648/625: Difference between revisions

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**Imported revision 248655011 - 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 = diminished comma, major diesis
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-26 12:24:56 UTC</tt>.<br>
| Color name = g<sup>4</sup>2, quadgu 2nd,<br>Quadgu comma
: The original revision id was <tt>248655011</tt>.<br>
| Sound = jid_648_625_pluck_adu_dr220.mp3
: The revision comment was: <tt></tt><br>
| Comma = yes
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">The interval 648/625 of 62.565 cents known as the diminished comma or major diesis, is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)^4/2. Tempering it out leads to [[Diminished family|diminished temperament]].</pre></div>
The interval '''648/625''' is known as the '''diminished comma''' or '''major diesis'''. It is the amount by which four [[6/5]] minor thirds exceed an [[2/1|octave]], in other words (6/5)<sup>4</sup> / 2.
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;648_625&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The interval 648/625 of 62.565 cents known as the diminished comma or major diesis, is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)^4/2. Tempering it out leads to &lt;a class="wiki_link" href="/Diminished%20family"&gt;diminished temperament&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
== Approximations ==
This interval is approximately one step of [[19edo]], which is the amount by which four 19edo minor thirds exceed an octave.  
 
== Temperaments ==
Tempering out this comma leads to the [[5-limit]] [[diminished (temperament)|diminished]] temperament.
 
[[Category:Diminished]]
[[Category:Commas named for their regular temperament properties]]

Latest revision as of 07:52, 3 November 2024

Interval information
Ratio 648/625
Factorization 23 × 34 × 5-4
Monzo [3 4 -4⟩
Size in cents 62.56515¢
Names diminished comma,
major diesis
Color name g42, quadgu 2nd,
Quadgu comma
FJS name [math]\displaystyle{ \text{d2}_{5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 18.6276
Weil norm (log2 max(n, d)) 18.6797
Wilson norm (sopfr(nd)) 38
Comma size medium

[sound info]
Open this interval in xen-calc

The interval 648/625 is known as the diminished comma or major diesis. It is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)4 / 2.

Approximations

This interval is approximately one step of 19edo, which is the amount by which four 19edo minor thirds exceed an octave.

Temperaments

Tempering out this comma leads to the 5-limit diminished temperament.

Retrieved from "https://en.xen.wiki/index.php?title=648/625&oldid=163558"