25/16: Difference between revisions

Interval information
Ratio	25/16
Factorization	2-4 × 52
Monzo	[-4 0 2⟩
Size in cents	772.6274¢
Names	classic(al) augmented fifth,; diptolemaic augmented fifth
Color name	yy5, yoyo 5th
FJS name	[math]\displaystyle{ \text{A5}^{5,5} }[/math]
Special properties	reduced,; reduced harmonic
Tenney norm (log2 nd)	8.64386
Weil norm (log2 max(n, d))	9.28771
Wilson norm (sopfr(nd))	18
	https://en.xen.wiki/w/File:Jid_25_16_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

VisualWikitext

Latest revision as of 13:07, 3 November 2025

25/16, the classic(al) augmented fifth is the interval obtained by stacking two 5/4 major thirds, however, it gains additional isoharmonic identity from its position between 11/8 and 7/4, so it can frequently be used in conjunction with those, even in chords.

While this interval has been referred to as the classic augmented fifth or classical augmented fifth for some time, the term diptolemaic was coined on Discord by Flora Canou while discussing a proposal for a consistent naming scheme for different 5-limit intervals with Aura. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the diptolemaic augmented fifth.

Approximation

Edo approximations for 25/16 (772.63 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
3	2\3	800.00	+27.37	+6.84
11	7\11	763.64	-8.99	-8.24
14	9\14	771.43	-1.20	-1.40
17	11\17	776.47	+3.84	+5.44
25	16\25	768.00	-4.63	-9.64
28	18\28	771.43	-1.20	-2.80
31	20\31	774.19	+1.57	+4.05
42	27\42	771.43	-1.20	-4.20
45	29\45	773.33	+0.71	+2.65
48	31\48	775.00	+2.37	+9.49
56	36\56	771.43	-1.20	-5.59
59	38\59	772.88	+0.25	+1.25
62	40\62	774.19	+1.57	+8.09
70	45\70	771.43	-1.20	-6.99
73	47\73	772.60	-0.02	-0.15
76	49\76	773.68	+1.06	+6.69

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox Interval
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| Name = classic(al) augmented fifth, diptolemaic augmented fifth
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-09 22:15:05 UTC</tt>.<br>
+| Color name = yy5, yoyo 5th
-: The original revision id was <tt>513416126</tt>.<br>
+| Sound = jid_25_16_pluck_adu_dr220.mp3
-: 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">**25/16**
-|-4 0 2&gt;
-.6274 cents
-[[media type="file" key="jid_25_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_25_16_pluck_adu_dr220.mp3|sound sample]]
-The classic ([[5-limit]]) augmented fifth.
+'''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords.
-</pre></div>
-<h4>Original HTML content:</h4>
+While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.
-<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;25_16&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;25/16&lt;/strong&gt;&lt;br /&gt;
+== Approximation ==
-|-4 0 2&amp;gt;&lt;br /&gt;
+{{Interval edo approximation|25/16}}
-.6274 cents&lt;br /&gt;
+== See also ==
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_25_16_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_25_16_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;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_25_16_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_25_16_pluck_adu_dr220.mp3/513415234/jid_25_16_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_25_16_pluck_adu_dr220.mp3/513415234/jid_25_16_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
+* [[32/25]] – its [[octave complement]]
-&lt;br /&gt;
-The classic (&lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;) augmented fifth.&lt;/body&gt;&lt;/html&gt;</pre></div>
+[[Category:Fifth]]
+[[Category:Augmented fifth]]

25/16: Difference between revisions

Latest revision as of 13:07, 3 November 2025

Approximation

See also

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