104
| 0.0163
| 2.57
|-
| 2.3.5.7
| 4375/4374, {{monzo| -1 4 11 -1 }}, {{monzo| -57 16 10 3 }}
| {{Mapping| 1889 2994 4386 5303 }}
| +0.0131
| 0.0149
| 2.35
|-
| 2.3.5.7.11
| 4375/4374, 151263/151250, 820125/819896, {{monzo| -28 7 7 -1 1 }}
| {{Mapping| 1889 2994 4386 5303 6535 }}
| +0.0055
| 0.0201
| 3.16
|-
| 2.3.5.7.11.13
| 4225/4224, 4375/4374, 6656/6655, 151263/151250, 4100625/4100096
| {{Mapping| 1889 2994 4386 5303 6535 6990 }}
| +0.0084
| 0.0194
| 3.05
|-
| 2.3.5.7.11.13.17
| 4225/4224, 4375/4374, 6656/6655, 12376/12375, 14875/14872, 194481/194480
| {{Mapping| 1889 2994 4386 5303 6535 6990 7721 }}
| +0.0120
| 0.0200
| 3.15
|-
| 2.3.5.7.11.13.17.19
| 4225/4224, 4375/4374, 5985/5984, 6175/6174, 6656/6655, 12376/12375, 61965/61952
| {{Mapping| 1889 2994 4386 5303 6535 6990 7721 8024 }}
| +0.0167
| 0.0226
| 3.56
|}
 
=== 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
| 392\1889
| 249.021
| {{Monzo| -26 18 1 }}
| [[Monzismic]]
|-
| 1
| 707\1889
| 449.127
| 35/27
| [[Semidimi]]
|}
<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]]
* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] | [https://francium223.bandcamp.com/track/scoop Bandcamp] | [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]
* "The Technological Harbinger of Death" from ''Void'' (2025) – [https://open.spotify.com/track/3LDPz84VhVrTDgPLHQXWyJ YouTube] | [https://francium223.bandcamp.com/track/the-technological-harbinger-of-death Bandcamp] | [https://www.youtube.com/watch?v=CEeXQsHpCc8 YouTube]
* "Don't Worry" from ''Don't'' (2025) – [https://open.spotify.com/track/3Kd1Ql1nYOBMhFWi94ljEP Spotify] | [https://francium223.bandcamp.com/track/dont-worry Bandcamp] | [https://www.youtube.com/watch?v=8CCFVZkxIgk YouTube]
 
[[Category:Monzismic]]
Retrieved from "https://en.xen.wiki/w/1889edo"