8/5: Difference between revisions

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**Imported revision 513184188 - Original comment: **
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<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 = just minor sixth, classic(al) minor sixth, ptolemaic minor sixth
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 12:18:17 UTC</tt>.<br>
| Color name = g6, gu 6th
: The original revision id was <tt>513184188</tt>.<br>
| Sound = jid_8_5_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>
{{Wikipedia|Minor sixth}}
<h4>Original Wikitext content:</h4>
In [[5-limit]] [[just intonation]], '''8/5''' is the '''just minor sixth''', '''classic(al) minor sixth''', or '''ptolemaic minor sixth'''<ref>For reference, see [[5-limit]]. </ref>, measuring about 813.7{{cent}}. It is the [[octave-reduced]] fifth [[subharmonic]], and thus the inversion of [[5/4]], the classic major third. It appears in chords where the 1/1 is higher than the 5/4, such as 5:6:8 (a first-inversion major triad). It is a large half step of [[16/15]] (about 111.7{{cent}}) sharp of [[3/2]], and a syntonic comma ([[81/80]], about 21.5{{cent}}) sharp of the [[Pythagorean tuning|Pythagorean]] minor sixth of [[128/81]] (about 792.2{{cent}}).
<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">**8/5**
== Approximation ==
|3 0 -1&gt;
{{Interval edo approximation|8/5}}
813.68629 cents
== See also ==
[[media type="file" key="jid_8_5_pluck_adu_dr220.mp3"]]
* [[5/4]] – its [[octave complement]]
* [[15/8]] – its [[twelfth complement]]
* [[Ed8/5]]
* [[Gallery of just intervals]]
{{todo|expand}}


In [[5-limit]] [[Just Intonation]], 8/5 is a minor sixth, measuring about 813.7¢. It is the 5th subharmonic, and thus the inversion of [[5_4|5/4]], the classic major third. It appears in chords where the 1/1 is higher than the 5/4, such as 5:6:8 (a first-inversion major triad). It is a large half step of [[16_15|16/15]] (about 111.7¢) away from [[3_2|3/2]], and an [[81_80|81/80]] (about 21.5¢) away from the Pythagorean ([[3-limit]]) minor sixth of [[128_81|128/81]] (about 792.2¢).
== Notes ==
<references/>


See: [[Gallery of Just Intervals]]</pre></div>
[[Category:Sixth]]
<h4>Original HTML content:</h4>
[[Category:Minor sixth]]
<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;8_5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;8/5&lt;/strong&gt;&lt;br /&gt;
|3 0 -1&amp;gt;&lt;br /&gt;
813.68629 cents&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_8_5_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_8_5_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_8_5_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;br /&gt;
&lt;br /&gt;
In &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 8/5 is a minor sixth, measuring about 813.7¢. It is the 5th subharmonic, and thus the inversion of &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, the classic major third. It appears in chords where the 1/1 is higher than the 5/4, such as 5:6:8 (a first-inversion major triad). It is a large half step of &lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt; (about 111.7¢) away from &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, and an &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt; (about 21.5¢) away from the Pythagorean (&lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt;) minor sixth of &lt;a class="wiki_link" href="/128_81"&gt;128/81&lt;/a&gt; (about 792.2¢).&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 13:05, 3 November 2025

Interval information
Ratio 8/5
Factorization 23 × 5-1
Monzo [3 0 -1⟩
Size in cents 813.6863¢
Names just minor sixth,
classic(al) minor sixth,
ptolemaic minor sixth
Color name g6, gu 6th
FJS name [math]\displaystyle{ \text{m6}_{5} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 5.32193
Weil norm (log2 max(n, d)) 6
Wilson norm (sopfr(nd)) 11

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

In 5-limit just intonation, 8/5 is the just minor sixth, classic(al) minor sixth, or ptolemaic minor sixth[1], measuring about 813.7 ¢. It is the octave-reduced fifth subharmonic, and thus the inversion of 5/4, the classic major third. It appears in chords where the 1/1 is higher than the 5/4, such as 5:6:8 (a first-inversion major triad). It is a large half step of 16/15 (about 111.7 ¢) sharp of 3/2, and a syntonic comma (81/80, about 21.5 ¢) sharp of the Pythagorean minor sixth of 128/81 (about 792.2 ¢).

Approximation

Edo approximations for 8/5 (813.69 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
3 2\3 800.00 -13.69 -3.42
6 4\6 800.00 -13.69 -6.84
22 15\22 818.18 +4.50 +8.24
25 17\25 816.00 +2.31 +4.82
28 19\28 814.29 +0.60 +1.40
31 21\31 812.90 -0.78 -2.02
34 23\34 811.76 -1.92 -5.44
37 25\37 810.81 -2.88 -8.87
50 34\50 816.00 +2.31 +9.64
53 36\53 815.09 +1.41 +6.22
56 38\56 814.29 +0.60 +2.80
59 40\59 813.56 -0.13 -0.62
62 42\62 812.90 -0.78 -4.05
65 44\65 812.31 -1.38 -7.47

See also

Notes

  1. ↑ For reference, see 5-limit.
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