User:Em: Difference between revisions

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[Image]

<small>(For a diagram of the harmonic series up to the 49th partial, see [https://heji.plainsound.org/ The Helmholtz-Ellis JI Pitch Notation Legend and Series])</small>

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

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[Video]

This audio was created using [https://www.klingbeil.com/spear/ Spear]: a free, downloadable spectral analysis software allowing users to explore and edit individual frequencies within recorded sounds.

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

== Mathematical Formula and Ratio Notation ==

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Beginning at the seventh partial, intervals in the harmonic series begin to deviate significantly from what is seen commonly in 12EDO. Therefore, these intervals are referenced based on their relative positions in the harmonic series. 12EDO interval nomenclature (minor third, perfect fifth, etc.) fails to accurately represent these relationships. For instance, the harmonic series contains an infinite number of ''different'' minor thirds. This is why 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 ways one might think of these ratios.

1) 6:5 represents the 6th and 5th partials in the harmonic series

* 6:5 represents the 6th and 5th partials of the harmonic series

** [Image]

[~~image~~]

* 6:5 represents the mathematical relationship between the frequencies of the two pitches

** [Image]

~~2) 6:5 represents~~ the mathematical ~~relationship between the frequencies of the two pitches~~

In reality, these frames of reference are one and the same, given that the harmonic series is itself based on these mathematical relationships.

~~[image]~~

~~In reality, these frames of reference are one and the same, given that the harmonic series is itself based on these mathematical relationships.~~ 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 this very same 6:5 minor third. For more information about how pitch is perceived, see [a page that doesn't exist yet on general psychoacoustics which includes a section explaining how at 20hz, we begin to perceive pitch instead of rhythm.]

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 this very same 6:5 minor third. For more information about how pitch is perceived, see [a page that doesn't exist yet on general psychoacoustics which includes a section explaining how at 20hz, we begin to perceive pitch instead of rhythm.]

=== Terminology ===

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== Advanced Concepts ==

The harmonic series is a fractal, in that it contains an infinite number of harmonic series within it. For example, by isolating every numbered partial with a given factor, one finds that the harmonic series manifests within this subset of the original harmonic series. For example, see the diagram below which isolates every multiple of 5:

=== The Motherchord ===

The harmonic series is a fractal, in that it contains an infinite number of harmonic series within it. For example, by isolating every numbered partial with a given factor, one finds that the harmonic series manifests within this subset of the original harmonic series. For example, see the diagram below which isolates every partial multiple of 5:

[Image]

For more information on this concept, [see the '''motherchord''' section in [[Primodality]] - does not exist yet]

=== 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]]

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

@@ Line 13: / Line 13: @@
 [Image]
+<small>(For a diagram of the harmonic series up to the 49th partial, see [https://heji.plainsound.org/ The Helmholtz-Ellis JI Pitch Notation Legend and Series])</small>
 The lowest frequency (or '''partial''') in a given harmonic series is called the '''fundamental'''. While the fundamental is generally the main audible pitch of a given sound, the harmonic series contains an infinitely proliferating sequence of higher partials called '''overtones'''. With practice, one can learn to hear and identify specific overtones:
@@ Line 32: / Line 34: @@
 [Video]
-This audio was created using [https://www.klingbeil.com/spear/ Spear]: a free, downloadable spectral analysis software allowing users to explore and edit individual frequencies within recorded sounds.
+<small>This audio was created using [https://www.klingbeil.com/spear/ Spear]: a free, downloadable spectral analysis software allowing users to explore and edit individual frequencies within recorded sounds.</small>
 == Mathematical Formula and Ratio Notation ==
@@ Line 42: / Line 44: @@
 Beginning at the seventh partial, intervals in the harmonic series begin to deviate significantly from what is seen commonly in 12EDO. Therefore, these intervals are referenced based on their relative positions in the harmonic series. 12EDO interval nomenclature (minor third, perfect fifth, etc.) fails to accurately represent these relationships. For instance, the harmonic series contains an infinite number of ''different'' minor thirds. This is why 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 ways one might think of these ratios.
-) 6:5 represents the 6th and 5th partials in the harmonic series
+* 6:5 represents the 6th and 5th partials of the harmonic series
+** [Image]
-[image]
+* 6:5 represents the mathematical relationship between the frequencies of the two pitches
+** [Image]
-) 6:5 represents the mathematical relationship between the frequencies of the two pitches
+In reality, these frames of reference are one and the same, given that the harmonic series is itself based on these mathematical relationships.
-[image]
-In reality, these frames of reference are one and the same, given that the harmonic series is itself based on these mathematical relationships. 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 this very same 6:5 minor third. For more information about how pitch is perceived, see [a page that doesn't exist yet on general psychoacoustics which includes a section explaining how at 20hz, we begin to perceive pitch instead of rhythm.]
+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 this very same 6:5 minor third. For more information about how pitch is perceived, see [a page that doesn't exist yet on general psychoacoustics which includes a section explaining how at 20hz, we begin to perceive pitch instead of rhythm.]
 === Terminology ===
@@ Line 60: / Line 62: @@
 == Advanced Concepts ==
-The harmonic series is a fractal, in that it contains an infinite number of harmonic series within it. For example, by isolating every numbered partial with a given factor, one finds that the harmonic series manifests within this subset of the original harmonic series. For example, see the diagram below which isolates every multiple of 5:
+=== The Motherchord ===
+The harmonic series is a fractal, in that it contains an infinite number of harmonic series within it. For example, by isolating every numbered partial with a given factor, one finds that the harmonic series manifests within this subset of the original harmonic series. For example, see the diagram below which isolates every partial multiple of 5:
 [Image]
 For more information on this concept, [see the '''motherchord''' section in [[Primodality]] - does not exist yet]
+=== 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]]
 == See also[edit | edit source] ==