32/25: Difference between revisions

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**Imported revision 301074604 - Original comment: **
 
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
 
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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 = classic(al) diminished fourth, diptolemaic diminished fourth
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 21:53:56 UTC</tt>.<br>
| Color name = gg4, gugu 4th
: The original revision id was <tt>301074604</tt>.<br>
| Sound = jid_32_25_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>
'''32/25''', the '''classic(al) diminished fourth''' or '''diptolemaic diminished fourth''', is the interval between [[5/4]] and [[8/5]]. It is [[225/224]] flat of [[9/7]], and tempering out 225/224 makes 1-5/4-8/5 into the [[marvel chords|marvel triad]]. It is also [[176/175]] sharp of [[14/11]], and tempering out 176/175 makes 1-5/4-8/5 into the [[valinorsmic chords|valinorsmic augmented triad]]. In terms of interval regions, it can be treated as a supermajor third.
<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">32/25, the classic diminished fourth, is the interval between [[5_4|5/4]] and [[8_5|8/5]]. It is 225/224 flat of [[9_7|9/7]], and tempering out 225/224 makes 1-5/4-8/5 into the [[marvel chords|marvel triad]]. It is also 176/175 sharp of [[14_11|14/11]], and tempering out 176/175 makes 1-5/4-8/5 into the [[valinorsmic chords|valinorsmic augmented triad]].</pre></div>
== Approximation ==
<h4>Original HTML content:</h4>
{{Interval edo approximation|32/25}}
<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;32_25&lt;/title&gt;&lt;/head&gt;&lt;body&gt;32/25, the classic diminished fourth, is the interval between &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; and &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;. It is 225/224 flat of &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;, and tempering out 225/224 makes 1-5/4-8/5 into the &lt;a class="wiki_link" href="/marvel%20chords"&gt;marvel triad&lt;/a&gt;. It is also 176/175 sharp of &lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;, and tempering out 176/175 makes 1-5/4-8/5 into the &lt;a class="wiki_link" href="/valinorsmic%20chords"&gt;valinorsmic augmented triad&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
== See also ==
* [[25/16]] – its [[octave complement]]
* [[75/64]] – its [[fifth complement]]
 
[[Category:Fourth]]
[[Category:Diminished fourth]]

Latest revision as of 13:14, 3 November 2025

Interval information
Ratio 32/25
Factorization 25 × 5-2
Monzo [5 0 -2⟩
Size in cents 427.3726¢
Names classic(al) diminished fourth,
diptolemaic diminished fourth
Color name gg4, gugu 4th
FJS name [math]\displaystyle{ \text{d4}_{5,5} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 9.64386
Weil norm (log2 max(n, d)) 10
Wilson norm (sopfr(nd)) 20

[sound info]
Open this interval in xen-calc

32/25, the classic(al) diminished fourth or diptolemaic diminished fourth, is the interval between 5/4 and 8/5. It is 225/224 flat of 9/7, and tempering out 225/224 makes 1-5/4-8/5 into the marvel triad. It is also 176/175 sharp of 14/11, and tempering out 176/175 makes 1-5/4-8/5 into the valinorsmic augmented triad. In terms of interval regions, it can be treated as a supermajor third.

Approximation

Edo approximations for 32/25 (427.37 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
3 1\3 400.00 -27.37 -6.84
11 4\11 436.36 +8.99 +8.24
14 5\14 428.57 +1.20 +1.40
17 6\17 423.53 -3.84 -5.44
25 9\25 432.00 +4.63 +9.64
28 10\28 428.57 +1.20 +2.80
31 11\31 425.81 -1.57 -4.05
42 15\42 428.57 +1.20 +4.20
45 16\45 426.67 -0.71 -2.65
48 17\48 425.00 -2.37 -9.49
56 20\56 428.57 +1.20 +5.59
59 21\59 427.12 -0.25 -1.25
62 22\62 425.81 -1.57 -8.09
70 25\70 428.57 +1.20 +6.99
73 26\73 427.40 +0.02 +0.15
76 27\76 426.32 -1.06 -6.69

See also

Retrieved from "https://en.xen.wiki/index.php?title=32/25&oldid=216086"