Sintel: Created page with "An '''undertone scale''' is a scale made from an octave-spanning segment of the subharmonic series, repeated at the octave. It is the inverse of an overtone scale. For example, the subharmonics 16 through 32 form the scale subharmonics 16–32. Undertone scales are also called '''modes of the subharmonic series''', or '''aliquot scales'''.''1/1, The Journal of the Just Intonation Network'', Volume 4, Number 1, Winter 1988, p.6, M..."

2026-10-11T01:41:02Z

Created page with "An '''undertone scale''' is a scale made from an octave-spanning segment of the subharmonic series, repeated at the octave. It is the inverse of an overtone scale. For example, the subharmonics 16 through 32 form the scale subharmonics 16–32. Undertone scales are also called '''modes of the subharmonic series''', or '''aliquot scales'''.<ref>''1/1, The Journal of the Just Intonation Network'', Volume 4, Number 1, Winter 1988, p.6, M..."

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An '''undertone scale''' is a [[scale]] made from an octave-spanning segment of the [[subharmonic series]], repeated at the octave. It is the inverse of an [[overtone scale]]. For example, the subharmonics 16 through 32 form the scale [[Subharmonics 16–32|subharmonics 16–32]]. Undertone scales are also called '''modes of the subharmonic series''', or '''aliquot scales'''.<ref>''1/1, The Journal of the Just Intonation Network'', Volume 4, Number 1, Winter 1988, p.6, Michael Sloper.</ref>

Undertone scales are much less commonly used than overtone scales, and fewer of them have been explored.

== Construction ==
The ''n''th through ''2n''th subharmonics have the frequencies ''1/n'', ''1/(n + 1)'', ..., ''1/(2n)'', relative to the fundamental. Starting on the lowest of these and ascending, they form the ratios

: ''2n/2n'', ''2n/(2n − 1)'', ''2n/(2n − 2)'', ..., ''2n/n''

above the root, which spans one octave. For example, subharmonics 3–6 are 1/1, 6/5, 3/2 and 2/1 (the [[just minor triad]]).

The steps of an undertone scale are [[superparticular]] ratios, as in an overtone scale, but they get larger as the scale ascends (for example 10/9, 9/8, 8/7, 7/6, 6/5 for subharmonics 5–10), whereas the steps of an overtone scale get smaller. In terms of string length, the steps are equal increments of length (see [[EDL]]).

== Relation to overtone scales ==
The undertone scale made of subharmonics ''n''–2''n'' is the inverse of the overtone scale made of harmonics ''n''–2''n'': its intervals are those of the overtone scale in reverse order. So [[Subharmonics 3–6|subharmonics 3–6]] has steps 6/5, 5/4, 4/3, where [[Harmonics 3–6|harmonics 3–6]] has steps 4/3, 5/4, 6/5.

== Terminology ==
The terms ''subharmonic'' and ''undertone'' are used interchangeably here, although they are not exact synonyms; see [[subharmonic series]]. Modes are numbered by subharmonic: mode ''n'' of the subharmonic series is the segment ''n''–2''n''. The label "under-''n''" (''n/'') can be used in the same sense as "over-''n''" (''/n''), see [[Overtone scale#Over-n scales]].

== See also ==
* [[Subharmonic series]]
* [[Overtone scale]]
* [[Otonality and utonality]]
* [[IFDO]]: An alternative framework for describing scales which overlaps substantially with undertone scales

== References ==
<references />

{{Navbox subharmonics}}

[[Category:Undertone scale| ]] 
[[Category:Just intonation]]
[[Category:Scale]]
[[Category:Subharmonic series]]

Undertone scale - Revision history