74edo: 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:genewardsmith|genewardsmith]] and made on <tt>2011-11-21 00:46:14 UTC</tt>.<br>~~

~~: The original revision id was <tt>277565016</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">//74edo// divides the [[octave]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out 81/80 in the [[5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and 144/143 and 847/845 in the [[13-limit]]. Discarding 847/845 from that gives [[Meantone family|13-limit meantone]], aka 13-limit huygens, for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.

~~74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.</pre></div>~~

== Theory ==

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

74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone.

~~<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>~~74edo</title></head><body><em>74edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 74 equal parts of size 16.216 <a class="wiki_link" href="/cent">cent</a>s each. It is most notable as a ~~<a class="wiki_link" href="/~~meantone~~">meantone</a>~~ tuning, tempering out 81/80 in the ~~<a class="wiki_link" href="/~~5-limit~~"&gt~~;~~5-limit</a>; 81/80 and~~ 126/125 (and ~~hence~~ 225/224) in the ~~<a class="wiki_link" href="/7-limit">~~7-limit~~</a>~~; 99/98, 176/175 and 441/440 in the ~~<a class="wiki_link" href="/~~11-limit~~">11-limit</a>~~; and 144/143 and 847/845 in the ~~<a class="wiki_link" href="/~~13-limit~~">13-limit</a>~~. Discarding 847/845 from that gives ~~<a class="wiki_link" href="/Meantone%20family">~~13-limit meantone~~</a>, aka 13-limit huygens~~, for which 74edo gives the ~~<a class="wiki_link" href="/optimal%20patent%20val">~~optimal patent val~~</a>~~; and discarding 144/143 gives a 13-limit 62&~~amp;~~amp;74 temperament with half-octave period and two parallel tracks of meantone.~~<br />~~

~~<br />~~

74edo tunes [[harmonic]] [[11/1|11]] only 1/30 of a cent sharp, and [[13/1|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.~~&lt~~;/~~body><~~/~~html>~~</~~pre~~></~~div~~>

=== Odd harmonics ===

=== Subsets and supersets ===

Since 74 factors into {{factorization|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets; of these, 37edo has the same highly accurate prime harmonics in the no-3s [[13-limit]].

== Intervals ==

== Notation ==

===Ups and downs notation===

74edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).

Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

=== Sagittal notation ===

==== Evo flavor ====

File:74-EDO_Evo_Sagittal.svg

desc none

rect 80 0 300 50 [[Sagittal_notation]]

rect 300 0 685 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]

rect 20 80 180 106 [[1701/1664]]

rect 180 80 300 106 [[36/35]]

rect 300 80 460 106 [[1053/1024]]

default [[File:74-EDO_Evo_Sagittal.svg]]

</imagemap>

==== Revo flavor ====

File:74-EDO_Revo_Sagittal.svg

desc none

rect 80 0 300 50 [[Sagittal_notation]]

rect 300 0 631 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]

rect 20 80 180 106 [[1701/1664]]

rect 180 80 300 106 [[36/35]]

rect 300 80 460 106 [[1053/1024]]

default [[File:74-EDO_Revo_Sagittal.svg]]

</imagemap>

In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

== Instruments ==

* [[Lumatone mapping for 74edo]]

== Music ==

=== Modern renderings ===

; {{W|Scott Joplin}}

* [https://www.youtube.com/watch?v=QBqzUWr6gXk ''Maple Leaf Rag''] (1899) – rendered by Francium (2024)

* [https://www.youtube.com/watch?v=oDTF5h9tsSU ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)

=== 21st century ===

; [[Claudi Meneghin]]

* ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] | [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025)

[[Category:Meantone]]

[[Category:Listen]]

[[Category:Historical]]

@@ 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>2011-11-21 00:46:14 UTC</tt>.<br>
-: The original revision id was <tt>277565016</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">//74edo// divides the [[octave]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out 81/80 in the [[5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and 144/143 and 847/845 in the [[13-limit]]. Discarding 847/845 from that gives [[Meantone family|13-limit meantone]], aka 13-limit huygens, for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives a 13-limit 62&amp;74 temperament with half-octave period and two parallel tracks of meantone.
-tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.</pre></div>
+== Theory ==
-<h4>Original HTML content:</h4>
+edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 &amp; 74 temperament with half-octave period and two parallel tracks of meantone.
-<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;74edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;74edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 74 equal parts of size 16.216 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It is most notable as a &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; tuning, tempering out 81/80 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;; 81/80 and 126/125 (and hence 225/224) in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;; 99/98, 176/175 and 441/440 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;; and 144/143 and 847/845 in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;. Discarding 847/845 from that gives &lt;a class="wiki_link" href="/Meantone%20family"&gt;13-limit meantone&lt;/a&gt;, aka 13-limit huygens, for which 74edo gives the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt;; and discarding 144/143 gives a 13-limit 62&amp;amp;74 temperament with half-octave period and two parallel tracks of meantone.&lt;br /&gt;
-&lt;br /&gt;
+edo tunes [[harmonic]] [[11/1|11]] only 1/30 of a cent sharp, and [[13/1|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.
-tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.&lt;/body&gt;&lt;/html&gt;</pre></div>
+=== Odd harmonics ===
+{{Harmonics in equal|74}}
+=== Subsets and supersets ===
+Since 74 factors into {{factorization|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets; of these, 37edo has the same highly accurate prime harmonics in the no-3s [[13-limit]].
+== Intervals ==
+{{Interval table}}
+== Notation ==
+===Ups and downs notation===
+edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
+{{Sharpness-sharp5a}}
+Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
+{{Sharpness-sharp5}}
+=== Sagittal notation ===
+==== Evo flavor ====
+<imagemap>
+File:74-EDO_Evo_Sagittal.svg
+desc none
+rect 80 0 300 50 [[Sagittal_notation]]
+rect 300 0 685 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
+rect 20 80 180 106 [[1701/1664]]
+rect 180 80 300 106 [[36/35]]
+rect 300 80 460 106 [[1053/1024]]
+default [[File:74-EDO_Evo_Sagittal.svg]]
+</imagemap>
+==== Revo flavor ====
+<imagemap>
+File:74-EDO_Revo_Sagittal.svg
+desc none
+rect 80 0 300 50 [[Sagittal_notation]]
+rect 300 0 631 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
+rect 20 80 180 106 [[1701/1664]]
+rect 180 80 300 106 [[36/35]]
+rect 300 80 460 106 [[1053/1024]]
+default [[File:74-EDO_Revo_Sagittal.svg]]
+</imagemap>
+In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
+== Instruments ==
+* [[Lumatone mapping for 74edo]]
+== Music ==
+=== Modern renderings ===
+; {{W|Scott Joplin}}
+* [https://www.youtube.com/watch?v=QBqzUWr6gXk ''Maple Leaf Rag''] (1899) – rendered by Francium (2024)
+* [https://www.youtube.com/watch?v=oDTF5h9tsSU ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)
+=== 21st century ===
+; [[Claudi Meneghin]]
+* ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] | [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025)
+[[Category:Meantone]]
+[[Category:Listen]]
+[[Category:Historical]]