Skip-fifteen scale - Revision history

Fredg999 category edits: Moving from Category:Dwarf to Category:Dwarves using Cat-a-lot

2023-04-23T20:30:44Z

Moving from Category:Dwarf to Category:Dwarves using Cat-a-lot

← Older revision		Revision as of 20:30, 23 April 2023
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	[[Category:heptatonic]]		[[Category:heptatonic]]
	[[Category:just_intonation]]		[[Category:just_intonation]]
	[[Category:~~Dwarf~~]]		[[Category:Dwarves]]
	[[Category:7-tone scales]]		[[Category:7-tone scales]]

BudjarnLambeth: Added 2 categories

2023-04-15T08:00:59Z

Added 2 categories

← Older revision		Revision as of 08:00, 15 April 2023
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	[[Category:heptatonic]]		[[Category:heptatonic]]
	[[Category:just_intonation]]		[[Category:just_intonation]]
			[[Category:Dwarf]]
			[[Category:7-tone scales]]

Spt3125: formatting

2018-12-08T02:51:54Z

formatting

← Older revision		Revision as of 02:51, 8 December 2018
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	There are actually two '''skip-fifteen scales''', a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).		There are actually two '''skip-fifteen scales''', a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).

	I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the [[Dwarves\|dwarf scale]] for the 13-limit 7edo patent val. It is epimorphic and [[~~constant_structure\|~~constant structure]]. It is also the 13-limit otonal heptad, and has been listed here as [[~~oheptad\|~~oheptad]], and the utonal version as [[~~uheptad\|~~uheptad]].]		I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the [[Dwarves\|dwarf scale]] for the 13-limit 7edo patent val. It is epimorphic and [[constant structure]]. It is also the 13-limit otonal heptad, and has been listed here as [[oheptad]], and the utonal version as [[uheptad]].]

	A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.		A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.
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	\| \| 128.298		\| \| 128.298
	\|}		\|}

	~~== ==~~

	==Utonal skip15 scale==		==Utonal skip15 scale==
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	Although it's also possible to include the fifteenth (sub)harmonic, thus generating an octatonic scale, I believe it's better to omit it. Specifically, this helps ensure that:		Although it's also possible to include the fifteenth (sub)harmonic, thus generating an octatonic scale, I believe it's better to omit it. Specifically, this helps ensure that:

	~~<ul><li>~~Every interval one step wide is perceived as a (major or neutral) tone, and~~</li><li>~~Every interval two steps wide is perceived as a third, and~~</li><li>~~The 15:13 interval (which is tonally ambiguous in that it is almost halfway between a third and a whole tone) is omitted. Omitting this interval ensures a clear separation between tones and thirds.~~</li><li>~~It is possible to cycle through all the pitch classes by taking the steps two at a time. In combination with the last property, this makes a circle of (unequal) thirds. This circle of thirds is 4:5:6:7:9:11:13:16 (or its utonal counterpart), a [https://en.wikipedia.org/wiki/Fifteenth double octave]-repeating scale in which every interval is a third. There are seven different types of thirds used in the circle, each type occurring exactly once in the circle: supermajor (9:7), wide major (13:11), major (5:4), wide neutral (16:13), narrow neutral (11:9), minor (6:5), and subminor (7:6).~~</li></ul>~~		* Every interval one step wide is perceived as a (major or neutral) tone, and
			* Every interval two steps wide is perceived as a third, and
			* The 15:13 interval (which is tonally ambiguous in that it is almost halfway between a third and a whole tone) is omitted. Omitting this interval ensures a clear separation between tones and thirds.
			* It is possible to cycle through all the pitch classes by taking the steps two at a time. In combination with the last property, this makes a circle of (unequal) thirds. This circle of thirds is 4:5:6:7:9:11:13:16 (or its utonal counterpart), a [https://en.wikipedia.org/wiki/Fifteenth double octave]-repeating scale in which every interval is a third. There are seven different types of thirds used in the circle, each type occurring exactly once in the circle: supermajor (9:7), wide major (13:11), major (5:4), wide neutral (16:13), narrow neutral (11:9), minor (6:5), and subminor (7:6).

	There is also a "phantom third" (14:11) which is not part of the circle of thirds, but appears in the skip15 scales as an interval three (rather than two) steps wide. This phantom third means that neither skip15 scale is [[Rothenberg_propriety\|proper]] (since it's narrower than the supermajor third, which occurs as a two-step interval in the scales).		There is also a "phantom third" (14:11) which is not part of the circle of thirds, but appears in the skip15 scales as an interval three (rather than two) steps wide. This phantom third means that neither skip15 scale is [[Rothenberg_propriety\|proper]] (since it's narrower than the supermajor third, which occurs as a two-step interval in the scales).
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	The skip15 scales (and the circle of thirds) can be approximated in many high edos, which are capable of distinguishing between all eight different thirds (the seven that are part of the circle, plus the "phantom" 11:14) third. Note that in order to ensure that every third has a unique approximation, it may be necessary to use a non-patent val in some cases.		The skip15 scales (and the circle of thirds) can be approximated in many high edos, which are capable of distinguishing between all eight different thirds (the seven that are part of the circle, plus the "phantom" 11:14) third. Note that in order to ensure that every third has a unique approximation, it may be necessary to use a non-patent val in some cases.

	[[Category:heptatonic]]		[[Category:heptatonic]]
	[[Category:just_intonation]]		[[Category:just_intonation]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>genewardsmith: Imported revision 565339669 - Original comment:

2015-11-05T13:13:53Z

**Imported revision 565339669 - Original comment: **

Wikispaces>genewardsmith: Imported revision 565192191 - Original comment:

2015-11-04T14:27:46Z

**Imported revision 565192191 - Original comment: **

← Older revision		Revision as of 14:27, 4 November 2015
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~MasonGreen1~~\|~~MasonGreen1~~]] and made on <tt>2015-11-~~01 23~~:02:02 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2015-11-04 14:27:46 UTC</tt>.<br>
	: The original revision id was <tt>~~564704053~~</tt>.<br>		: The original revision id was <tt>565192191</tt>.<br>
	: The revision comment was: <tt></tt><br>		: 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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	<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">There are actually two skip-fifteen scales, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).		<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">There are actually two skip-fifteen scales, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).

	I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting.		I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the [[Dwarves\|dwarf scale]] for the 13-limit 7edo patent val. It is epimorphic and [[constant structure]].]

	A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.		A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.
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	<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>Skip-fifteen scale</title></head><body>There are actually two <strong>skip-fifteen scales</strong>, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).<br />		<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>Skip-fifteen scale</title></head><body>There are actually two <strong>skip-fifteen scales</strong>, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).<br />
	<br />		<br />
	I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting.<br />		I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the <a class="wiki_link" href="/Dwarves">dwarf scale</a> for the 13-limit 7edo patent val. It is epimorphic and <a class="wiki_link" href="/constant%20structure">constant structure</a>.]<br />
	<br />		<br />
	A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.<br />		A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.<br />

Wikispaces>MasonGreen1: Imported revision 564704053 - Original comment:

2015-11-01T23:02:02Z

**Imported revision 564704053 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-01 23:02:02 UTC</tt>.<br>
: The original revision id was <tt>564704053</tt>.<br>
: 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>
<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">There are actually two **skip-fifteen scales**, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).

I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting.

A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.

==Otonal skip15 scale==

|| Corresponding harmonic || Cents || Distance above last note ||
|| 8 (or 16) || 0 || (231.174) ||
|| 9 || 203.910 || 203.910 ||
|| 10 || 386.314 || 182.404 ||
|| 11 || 551.318 || 165.004 ||
|| 12 || 701.955 || 150.637 ||
|| 13 || 840.528 || 138.573 ||
|| 14 || 968.826 || 128.298 ||
== ==
==Utonal skip15 scale==

|| Corresponding subharmonic || Cents || Distance above last note ||
|| 1/16 (or 1/8) || 0 || (203.174) ||
|| 1/14 || 231.174 || 231.174 ||
|| 1/13 || 359.472 || 128.298 ||
|| 1/12 || 498.045 || 138.573 ||
|| 1/11 || 648.682 || 150.637 ||
|| 1/10 || 813.686 || 165.004 ||
|| 1/9 || 996.090 || 182.404 ||

==Why skip the 15?==

Although it's also possible to include the fifteenth (sub)harmonic, thus generating an octatonic scale, I believe it's better to omit it. Specifically, this helps ensure that:

* Every interval one step wide is perceived as a (major or neutral) tone, and
* Every interval two steps wide is perceived as a third, and
* The 15:13 interval (which is tonally ambiguous in that it is almost halfway between a third and a whole tone) is omitted. Omitting this interval ensures a clear separation between tones and thirds.
* It is possible to cycle through all the pitch classes by taking the steps two at a time. In combination with the last property, this makes a circle of (unequal) thirds. This circle of thirds is 4:5:6:7:9:11:13:16 (or its utonal counterpart), a [[https://en.wikipedia.org/wiki/Fifteenth|double octave]]-repeating scale in which every interval is a third. There are seven different types of thirds used in the circle, each type occurring exactly once in the circle: supermajor (9:7), wide major (13:11), major (5:4), wide neutral (16:13), narrow neutral (11:9), minor (6:5), and subminor (7:6).

There is also a "phantom third" (14:11) which is not part of the circle of thirds, but appears in the skip15 scales as an interval three (rather than two) steps wide. This phantom third means that neither skip15 scale is [[Rothenberg propriety|proper]] (since it's narrower than the supermajor third, which occurs as a two-step interval in the scales).

The "Barbados third" or "fird" (13:10), which is 454.217 cents, also occurs in the skip15 scale but not in the circle. However, this interval is also sometimes considered a narrowed fourth rather than as a third.

==Approximations==

The skip15 scales (and the circle of thirds) can be approximated in many high edos, which are capable of distinguishing between all eight different thirds (the seven that are part of the circle, plus the "phantom" 11:14) third. Note that in order to ensure that every third has a unique approximation, it may be necessary to use a non-patent val in some cases.</pre></div>
<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"><html><head><title>Skip-fifteen scale</title></head><body>There are actually two <strong>skip-fifteen scales</strong>, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).<br />
<br />
I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting.<br />
<br />
A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.<br />
<br />
<h2 id="toc0"><a name="x-Otonal skip15 scale"></a>Otonal skip15 scale</h2>
<br />

<table class="wiki_table">
<tr>
<td>Corresponding harmonic<br />
</td>
<td>Cents<br />
</td>
<td>Distance above last note<br />
</td>
</tr>
<tr>
<td>8 (or 16)<br />
</td>
<td>0<br />
</td>
<td>(231.174)<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>203.910<br />
</td>
<td>203.910<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>386.314<br />
</td>
<td>182.404<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>551.318<br />
</td>
<td>165.004<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>701.955<br />
</td>
<td>150.637<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>840.528<br />
</td>
<td>138.573<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>968.826<br />
</td>
<td>128.298<br />
</td>
</tr>
</table>

<h2 id="toc1"> </h2>
<h2 id="toc2"><a name="x-Utonal skip15 scale"></a>Utonal skip15 scale</h2>
<br />

<table class="wiki_table">
<tr>
<td>Corresponding subharmonic<br />
</td>
<td>Cents<br />
</td>
<td>Distance above last note<br />
</td>
</tr>
<tr>
<td>1/16 (or 1/8)<br />
</td>
<td>0<br />
</td>
<td>(203.174)<br />
</td>
</tr>
<tr>
<td>1/14<br />
</td>
<td>231.174<br />
</td>
<td>231.174<br />
</td>
</tr>
<tr>
<td>1/13<br />
</td>
<td>359.472<br />
</td>
<td>128.298<br />
</td>
</tr>
<tr>
<td>1/12<br />
</td>
<td>498.045<br />
</td>
<td>138.573<br />
</td>
</tr>
<tr>
<td>1/11<br />
</td>
<td>648.682<br />
</td>
<td>150.637<br />
</td>
</tr>
<tr>
<td>1/10<br />
</td>
<td>813.686<br />
</td>
<td>165.004<br />
</td>
</tr>
<tr>
<td>1/9<br />
</td>
<td>996.090<br />
</td>
<td>182.404<br />
</td>
</tr>
</table>

<br />
<h2 id="toc3"><a name="x-Why skip the 15?"></a>Why skip the 15?</h2>
<br />
Although it's also possible to include the fifteenth (sub)harmonic, thus generating an octatonic scale, I believe it's better to omit it. Specifically, this helps ensure that:<br />
<br />
<ul><li>Every interval one step wide is perceived as a (major or neutral) tone, and</li><li>Every interval two steps wide is perceived as a third, and</li><li>The 15:13 interval (which is tonally ambiguous in that it is almost halfway between a third and a whole tone) is omitted. Omitting this interval ensures a clear separation between tones and thirds.</li><li>It is possible to cycle through all the pitch classes by taking the steps two at a time. In combination with the last property, this makes a circle of (unequal) thirds. This circle of thirds is 4:5:6:7:9:11:13:16 (or its utonal counterpart), a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Fifteenth" rel="nofollow">double octave</a>-repeating scale in which every interval is a third. There are seven different types of thirds used in the circle, each type occurring exactly once in the circle: supermajor (9:7), wide major (13:11), major (5:4), wide neutral (16:13), narrow neutral (11:9), minor (6:5), and subminor (7:6).</li></ul><br />
There is also a &quot;phantom third&quot; (14:11) which is not part of the circle of thirds, but appears in the skip15 scales as an interval three (rather than two) steps wide. This phantom third means that neither skip15 scale is <a class="wiki_link" href="/Rothenberg%20propriety">proper</a> (since it's narrower than the supermajor third, which occurs as a two-step interval in the scales).<br />
<br />
The &quot;Barbados third&quot; or &quot;fird&quot; (13:10), which is 454.217 cents, also occurs in the skip15 scale but not in the circle. However, this interval is also sometimes considered a narrowed fourth rather than as a third.<br />
<br />
<h2 id="toc4"><a name="x-Approximations"></a>Approximations</h2>
<br />
The skip15 scales (and the circle of thirds) can be approximated in many high edos, which are capable of distinguishing between all eight different thirds (the seven that are part of the circle, plus the &quot;phantom&quot; 11:14) third. Note that in order to ensure that every third has a unique approximation, it may be necessary to use a non-patent val in some cases.</body></html></pre></div>

← Older revision		Revision as of 13:13, 5 November 2015
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2015-11-~~04 14~~:27:46 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2015-11-05 13:13:53 UTC</tt>.<br>
	: The original revision id was <tt>~~565192191~~</tt>.<br>		: The original revision id was <tt>565339669</tt>.<br>
	: The revision comment was: <tt></tt><br>		: 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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 8:		Line 8:
	<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">There are actually two skip-fifteen scales, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).		<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">There are actually two skip-fifteen scales, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).

	I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the [[Dwarves\|dwarf scale]] for the 13-limit 7edo patent val. It is epimorphic and [[constant structure]].]		I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the [[Dwarves\|dwarf scale]] for the 13-limit 7edo patent val. It is epimorphic and [[constant structure]]. It is also the 13-limit otonal heptad, and has been listed here as [[http://xenharmonic.wikispaces.com/oheptad\|oheptad]], and the utonal version as [[http://xenharmonic.wikispaces.com/uheptad\|uheptad]].]

	A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.		A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.
Line 53:		Line 53:
	<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>Skip-fifteen scale</title></head><body>There are actually two <strong>skip-fifteen scales</strong>, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).<br />		<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>Skip-fifteen scale</title></head><body>There are actually two <strong>skip-fifteen scales</strong>, a utonal and an otonal version. Both are heptatonic scales (seven tones per octave).<br />
	<br />		<br />
	I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the <a class="wiki_link" href="/Dwarves">dwarf scale</a> for the 13-limit 7edo patent val. It is epimorphic and <a class="wiki_link" href="/constant%20structure">constant structure</a>.]<br />		I (Mason Green) am not sure if anyone else has written about this type of scale before. It might be a re-discovery, but I find it interesting. [In fact, the otonal skip15 is the <a class="wiki_link" href="/Dwarves">dwarf scale</a> for the 13-limit 7edo patent val. It is epimorphic and <a class="wiki_link" href="/constant%20structure">constant structure</a>. It is also the 13-limit otonal heptad, and has been listed here as <a href="http://xenharmonic.wikispaces.com/oheptad">oheptad</a>, and the utonal version as <a href="http://xenharmonic.wikispaces.com/uheptad">uheptad</a>.]<br />
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	A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.<br />		A skip-fifteen scale is the octave-repeating scale in just intonation consisting of all the harmonics between 8 and 16, but skipping the 15th (hence the name). The utonal version instead uses the subharmonics between 1/16 and 1/8, excluding 1/15.<br />