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Joined 16 October 2024
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====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.[[File:(a) (e) (i) (o) (u) Video.mov|Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced|alt=|thumb|left]] | 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.[[File:(a) (e) (i) (o) (u) Video.mov|Vocalist sings on alternating vowels as harmonic partials are gradually reintroduced|alt=|thumb|left]] | ||
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== Advanced Concepts== | == Advanced Concepts== | ||
===The | ===The Harmonic Series As A Fractal=== | ||
The 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. | ||
===Prime Partials=== | ===Prime Partials=== | ||
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!Title | !Title | ||
!Author | !Author | ||
|- | |- | ||
|The Arithmetic Of Listening | |The Arithmetic Of Listening | ||
|Gann, Kyle | |Gann, Kyle | ||
|- | |- | ||
| Harmonic Experience: Tonal Harmony From Its Natural Origins to Its Modern Expression | | Harmonic Experience: Tonal Harmony From Its Natural Origins to Its Modern Expression | ||
|Mathieu, W. A. | |Mathieu, W. A. | ||
|- | |- | ||
|An Introduction To the Harmonic Series And Logarithmic Integrals-For High School Students Up To Researchers | |An Introduction To the Harmonic Series And Logarithmic Integrals-For High School Students Up To Researchers | ||
|Olaikhan, Ali | |Olaikhan, Ali | ||
|} | |} | ||