18/17: Difference between revisions

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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 = small septendecimal semitone

~~: This revision was by author [[User:Andrew_Heathwaite~~|~~Andrew_Heathwaite]] and made on <tt>2011-12-07 01:08:49 UTC</tt>.<br>~~

| Color name = 17u1, su unison

~~: The original revision id was <tt>283155952</tt>.<br>~~

| Sound = jid_18_17_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">In [[17-limit]] [[Just Intonation]], 18/17 is the "~~small septendecimal semitone~~" of about 98.955¢. It is very close to [[12edo]]'s "half step" of 100¢~~, ~~as well as to the "large septendecimal semitone" of [[17_16~~|~~17/16]]~~.

~~See:~~ [[~~Gallery~~ of ~~Just Intervals~~]]</~~pre></div>~~

In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).

~~<h4>Original HTML content:<~~/~~h4>~~

== Approximation ==

~~<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"><html><head><title>18_17<~~/~~title></head><body>In <~~a class~~="wiki_link" href="/~~17-limit~~">~~17~~-limit<~~/~~a> <a class="wiki_link" href="~~/~~Just%20Intonation">Just Intonation<~~/a~~>~~, 18/~~17 is~~ the ~~&quot;~~small septendecimal semitone~~&quot; of about 98~~.~~955¢~~. It is ~~very close~~ to ~~<a class~~=~~"wiki_link" href~~="/~~12edo">12edo<~~/a~~>~~'s &~~amp;quot;half step&quot~~; of ~~100¢~~, as well ~~as to~~ the ~~&quot;large septendecimal semitone&quot;~~ of ~~<~~a ~~class="wiki_link" href="~~/~~17_16">~~17/~~16</a>~~.~~<br />~~

~~<br />~~

== Terminology and notation ==

See~~: <a class~~=~~"wiki_link" href~~="/Gallery~~%20of%20Just%20Intervals">Gallery~~ of ~~Just Intervals</a></body></html>~~</~~pre></div~~>

Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.

For 18/17 specifically:

* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].

* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]].

The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16.

== Temperaments ==

{{w|Vincenzo Galilei}} (1520-1591) proposed a tuning based on eleven 18/17 semitones and one larger semitone of about 111.5{{cent}} (the [[octave complement]])<ref>Barbour, J. Murray. ''[https://archive.org/details/tuningtemperamen00barb/page/n7/mode/2up Tuning and temperament: a historical survey]'', p. 57.</ref>. This [[well temperament]] provides seven wide perfect fifths of about 705.2{{cent}} and five narrow perfect fifths of about 692.7{{cent}}, whose distribution is [[maximally even]] instead of grouping together the wide and the narrow fifths along the [[circle of fifths]], as is often the case in other well temperaments.

The following [[linear temperament]]s are [[generate]]d by a [[~]]18/17 in the 2.3.5.17 and 2.3.5.17.19 [[subgroup]]s:

* [[Quintaleap]]

* [[Quindromeda]]

* [[Schismatic_family#Quintilischis_(2.3.5.17)|Quintilischis]].

Note that all of these reach [[4/3]] as a stack of five 18/17 intervals (tempering out the [[quinticular comma]]).

Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.

== See also ==

* [[17/9]] – its [[octave complement]]

* [[17/12]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

== References ==

[[Category:Second]]

[[Category:Chroma]]

[[Category:Semitone]]

[[Category:Commas named after their interval size]]

@@ 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>
+| Name = small septendecimal semitone
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-07 01:08:49 UTC</tt>.<br>
+| Color name = 17u1, su unison
-: The original revision id was <tt>283155952</tt>.<br>
+| Sound = jid_18_17_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">In [[17-limit]] [[Just Intonation]], 18/17 is the "small septendecimal semitone" of about 98.955¢. It is very close to [[12edo]]'s "half step" of 100¢, as well as to the "large septendecimal semitone" of [[17_16|17/16]].
-See: [[Gallery of Just Intervals]]</pre></div>
+In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99{{cent}}. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢).
-<h4>Original HTML content:</h4>
+== Approximation ==
-<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;18_17&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 18/17 is the &amp;quot;small septendecimal semitone&amp;quot; of about 98.955¢. It is very close to &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;'s &amp;quot;half step&amp;quot; of 100¢, as well as to the &amp;quot;large septendecimal semitone&amp;quot; of &lt;a class="wiki_link" href="/17_16"&gt;17/16&lt;/a&gt;.&lt;br /&gt;
+{{Interval edo approximation|25/24}}
-&lt;br /&gt;
+== Terminology and notation ==
-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>
+Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.
+For 18/17 specifically:
+* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].
+* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]].
+The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 17/16.
+== Temperaments ==
+{{w|Vincenzo Galilei}} (1520-1591) proposed a tuning based on eleven 18/17 semitones and one larger semitone of about 111.5{{cent}} (the [[octave complement]])<ref>Barbour, J. Murray. ''[https://archive.org/details/tuningtemperamen00barb/page/n7/mode/2up Tuning and temperament: a historical survey]'', p.&nbsp;57.</ref>. This [[well temperament]] provides seven wide perfect fifths of about 705.2{{cent}} and five narrow perfect fifths of about 692.7{{cent}}, whose distribution is [[maximally even]] instead of grouping together the wide and the narrow fifths along the [[circle of fifths]], as is often the case in other well temperaments.
+The following [[linear temperament]]s are [[generate]]d by a [[~]]18/17 in the 2.3.5.17 and 2.3.5.17.19 [[subgroup]]s:
+* [[Quintaleap]]
+* [[Quindromeda]]
+* [[Schismatic_family#Quintilischis_(2.3.5.17)|Quintilischis]].
+{{todo|complete list}}
+Note that all of these reach [[4/3]] as a stack of five 18/17 intervals (tempering out the [[quinticular comma]]).
+Some [[12th-octave temperaments]] treat ~18/17 as the period, including [[compton]]'s 17-limit extension.
+== See also ==
+* [[17/9]] – its [[octave complement]]
+* [[17/12]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+== References ==
+<references/>
+[[Category:Second]]
+[[Category:Chroma]]
+[[Category:Semitone]]
+[[Category:Commas named after their interval size]]