Overtone scale: Difference between revisions

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This page was originally developed by [[Andrew Heathwaite]], but others are welcome to add to it. For another take on the subject, see [[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]. This article focuses on a systematic approach to building modes of the harmonic series and taking subsets of it, with attention paid to the different kinds of relationships available depending on the starting pitch, or tonic notes. It is not concerned with "purity", "consonance", "naturalness" or avoidance of "dissonance." Here, what might be called dissonant is instead called complex, and the reader is encouraged to explore the sounds of harmonic ratios ranging from the simplest to the most complex. This does not mean that the more complex intervals can be treated exactly the same way as the simpler ones, but that different levels of complexity can be valuable to explore in a tuning system. The usefulness of all this is left to each composer to determine through experimentation.

== Introduction - Modes of the Harmonic Series ==

One way of using the [[~~OverToneSeries|~~overtone series]] to generate scalar material is to take an octave-long subset of the series and make it repeat at the octave. So for instance, starting at the fifth overtone and continuing up the sequence to the tenth overtone (which is a doubling of five, and thus an octave higher) produces a pentatonic scale:

One way of using the [[overtone series]] to generate scalar material is to take an octave-long subset of the series and make it repeat at the octave. So for instance, starting at the fifth overtone and continuing up the sequence to the tenth overtone (which is a doubling of five, and thus an octave higher) produces a pentatonic scale:

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 This page was originally developed by [[Andrew Heathwaite]], but others are welcome to add to it. For another take on the subject, see [[Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page]]. This article focuses on a systematic approach to building modes of the harmonic series and taking subsets of it, with attention paid to the different kinds of relationships available depending on the starting pitch, or tonic notes. It is not concerned with "purity", "consonance", "naturalness" or avoidance of "dissonance." Here, what might be called dissonant is instead called complex, and the reader is encouraged to explore the sounds of harmonic ratios ranging from the simplest to the most complex. This does not mean that the more complex intervals can be treated exactly the same way as the simpler ones, but that different levels of complexity can be valuable to explore in a tuning system. The usefulness of all this is left to each composer to determine through experimentation.
 == Introduction - Modes of the Harmonic Series ==
-One way of using the [[OverToneSeries|overtone series]] to generate scalar material is to take an octave-long subset of the series and make it repeat at the octave. So for instance, starting at the fifth overtone and continuing up the sequence to the tenth overtone (which is a doubling of five, and thus an octave higher) produces a pentatonic scale:
+One way of using the [[overtone series]] to generate scalar material is to take an octave-long subset of the series and make it repeat at the octave. So for instance, starting at the fifth overtone and continuing up the sequence to the tenth overtone (which is a doubling of five, and thus an octave higher) produces a pentatonic scale:
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