Harmonic Scale

Harmonic series on C, partials 1-5 numbered <phonos file="Harmonic series klang.mid">Play</phonos>.

File:Harmonic series klang G.png

Harmonic series on G, partials 1-5 numbered .

The Harmonic Scale is a "super-Just" musical scale allowing extended just intonation, beyond 5-limit to the 19th harmonic (<phonos file="19th harmonic on C.mid">Play</phonos>), and free modulation through the use of synthesizers. Transpositions and tuning tables are controlled by the left hand on the appropriate note on a one-octave keyboard.

For example, if the harmonic scale is tuned to a fundamental of C then harmonics 16-32 are as follows:

Notation			Harmonics	Cents
C	C	C	<phonos file="Unison on C.mid">16</phonos>	0
C♯	C17♯	D♭	<phonos file="Minor diatonic semitone on C.mid">17</phonos>	104.96
D	D	D♮	<phonos file="Major tone on C.mid">18</phonos>	203.91
E♭	E19♭	E♭	<phonos file="19th harmonic on C.mid">19</phonos>	297.51
E♮	E♮	E↓	<phonos file="Just major third on C.mid">20</phonos>	386.31
F	F+	F	<phonos file="Twenty-first harmonic on C.mid">21</phonos>	470.78
F♯	F↑	Fx14px♯	<phonos file="Eleventh harmonic on C.mid">22</phonos>	551.32
G	G	G	<phonos file="Just perfect fifth on C.mid">24</phonos>	701.96
A♭	A♭	A♭	<phonos file="Tridecimal neutral sixth on C.mid">26</phonos>	840.53
A♮	A♮+	A♮	<phonos file="Pythagorean major sixth on C.mid">27</phonos>	905.87
B♭	B♭	B♭	<phonos file="Harmonic seventh on C.mid">28</phonos>	968.83
B♮	B♮	B♮↓	<phonos file="Just major seventh on C.mid">30</phonos>	1088.27
C'	C'	C'	<phonos file="Perfect octave on C.mid">32</phonos>	1200

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.

File:Harmonic scale chromatic on C and G.png

Harmonic Scales chromatic on C and G.

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 and Frans Richter Herf.

Number of notes

Though described by Carlos as containing, "144 [=12²] distinct pitches to the octave," the twelve scales include 78 (=^12(12+1)⁄₂) notes per octave.

Technically there should then be duplicates and thus 57 (=78-21) pitches (21=⁶⁽⁶⁺¹⁾⁄₂). For example, a perfect fifth above G (D) is the major tone above C.

External links

• "Wendy Carlos Harmonic scale", Microtonal-Synthesis.com.