Harmonic series: Difference between revisions

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The '''harmonic series''' ~~(or '''overtone 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]]; the ~~term~~ ''overtone'', ~~which~~ is ~~not an exact synonym~~, is ~~also used in~~ the ~~same sense by many people~~.

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.

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

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* Tuning to the first several harmonics over one fundamental;

* Tuning to an octave-repeating slice of the harmonic series for use as a scale (for instance ~~overtones~~ 8 though 16, [[otones12-24|12 through 24]], [[otones20-40|20 through 40]]... see [[overtone scales]]);

* Tuning to an octave-repeating slice of the harmonic series for use as a scale (for instance harmonics 8 though 16, [[otones12-24|12 through 24]], [[otones20-40|20 through 40]]... see [[overtone scales]]);

* Tuning to the overtones of the overtones & the undertones of the undertones. (This can produce complex scales such as [[Harry Partch]]'s 43-tone Monophonic; this kind of thing is more often called "just intonation" than "overtone music".)

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 {{Wikipedia|Harmonic series (music)}}
-The '''harmonic series''' (or '''overtone 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]]; the term ''overtone'', which is not an exact synonym, is also used in the same sense by many people.
+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.
 In [[just intonation]] theory, the harmonic series is often treated as the foundation of consonance.
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 * Tuning to the first several harmonics over one fundamental;
-* Tuning to an octave-repeating slice of the harmonic series for use as a scale (for instance overtones 8 though 16, [[otones12-24|12 through 24]], [[otones20-40|20 through 40]]... see [[overtone scales]]);
+* Tuning to an octave-repeating slice of the harmonic series for use as a scale (for instance harmonics 8 though 16, [[otones12-24|12 through 24]], [[otones20-40|20 through 40]]... see [[overtone scales]]);
 * Tuning to the overtones of the overtones & the undertones of the undertones. (This can produce complex scales such as [[Harry Partch]]'s 43-tone Monophonic; this kind of thing is more often called "just intonation" than "overtone music".)