Harmonic major scale
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In music theory, the harmonic major scale is a musical scale which found occasional use during the common practice era and is now occasionally employed, most often in jazz. It was named by Rimsky-Korsakov. In George Russell's Lydian Chromatic Concept it is the fifth mode (V) of the Lydian Diminished scale.
It may be considered as a major scale with the sixth degree lowered, Ionian ♭13, or the harmonic minor scale with the third degree raised. It may also be generated by reversing the succession of intervals in the harmonic minor scale. It contains the following chords types Dom 7 ♭9, Dom 7 ♭9 ♯9(♯5), and dim.
The Harmonic Major scale has its own set of modes, completely separate from the Harmonic Minor, Melodic Minor, and Major modes, depending on which note is taken to be tonic.
For example, an A major scale consists of the notes: A B C♯ D E F♯ G♯; whereas an A harmonic major scale consists of the notes: A B C♯ D E F G♯. Notice the sixth note in the sequence is lowered, from F♯ to F. The A harmonic major scale can also be obtained from the A harmonic minor scale, which is A B C D E F G♯, by raising the C to C♯. The E harmonic major scale may be derived from the A melodic minor scale with a raised fourth: A B C D# E F# G#.
The harmonic major scale may also be considered a synthetic scale, primarily used for implying and relating to various altered chords, with major and minor qualities in each tetrachord. Thus the musical effect of the harmonic major scale is a sound intermediate between harmonic minor and diatonic major, and partaking of both. The harmonic major scale may be used in any system of meantone tuning, such as 19 equal temperament or 31 equal temperament, as well as 12 equal temperament.
One interesting property of this scale is that for any diatonic scale, there is a relative major or minor mode, and if each of these is made harmonic major or harmonic minor, the accidental required in each "harmonic" scale is actually the same note spelled enharmonically. For example, A-flat in C harmonic major and G-sharp in A harmonic minor; i.e., A harmonic minor is an "enharmonic mode" of C harmonic major.
The harmonic major scale has the diatonic thirds property, which means that the interval between notes two steps apart (e.g. C and E, D and F, etc.) are separated by the chromatic interval of three or four semitones. In this sense it generalizes a property of the familiar diatonic scale. There are only seven such scales in equal temperament, including whole tone, hexatonic, diatonic, acoustic, harmonic minor, harmonic major, and octatonic. The harmonic major scale is also one of the five proper seven-note scales of equal temperament. Like five of those other six scales, it is a complete circle of thirds; starting from the tonic the pattern is MmmmMMm, where M is a major third and m is a minor third.
Further reading 
- Peter Burt, The Music of Toru Takemitsu, Cambridge University Press, 2001, ISBN 0-521-78220-1.
- Hewitt, Michael. 2013. Musical Scales of the World. The Note Tree. ISBN 978-0957547001.
- Nikolai Rimsky-Korsakov, Practical Manual of Harmony, Carl Fischer, LLC, 2005, ISBN 978-0-8258-5699-0
- Nicolas Slonimsky, Thesaurus of Scales and Melodic Patterns, Music Sales America; First Edition, 1947, ISBN 978-0-8256-1449-1
- Yamaguchi, Masaya. 2006. The Complete Thesaurus of Musical Scales, revised edition. New York: Masaya Music Services. ISBN 0-9676353-0-6.
- Bret Willmott, Mel Bay's Complete Book of Harmony Theory and Voicing, Mel Bay Publications, 1994, ISBN 1-56222-994-X
- "Dan Haerle: The Jazz Language" Studio P/R, Miami, Florida, USA 1980; "Jazz Improvisation und Pentatonic" advance music, Rottenberg/N 1987. Featuring "logical delibaration" for "harmonic major chord-scale system" cited in Haunschild (2000).
- Dmitri Tymoczko. 2011. A Geometry of Music. New York: Oxford, Chapter 4.
- Burt, Peter (2001). The Music of Toru Takemitsu, p.100-101. ISBN 0-521-78220-1.
- Haunschild, Frank (2000). The New Harmony Book, p.122. ISBN 3-927190-68-3.
- Boyd, Bill (1996). Exploring Traditional Scales and Chords for Jazz Keyboard, p.27. ISBN 0-7935-6168-X.
- Holdsworth, Allan (1994). Just for the Curious, p.6. ISBN 0-7692-2015-0.
- Richard Lawn, Jeffrey L. Hellmer (1996). Jazz: theory and practice, p.43. ISBN 0-88284-722-8.
- Dmitri Tymoczko (2004). "Scale Networks and Debussy." Journal of Music Theory 48.2: 215-292.