Harmonic - Revision history

FloraC: Move opening see-also link to the end of the intro. - self link and misc. improvements

2026-07-28T06:15:07Z

Move opening see-also link to the end of the intro. - self link and misc. improvements

← Older revision		Revision as of 06:15, 28 July 2026
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	{{Wikipedia}}		{{Wikipedia}}
	~~{{See also\|Category:Harmonics}}~~
	A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].		A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].

	The timbre of a periodic sound, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f''~~...~~ where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The [[span]] between any two of these harmonics is a [[just interval]]. If the harmonics are numbered such that the fundamental is number 1, the octave is 2, etc., then the interval's ratio is given by the two numbers. For example the interval between the 3rd and 4th harmonics is 4/3.		The timbre of a periodic sound, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f'', … where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The [[span]] between any two of these harmonics is a [[just interval]]. If the harmonics are numbered such that the fundamental is number 1, the octave is 2, etc., then the interval's ratio is given by the two numbers. For example the interval between the 3rd and 4th harmonics is 4/3.

	The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.		The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.

	A '''subharmonic''' is a unit fraction of the fundamental frequency of a sound: ''f''/1, ''f''/2, ''f''/3, ''f''/4... It is an element of the [[subharmonic series]].		A '''subharmonic''' is a unit fraction of the fundamental frequency of a sound: ''f''/1, ''f''/2, ''f''/3, ''f''/4, …. It is an element of the [[subharmonic series]].

			For individual articles on each harmonic, see [[:Category: Harmonics]].

	== Odd harmonic ==		== Odd harmonic ==
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	== Prime harmonic ==		== Prime harmonic ==
	{{See also\|Category:Prime harmonics}}		{{See also\|Category: Prime harmonics}}

	A '''prime interval''' or '''prime harmonic''' is a harmonic which as a [[ratio]] of frequencies is a [[prime number]]; that is, a number such as 2, 3, 5, 7, 11, … which is divisible only by itself and 1. It is an element of the [[prime harmonic series]].		A '''prime interval''' or '''prime harmonic''' is a harmonic which as a [[ratio]] of frequencies is a [[prime number]]; that is, a number such as 2, 3, 5, 7, 11, … which is divisible only by itself and 1. It is an element of the [[prime harmonic series]].

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	== Highly composite harmonic ==		== Highly composite harmonic ==
	{{See also\|Category:Highly composite harmonics}}		{{See also\|Category: Highly composite harmonics}}

	A '''highly composite interval''' or '''highly composite harmonic''' is a harmonic which has a [[ratio]] of frequencies is a [[highly composite number]]; that is, a number such as 1, 2, 4, 6, 12, … each of which has more divisors than the number before it.		A '''highly composite interval''' or '''highly composite harmonic''' is a harmonic which has a [[ratio]] of frequencies is a [[highly composite number]]; that is, a number such as 1, 2, 4, 6, 12, … each of which has more divisors than the number before it.

	Highly composite intervals are significant for having the largest number of ways to be approached through [[harmonic]] [[chord]]s for its size.		Highly composite intervals are significant for having the largest number of ways to be approached through harmonic [[chord]]s for its size.

	Highly composite intervals can be thought of as the opposite of prime harmonics, since highly composite numbers are "antiprime", but they are not complementary sets, as they share a common element (2/1) and there are infinitely many harmonics which are neither prime nor highly composite.		Highly composite intervals can be thought of as the opposite of prime harmonics, since highly composite numbers are "antiprime", but they are not complementary sets, as they share a common element (2/1) and there are infinitely many harmonics which are neither prime nor highly composite.

Fredg999: /* Prime harmonic */ Insert former see also links

2026-07-28T00:44:06Z

Prime harmonic: Insert former see also links

← Older revision		Revision as of 00:44, 28 July 2026
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	== Prime harmonic ==		== Prime harmonic ==
	{{See also\|Category:Prime harmonics}}		{{See also\|Category:Prime harmonics}}
	A '''prime interval''' or '''prime harmonic''' is a harmonic which as a [[ratio]] of frequencies is a [[prime number]]; that is, a number such as 2, 3, 5, 7, 11, … which is divisible only by itself and 1.		A '''prime interval''' or '''prime harmonic''' is a harmonic which as a [[ratio]] of frequencies is a [[prime number]]; that is, a number such as 2, 3, 5, 7, 11, … which is divisible only by itself and 1. It is an element of the [[prime harmonic series]].

	Any interval of [[just intonation\|just intonation (JI)]] can be expressed in terms of a product of prime intervals, allowing us to decompose a complex JI interval into simpler parts. A prime interval itself cannot be expressed by other prime intervals, so no prime intervals are redundant for reconstructing the entirety of JI. For those reasons and for the fact that prime intervals occur in [[harmonic series]], they form a very important [[basis]] (literally and mathematically) for JI.		Any interval of [[just intonation\|just intonation (JI)]] can be expressed in terms of a product of prime intervals, allowing us to decompose a complex JI interval into simpler parts. A prime interval itself cannot be expressed by other prime intervals, so no prime intervals are redundant for reconstructing the entirety of JI. For those reasons and for the fact that prime intervals occur in [[harmonic series]], they form a very important [[basis]] (literally and mathematically) for JI.
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	The [[monzo]] notation of each prime interval consists of all-zeros except for a single entry equal to 1: (2: {{monzo\| 1 }}, 3: {{monzo\| 0 1 }}, 5: {{monzo\| 0 0 1 }}, 7: {{monzo\| 0 0 0 1 }}, 11: {{monzo\| 0 0 0 0 1 }}, …)		The [[monzo]] notation of each prime interval consists of all-zeros except for a single entry equal to 1: (2: {{monzo\| 1 }}, 3: {{monzo\| 0 1 }}, 5: {{monzo\| 0 0 1 }}, 7: {{monzo\| 0 0 0 1 }}, 11: {{monzo\| 0 0 0 0 1 }}, …)

			Prime harmonics are often used to define [[harmonic limit]]s, also known as prime limits.

	== Highly composite harmonic ==		== Highly composite harmonic ==

Fredg999: Merge odd harmonic, prime interval and highly composite interval

2026-07-28T00:41:08Z

Merge odd harmonic, prime interval and highly composite interval

← Older revision		Revision as of 00:41, 28 July 2026
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	{{Wikipedia\|~~Harmonic~~}}		{{Wikipedia}}
			{{See also\|Category:Harmonics}}
	A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].		A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].

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	The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.		The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.

	A '''subharmonic''' is a unit fraction of the fundamental frequency of a sound. It is an element of the [[subharmonic series]].		A '''subharmonic''' is a unit fraction of the fundamental frequency of a sound: ''f''/1, ''f''/2, ''f''/3, ''f''/4... It is an element of the [[subharmonic series]].

	== ~~Individual pages~~ ==		== Odd harmonic ==
	See [[:Category: ~~Harmonics~~]].		An '''odd harmonic''' is a harmonic where the [[frequency ratio]] is an odd number. The first few odd harmonics are [[1/1]], [[3/1]], [[5/1]], [[7/1]], [[9/1]], [[11/1]], etc. Odd harmonics are significant in that they create distinct [[pitch class]]es, since any even harmonic is a whole number of [[octave]]s above an odd harmonic.

			An [[odd limit]] is the set of all [[just interval]]s where the largest odd factor in the numerator and denominator both do not exceed a specified bound. For example, the [[5-odd-limit]] consists of all ratios where the only allowable odd factors are 1, 3, and 5; those being [[1/1]], [[6/5]], [[5/4]], [[4/3]], [[3/2]], [[8/5]], [[5/3]], and any whole number of octaves above those intervals.

			We can also restrict the set of usable intervals to only allow odd harmonics. Such intervals include [[3/1]], [[5/3]], [[9/7]], [[27/25]], etc. Here, using [[3/1]] as the [[interval of equivalence]] (a "tritave") is natural, since the 3rd harmonic is the smallest odd harmonic after the fundamental. [[Edt]]s divide the tritave into a whole number of equal steps, analogous to how [[edo]]s divide the octave.

			== Prime harmonic ==
			{{See also\|Category:Prime harmonics}}
			A '''prime interval''' or '''prime harmonic''' is a harmonic which as a [[ratio]] of frequencies is a [[prime number]]; that is, a number such as 2, 3, 5, 7, 11, … which is divisible only by itself and 1.

			Any interval of [[just intonation\|just intonation (JI)]] can be expressed in terms of a product of prime intervals, allowing us to decompose a complex JI interval into simpler parts. A prime interval itself cannot be expressed by other prime intervals, so no prime intervals are redundant for reconstructing the entirety of JI. For those reasons and for the fact that prime intervals occur in [[harmonic series]], they form a very important [[basis]] (literally and mathematically) for JI.

			For example, the [[octave]] is a prime interval whereas the intervals [[5/3]] or even [[1/1]] are not. In traditional ratio notation, the prime intervals are [[2/1]], [[3/1]], [[5/1]], [[7/1]], [[11/1]] etc.

			The [[monzo]] notation of each prime interval consists of all-zeros except for a single entry equal to 1: (2: {{monzo\| 1 }}, 3: {{monzo\| 0 1 }}, 5: {{monzo\| 0 0 1 }}, 7: {{monzo\| 0 0 0 1 }}, 11: {{monzo\| 0 0 0 0 1 }}, …)

			== Highly composite harmonic ==
			{{See also\|Category:Highly composite harmonics}}
			A '''highly composite interval''' or '''highly composite harmonic''' is a harmonic which has a [[ratio]] of frequencies is a [[highly composite number]]; that is, a number such as 1, 2, 4, 6, 12, … each of which has more divisors than the number before it.

			Highly composite intervals are significant for having the largest number of ways to be approached through [[harmonic]] [[chord]]s for its size.

			Highly composite intervals can be thought of as the opposite of prime harmonics, since highly composite numbers are "antiprime", but they are not complementary sets, as they share a common element (2/1) and there are infinitely many harmonics which are neither prime nor highly composite.

	== See also ==		== See also ==
	* [[Mixed timbre]]		* [[Mixed timbre]]
	* [[Prime interval]]
	* [[Odd harmonic]]

	[[Category:Harmonic\| ]] <!-- main article -->		[[Category:Harmonic\| ]] <!-- main article -->
	[[Category:Psychoacoustics]]		[[Category:Psychoacoustics]]
	[[Category:Terms]]		[[Category:Terms]]

Fredg999: Internal link

2026-07-27T04:17:59Z

Internal link

← Older revision		Revision as of 04:17, 27 July 2026
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	A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].		A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].

	The timbre of a periodic sound, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f''... where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The span between any two of these harmonics is a [[just interval]]. If the harmonics are numbered such that the fundamental is number 1, the octave is 2, etc., then the interval's ratio is given by the two numbers. For example the interval between the 3rd and 4th harmonics is 4/3.		The timbre of a periodic sound, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f''... where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The [[span]] between any two of these harmonics is a [[just interval]]. If the harmonics are numbered such that the fundamental is number 1, the octave is 2, etc., then the interval's ratio is given by the two numbers. For example the interval between the 3rd and 4th harmonics is 4/3.

	The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.		The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.

FloraC: + links

2026-03-18T09:48:43Z

+ links

← Older revision		Revision as of 09:48, 18 March 2026
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	== See also ==		== See also ==
	* [[Mixed timbre]]		* [[Mixed timbre]]
			* [[Prime interval]]
			* [[Odd harmonic]]

	[[Category:Harmonic\| ]] <!-- main article -->		[[Category:Harmonic\| ]] <!-- main article -->
	[[Category:Psychoacoustics]]		[[Category:Psychoacoustics]]
	[[Category:Terms]]		[[Category:Terms]]

TallKite: added a sentence about the importance of calling the fundamental, not the octave, the first harmonic.

2025-05-15T02:29:30Z

added a sentence about the importance of calling the fundamental, not the octave, the first harmonic.

← Older revision		Revision as of 02:29, 15 May 2025
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	A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].		A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].

	The timbre of a periodic sound, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f''... where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The span between any two of these harmonics is ~~called~~ a [[just interval]].		The timbre of a periodic sound, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f''... where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The span between any two of these harmonics is a [[just interval]]. If the harmonics are numbered such that the fundamental is number 1, the octave is 2, etc., then the interval's ratio is given by the two numbers. For example the interval between the 3rd and 4th harmonics is 4/3.

	The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.		The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.

Sintel: "harmonic oscillator" means something else

2025-05-14T22:55:56Z

"harmonic oscillator" means something else

← Older revision		Revision as of 22:55, 14 May 2025
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	A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].		A '''harmonic''' is a whole-number multiple of the fundamental frequency of a sound. It is an element of the [[harmonic series]].

	The timbre of ~~harmonic oscillators~~, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f''... where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The span between any two of these harmonics is called a [[just interval]].		The timbre of a periodic sound, such as a bowed violin or the human voice, contains a nearly infinite amount of harmonic [[partial]]s, starting with 1''f'', 2''f'', 3''f'', 4''f''... where ''f'' is the fundamental frequency. Each of these harmonics has a distinct amplitude, generally decreasing as the 'height' of the harmonic increases. The span between any two of these harmonics is called a [[just interval]].

	The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.		The ancient Greeks called these harmonics "multiples", and considered them to be a unique interval class separate from [[superparticular]] and [[superpartient]] intervals.

FloraC: +link to the category of individual pages

2024-02-21T09:07:15Z

+link to the category of individual pages

← Older revision		Revision as of 09:07, 21 February 2024
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	A '''subharmonic''' is a unit fraction of the fundamental frequency of a sound. It is an element of the [[subharmonic series]].		A '''subharmonic''' is a unit fraction of the fundamental frequency of a sound. It is an element of the [[subharmonic series]].

			== Individual pages ==
			See [[:Category: Harmonics]].

	== See also ==		== See also ==

	* [[Mixed timbre]]		* [[Mixed timbre]]

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

2023-03-02T03:53:56Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 03:53, 2 March 2023
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	[[Category:Psychoacoustics]]		[[Category:Psychoacoustics]]
	[[Category:Terms]]		[[Category:Terms]]
	~~[[Category:Theory]]~~

Fredg999: Categories

2021-12-26T00:38:22Z

← Older revision		Revision as of 00:38, 26 December 2021
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	[[Category:Harmonic\| ]] <!-- main article -->		[[Category:Harmonic\| ]] <!-- main article -->
	[[Category:Psychoacoustics]]		[[Category:Psychoacoustics]]
			[[Category:Terms]]
	[[Category:Theory]]		[[Category:Theory]]