Subharmonic series: Difference between revisions
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{{Wikipedia|Undertone series}} | {{Wikipedia|Undertone series}} | ||
The '''subharmonic series''' (or '''undertone series''') is a sequence of | The '''subharmonic series''' (or '''undertone series''') is a sequence of [[pitch|tone]]s generated by unit-fraction frequency [[ratio]]s under a fundamental: [[1/1]], 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, ... ad infinitum. Each member of this series is a [[subharmonic]]. The term '''undertone''', which is not an exact synonym, is also used in the same sense by many people, especially because undertones do not occur as partials of a sound's timbre. | ||
== Relation to the harmonic series == | |||
The subharmonic series is the inverse of the [[harmonic series]]. The ''n''th subharmonic lies below the fundamental by the same interval that the ''n''th harmonic lies above it, so every interval of one series has a mirror image in the other. | |||
Each octave-reduced subharmonic is the octave complement of the octave-reduced harmonic with the same number. | |||
{| class="wikitable center-all" | |||
! ''n'' | |||
! Harmonic ''n'' | |||
! Cents | |||
! Subharmonic ''n'' | |||
! Cents | |||
|- | |||
| 3 | |||
| [[3/2]] | |||
| 702.0 | |||
| [[4/3]] | |||
| 498.0 | |||
|- | |||
| 5 | |||
| [[5/4]] | |||
| 386.3 | |||
| [[8/5]] | |||
| 813.7 | |||
|- | |||
| 7 | |||
| [[7/4]] | |||
| 968.8 | |||
| [[8/7]] | |||
| 231.2 | |||
|- | |||
| 9 | |||
| [[9/8]] | |||
| 203.9 | |||
| [[16/9]] | |||
| 996.1 | |||
|- | |||
| 11 | |||
| [[11/8]] | |||
| 551.3 | |||
| [[16/11]] | |||
| 648.7 | |||
|- | |||
| 13 | |||
| [[13/8]] | |||
| 840.5 | |||
| [[16/13]] | |||
| 359.5 | |||
|} | |||
As in the harmonic series, the steps between adjacent members are [[superparticular]] ratios. The interval from the (''n'' + 1)th subharmonic up to the ''n''th is (''n'' + 1)/''n'', so the steps get smaller the further down the series goes. | |||
== Chords and scales == | |||
Any material taken from the subharmonic series is a ''utonality'' in [[Harry Partch]]'s terminology (see [[otonality and utonality]]). For example, the subharmonics 4, 5 and 6, from highest to lowest, are in the ratio 1/6 : 1/5 : 1/4, which is 10:12:15, the just minor triad. It is the utonal counterpart of the major triad 4:5:6 built from the harmonics 4, 5 and 6. | |||
A segment of the series that spans one octave, repeated at the octave, forms an [[undertone scale]], the inverse of an [[overtone scale]]. | |||
== See also == | == See also == | ||
* [[Harmonic series]] | * [[Harmonic series]] | ||
* [[Undertone scale]]s | |||
* [[Otonality and utonality]] | |||
* [[Undertone sequence]] | * [[Undertone sequence]] | ||
* [[Undertone division]] | * [[Undertone division]] | ||
* [[IFDO]] | |||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||
[[Category:Xenharmonic series]] | [[Category:Xenharmonic series]] | ||
[[Category:Subharmonic series]] | [[Category:Subharmonic series]] | ||