31/16 - Revision history

Pailiaq: /* Approximations */

2026-02-25T07:26:27Z

Approximations

← Older revision		Revision as of 07:26, 25 February 2026
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	== Approximation ==		== Approximation ==
	31/16 is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent\|¢]] sharp of 31/16.		31/16 is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent\|¢]] sharp of 31/16.
			{{Interval edo approximation}}

	== See also ==		== See also ==

TallKite at 20:49, 24 September 2024

2024-09-24T20:49:26Z

← Older revision		Revision as of 20:49, 24 September 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = tricesimoprimal ultramajor seventh, tricesimoprimal semidiminished octave, octave-reduced 31st harmonic		\| Name = tricesimoprimal ultramajor seventh, tricesimoprimal semidiminished octave, octave-reduced 31st harmonic
	\| Color name = thiwo 7th		\| Color name = 31o7, thiwo 7th
	\| Sound = jid_31_16_pluck_adu_dr220.mp3		\| Sound = jid_31_16_pluck_adu_dr220.mp3
	}}		}}

FloraC: Expansion

2024-07-26T05:10:42Z

Expansion

← Older revision		Revision as of 05:10, 26 July 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = octave-reduced 31st harmonic		\| Name = tricesimoprimal ultramajor seventh, tricesimoprimal semidiminished octave, octave-reduced 31st harmonic
	\| Color name = thiwo 7th		\| Color name = thiwo 7th
	\| Sound = jid_31_16_pluck_adu_dr220.mp3		\| Sound = jid_31_16_pluck_adu_dr220.mp3
	}}		}}

	'''31/16''' is the [[~~Octave~~ reduction\|octave-reduced]] 31st [[harmonic]]. It is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent\|¢]] sharp of 31/16.		In [[31-limit]] [[just intonation]], '''31/16''' is either the '''tricesimoprimal ultramajor seventh''' or '''tricesimoprimal semidiminished octave''', which is also the [[octave reduction\|octave-reduced]] [[31/1\|31st]] [[harmonic]]. It is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[248/243]], and flat of the octave by [[32/31]].

			== Approximation ==
			31/16 is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent\|¢]] sharp of 31/16.

			== See also ==
			* [[32/31]] – its [[octave complement]]
			* [[48/31]] – its [[twelfth complement]]

	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Supermajor seventh]]		[[Category:Supermajor seventh]]
	[[Category:~~todo~~:~~expand~~]]		[[Category:Octave]]
			[[Category:Suboctave]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T14:55:58Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 14:55, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 31/16~~
	~~\| Monzo = -4 0 0 0 0 0 0 0 0 0 1~~
	~~\| Cents = 1145.03557~~
	\| Name = octave-reduced 31st harmonic		\| Name = octave-reduced 31st harmonic
	\| Color name = thiwo 7th		\| Color name = thiwo 7th
	~~\| FJS name = M7<sup>31</sup>~~
	\| Sound = jid_31_16_pluck_adu_dr220.mp3		\| Sound = jid_31_16_pluck_adu_dr220.mp3
	}}		}}
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	'''31/16''' is the [[Octave reduction\|octave-reduced]] 31st [[harmonic]]. It is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent\|¢]] sharp of 31/16.		'''31/16''' is the [[Octave reduction\|octave-reduced]] 31st [[harmonic]]. It is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent\|¢]] sharp of 31/16.

	~~[[Category:31-limit]]~~
	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Supermajor seventh]]		[[Category:Supermajor seventh]]
	~~[[Category:Octave-reduced harmonics]]~~
	[[Category:todo:expand]]		[[Category:todo:expand]]

Fredg999 category edits: Removing from Category:Pages with internal sound examples using Cat-a-lot

2022-02-22T23:46:45Z

Removing from Category:Pages with internal sound examples using Cat-a-lot

← Older revision		Revision as of 23:46, 22 February 2022
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	[[Category:Supermajor seventh]]		[[Category:Supermajor seventh]]
	[[Category:Octave-reduced harmonics]]		[[Category:Octave-reduced harmonics]]
	~~[[Category:Pages with internal sound examples]]~~

	[[Category:todo:expand]]		[[Category:todo:expand]]

Fredg999: Slight expansion, misc. edits, categories

2021-12-16T18:22:09Z

Slight expansion, misc. edits, categories

← Older revision		Revision as of 18:22, 16 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| JI glyph =~~
	\| Ratio = 31/16		\| Ratio = 31/16
	\| Monzo = -4 0 0 0 0 0 0 0 0 0 1		\| Monzo = -4 0 0 0 0 0 0 0 0 0 1
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	\| Name = octave-reduced 31st harmonic		\| Name = octave-reduced 31st harmonic
	\| Color name = thiwo 7th		\| Color name = thiwo 7th
	\| FJS name =		\| FJS name = M7<sup>31</sup>
	\| Sound = jid_31_16_pluck_adu_dr220.mp3		\| Sound = jid_31_16_pluck_adu_dr220.mp3
	}}		}}

	'''31/16''' ~~= 2<sup>−4</sup> ⋅ 31,~~ the octave-reduced 31st harmonic.		'''31/16''' is the [[Octave reduction\|octave-reduced]] 31st [[harmonic]]. It is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent\|¢]] sharp of 31/16.

	[[Category:~~Interval~~]]		[[Category:31-limit]]
			[[Category:Seventh]]
			[[Category:Supermajor seventh]]
			[[Category:Octave-reduced harmonics]]
			[[Category:Pages with internal sound examples]]

	[[Category:todo:expand]]		[[Category:todo:expand]]

TallKite at 22:19, 13 December 2020

2020-12-13T22:19:50Z

← Older revision		Revision as of 22:19, 13 December 2020
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	\| Cents = 1145.03557		\| Cents = 1145.03557
	\| Name = octave-reduced 31st harmonic		\| Name = octave-reduced 31st harmonic
	\| Color name =		\| Color name = thiwo 7th
	\| FJS name =		\| FJS name =
	\| Sound = jid_31_16_pluck_adu_dr220.mp3		\| Sound = jid_31_16_pluck_adu_dr220.mp3

Arseniiv: infoboxified

2020-11-08T17:23:35Z

infoboxified

← Older revision		Revision as of 17:23, 8 November 2020
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	~~'''~~31/16~~'''~~		{{Infobox Interval
	\|-4 0 0 0 0 0 0 0 0 0 1~~>~~		\| JI glyph =
			\| Ratio = 31/16
			\| Monzo = -4 0 0 0 0 0 0 0 0 0 1
			\| Cents = 1145.03557
			\| Name = octave-reduced 31st harmonic
			\| Color name =
			\| FJS name =
			\| Sound = jid_31_16_pluck_adu_dr220.mp3
			}}

	~~1145~~.~~0356 cents~~		'''31/16''' = 2<sup>−4</sup> ⋅ 31, the octave-reduced 31st harmonic.

	[[~~File~~:~~jid_31_16_pluck_adu_dr220.mp3]] [[:File:jid_31_16_pluck_adu_dr220.mp3\|sound sample~~]]		[[Category:Interval]]

	~~The 31st harmonic, octave-reduced.~~
	[[Category:todo:expand]]		[[Category:todo:expand]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		'''31/16'''
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:spt3125\|spt3125]] and made on <tt>2014-06-10 22:09:46 UTC</tt>.<br>~~
	~~: The original revision id was <tt>513548534</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">31/16
	\|-4 0 0 0 0 0 0 0 0 0 1>		\|-4 0 0 0 0 0 0 0 0 0 1>

	1145.0356 cents		1145.0356 cents
	~~[[media type="file" key="jid_31_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_31_16_pluck_adu_dr220.mp3\|sound sample]]~~

	~~The 31st harmonic, octave-reduced.</pre></div>~~		[[File:jid_31_16_pluck_adu_dr220.mp3]] [[:File:jid_31_16_pluck_adu_dr220.mp3\|sound sample]]
	~~<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"><html><head><title>31_16</title></head><body><strong>31/16</strong><br />~~		The 31st harmonic, octave-reduced.
	~~\|-4 0 0 0 0 0 0 0 0 0 1&gt;<br />~~		[[Category:todo:expand]]
	~~1145.0356 cents<br />~~
	~~<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/~~jid_31_16_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_31_16_pluck_adu_dr220.mp3&amp;quot;&quot; title=&quot;Local Media File~~&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http~~://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_31_16_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --> <a href="http://xenharmonic.wikispaces.com/file/view/jid_31_16_pluck_adu_dr220.mp3~~/513545544/jid_31_16_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_31_16_pluck_adu_dr220.mp3/513545544/jid_31_16_pluck_adu_dr220.mp3');">~~sound sample~~</a><br />~~
	~~<br />~~
	The 31st harmonic, octave-reduced.~~</body></html></pre></div>~~

Wikispaces>spt3125: Imported revision 513548534 - Original comment:

2014-06-10T22:09:46Z

**Imported revision 513548534 - Original comment: **

New page

<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:spt3125|spt3125]] and made on <tt>2014-06-10 22:09:46 UTC</tt>.<br>
: The original revision id was <tt>513548534</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">**31/16**
|-4 0 0 0 0 0 0 0 0 0 1>
1145.0356 cents
[[media type="file" key="jid_31_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_31_16_pluck_adu_dr220.mp3|sound sample]]

The 31st harmonic, octave-reduced.</pre></div>
<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"><html><head><title>31_16</title></head><body><strong>31/16</strong><br />
|-4 0 0 0 0 0 0 0 0 0 1&gt;<br />
1145.0356 cents<br />
<embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_31_16_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed> <a href="http://xenharmonic.wikispaces.com/file/view/jid_31_16_pluck_adu_dr220.mp3/513545544/jid_31_16_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_31_16_pluck_adu_dr220.mp3/513545544/jid_31_16_pluck_adu_dr220.mp3');">sound sample</a><br />
<br />
The 31st harmonic, octave-reduced.</body></html></pre></div>