Harmonic: Difference between revisions

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~~{{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]].

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.

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 ==

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== Prime harmonic ==

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 ==

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.

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 {{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]].
-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.
-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 ==
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 == 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]].
@@ Line 29: / Line 31: @@
 == 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.
-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.