Xenharmonic Wiki

Gothic comma: Difference between revisions

VisualWikitext
Wikispaces>genewardsmith
**Imported revision 248800765 - Original comment: **
 
Eufalesio (talk | contribs)
autopatrolled
647 edits
Updated color notation
 
(25 intermediate revisions by 13 users not shown)
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>
| Ratio = 134217728/129140163
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-27 13:45:10 UTC</tt>.<br>
| Name = gothic comma, 17-comma, Pythagorean gothma, Pythagorean double-diminished third
: The original revision id was <tt>248800765</tt>.<br>
| Color name = ssw3, sasawa 3rd,<br>17wM, sewama
: 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>
The '''gothic comma''', otherwise known as the '''17-comma''' or '''Pythagorean gothma''' ({{monzo|legend=1| 27 -17 }}, [[ratio]]: 134217728/129140163), is a [[3-limit]] interval of 66.765{{cent}}. It is the amount by which seventeen [[perfect fifth]]s fall short of ten [[octave]]s, or 2<sup>10</sup>/(3/2)<sup>17</sup>. If used as an interval in its own right, it is the '''Pythagorean double-diminished 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">134217728/129140163 = |27 -17&gt;, called the 17-comma, is an interval of 66.765 cents, is the amount by which seventeen fifths fall short of ten octaves, or 2^10/(3/2)^17. For EDOs up to 150 the 17-comma is tempered out if and only if 17 divides it, for example [[17edo]], [[34edo]] or [[68edo]].</pre></div>
 
<h4>Original HTML content:</h4>
== Temperaments ==
<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;17-comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;134217728/129140163 = |27 -17&amp;gt;, called the 17-comma, is an interval of 66.765 cents, is the amount by which seventeen fifths fall short of ten octaves, or 2^10/(3/2)^17. For EDOs up to 150 the 17-comma is tempered out if and only if 17 divides it, for example &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; or &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
Tempering out this comma in the 5-limit leads to the [[gothic]] temperament. For edos up to [[136edo|136]], the comma is tempered out if and only if 17 divides it, for example [[17edo]], [[34edo]] or [[68edo]].
 
== Terminology ==
The names were given by [[Flora Canou]] in 2023. The first term ''gothic comma'' draws two inspirations:
# the [[neogothic]] tuning available in 17edo, and
# the link of [[TAMNAMS Extension]] name and comma names by the analogy pair gothic : pytha<u>go</u>tonic :: mystery : pytha<u>mys</u>tonic.
Additionally, by coincidence, the term "gothic" fits into the naming scheme of the [[comptonesque]] temperament collection, representing Vector's project Not!Earth in which the Goths are a major culture group.
 
The second term ''Pythagorean gothma'' is part of a series of step names in the [[Pythagorean tuning|Pythagorean]] [[diatonic scale]], where ''gothma'' (adjective: ''gothmic'') refers to the double diminished 2-step, i.e. |3s - L|.
 
== See also ==
* [[Gallery of just intervals]]
* [[Medium comma]]
 
[[Category:Commas named for other reasons]]
Retrieved from "https://en.xen.wiki/w/Gothic_comma"