79edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

~~: This revision was by author [[User:Dodecaphobe|Dodecaphobe]] and made on <tt>2015-09-16 23:02:23 UTC</tt>.<br>~~

~~: The original revision id was <tt>559512369</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">=<span style="color: #790079; font-family: 'Times New Roman',Times,serif; font-size: 113%;">79 tone equal temperament</span>=

**79edo** divides the octave into 79 equal parts of 15.190 cents each. It tempers out 3125/3072 in the 5-~~limit, 4000/3969, 1728/1715 and 4375/4374 in the~~ 7-limit~~, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993~~ in ~~the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197~~ in the 13-~~limit. It provides the optimal patent val for~~ [[~~Orwellismic temperaments#Sentinel~~-11-limit~~|sentinel temperament~~]]~~. 79 is the 22nd prime EDO number~~.

== Theory ==

79edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] in the no-7 [[13-odd-limit]].

~~=Music=~~

Using the [[patent val]], it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit, [[1728/1715]], [[4000/3969]] and [[4375/4374]] in the 7-limit, [[99/98]], [[243/242]], [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit, and [[169/168]], [[275/273]], [[325/324]], [[351/350]], [[640/637]], [[1188/1183]], [[1575/1573]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It provides the [[optimal patent val]] for the [[sentinel]] temperament.

[[~~https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni|Saint Sebastian, By the Hands of Reni~~]] ~~by Silence and Secrecy (Julian Malerman)</pre></div>~~

~~<h4>Original HTML content:</h4>~~

The 79c val [[support]]s [[meantone]] with a tuning very close to [[1/7-comma meantone|1/7-comma]].

<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"><html><head><title>79edo</title></head><body><h1 id="toc0"><a name="x79 tone equal temperament"></a><span style="color: #790079; font-family: 'Times New Roman',~~Times,serif; font-size: 113%;">79 tone equal temperament</span></h1>~~

~~<br />~~

=== Odd harmonics ===

~~<strong>79edo</strong> divides the octave into 79 equal parts of 15.190 cents each. It~~ tempers out 3125/3072 in the 5-limit, 4000/3969~~, 1728/1715~~ and 4375/4374 in the 7-limit, 99/98, ~~1331/1323,~~ 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, ~~169~~/~~168~~, 640/637, 1188/1183, ~~325/324, 351/350,~~ 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for ~~<~~a ~~class~~=~~"wiki_link" href~~="/~~Orwellismic%20temperaments#Sentinel~~-~~11-limit">sentinel temperament<~~/a~~>~~. 79 is the ~~22nd prime EDO~~ number.~~&lt~~;br /~~>~~

~~<br~~ /~~>~~

~~<h1 id~~=~~"toc1"><a name~~="Music~~">&lt~~;/~~a&gt~~;~~Music<~~/~~h1&gt~~;

=== Subsets and supersets ===

~~<a class="wiki_link_ext" href="~~https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni~~" rel="nofollow">~~Saint Sebastian, By the Hands of Reni~~</a> by Silence and Secrecy~~ (~~Julian Malerman~~)~~</body></html></pre></div>~~

79edo is the 22nd prime edo, past [[73edo]] and before [[83edo]].

=== Miscellany ===

79edo adequately represents the [[Decaononic]] way of playing, as 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. A [[maximal evenness]] variant of such a scale can be generated by naively stacking six [[12edo]] diatonic majors and one Lydian [[tetrachord]]{{clarify}}. Since the final tetrachord does not have a 2nd degree, this results in 6 II's stretched over 6 + 7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9{{clarify}}. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.

== Intervals ==

== Regular temperament properties ==

79edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]], [[meantone]], and [[sentinel]].

== Scales ==

=== Mos scales ===

* Bluebirds[6, 7, 13, 20, 33…]

* Meantone[7, 12, 19, 31…]

* Oceanfront[7, 12, 17, 22, 27…]

** Subsets of the above: see [[oceanfront scales]]

* Sentinel[5, 8, 11, 14, 17, 31…]

=== Others ===

* [[Meantone]] Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)

== Instruments ==

=== Lumatone ===

* [[Lumatone mapping for 79edo]]

=== Skip fretting ===

'''Skip fretting system 79 7 19''' is a [[skip fretting]] system for [[79edo]]. All examples are for 5-string bass.

; Harmonics

1/1: string 2 open

2/1: string 1 fret 14

3/2: string 5 fret 21

5/4: string 5 fret 18

7/4: string 5 fret 2

11/8: string 4 fret 11

13/8: string 5 fret 11

17/16: string 2 fret 1

19/16: string 5 fret 6

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/watch?v=qj6tmkMvQMU ''microtonal improvisation in 79edo''] (2025)

; [[User:Francium|Francium]]

* [https://www.youtube.com/watch?v=gAELEuSZra8 ''Gold''] (2022)

; Silence and Secrecy ([[Julian Malerman]])

* [https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni ''Saint Sebastian, By the Hands of Reni''] (2014)

[[Category:Listen]]

@@ 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:Dodecaphobe|Dodecaphobe]] and made on <tt>2015-09-16 23:02:23 UTC</tt>.<br>
-: The original revision id was <tt>559512369</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">=&lt;span style="color: #790079; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;79 tone equal temperament&lt;/span&gt;=
-**79edo** divides the octave into 79 equal parts of 15.190 cents each. It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for [[Orwellismic temperaments#Sentinel-11-limit|sentinel temperament]]. 79 is the 22nd prime EDO number.
+== Theory ==
+edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] in the no-7 [[13-odd-limit]].
-=Music=
+Using the [[patent val]], it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit, [[1728/1715]], [[4000/3969]] and [[4375/4374]] in the 7-limit, [[99/98]], [[243/242]], [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit, and [[169/168]], [[275/273]], [[325/324]], [[351/350]], [[640/637]], [[1188/1183]], [[1575/1573]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It provides the [[optimal patent val]] for the [[sentinel]] temperament.
-[[https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni|Saint Sebastian, By the Hands of Reni]] by Silence and Secrecy (Julian Malerman)</pre></div>
-<h4>Original HTML content:</h4>
+The 79c val [[support]]s [[meantone]] with a tuning very close to [[1/7-comma meantone|1/7-comma]].
-<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;79edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x79 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #790079; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;79 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
- &lt;br /&gt;
+=== Odd harmonics ===
-&lt;strong&gt;79edo&lt;/strong&gt; divides the octave into 79 equal parts of 15.190 cents each. It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for &lt;a class="wiki_link" href="/Orwellismic%20temperaments#Sentinel-11-limit"&gt;sentinel temperament&lt;/a&gt;. 79 is the 22nd prime EDO number.&lt;br /&gt;
+{{Harmonics in equal|79}}
-&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;
+=== Subsets and supersets ===
- &lt;a class="wiki_link_ext" href="https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni" rel="nofollow"&gt;Saint Sebastian, By the Hands of Reni&lt;/a&gt; by Silence and Secrecy (Julian Malerman)&lt;/body&gt;&lt;/html&gt;</pre></div>
+edo is the 22nd prime edo, past [[73edo]] and before [[83edo]].
+=== Miscellany ===
+edo adequately represents the [[Decaononic]] way of playing, as 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. A [[maximal evenness]] variant of such a scale can be generated by naively stacking six [[12edo]] diatonic majors and one Lydian [[tetrachord]]{{clarify}}. Since the final tetrachord does not have a 2nd degree, this results in 6 II's stretched over 6 + 7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9{{clarify}}. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.
+== Intervals ==
+{{Interval table}}
+== Regular temperament properties ==
+edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]], [[meantone]], and [[sentinel]].
+{{todo|expand}}
+== Scales ==
+=== Mos scales ===
+* Bluebirds[6, 7, 13, 20, 33…]
+* Meantone[7, 12, 19, 31…]
+* Oceanfront[7, 12, 17, 22, 27…]
+** Subsets of the above: see [[oceanfront scales]]
+* Sentinel[5, 8, 11, 14, 17, 31…]
+=== Others ===
+* [[Meantone]] Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)
+== Instruments ==
+=== Lumatone ===
+* [[Lumatone mapping for 79edo]]
+=== Skip fretting ===
+'''Skip fretting system 79 7 19''' is a [[skip fretting]] system for [[79edo]]. All examples are for 5-string bass.
+; Harmonics
+/1: string 2 open
+/1: string 1 fret 14
+/2: string 5 fret 21
+/4: string 5 fret 18
+/4: string 5 fret 2
+/8: string 4 fret 11
+/8: string 5 fret 11
+/16: string 2 fret 1
+/16: string 5 fret 6
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/watch?v=qj6tmkMvQMU ''microtonal improvisation in 79edo''] (2025)
+; [[User:Francium|Francium]]
+* [https://www.youtube.com/watch?v=gAELEuSZra8 ''Gold''] (2022)
+; Silence and Secrecy ([[Julian Malerman]])
+* [https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni ''Saint Sebastian, By the Hands of Reni''] (2014)
+[[Category:Listen]]