Bohpier/Chords - Revision history

Lériendil: Lériendil moved page Chords of bohpier to Bohpier/Chords

2025-06-22T21:47:34Z

Lériendil moved page Chords of bohpier to Bohpier/Chords

← Older revision	Revision as of 21:47, 22 June 2025
(No difference)

ArrowHead294 at 13:06, 10 March 2025

2025-03-10T13:06:45Z

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BudjarnLambeth: Categorised this uncategorised page

2023-04-25T10:57:10Z

Categorised this uncategorised page

← Older revision		Revision as of 10:57, 25 April 2023
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	\| \| otonal		\| \| otonal
	\|}		\|}
			[[Category:Lists of chords]]
			[[Category:Bohpier]]
			[[Category:Bohlen-Pierce]]
			[[Category:11-limit]]
			[[Category:Dyadic chords]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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Wikispaces>genewardsmith: Imported revision 290312079 - Original comment:

2012-01-08T01:47:58Z

**Imported revision 290312079 - Original comment: **

← Older revision		Revision as of 01:47, 8 January 2012
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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:~~keenanpepper~~\|~~keenanpepper~~]] and made on <tt>2012-01-08 00:18:34 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2012-01-08 01:47:58 UTC</tt>.<br>
	: The original revision id was <tt>~~290308213~~</tt>.<br>		: The original revision id was <tt>290312079</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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier\|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.		<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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier\|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.

	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals may be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.

	In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the [[sensamagic chords]] exist in strict Bohlen-Pierce.		In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the [[sensamagic chords]] exist in strict Bohlen-Pierce.
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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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<br />
	<br />		<br />
	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals may be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />
	<br />		<br />
	In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the <a class="wiki_link" href="/sensamagic%20chords">sensamagic chords</a> exist in strict Bohlen-Pierce.<br />		In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the <a class="wiki_link" href="/sensamagic%20chords">sensamagic chords</a> exist in strict Bohlen-Pierce.<br />

Wikispaces>keenanpepper: Imported revision 290308213 - Original comment:

2012-01-08T00:18:34Z

**Imported revision 290308213 - Original comment: **

← Older revision		Revision as of 00:18, 8 January 2012
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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:keenanpepper\|keenanpepper]] and made on <tt>2012-01-08 00:18:12 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-01-08 00:18:34 UTC</tt>.<br>
	: The original revision id was <tt>~~290308191~~</tt>.<br>		: The original revision id was <tt>290308213</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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	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.

	In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the sensamagic chords exist in strict Bohlen-Pierce.		In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the [[sensamagic chords]] exist in strict Bohlen-Pierce.

	=Triads=		=Triads=
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	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />
	<br />		<br />
	In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the sensamagic chords exist in strict Bohlen-Pierce.<br />		In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the <a class="wiki_link" href="/sensamagic%20chords">sensamagic chords</a> exist in strict Bohlen-Pierce.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>		<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>

Wikispaces>keenanpepper: Imported revision 290308191 - Original comment:

2012-01-08T00:18:12Z

**Imported revision 290308191 - Original comment: **

← Older revision		Revision as of 00:18, 8 January 2012
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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:~~genewardsmith~~\|~~genewardsmith~~]] and made on <tt>2012-01-~~05 19~~:14:13 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-01-08 00:18:12 UTC</tt>.<br>
	: The original revision id was <tt>~~289920687~~</tt>.<br>		: The original revision id was <tt>290308191</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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	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.

	=Triads=		In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the sensamagic chords exist in strict Bohlen-Pierce.

			=Triads=
	\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|		\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|
	\|\| 1 \|\| 0-1-4 \|\| 1-12/11-7/5 \|\| swetismic \|\|		\|\| 1 \|\| 0-1-4 \|\| 1-12/11-7/5 \|\| swetismic \|\|
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	\|\| 48 \|\| 0-23-26 \|\| 1-7/4-9/8 \|\| otonal \|\|		\|\| 48 \|\| 0-23-26 \|\| 1-7/4-9/8 \|\| otonal \|\|

	=Tetrads=		=Tetrads=
	\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|		\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|
	\|\| 1 \|\| 0-1-4-7 \|\| 1-12/11-7/5-9/5 \|\| octarod \|\|		\|\| 1 \|\| 0-1-4-7 \|\| 1-12/11-7/5-9/5 \|\| octarod \|\|
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	\|\| 65 \|\| 0-19-23-26 \|\| 1-5/4-7/4-9/8 \|\| otonal \|\|		\|\| 65 \|\| 0-19-23-26 \|\| 1-5/4-7/4-9/8 \|\| otonal \|\|

	=Pentads=		=Pentads=
	\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|		\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|
	\|\| 1 \|\| 0-3-4-7-10 \|\| 1-9/7-7/5-9/5-7/6 \|\| octarod \|\|		\|\| 1 \|\| 0-3-4-7-10 \|\| 1-9/7-7/5-9/5-7/6 \|\| octarod \|\|
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	\|\| 35 \|\| 0-13-19-23-26 \|\| 1-3/2-5/4-7/4-9/8 \|\| otonal \|\|		\|\| 35 \|\| 0-13-19-23-26 \|\| 1-3/2-5/4-7/4-9/8 \|\| otonal \|\|

	=Hexads=		=Hexads=
	\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|		\|\| Number \|\| Chord \|\| Transversal \|\| Type \|\|
	\|\| 1 \|\| 0-3-6-7-10-13 \|\| 1-9/7-5/3-9/5-7/6-3/2 \|\| octarod \|\|		\|\| 1 \|\| 0-3-6-7-10-13 \|\| 1-9/7-5/3-9/5-7/6-3/2 \|\| octarod \|\|
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	\|\| 5 \|\| 0-3-7-10-13-14 \|\| 1-9/7-9/5-7/6-3/2-18/11 \|\| octarod \|\|		\|\| 5 \|\| 0-3-7-10-13-14 \|\| 1-9/7-9/5-7/6-3/2-18/11 \|\| octarod \|\|
	\|\| 6 \|\| 0-3-7-13-14-26 \|\| 1-9/7-9/5-3/2-18/11-9/8 \|\| utonal \|\|		\|\| 6 \|\| 0-3-7-13-14-26 \|\| 1-9/7-9/5-3/2-18/11-9/8 \|\| utonal \|\|
	\|\| 7 \|\| 0-12-13-19-23-26 \|\| 1-11/8-3/2-5/4-7/4-9/8 \|\| otonal \|\|		\|\| 7 \|\| 0-12-13-19-23-26 \|\| 1-11/8-3/2-5/4-7/4-9/8 \|\| otonal \|\|</pre></div>
	</pre></div>
	<h4>Original HTML content:</h4>		<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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<br />
	<br />		<br />
	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />
			<br />
			In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the sensamagic chords exist in strict Bohlen-Pierce.<br />
	<br />		<br />
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Wikispaces>genewardsmith: Imported revision 289920687 - Original comment:

2012-01-05T19:14:13Z

**Imported revision 289920687 - Original comment: **

← Older revision		Revision as of 19:14, 5 January 2012
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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:genewardsmith\|genewardsmith]] and made on <tt>2012-01-05 19:13~~:42~~ UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2012-01-05 19:14:13 UTC</tt>.<br>
	: The original revision id was <tt>~~289920621~~</tt>.<br>		: The original revision id was <tt>289920687</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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier\|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.		<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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier\|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.

	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-~~limitbohpier~~ is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.

	=Triads=		=Triads=
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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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<br />
	<br />		<br />
	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-~~limitbohpier~~ is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>		<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>

Wikispaces>genewardsmith: Imported revision 289920621 - Original comment:

2012-01-05T19:13:42Z

**Imported revision 289920621 - Original comment: **

← Older revision		Revision as of 19:13, 5 January 2012
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>~~2011~~-12-~~28 16~~:18:41 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2012-01-05 19:13:42 UTC</tt>.<br>
	: The original revision id was <tt>~~288679822~~</tt>.<br>		: The original revision id was <tt>289920621</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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier\|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.		<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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier\|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.

	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of ~~bohpier~~ is the [[Bohlen-Pierce]] scale. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limitbohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.

	=Triads=		=Triads=
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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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<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>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<br />
	<br />		<br />
	Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of ~~bohpier~~ is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />		Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limitbohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>		<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>

Wikispaces>genewardsmith: Imported revision 288679822 - Original comment:

2011-12-28T16:18:41Z

**Imported revision 288679822 - Original comment: **

Show changes

Bohpier/Chords - Revision history

Lériendil: Lériendil moved page Chords of bohpier to Bohpier/Chords

ArrowHead294 at 13:06, 10 March 2025

BudjarnLambeth: Categorised this uncategorised page

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>genewardsmith: **Imported revision 290312079 - Original comment: **

Wikispaces>keenanpepper: **Imported revision 290308213 - Original comment: **

Wikispaces>keenanpepper: **Imported revision 290308191 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 289920687 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 289920621 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 288679822 - Original comment: **

Wikispaces>genewardsmith: Imported revision 290312079 - Original comment:

Wikispaces>keenanpepper: Imported revision 290308213 - Original comment:

Wikispaces>keenanpepper: Imported revision 290308191 - Original comment:

Wikispaces>genewardsmith: Imported revision 289920687 - Original comment:

Wikispaces>genewardsmith: Imported revision 289920621 - Original comment:

Wikispaces>genewardsmith: Imported revision 288679822 - Original comment: