Harmonic series: Difference between revisions

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The '''harmonic series''' is a sequence of notes generated by whole-number frequency [[ratio]]s over a fundamental: [[1/1]], [[2/1]], [[3/1]], [[4/1]], [[5/1]], [[6/1]], [[7/1]]~~...~~ ad infinitum. Each member of this series is a [[harmonic]] (which is short for "harmonic partial").

The '''harmonic series''' is a sequence of notes generated by whole-number frequency [[ratio]]s over a fundamental: [[1/1]], [[2/1]], [[3/1]], [[4/1]], [[5/1]], [[6/1]], [[7/1]]… ad infinitum. Each member of this series is a [[harmonic]] (which is short for "harmonic partial").

Note that the terms ''overtone'' and '''overtone series''' are not quite synonymous with "harmonic" and "harmonic series". ~~"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 the preferred standard.

Note that the terms ''overtone'' and '''overtone series''' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage are 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.

In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance.

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 {{Wikipedia|Harmonic series (music)}}
-The '''harmonic series''' is a sequence of notes generated by whole-number frequency [[ratio]]s over a fundamental: [[1/1]], [[2/1]], [[3/1]], [[4/1]], [[5/1]], [[6/1]], [[7/1]]... ad infinitum. Each member of this series is a [[harmonic]] (which is short for "harmonic partial").
+The '''harmonic series''' is a sequence of notes generated by whole-number frequency [[ratio]]s over a fundamental: [[1/1]], [[2/1]], [[3/1]], [[4/1]], [[5/1]], [[6/1]], [[7/1]]… ad infinitum. Each member of this series is a [[harmonic]] (which is short for "harmonic partial").
-Note that the terms ''overtone'' and '''overtone series''' are not quite synonymous with "harmonic" and "harmonic series". "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 the preferred standard.
+Note that the terms ''overtone'' and '''overtone series''' are not quite synonymous with ''harmonic'' and ''harmonic series'', respectively, although interchangeable usage are 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.
 In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance.