Diatonic hexachord

Diatonic hexachord
Component intervals from root
	major sixth
	perfect fifth
	perfect fourth
	major third
	major second
	root
Forte no. / Complement
	6-32 / 6-32
Interval vector
	<1,4,3,2,5,0>

Last updated January 23, 2026

William Daman (ca.1540-1591) - Ut Re Mi Fa Sol La à3 from XX konincklycke fantasien. Mathysz press, Amsterdam (1648)

Alfonso Ferrabosco the Elder (1543-1588) - Ut re mi fa sol la à3 from John Baldwyne’s Commonplace Book, London. GB-Lbl, R.M.24.d.2 (ca.1590-1606)

Alfonso Ferrabosco the Younger (ca.1575-1628) - Fantasia 'On the Hexachord' à4, VdGS No.10 - The Hexachord Ascending, Oxford. Christ College, Mus.Ms.436 (ca.1630)

Hexachord Fantasias performed by Phillip W. Serna, Treble, Tenor & Bass Viols

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The diatonic, Guidonian, or major hexachord (6-32^[1]^[2]^[3]) is a hexachord consisting of six consecutive pitches from the diatonic scale that are also a consecutive segment of the circle of fifths: F C G D A E = C D E F G A = "do-re-mi-fa-sol-la".

It is the thirty-second hexachord as ordered by Forte number, and its complement is the diatonic hexachord at the tritone. If the circle of fifths transformation is applied to the diatonic hexachord the chromatic hexachord results.^[4] It is source set C.

Hugo Riemann points out that the hexachord consists of three overlapping (diatonic) tetrachords: Lydian, Phrygian, and Dorian; as well as two overlapping pentatonic scales (which are major pentatonic and mixolydian pentatonic).^[5] Richard Crocker made the case that, in the words of Stefano Mengozzi, "the Guidonian hexachord was the most important diatonic unit for practical musicians from the Carolingian era to the seventeenth century".^[6]

More generally diatonic hexachord may refer to any hexachordal subset of the diatonic septad (7-35): 6-Z25, 6-Z26, 6-32, or 6-33. The minor hexachord is 6-33 (0 2 3 5 7 9 = C D E♭ F G A).

References

↑ Morris, Robert (2010). The Whistling Blackbird: Essays and Talks on New Music, p.65. University Rochester Press. ISBN 978-1-58046-349-2.
↑ Chikinda, Michael Wayne (2008). Processes of Redemption and the Aesthetic of the Fragment in the Early Twelve-tone Works of Luigi Dallapiccola, p.66. ISBN 978-0-549-73561-8.
↑ Forte, Allen (1978). The Harmonic Organization of the Rite of Spring, p.34. Yale University Press. ISBN 978-0-300-10537-7.
↑ Babbitt, Milton (1987). Milton Babbitt: Words about Music, p.93. University of Wisconsin Press. ISBN 978-0-299-10794-9.
↑ Riemann, Hugo (1916). Folkloristische Tonalitätsstudien, p.39. Leipzig: Breitkopf und Härtel. Cited in (2011). The Oxford Handbook of Neo-Riemannian Music Theories, p.155-56. ISBN 978-0-19-532133-3.
↑ Crocker, R.L. (1968 and 1972). "Perchè Zarlino diede una nuova numerazione ai modi?", Rivista italiana di musicologia 3: 48-58 and "Hermann's Major Sixth", JAMS 25: 19-37. Cited in: Mengozzi, Stefano (2010). The Renaissance Reform of Medieval Music Theory: Guido of Arezzo Between Myth and History, p.19 (n.2). ISBN 978-0-521-88415-0.

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[1] Morris, Robert (2010). The Whistling Blackbird: Essays and Talks on New Music, p.65. University Rochester Press. ISBN 978-1-58046-349-2.

[2] Chikinda, Michael Wayne (2008). Processes of Redemption and the Aesthetic of the Fragment in the Early Twelve-tone Works of Luigi Dallapiccola, p.66. ISBN 978-0-549-73561-8.

[3] Forte, Allen (1978). The Harmonic Organization of the Rite of Spring, p.34. Yale University Press. ISBN 978-0-300-10537-7.

[4] Babbitt, Milton (1987). Milton Babbitt: Words about Music, p.93. University of Wisconsin Press. ISBN 978-0-299-10794-9.

[5] Riemann, Hugo (1916). Folkloristische Tonalitätsstudien, p.39. Leipzig: Breitkopf und Härtel. Cited in (2011). The Oxford Handbook of Neo-Riemannian Music Theories, p.155-56. ISBN 978-0-19-532133-3.

[6] Crocker, R.L. (1968 and 1972). "Perchè Zarlino diede una nuova numerazione ai modi?", Rivista italiana di musicologia 3: 48-58 and "Hermann's Major Sixth", JAMS 25: 19-37. Cited in: Mengozzi, Stefano (2010). The Renaissance Reform of Medieval Music Theory: Guido of Arezzo Between Myth and History, p.19 (n.2). ISBN 978-0-521-88415-0.

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Diatonic hexachord

See also

References