Twelfth complement

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Analogous to the octave complement, the twelfth or tritave complement of a given twelfth-reduced interval is its interval distance from the perfect twelfth (3/1). It seems to be very useful as a way of conceptualizing and constructing semiquartal triads in extended voices, and even as a way of describing the relationships between different hemitwelfths.


The thought that the minor seventh and the major sixth complement or contrast each other is discussed in Flora Canou's 2022 essay Analysis on the 13-limit Just Intonation Space: Episode I. In "Chapter VII. Septimal Chord Construction", it is suggested that the triads 1–7/4–3 and 1–12/7–3 are the septimal counterparts of the classical triads and that they come out superior to 1–7/6–4/3 and 1–8/7–4/3, which are formed on fourth complements.


The following interval pairs are twelfth complementary to each other

See also