Mixed timbre - Revision history

Fredg999: Mark term as idiosyncratic, categories

2023-12-12T20:34:08Z

Mark term as idiosyncratic, categories

← Older revision		Revision as of 20:34, 12 December 2023
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	A '''mixed timbre''' is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same "clear" quality that distinguishes harmonic timbres from the more "opaque" or bell-like inharmonic ones. The term mixed timbre was coined by [[Mason Green]], although the concept may have been proposed before.		A '''mixed timbre'''{{idiosyncratic}} is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same "clear" quality that distinguishes harmonic timbres from the more "opaque" or bell-like inharmonic ones. The term mixed timbre was coined by [[Mason Green]], although the concept may have been proposed before.

	Mixed timbres are ideal for use with tunings that ''almost,'' but not quite, provide satisfactory approximations for certain intervals. For example, [[22edo]] is a fairly good [[11-limit]] system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by [[Paul Erlich]] among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.		Mixed timbres are ideal for use with tunings that ''almost,'' but not quite, provide satisfactory approximations for certain intervals. For example, [[22edo]] is a fairly good [[11-limit]] system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by [[Paul Erlich]] among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.
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	It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old [[12edo]] can, as well (if you use a timbre with the 5th and 7th partials bent up).		It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old [[12edo]] can, as well (if you use a timbre with the 5th and 7th partials bent up).

	~~[[Category:Terms]]~~
	[[Category:Timbre]]		[[Category:Timbre]]

Fredg999: Fixed internal link

2021-12-12T03:12:25Z

Fixed internal link

← Older revision		Revision as of 03:12, 12 December 2021
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	However, with most harmonic timbres, neither of these intervals ''sounds'' particularly consonant. The tritone is too far apart from both 7:5 and 10:7 to sound like either. By introducing some inharmonicity, though, it is possible to make these intervals sound much sweeter, as consonances should. That way, 22edo will not sound nearly as "out of tune" as it otherwise would.		However, with most harmonic timbres, neither of these intervals ''sounds'' particularly consonant. The tritone is too far apart from both 7:5 and 10:7 to sound like either. By introducing some inharmonicity, though, it is possible to make these intervals sound much sweeter, as consonances should. That way, 22edo will not sound nearly as "out of tune" as it otherwise would.

	Mixed timbres are one way to do this. A mixed timbre contains '''mixed [[~~partials~~]]''', which are partials consisting of two or more closely-spaced frequency components (they must be close enough that they are perceived as one "beating" partial rather than separate entities). One of the components is a perfect harmonic multiple of the fundamental, and the other(s) are slightly higher or lower.		Mixed timbres are one way to do this. A mixed timbre contains '''mixed [[partial]]s''', which are partials consisting of two or more closely-spaced frequency components (they must be close enough that they are perceived as one "beating" partial rather than separate entities). One of the components is a perfect harmonic multiple of the fundamental, and the other(s) are slightly higher or lower.

	For example, we could imagine a mixed partial consisting of one component at 3''f'', where ''f'' is the fundamental frequency, and a second component with half the amplitude at ''3.03f''. Because of the harmonic component, this partial maintains some semblance of (imperfect) mode-locking with the fundamental, which results in a more stable timbre. Interference between the two components causes this partial to "beat", but beats on overtones are generally ''much'' less noticeable than beats on the fundamental, and because the inharmonic component is smaller to begin with, the beating will not be very noticeable and the timbre will sound very close to a perfectly harmonic one.		For example, we could imagine a mixed partial consisting of one component at 3''f'', where ''f'' is the fundamental frequency, and a second component with half the amplitude at ''3.03f''. Because of the harmonic component, this partial maintains some semblance of (imperfect) mode-locking with the fundamental, which results in a more stable timbre. Interference between the two components causes this partial to "beat", but beats on overtones are generally ''much'' less noticeable than beats on the fundamental, and because the inharmonic component is smaller to begin with, the beating will not be very noticeable and the timbre will sound very close to a perfectly harmonic one.

Keenan Pepper category edits: Moving from Category:Term to Category:Terms using Cat-a-lot

2020-12-04T22:44:58Z

Moving from Category:Term to Category:Terms using Cat-a-lot

← Older revision		Revision as of 22:44, 4 December 2020
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	It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old [[12edo]] can, as well (if you use a timbre with the 5th and 7th partials bent up).		It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old [[12edo]] can, as well (if you use a timbre with the 5th and 7th partials bent up).

	[[Category:~~Term~~]]		[[Category:Terms]]
	[[Category:Timbre]]		[[Category:Timbre]]

Xenwolf: added cats, also some links. Interestingly (or better said sadly) this page is orphaned.

2020-06-12T20:37:02Z

added cats, also some links. Interestingly (or better said sadly) this page is orphaned.

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>xenwolf: Imported revision 575527913 - Original comment: let's try

2016-02-22T15:27:37Z

**Imported revision 575527913 - Original comment: let's try**

← Older revision		Revision as of 15:27, 22 February 2016
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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>2016-02-22 01:12:02 UTC</tt>.<br>		: This revision was by author [[User:xenwolf\|xenwolf]] and made on <tt>2016-02-22 15:27:37 UTC</tt>.<br>
	: The original revision id was <tt>~~575446979~~</tt>.<br>		: The original revision id was <tt>575527913</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt>let's try</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>
	<h4>Original Wikitext content:</h4>		<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 mixed timbre is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same "clear" quality that distinguishes harmonic timbres from the more "opaque" or bell-like inharmonic ones. The term mixed timbre was coined by ~~me (~~Mason Green), although the concept may have been proposed before~~; I'm not entirely sure~~.		<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 mixed timbre is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same "clear" quality that distinguishes harmonic timbres from the more "opaque" or bell-like inharmonic ones. The term mixed timbre was coined by [[Mason Green]], although the concept may have been proposed before.

	Mixed timbres are ideal for use with tunings that //almost,// but not quite, provide satisfactory approximations for certain intervals. For example, [[22edo]] is a fairly good 11-limit system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by Paul Erlich among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.		Mixed timbres are ideal for use with tunings that //almost,// but not quite, provide satisfactory approximations for certain intervals. For example, [[22edo]] is a fairly good 11-limit system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by Paul Erlich among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.
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	It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old 12edo can, as well (if you use a timbre with the 5th and 7th partials bent up).</pre></div>		It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old 12edo can, as well (if you use a timbre with the 5th and 7th partials bent up).</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>mixed timbre</title></head><body>A <strong>mixed timbre</strong> is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same &quot;clear&quot; quality that distinguishes harmonic timbres from the more &quot;opaque&quot; or bell-like inharmonic ones. The term mixed timbre was coined by ~~me (~~Mason Green), although the concept may have been proposed before~~; I'm not entirely sure~~.<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>mixed timbre</title></head><body>A <strong>mixed timbre</strong> is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same &quot;clear&quot; quality that distinguishes harmonic timbres from the more &quot;opaque&quot; or bell-like inharmonic ones. The term mixed timbre was coined by <a class="wiki_link" href="/Mason%20Green">Mason Green</a>, although the concept may have been proposed before.<br />
	<br />		<br />
	Mixed timbres are ideal for use with tunings that <em>almost,</em> but not quite, provide satisfactory approximations for certain intervals. For example, <a class="wiki_link" href="/22edo">22edo</a> is a fairly good 11-limit system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by Paul Erlich among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.<br />		Mixed timbres are ideal for use with tunings that <em>almost,</em> but not quite, provide satisfactory approximations for certain intervals. For example, <a class="wiki_link" href="/22edo">22edo</a> is a fairly good 11-limit system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by Paul Erlich among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.<br />

Wikispaces>MasonGreen1: Imported revision 575446979 - Original comment:

2016-02-22T01:12:02Z

**Imported revision 575446979 - Original comment: **

Wikispaces>MasonGreen1: Imported revision 575446935 - Original comment:

2016-02-22T01:11:02Z

**Imported revision 575446935 - Original comment: **

← Older revision		Revision as of 01:11, 22 February 2016
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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>2016-02-15 22:24:24 UTC</tt>.<br>		: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-02-22 01:11:02 UTC</tt>.<br>
	: The original revision id was <tt>~~574925935~~</tt>.<br>		: The original revision id was <tt>575446935</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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	If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.		If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.

			Another tuning that would benefit a great deal from this is [[17edo]], which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial //way// up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound //too// inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the "5:4" and "5:6" onto a neutral third.

	Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.		Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.
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	<br />		<br />
	If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.<br />		If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.<br />
			<br />
			Another tuning that would benefit a great deal from this is <a class="wiki_link" href="/17edo">17edo</a>, which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial <em>way</em> up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound <em>too</em> inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the &quot;5:4&quot; and &quot;5:6&quot; onto a neutral third.<br />
	<br />		<br />
	Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.<br />		Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.<br />

Wikispaces>MasonGreen1: Imported revision 574925935 - Original comment:

2016-02-15T22:24:24Z

**Imported revision 574925935 - 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>2016-02-15 22:24:24 UTC</tt>.<br>
: The original revision id was <tt>574925935</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 **mixed timbre** is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same "clear" quality that distinguishes harmonic timbres from the more "opaque" or bell-like inharmonic ones. The term mixed timbre was coined by me (Mason Green), although the concept may have been proposed before; I'm not entirely sure.

Mixed timbres are ideal for use with tunings that //almost,// but not quite, provide satisfactory approximations for certain intervals. For example, [[22edo]] is a fairly good 11-limit system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by Paul Erlich among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.

However, with most harmonic timbres, neither of these intervals //sounds// particularly consonant. The tritone is too far apart from both 7:5 and 10:7 to sound like either. By introducing some inharmonicity, though, it is possible to make these intervals sound much sweeter, as consonances should. That way, 22edo will not sound nearly as "out of tune" as it otherwise would.

Mixed timbres are one way to do this. A mixed timbre contains **mixed partials**, which are partials consisting of two or more closely-spaced frequency components (they must be close enough that they are perceived as one "beating" partial rather than separate entities). One of the components is a perfect harmonic multiple of the fundamental, and the other(s) are slightly higher or lower.

For example, we could imagine a mixed partial consisting of one component at 3//f//, where //f// is the fundamental frequency, and a second component with half the amplitude at //3.03f//. Because of the harmonic component, this partial maintains some semblance of (imperfect) mode-locking with the fundamental, which results in a more stable timbre. Interference between the two components causes this partial to "beat", but beats on overtones are generally //much// less noticeable than beats on the fundamental, and because the inharmonic component is smaller to begin with, the beating will not be very noticeable and the timbre will sound very close to a perfectly harmonic one.

This mixed overtone will have an effective pitch which is a weighted average of its two components; in this case, about 5-6 cents above 3//f//. Thus, we can say that the pitch of this overtone has been "bent up" through the addition of the inharmonic component. Assuming octave equivalence and that the 2nd, 4th, 8th, etc. are all perfectly harmonic, it might be inferred that the ideal width of a fifth, when using this timbre, will be somewhere around ~707 cents. This may make a huge difference if we are using a tuning where the fifths are already very sharp to begin with (for example, 22edo or 27edo).

If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.

Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.

In fact, it's quite likely that many if not most of the "perfectly harmonic" timbres in nature, including the human voice, are in fact mixed timbres. Few if any physical objects are //completely// free of inharmonicity, and mode-locking is not always perfect ([[https://en.wikipedia.org/wiki/Injection_locking#Injection_pulling|injection pulling]] can occur as often as injection locking). Because of this, a mixed timbre may in fact sound more organic, or less artificial, than a perfectly harmonic one.

It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old 12edo can, as well (if you use a timbre with the 5th and 7th partials bent up).</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>mixed timbre</title></head><body>A <strong>mixed timbre</strong> is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same &quot;clear&quot; quality that distinguishes harmonic timbres from the more &quot;opaque&quot; or bell-like inharmonic ones. The term mixed timbre was coined by me (Mason Green), although the concept may have been proposed before; I'm not entirely sure.<br />
<br />
Mixed timbres are ideal for use with tunings that <em>almost,</em> but not quite, provide satisfactory approximations for certain intervals. For example, <a class="wiki_link" href="/22edo">22edo</a> is a fairly good 11-limit system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by Paul Erlich among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.<br />
<br />
However, with most harmonic timbres, neither of these intervals <em>sounds</em> particularly consonant. The tritone is too far apart from both 7:5 and 10:7 to sound like either. By introducing some inharmonicity, though, it is possible to make these intervals sound much sweeter, as consonances should. That way, 22edo will not sound nearly as &quot;out of tune&quot; as it otherwise would.<br />
<br />
Mixed timbres are one way to do this. A mixed timbre contains <strong>mixed partials</strong>, which are partials consisting of two or more closely-spaced frequency components (they must be close enough that they are perceived as one &quot;beating&quot; partial rather than separate entities). One of the components is a perfect harmonic multiple of the fundamental, and the other(s) are slightly higher or lower.<br />
<br />
For example, we could imagine a mixed partial consisting of one component at 3<em>f</em>, where <em>f</em> is the fundamental frequency, and a second component with half the amplitude at <em>3.03f</em>. Because of the harmonic component, this partial maintains some semblance of (imperfect) mode-locking with the fundamental, which results in a more stable timbre. Interference between the two components causes this partial to &quot;beat&quot;, but beats on overtones are generally <em>much</em> less noticeable than beats on the fundamental, and because the inharmonic component is smaller to begin with, the beating will not be very noticeable and the timbre will sound very close to a perfectly harmonic one.<br />
<br />
This mixed overtone will have an effective pitch which is a weighted average of its two components; in this case, about 5-6 cents above 3<em>f</em>. Thus, we can say that the pitch of this overtone has been &quot;bent up&quot; through the addition of the inharmonic component. Assuming octave equivalence and that the 2nd, 4th, 8th, etc. are all perfectly harmonic, it might be inferred that the ideal width of a fifth, when using this timbre, will be somewhere around ~707 cents. This may make a huge difference if we are using a tuning where the fifths are already very sharp to begin with (for example, 22edo or 27edo).<br />
<br />
If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.<br />
<br />
Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.<br />
<br />
In fact, it's quite likely that many if not most of the &quot;perfectly harmonic&quot; timbres in nature, including the human voice, are in fact mixed timbres. Few if any physical objects are <em>completely</em> free of inharmonicity, and mode-locking is not always perfect (<a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Injection_locking#Injection_pulling" rel="nofollow">injection pulling</a> can occur as often as injection locking). Because of this, a mixed timbre may in fact sound more organic, or less artificial, than a perfectly harmonic one.<br />
<br />
It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old 12edo can, as well (if you use a timbre with the 5th and 7th partials bent up).</body></html></pre></div>

← Older revision		Revision as of 20:37, 12 June 2020
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	A '''mixed timbre''' is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same "clear" quality that distinguishes harmonic timbres from the more "opaque" or bell-like inharmonic ones. The term mixed timbre was coined by [[~~Mason_Green\|~~Mason Green]], although the concept may have been proposed before.		A '''mixed timbre''' is a type of musical timbre that is intermediate between a perfectly harmonic (mode-locked) timbre and an inharmonic one. These types of timbres introduce a slight amount of inharmonicity, with partials being bent up or down by a few cents, while also maintaining the same "clear" quality that distinguishes harmonic timbres from the more "opaque" or bell-like inharmonic ones. The term mixed timbre was coined by [[Mason Green]], although the concept may have been proposed before.

	Mixed timbres are ideal for use with tunings that ''almost,'' but not quite, provide satisfactory approximations for certain intervals. For example, [[~~22edo\|~~22edo]] is a fairly good 11-limit system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by Paul Erlich among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.		Mixed timbres are ideal for use with tunings that ''almost,'' but not quite, provide satisfactory approximations for certain intervals. For example, [[22edo]] is a fairly good [[11-limit]] system, and it also allows for a great deal of new modal and tonal possibilities, which have been written about by [[Paul Erlich]] among others. Some of these scales sound much better if the 600-cent tritone is treated as a consonance rather than a dissonance. Similarly, it might be a good idea to treat the tempered whole tone (~218 cents) as a consonance as well, since it occurs in inversions of the harmonic seventh chord.

	However, with most harmonic timbres, neither of these intervals ''sounds'' particularly consonant. The tritone is too far apart from both 7:5 and 10:7 to sound like either. By introducing some inharmonicity, though, it is possible to make these intervals sound much sweeter, as consonances should. That way, 22edo will not sound nearly as "out of tune" as it otherwise would.		However, with most harmonic timbres, neither of these intervals ''sounds'' particularly consonant. The tritone is too far apart from both 7:5 and 10:7 to sound like either. By introducing some inharmonicity, though, it is possible to make these intervals sound much sweeter, as consonances should. That way, 22edo will not sound nearly as "out of tune" as it otherwise would.

	Mixed timbres are one way to do this. A mixed timbre contains '''mixed partials''', which are partials consisting of two or more closely-spaced frequency components (they must be close enough that they are perceived as one "beating" partial rather than separate entities). One of the components is a perfect harmonic multiple of the fundamental, and the other(s) are slightly higher or lower.		Mixed timbres are one way to do this. A mixed timbre contains '''mixed [[partials]]''', which are partials consisting of two or more closely-spaced frequency components (they must be close enough that they are perceived as one "beating" partial rather than separate entities). One of the components is a perfect harmonic multiple of the fundamental, and the other(s) are slightly higher or lower.

	For example, we could imagine a mixed partial consisting of one component at 3''f'', where ''f'' is the fundamental frequency, and a second component with half the amplitude at ''3.03f''. Because of the harmonic component, this partial maintains some semblance of (imperfect) mode-locking with the fundamental, which results in a more stable timbre. Interference between the two components causes this partial to "beat", but beats on overtones are generally ''much'' less noticeable than beats on the fundamental, and because the inharmonic component is smaller to begin with, the beating will not be very noticeable and the timbre will sound very close to a perfectly harmonic one.		For example, we could imagine a mixed partial consisting of one component at 3''f'', where ''f'' is the fundamental frequency, and a second component with half the amplitude at ''3.03f''. Because of the harmonic component, this partial maintains some semblance of (imperfect) mode-locking with the fundamental, which results in a more stable timbre. Interference between the two components causes this partial to "beat", but beats on overtones are generally ''much'' less noticeable than beats on the fundamental, and because the inharmonic component is smaller to begin with, the beating will not be very noticeable and the timbre will sound very close to a perfectly harmonic one.

	This mixed overtone will have an effective pitch which is a weighted average of its two components; in this case, about 5-6 cents above 3''f''. Thus, we can say that the pitch of this overtone has been "bent up" through the addition of the inharmonic component. Assuming octave equivalence and that the 2nd, 4th, 8th, etc. are all perfectly harmonic, it might be inferred that the ideal width of a fifth, when using this timbre, will be somewhere around ~707 cents. This may make a huge difference if we are using a tuning where the fifths are already very sharp to begin with (for example, 22edo or 27edo).		This mixed overtone will have an effective pitch which is a weighted average of its two components; in this case, about 5-6 cents above 3''f''. Thus, we can say that the pitch of this overtone has been "bent up" through the addition of the inharmonic component. Assuming [[octave equivalence]] and that the 2nd, 4th, 8th, etc. are all perfectly harmonic, it might be inferred that the ideal width of a fifth, when using this timbre, will be somewhere around ~707 cents. This may make a huge difference if we are using a tuning where the fifths are already very sharp to begin with (for example, 22edo or 27edo).

	If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.		If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.

	Another tuning that would benefit a great deal from this is [[~~17edo\|~~17edo]], which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial ''way'' up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound ''too'' inharmonic. Using the flat val for 5 will result in a different timbre with a more xenharmonic effect, since it maps both the "5:4" and "5:6" onto a neutral third.		Another tuning that would benefit a great deal from this is [[17edo]], which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial ''way'' up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound ''too'' inharmonic. Using the flat val for 5 will result in a different timbre with a more [[xenharmonic]] effect, since it maps both the "5:4" and "5:6" onto a neutral third.

	Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.		Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an [[idiophone]]. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.

	In fact, it's quite likely that many if not most of the "perfectly harmonic" timbres in nature, including the human voice, are in fact mixed timbres. Few if any physical objects are ''completely'' free of inharmonicity, and mode-locking is not always perfect ([https://en.wikipedia.org/wiki/Injection_locking#Injection_pulling injection pulling] can occur as often as injection locking). Because of this, a mixed timbre may in fact sound more organic, or less artificial, than a perfectly harmonic one.		In fact, it's quite likely that many if not most of the "perfectly harmonic" timbres in nature, including the human voice, are in fact mixed timbres. Few if any physical objects are ''completely'' free of inharmonicity, and mode-locking is not always perfect ([https://en.wikipedia.org/wiki/Injection_locking#Injection_pulling injection pulling] can occur as often as injection locking). Because of this, a mixed timbre may in fact sound more organic, or less artificial, than a perfectly harmonic one.

	It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old 12edo can, as well (if you use a timbre with the 5th and 7th partials bent up).		It's not just xenharmonic tunings that can benefit from using mixed timbres; even plain old [[12edo]] can, as well (if you use a timbre with the 5th and 7th partials bent up).

			[[Category:Term]]
			[[Category:Timbre]]

← Older revision		Revision as of 01:12, 22 February 2016
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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>2016-02-22 01:11:02 UTC</tt>.<br>		: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-02-22 01:12:02 UTC</tt>.<br>
	: The original revision id was <tt>~~575446935~~</tt>.<br>		: The original revision id was <tt>575446979</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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	If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.		If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.

	Another tuning that would benefit a great deal from this is [[17edo]], which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial //way// up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound //too// inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the "5:4" and "5:6" onto a neutral third.		Another tuning that would benefit a great deal from this is [[17edo]], which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial //way// up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound //too// inharmonic. Using the flat val for 5 will result in a different timbre with a more xenharmonic effect, since it maps both the "5:4" and "5:6" onto a neutral third.

	Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.		Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.
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	If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.<br />		If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.<br />
	<br />		<br />
	Another tuning that would benefit a great deal from this is <a class="wiki_link" href="/17edo">17edo</a>, which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial <em>way</em> up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound <em>too</em> inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the &quot;5:4&quot; and &quot;5:6&quot; onto a neutral third.<br />		Another tuning that would benefit a great deal from this is <a class="wiki_link" href="/17edo">17edo</a>, which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial <em>way</em> up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound <em>too</em> inharmonic. Using the flat val for 5 will result in a different timbre with a more xenharmonic effect, since it maps both the &quot;5:4&quot; and &quot;5:6&quot; onto a neutral third.<br />
	<br />		<br />
	Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.<br />		Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.<br />