User:Em/Harmonic Series - Revision history

Em: Edited wording for clarity and professionalism, as well as for technical precision in the first paragraph. (It was pointed out that I should specify that while the harmonic series is physically real, its manifestation is often imprecise).

2024-10-27T03:25:14Z

Edited wording for clarity and professionalism, as well as for technical precision in the first paragraph. (It was pointed out that I should specify that while the harmonic series is physically real, its manifestation is often imprecise).

← Older revision		Revision as of 03:25, 27 October 2024
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	== Overview ==		== Overview ==
	The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. ~~This phenomenon~~ can be observed in many pitched sounds.		The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. Though its manifestation is often imprecise, the harmonic series can be observed in many pitched sounds.

	The '''fundamental''' is the lowest frequency (or '''partial''') in a given harmonic series. While the fundamental is generally the main audible pitch of a given sound, the harmonic series contains an infinitely proliferating pattern of higher partials, which are called '''overtones'''. With practice, one can learn to hear and identify specific overtones:		The '''fundamental''' is the lowest frequency (or '''partial''') in a given harmonic series. While the fundamental is generally the main audible pitch of a given sound, the harmonic series contains an infinitely proliferating pattern of higher partials, which are called '''overtones'''. With practice, one can learn to hear and identify specific overtones:
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	<small>(For a diagram of the harmonic series up to the 49th partial, see [https://www.diva-portal.org/smash/get/diva2:1869939/FULLTEXT03.pdf The Helmholtz-Ellis JI Pitch Notation Legend and Series])</small>		<small>(For a diagram of the harmonic series up to the 49th partial, see [https://www.diva-portal.org/smash/get/diva2:1869939/FULLTEXT03.pdf The Helmholtz-Ellis JI Pitch Notation Legend and Series])</small>

	=== ~~The~~ Harmonic Series ~~In Real Life~~ ===		=== Manifestations of the Harmonic Series ===
	[[File:Cello natural harmonics.png\|left\|thumb\|Cello Harmonics]]		[[File:Cello natural harmonics.png\|left\|thumb\|Cello Harmonics]]

	==== Musical Instruments ====		==== Musical Instruments ====
	Many musicians are already familiar with the harmonic series, even if they may not realize it. For example: the natural harmonics of a string instrument (bowed or strummed) and the open notes on a French horn are two manifestations of the harmonic series. Using the cello as an example, the low, open C string acts as the fundamental of its harmonic series. In this case, the first available natural harmonic is C one octave up, then G, C, E, G etc. To play these harmonics, one effectively shortens the length of the string, at ratios that match those in the harmonic series.		Many musicians are already familiar with the harmonic series, even if they may not realize it. For example: the natural harmonics of a string instrument (bowed or strummed) and the open notes on a French horn are two manifestations of the harmonic series. Using the cello as an example, the low, open C string acts as the fundamental of its harmonic series. In this case, the first available natural harmonic is C one octave up, then G, C, E, G etc. To play these harmonics, one effectively shortens the length of the string, at ratios that match those in the harmonic series.
	~~Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced~~



	[[File:(a) (e) (i) (o) (u) Video.mov\|thumb\|Singer singing on different vowels as partials are gradually reintroduced\|alt=\|left\|0x0px]]		[[File:(a) (e) (i) (o) (u) Video.mov\|thumb\|Singer singing on different vowels as partials are gradually reintroduced\|alt=\|left\|0x0px]]


	==== Timbre ====		==== Timbre ====
	The harmonic series is also responsible for timbre: one can easily identify the sound of a trumpet, violin, or electric guitar, even if they play the same pitch. This is because while the same set of frequencies is (mostly) present in all these sounds, some partials will be more prominent than others depending on the sound source. This also applies to speech and singing, as different vowel formants are distinguished by their unique harmonic identity.		The harmonic series is also responsible for timbre: It is how one can easily identify the sound of a trumpet, violin, or electric guitar, even if they play the same pitch. This is because while the same set of frequencies is (mostly) present in all these sounds, some partials will be more prominent than others depending on the sound source. This also applies to speech and singing, as different vowel formants are distinguished by their unique harmonic identity.

	In this video, individual harmonic partials are gradually re-introduced to a recording of a singer alternating between different vowels. A psychoacoustic illusion is created where at a certain point, the the individual frequencies are suddenly interpreted by the brain as one, timbrally unique and recognizable sound: the human voice. Also note how the intensity of each partial varies depending on the vowel being sung.		In this video, individual harmonic partials are gradually re-introduced to a recording of a singer alternating between different vowels. A psychoacoustic illusion is created where at a certain point, the the individual frequencies are suddenly interpreted by the brain as one, timbrally unique and recognizable sound: the human voice. Also note how the intensity of each partial varies depending on the vowel being sung.
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	These two frames of reference are fundamentally the same.		These two frames of reference are fundamentally the same.

	~~Interestingly, if~~ one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see [psychoacoustics page that does not exist yet].		If one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see [psychoacoustics page that does not exist yet].

	=== Terminology ===		=== Terminology ===

Em: Em moved page User:Em/HarmonicSeries to User:Em/Harmonic Series: Easier to find

2024-10-25T17:28:26Z

Em moved page User:Em/HarmonicSeries to User:Em/Harmonic Series: Easier to find

← Older revision	Revision as of 17:28, 25 October 2024
(No difference)

Em: .

2024-10-24T02:01:49Z

← Older revision		Revision as of 02:01, 24 October 2024
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	== Overview ==		== Overview ==
	~~Harmonic Series~~
	The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. This phenomenon can be observed in many pitched sounds.		The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. This phenomenon can be observed in many pitched sounds.

Em: .

2024-10-23T20:51:06Z

← Older revision		Revision as of 20:51, 23 October 2024
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	= Harmonic series~~[edit \| edit source]~~ =		= Harmonic series =
	[[Harmonic series#mw-head\|Jump to navigation]][[Harmonic series#searchInput\|Jump to search]]		[[Harmonic series#mw-head\|Jump to navigation]][[Harmonic series#searchInput\|Jump to search]]

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	'''Harmonic series (music)'''		'''Harmonic series (music)'''

	== Prerequisite Knowledge~~[edit \| edit source]~~ ==		== Prerequisite Knowledge ==
	[[Hertz]]		[[Hertz]]

	== Overview~~[edit \| edit source]~~ ==		== Overview ==
	Harmonic Series		Harmonic Series
	The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. This phenomenon can be observed in many pitched sounds.		The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. This phenomenon can be observed in many pitched sounds.
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	<small>(For a diagram of the harmonic series up to the 49th partial, see [https://www.diva-portal.org/smash/get/diva2:1869939/FULLTEXT03.pdf The Helmholtz-Ellis JI Pitch Notation Legend and Series])</small>		<small>(For a diagram of the harmonic series up to the 49th partial, see [https://www.diva-portal.org/smash/get/diva2:1869939/FULLTEXT03.pdf The Helmholtz-Ellis JI Pitch Notation Legend and Series])</small>

	=== The Harmonic Series In Real Life~~[edit \| edit source]~~ ===		=== The Harmonic Series In Real Life ===
	[[File:Cello natural harmonics.png\|left\|thumb\|Cello Harmonics]]		[[File:Cello natural harmonics.png\|left\|thumb\|Cello Harmonics]]

	==== Musical Instruments~~[edit \| edit source]~~ ====		==== Musical Instruments ====
	Many musicians are already familiar with the harmonic series, even if they may not realize it. For example: the natural harmonics of a string instrument (bowed or strummed) and the open notes on a French horn are two manifestations of the harmonic series. Using the cello as an example, the low, open C string acts as the fundamental of its harmonic series. In this case, the first available natural harmonic is C one octave up, then G, C, E, G etc. To play these harmonics, one effectively shortens the length of the string, at ratios that match those in the harmonic series.		Many musicians are already familiar with the harmonic series, even if they may not realize it. For example: the natural harmonics of a string instrument (bowed or strummed) and the open notes on a French horn are two manifestations of the harmonic series. Using the cello as an example, the low, open C string acts as the fundamental of its harmonic series. In this case, the first available natural harmonic is C one octave up, then G, C, E, G etc. To play these harmonics, one effectively shortens the length of the string, at ratios that match those in the harmonic series.
	Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced		Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced
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	[[File:(a) (e) (i) (o) (u) Video.mov\|thumb\|Singer singing on different vowels as partials are gradually reintroduced\|alt=\|left\|0x0px]]		[[File:(a) (e) (i) (o) (u) Video.mov\|thumb\|Singer singing on different vowels as partials are gradually reintroduced\|alt=\|left\|0x0px]]

	==== Timbre~~[edit \| edit source]~~ ====		==== Timbre ====
	The harmonic series is also responsible for timbre: one can easily identify the sound of a trumpet, violin, or electric guitar, even if they play the same pitch. This is because while the same set of frequencies is (mostly) present in all these sounds, some partials will be more prominent than others depending on the sound source. This also applies to speech and singing, as different vowel formants are distinguished by their unique harmonic identity.		The harmonic series is also responsible for timbre: one can easily identify the sound of a trumpet, violin, or electric guitar, even if they play the same pitch. This is because while the same set of frequencies is (mostly) present in all these sounds, some partials will be more prominent than others depending on the sound source. This also applies to speech and singing, as different vowel formants are distinguished by their unique harmonic identity.

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	<small>This audio was created using Spear: a free, downloadable spectral analysis software allowing users to explore and edit individual frequencies within recorded sounds.</small>		<small>This audio was created using Spear: a free, downloadable spectral analysis software allowing users to explore and edit individual frequencies within recorded sounds.</small>

	== Mathematical Formula and Ratio Notation~~[edit \| edit source]~~ ==		== Mathematical Formula and Ratio Notation ==
	The mathematical formula for the harmonic series is simple: each positive-integer multiple of the fundamental frequency represents one overtone. For example, if the fundamental frequency is 100Hz, the partials, in ascending order, will be 100Hz, 200Hz, 300Hz, 400Hz, etc...		The mathematical formula for the harmonic series is simple: each positive-integer multiple of the fundamental frequency represents one overtone. For example, if the fundamental frequency is 100Hz, the partials, in ascending order, will be 100Hz, 200Hz, 300Hz, 400Hz, etc...

	Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. With a new partial at every interval of 100Hz, the number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].		Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. With a new partial at every interval of 100Hz, the number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].

	=== Musical Intervals As Ratios~~[edit \| edit source]~~ ===		=== Musical Intervals As Ratios ===
	Beginning with the seventh partial, intervals in the harmonic series begin to deviate significantly from those used in 12EDO. 12EDO interval nomenclature (minor third, perfect fifth, etc.) fails to accurately represent these relationships because, for instance, the harmonic series contains an infinite number of ''different'' minor thirds. Therefore, it is standard in [[Just intonation\|Just Intonation]] to use ratios (such as 6:5) to refer to a specific ''type'' of minor third. There are two main ways in which one might think of these ratios:		Beginning with the seventh partial, intervals in the harmonic series begin to deviate significantly from those used in 12EDO. 12EDO interval nomenclature (minor third, perfect fifth, etc.) fails to accurately represent these relationships because, for instance, the harmonic series contains an infinite number of ''different'' minor thirds. Therefore, it is standard in [[Just intonation\|Just Intonation]] to use ratios (such as 6:5) to refer to a specific ''type'' of minor third. There are two main ways in which one might think of these ratios:

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	Interestingly, if one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see [psychoacoustics page that does not exist yet].		Interestingly, if one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see [psychoacoustics page that does not exist yet].

	=== Terminology~~[edit \| edit source]~~ ===		=== Terminology ===
	Note that the terms ''overtone'' and ''overtone series'' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage is also attested. Technically speaking, ''overtone series'' excludes the starting fundamental, so the 2nd harmonic is the 1st overtone. Because of that distinction, the math of the "overtone series" is off by one. So, "harmonic series" is arguably the preferred standard. Likewise, the standard way to refer to frequencies in the harmonic series is by using numbered '''partials''' (beginning with the fundamental as the first partial), not overtones.		Note that the terms ''overtone'' and ''overtone series'' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage is also attested. Technically speaking, ''overtone series'' excludes the starting fundamental, so the 2nd harmonic is the 1st overtone. Because of that distinction, the math of the "overtone series" is off by one. So, "harmonic series" is arguably the preferred standard. Likewise, the standard way to refer to frequencies in the harmonic series is by using numbered '''partials''' (beginning with the fundamental as the first partial), not overtones.

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	The [[subharmonic series]] (or undertone series) is the inversion of the harmonic series: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum. The words otonal (referring to overtones) and utonal (referring to undertones) are used to refer to the harmonic and subharmonic series, respectively.		The [[subharmonic series]] (or undertone series) is the inversion of the harmonic series: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum. The words otonal (referring to overtones) and utonal (referring to undertones) are used to refer to the harmonic and subharmonic series, respectively.

	== Advanced Concepts~~[edit \| edit source]~~ ==		== Advanced Concepts ==

	=== The Harmonic Series As A Fractal~~[edit \| edit source]~~ ===		=== The Harmonic Series As A Fractal ===
	The harmonic series contains an infinite number of harmonic series within it. By isolating every numbered partial with a given factor, one finds that an entire harmonic series manifests within this smaller subset of the original harmonic series. [Add example and image]		The harmonic series contains an infinite number of harmonic series within it. By isolating every numbered partial with a given factor, one finds that an entire harmonic series manifests within this smaller subset of the original harmonic series. [Add example and image]

	=== Prime Partials~~[edit \| edit source]~~ ===		=== Prime Partials ===
	Prime-numbered partials are sometime referred to simply as "primes". These partials are of interest because each new prime produces a unique interval not present in any of the lower partials. For more information on this, see: [[Prime interval]]		Prime-numbered partials are sometime referred to simply as "primes". These partials are of interest because each new prime produces a unique interval not present in any of the lower partials. For more information on this, see: [[Prime interval]]

	== Further Reading~~[edit \| edit source]~~ ==		== Further Reading ==
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
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	\|}		\|}

	== See also~~[edit \| edit source][edit \| edit source]~~ ==		== See also ==

	* [[Subharmonic series]]		* [[Subharmonic series]]
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	* [[8th Octave Overtone Tuning]]		* [[8th Octave Overtone Tuning]]

	=== External links~~[edit \| edit source][edit \| edit source]~~ ===		=== External links ===

	* Spectral music article on Wikipedia		* Spectral music article on Wikipedia

Em: .

2024-10-23T20:49:52Z

← Older revision		Revision as of 20:49, 23 October 2024
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	These two frames of reference are fundamentally the same.		These two frames of reference are fundamentally the same.

	Interestingly, if one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see psychoacoustics.		Interestingly, if one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see [psychoacoustics page that does not exist yet].

	=== Terminology[edit \| edit source] ===		=== Terminology[edit \| edit source] ===
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	=== The Harmonic Series As A Fractal[edit \| edit source] ===		=== The Harmonic Series As A Fractal[edit \| edit source] ===
	The harmonic series contains an infinite number of harmonic series within it. By isolating every numbered partial with a given factor, one finds that an entire harmonic series manifests within this smaller subset of the original harmonic series.		The harmonic series contains an infinite number of harmonic series within it. By isolating every numbered partial with a given factor, one finds that an entire harmonic series manifests within this smaller subset of the original harmonic series. [Add example and image]

	=== Prime Partials[edit \| edit source] ===		=== Prime Partials[edit \| edit source] ===

Em: .

2024-10-23T20:48:59Z

← Older revision		Revision as of 20:48, 23 October 2024
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	[[File:(a) (e) (i) (o) (u) Video.mov~~\|center~~\|thumb\|Singer singing on different vowels as partials are gradually reintroduced]]		[[File:(a) (e) (i) (o) (u) Video.mov\|thumb\|Singer singing on different vowels as partials are gradually reintroduced\|alt=\|left\|0x0px]]

	==== Timbre[edit \| edit source] ====		==== Timbre[edit \| edit source] ====

Em: .

2024-10-23T20:48:36Z

New page

= Harmonic series[edit | edit source] =
[[Harmonic series#mw-head|Jump to navigation]][[Harmonic series#searchInput|Jump to search]]

English Wikipedia has an article on:

'''Harmonic series (music)'''

== Prerequisite Knowledge[edit | edit source] ==
[[Hertz]]

== Overview[edit | edit source] ==
Harmonic Series
The harmonic series describes a pattern of frequencies naturally occurring as a real, physical (not theoretical or psychoacoustic) phenomenon. This phenomenon can be observed in many pitched sounds.

The '''fundamental''' is the lowest frequency (or '''partial''') in a given harmonic series. While the fundamental is generally the main audible pitch of a given sound, the harmonic series contains an infinitely proliferating pattern of higher partials, which are called '''overtones'''. With practice, one can learn to hear and identify specific overtones:

[https://www.youtube.com/watch?v=hDLhe-NkH2A&ab_channel=mannfishh Learn To Hear Harmonics!! By Mannfish]

The approach of creating music based on intervallic relationships derived from the harmonic series relationships is called [[Just intonation|Just Intonation]].

(For a diagram of the harmonic series up to the 49th partial, see [https://www.diva-portal.org/smash/get/diva2:1869939/FULLTEXT03.pdf The Helmholtz-Ellis JI Pitch Notation Legend and Series])

=== The Harmonic Series In Real Life[edit | edit source] ===
[[File:Cello natural harmonics.png|left|thumb|Cello Harmonics]]

==== Musical Instruments[edit | edit source] ====
Many musicians are already familiar with the harmonic series, even if they may not realize it. For example: the natural harmonics of a string instrument (bowed or strummed) and the open notes on a French horn are two manifestations of the harmonic series. Using the cello as an example, the low, open C string acts as the fundamental of its harmonic series. In this case, the first available natural harmonic is C one octave up, then G, C, E, G etc. To play these harmonics, one effectively shortens the length of the string, at ratios that match those in the harmonic series.
Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced

[[File:(a) (e) (i) (o) (u) Video.mov|center|thumb|Singer singing on different vowels as partials are gradually reintroduced]]

==== Timbre[edit | edit source] ====
The harmonic series is also responsible for timbre: one can easily identify the sound of a trumpet, violin, or electric guitar, even if they play the same pitch. This is because while the same set of frequencies is (mostly) present in all these sounds, some partials will be more prominent than others depending on the sound source. This also applies to speech and singing, as different vowel formants are distinguished by their unique harmonic identity.

In this video, individual harmonic partials are gradually re-introduced to a recording of a singer alternating between different vowels. A psychoacoustic illusion is created where at a certain point, the the individual frequencies are suddenly interpreted by the brain as one, timbrally unique and recognizable sound: the human voice. Also note how the intensity of each partial varies depending on the vowel being sung.

This audio was created using Spear: a free, downloadable spectral analysis software allowing users to explore and edit individual frequencies within recorded sounds.

== Mathematical Formula and Ratio Notation[edit | edit source] ==
The mathematical formula for the harmonic series is simple: each positive-integer multiple of the fundamental frequency represents one overtone. For example, if the fundamental frequency is 100Hz, the partials, in ascending order, will be 100Hz, 200Hz, 300Hz, 400Hz, etc...

Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. With a new partial at every interval of 100Hz, the number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].

=== Musical Intervals As Ratios[edit | edit source] ===
Beginning with the seventh partial, intervals in the harmonic series begin to deviate significantly from those used in 12EDO. 12EDO interval nomenclature (minor third, perfect fifth, etc.) fails to accurately represent these relationships because, for instance, the harmonic series contains an infinite number of ''different'' minor thirds. Therefore, it is standard in [[Just intonation|Just Intonation]] to use ratios (such as 6:5) to refer to a specific ''type'' of minor third. There are two main ways in which one might think of these ratios:

* 6:5 represents the 6th and 5th partials of the harmonic series
* 6:5 is the mathematical ratio of the two pitches' frequencies (600Hz and 500Hz, for example).

These two frames of reference are fundamentally the same.

Interestingly, if one were to record themself clapping a 6:5 polyrhythm (6 eighth notes over an eighth note quintuplet), then speed up the audio by a factor of 1000, one would hear the same 6:5 minor third described above. For more information about how pitch is perceived, see psychoacoustics.

=== Terminology[edit | edit source] ===
Note that the terms ''overtone'' and ''overtone series'' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage is also attested. Technically speaking, ''overtone series'' excludes the starting fundamental, so the 2nd harmonic is the 1st overtone. Because of that distinction, the math of the "overtone series" is off by one. So, "harmonic series" is arguably the preferred standard. Likewise, the standard way to refer to frequencies in the harmonic series is by using numbered '''partials''' (beginning with the fundamental as the first partial), not overtones.

Also note that interval ratios are always notated with the greater number first. In order to change the order of the two pitches, one must use the ratio's '''reciprocal.''' For example, to represent a major sixth instead of a minor third, one must notate the interval as 10:6, not 5:6.

The [[subharmonic series]] (or undertone series) is the inversion of the harmonic series: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7... ad infinitum. The words otonal (referring to overtones) and utonal (referring to undertones) are used to refer to the harmonic and subharmonic series, respectively.

== Advanced Concepts[edit | edit source] ==

=== The Harmonic Series As A Fractal[edit | edit source] ===
The harmonic series contains an infinite number of harmonic series within it. By isolating every numbered partial with a given factor, one finds that an entire harmonic series manifests within this smaller subset of the original harmonic series.

=== Prime Partials[edit | edit source] ===
Prime-numbered partials are sometime referred to simply as "primes". These partials are of interest because each new prime produces a unique interval not present in any of the lower partials. For more information on this, see: [[Prime interval]]

== Further Reading[edit | edit source] ==
{| class="wikitable"
|+
!Title
!Author
|-
|The Arithmetic Of Listening
|Gann, Kyle
|-
|Harmonic Experience: Tonal Harmony From Its Natural Origins to Its Modern Expression
|Mathieu, W. A.
|-
|An Introduction To the Harmonic Series And Logarithmic Integrals-For High School Students Up To Researchers
|Olaikhan, Ali
|}

== See also[edit | edit source][edit | edit source] ==

* [[Subharmonic series]]
* [[Gallery of just intervals]]
* [[Isoharmonic chords]]
* [[First Five Octaves of the Harmonic Series]]
* [[Overtone scales]]
* [[List of octave-reduced harmonics]]
* [[Prime harmonic series]]
* [[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]
* [[8th Octave Overtone Tuning]]

=== External links[edit | edit source][edit | edit source] ===

* Spectral music article on Wikipedia
* www.naturton-musik.de [<nowiki/>[[:Category:Pages containing dead links|''dead link'']]] - web site dedicated to overtone music (by Austrian composer Johannes Kotschy) - a lot of theory material and practical guides to write music based on the overtone series
* Overtone music network - a portal for overtone music.
* Oberton-Netzwerk (Xing) [<nowiki/>[[:Category:Pages containing dead links|''dead link'']]] - German-speaking group dedicated to overtone music on the social network platform Xing. Microtonal music in general is welcome, too.