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The half diminished scale is a seven-note musical scale. It is more commonly known as the Locrian 2 scale or the Aeolian 5 scale, names that avoid confusion with the diminished scale and the half-diminished seventh chord (minor seventh, diminished fifth). It is the sixth mode of the ascending melodic minor scale. : In the key of B, the half-diminished scale built on C is associated with C m75, which functions as a ii 7 chord in minor (see
chord-scale system The chord-scale system is a method of matching, from a list of possible chord (music), chords, a list of possible scale (music), scales.Mervyn Cooke, David Horn (2003). ''Cambridge Companions to Music, The Cambridge Companion to Jazz'', p.266. . ...
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References

Heptatonic scales Modes (music) Hemitonic scales Tritonic scales {{music-theory-stub