Saddle chord - Revision history

Fredg999: Update internal link, clarify 24edo explicity

2024-12-24T05:08:11Z

Update internal link, clarify 24edo explicity

← Older revision		Revision as of 05:08, 24 December 2024
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	Chords <span style="line-height: 1.5;">at or near local minima sound "clean" and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.</span>		Chords <span style="line-height: 1.5;">at or near local minima sound "clean" and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.</span>

	In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" dyads include many [[~~24edo\|~~quarter tone]]-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} with each note a quarter tone apart.		In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" dyads include many [[quarter tone]]-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} in [[24edo]] with each note a quarter tone apart.

	For triads and higher, though, there are other possibilities, corresponding to [https://en.wikipedia.org/wiki/Monkey_saddle monkey saddle] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.		For triads and higher, though, there are other possibilities, corresponding to [https://en.wikipedia.org/wiki/Monkey_saddle monkey saddle] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.

Fredg999: Categories, misc. edits, todo:add examples

2024-12-22T21:58:49Z

Categories, misc. edits, todo:add examples

← Older revision		Revision as of 21:58, 22 December 2024
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	A '''saddle chord''' is a chord that represents a ''saddle point'' in the [[~~Harmonic_Entropy\|~~harmonic entropy]] surface, rather than a local minimum or maximum. Because saddle points only occur in two-dimensional or higher surfaces, a saddle chord cannot be a dyad (since the harmonic entropy graph for dyads is a one-dimensional curve). It must be a triad, tetrad or higher.		A '''saddle chord''' is a chord that represents a ''saddle point'' in the [[harmonic entropy]] surface, rather than a local minimum or maximum. Because saddle points only occur in two-dimensional or higher surfaces, a saddle chord cannot be a dyad (since the harmonic entropy graph for dyads is a one-dimensional curve). It must be a triad, tetrad or higher.

	Chords <span style="line-height: 1.5;">at or near local minima sound "clean" and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.</span>		Chords <span style="line-height: 1.5;">at or near local minima sound "clean" and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.</span>

	In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" dyads include many [[~~quarter_tone~~\|quarter tone]]-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} with each note a quarter tone apart.		In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" dyads include many [[24edo\|quarter tone]]-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} with each note a quarter tone apart.

	For triads and higher, though, there are other possibilities, corresponding to [https://en.wikipedia.org/wiki/Monkey_saddle monkey saddle] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.		For triads and higher, though, there are other possibilities, corresponding to [https://en.wikipedia.org/wiki/Monkey_saddle monkey saddle] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.
	[[Category:~~chords~~]]

			{{todo\|add examples\|inline=1}}

			[[Category:Chord]]
	[[Category:Consonance and dissonance]]		[[Category:Consonance and dissonance]]
	~~[[Category:pentad]]~~
	~~[[Category:tetrad]]~~
	~~[[Category:triad]]~~

Fredg999 category edits: Removing from Category:Sonance using Cat-a-lot

2023-03-04T18:39:31Z

Removing from Category:Sonance using Cat-a-lot

← Older revision		Revision as of 18:39, 4 March 2023
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	[[Category:Consonance and dissonance]]		[[Category:Consonance and dissonance]]
	[[Category:pentad]]		[[Category:pentad]]
	~~[[Category:sonance]]~~
	[[Category:tetrad]]		[[Category:tetrad]]
	[[Category:triad]]		[[Category:triad]]

Fredg999 category edits: Removing from Category:Dissonance using Cat-a-lot

2023-03-04T18:39:15Z

Removing from Category:Dissonance using Cat-a-lot

← Older revision		Revision as of 18:39, 4 March 2023
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	[[Category:chords]]		[[Category:chords]]
	[[Category:Consonance and dissonance]]		[[Category:Consonance and dissonance]]
	~~[[Category:dissonance]]~~
	[[Category:pentad]]		[[Category:pentad]]
	[[Category:sonance]]		[[Category:sonance]]
	[[Category:tetrad]]		[[Category:tetrad]]
	[[Category:triad]]		[[Category:triad]]

Fredg999 category edits: Moving from Category:Consonance to Category:Consonance and dissonance using Cat-a-lot

2023-03-04T18:38:54Z

Moving from Category:Consonance to Category:Consonance and dissonance using Cat-a-lot

← Older revision		Revision as of 18:38, 4 March 2023
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	For triads and higher, though, there are other possibilities, corresponding to [https://en.wikipedia.org/wiki/Monkey_saddle monkey saddle] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.		For triads and higher, though, there are other possibilities, corresponding to [https://en.wikipedia.org/wiki/Monkey_saddle monkey saddle] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.
	[[Category:chords]]		[[Category:chords]]
	[[Category:~~consonance~~]]		[[Category:Consonance and dissonance]]
	[[Category:dissonance]]		[[Category:dissonance]]
	[[Category:pentad]]		[[Category:pentad]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		A '''saddle chord''' is a chord that represents a ''saddle point'' in the [[Harmonic_Entropy\|harmonic entropy]] surface, rather than a local minimum or maximum. Because saddle points only occur in two-dimensional or higher surfaces, a saddle chord cannot be a dyad (since the harmonic entropy graph for dyads is a one-dimensional curve). It must be a triad, tetrad or higher.
	~~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>2015-11-29 13:34:45 UTC</tt>.<br>~~
	~~: The original revision id was <tt>568156139</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">A saddle chord is a chord that represents a //saddle point// in the [[harmonic entropy]] surface, rather than a local minimum or maximum. Because saddle points only occur in two-dimensional or higher surfaces, a saddle chord cannot be a dyad (since the harmonic entropy graph for dyads is a one-dimensional curve). It must be a triad, tetrad or higher.

	Chords ~~<~~span style="line-height: 1.5;"~~>~~at or near local minima sound "clean" and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.~~<~~/span~~>~~		Chords <span style="line-height: 1.5;">at or near local minima sound "clean" and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.</span>

	In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" dyads include many [[quarter tone]]-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} with each note a quarter tone apart.		In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" dyads include many [[quarter_tone\|quarter tone]]-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} with each note a quarter tone apart.

	For triads and higher, though, there are other possibilities, corresponding to [[https://en.wikipedia.org/wiki/Monkey_saddle\|monkey saddle]] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.~~</pre></div>~~		For triads and higher, though, there are other possibilities, corresponding to [https://en.wikipedia.org/wiki/Monkey_saddle monkey saddle] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.
	~~<h4>Original HTML content~~:~~</h4>~~		[[Category:chords]]
	~~<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>Saddle chord</title></head><body>A <strong>saddle chord</strong> is a chord that represents a <em>saddle point</em> in the <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> surface, rather than a local minimum or maximum. Because saddle points only occur in two-dimensional or higher surfaces, a saddle chord cannot be a dyad (since the harmonic entropy graph for dyads is a one-dimensional curve). It must be a triad, tetrad ~~or higher.<br />~~		[[Category:consonance]]
	~~<br />~~		[[Category:dissonance]]
	Chords <span style="line-height: 1.5;">at or near local minima sound &quot;clean&quot; and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:~~6 is a local minimum, and its approximation in 12edo is close by.</span><br />~~		[[Category:pentad]]
	~~<br />~~		[[Category:sonance]]
	In contrast, a chord at or near a local maximum sounds especially &quot;dirty&quot; and discordant. &quot;Dirty&quot; dyads include many <a class="wiki_link" href="/quarter%20tone">quarter tone</a>-based intervals. There are also dirty triads, for example, the quarter tone triad ~~{0,1,2} with each note a quarter tone apart.<br />~~		[[Category:tetrad]]
	~~<br />~~		[[Category:triad]]
	For triads and higher, though, there are other possibilities, corresponding to <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Monkey_saddle" rel="nofollow">monkey saddle</a> and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and &quot;dirty&quot; in terms of sounds.</body></html></pre></div>

Wikispaces>MasonGreen1: Imported revision 568156139 - Original comment:

2015-11-29T13:34:45Z

**Imported revision 568156139 - 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>2015-11-29 13:34:45 UTC</tt>.<br>
: The original revision id was <tt>568156139</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">A **saddle chord** is a chord that represents a //saddle point// in the [[harmonic entropy]] surface, rather than a local minimum or maximum. Because saddle points only occur in two-dimensional or higher surfaces, a saddle chord cannot be a dyad (since the harmonic entropy graph for dyads is a one-dimensional curve). It must be a triad, tetrad or higher.

Chords <span style="line-height: 1.5;">at or near local minima sound "clean" and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.</span>

In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" dyads include many [[quarter tone]]-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} with each note a quarter tone apart.

For triads and higher, though, there are other possibilities, corresponding to [[https://en.wikipedia.org/wiki/Monkey_saddle|monkey saddle]] and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and "dirty" in terms of sounds.</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>Saddle chord</title></head><body>A <strong>saddle chord</strong> is a chord that represents a <em>saddle point</em> in the <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> surface, rather than a local minimum or maximum. Because saddle points only occur in two-dimensional or higher surfaces, a saddle chord cannot be a dyad (since the harmonic entropy graph for dyads is a one-dimensional curve). It must be a triad, tetrad or higher.<br />
<br />
Chords <span style="line-height: 1.5;">at or near local minima sound &quot;clean&quot; and have a single primary approximation just intonation approximation. For example, the justly intoned major chord 4:5:6 is a local minimum, and its approximation in 12edo is close by.</span><br />
<br />
In contrast, a chord at or near a local maximum sounds especially &quot;dirty&quot; and discordant. &quot;Dirty&quot; dyads include many <a class="wiki_link" href="/quarter%20tone">quarter tone</a>-based intervals. There are also dirty triads, for example, the quarter tone triad {0,1,2} with each note a quarter tone apart.<br />
<br />
For triads and higher, though, there are other possibilities, corresponding to <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Monkey_saddle" rel="nofollow">monkey saddle</a> and horse saddle-type points. These chords do not have a single just approximation but rather are a compromise between multiple ones, and as such their harmonic entropy is not a local minimum (at least not in all directions). They are intermediate between consonant and &quot;dirty&quot; in terms of sounds.</body></html></pre></div>