Gothic comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>Andrew_Heathwaite
**Imported revision 282666630 - Original comment: **
Eufalesio (talk | contribs)
autopatrolled
647 edits
Updated color notation
 
(24 intermediate revisions by 12 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-05 21:41:08 UTC</tt>.<br>
| Name = gothic comma, 17-comma, Pythagorean gothma, Pythagorean double-diminished third
: The original revision id was <tt>282666630</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]].


See: [[comma]], [[Gallery of Just Intervals]]</pre></div>
== Temperaments ==
<h4>Original HTML content:</h4>
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]].
<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;br /&gt;
 
&lt;br /&gt;
== Terminology ==
See: &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;, &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>
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]]

Latest revision as of 14:47, 1 May 2026

Interval information
Ratio 134217728/129140163
Factorization 227 × 3-17
Monzo [27 -17⟩
Size in cents 66.76499¢
Names gothic comma,
17-comma,
Pythagorean gothma,
Pythagorean double-diminished third
Color name ssw3, sasawa 3rd,
17wM, sewama
FJS name [math]\displaystyle{ \text{dd3} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 53.9444
Weil norm (log2 max(n, d)) 54
Wilson norm (sopfr(nd)) 105
Comma size medium
Open this interval in xen-calc

The gothic comma, otherwise known as the 17-comma or Pythagorean gothma (monzo: [27 -17⟩, ratio: 134217728/129140163), is a 3-limit interval of 66.765 ¢. It is the amount by which seventeen perfect fifths fall short of ten octaves, or 210/(3/2)17. If used as an interval in its own right, it is the Pythagorean double-diminished third.

Temperaments

Tempering out this comma in the 5-limit leads to the gothic temperament. For edos up to 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:

  1. the neogothic tuning available in 17edo, and
  2. the link of TAMNAMS Extension name and comma names by the analogy pair gothic : pythagotonic :: mystery : pythamystonic.

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 diatonic scale, where gothma (adjective: gothmic) refers to the double diminished 2-step, i.e. |3s - L|.

See also

Retrieved from "https://en.xen.wiki/index.php?title=Gothic_comma&oldid=229281"