User:Em/Harmonic Series: Difference between revisions

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== 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:

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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>

=== ~~The~~ Harmonic Series ~~In Real Life~~ ===

=== Manifestations of the Harmonic Series ===

[[File:Cello natural harmonics.png|left|thumb|Cello Harmonics]]

==== 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.

~~Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced~~

==== 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.

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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 ===

@@ Line 10: / Line 10: @@
 == 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:
@@ Line 20: / Line 20: @@
 <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]]
 ==== 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.
-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]]
 ==== 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.
@@ Line 51: / Line 51: @@
 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 ===