The Harmonic Scale is a "Super-Just" musical scale

Musical scale

In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...

 allowing extended just intonation

Just intonation

In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

, beyond 5-limit

Limit (music)

In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...

 to the 19th harmonic

Harmonic

A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

 , and free modulation

Modulation (music)

In music, modulation is most commonly the act or process of changing from one key to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest...

 through the use of synthesizer

Synthesizer

A synthesizer is an electronic instrument capable of producing sounds by generating electrical signals of different frequencies. These electrical signals are played through a loudspeaker or set of headphones...

s. It includes 144 notes per octave

Octave

In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...

 and two circles of fifths

Circle of fifths

In music theory, the circle of fifths shows the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys...

.

For example, if the harmonic scale is tuned to a fundamental

Fundamental frequency

The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...

 of C then C is also the 16th and 32nd harmonic

Harmonic

A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

s, C is the 17th , D the 18th , E the 19th , E the 20th , F the 21st (a natural seventh above G, but not a great interval above C) , F the 22nd , G the 24th , A the 26th , A the 27th (a just fifth above D) , B the 28th , B the 30th , and some harmonics are not included.

It was used invented by Wendy Carlos

Wendy Carlos

Wendy Carlos is an American composer and electronic musician. Carlos first came to notice in the late 1960s with recordings made on the Moog synthesizer, then a relatively new and unknown instrument; most notable were LPs of synthesized Bach and the soundtrack for Stanley Kubrick's film A...

 and used on her album Beauty in the Beast

Beauty in the Beast

Beauty in the Beast is an album by Wendy Carlos using alternate tunings and scales and influenced by jazz and world music. On the back she includes a quote by Van Gogh: "I am always doing what I cannot do yet, in order to learn how to do it."...

(1986). Transpositions and tuning tables are controlled by left-hand on the appropriate note on a one-octave keyboard.