Saddle chord
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- This revision was by author MasonGreen1 and made on 2015-11-29 13:34:45 UTC.
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Original Wikitext content:
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.Original HTML content:
<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 "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><br />
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In contrast, a chord at or near a local maximum sounds especially "dirty" and discordant. "Dirty" 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 "dirty" in terms of sounds.</body></html>