The harmonic scale is a "super-just"
musical scale allowing extended
just intonation
In music, just intonation or pure intonation is the tuning of musical intervals
Interval may refer to:
Mathematics and physics
* Interval (mathematics), a range of numbers
** Partially ordered set#Intervals, its generalization from numbers to ...
, beyond 5-
limit
Limit or Limits may refer to:
Arts and media
* ''Limit'' (manga), a manga by Keiko Suenobu
* ''Limit'' (film), a South Korean film
* Limit (music), a way to characterize harmony
* "Limit" (song), a 2016 single by Luna Sea
* "Limits", a 2019 ...
to the 19th
harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
(), and free
modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
through the use of
synthesizer
A synthesizer (also spelled synthesiser) is an electronic musical instrument that generates audio signals. Synthesizers typically create sounds by generating waveforms through methods including subtractive synthesis, additive synthesis and ...
s.
Transpositions and
tuning tables are controlled by the left hand on the appropriate note on a one-octave keyboard.
[Milano, Dominic (November 1986)]
"A Many-Colored Jungle of Exotic Tunings"
''Keyboard''.
For example, if the harmonic scale is tuned to a
fundamental of C, then harmonics 16–32 are as follows:
Some harmonics are not included:
23, 25, 29, & 31. The 21st is a natural seventh above G, but not a great interval above C, and the 27th is a just fifth above D.
It was invented by
Wendy Carlos and used on three pieces on her album ''
Beauty in the Beast'' (1986): ''Just Imaginings'', ''That's Just It'', and ''Yusae-Aisae''. Versions of the scale have also been used by
Ezra Sims
Ezra Sims (January 16, 1928 in Birmingham, Alabama — January 30, 2015 in Boston, Massachusetts) was one of the pioneers in the field of microtonal composition. He invented a system of notation that was adopted by many microtonal composers after ...
, Franz Richter Herf and Gosheven.
Number of notes
Though described by Carlos as containing "
144 144 may refer to:
* 144 (number), the natural number following 143 and preceding 145
* AD 144, a year of the Julian calendar, in the second century AD
* 144 BC, a year of the pre-Julian Roman calendar
* 144 (film), ''144'' (film), a 2015 Indian com ...
122distinct pitches to the octave",
the twelve scales include
78 notes per
octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
.
Technically there should then be duplicates and thus 57 pitches . For example, a perfect fifth above G (D) is the major tone above C.
References
External links
Wendy Carlos Harmonic scale, ''Microtonal-Synthesis.com''.
19-limit tuning and intervals
Chromaticism
Musical scales
Wendy Carlos
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