(from Gk. hex: ‘six’, chordē: ‘string’).
A
term denoting a series of six notes ascending stepwise through two whole tones,
a semitone and two further whole tones, used as a complement to the eight-note
diatonic system (including B
and B
) in the teaching of practical music and music
theory, and thus in composition (particularly in the later period), from the
Middle Ages to the 17th century. The six notes of a hexachord are named after
the first syllables of the lines of the hymn Ut queant laxis: ut,
re, mi, fa, sol, la.
The concept of the hexachord as a mnemonic device for teaching plainchant melodies was first described by Guido of Arezzo, who expanded the tetrachordal structuring of melodies (deriving from the Greek tonal system) to include one tone either side of the tetrachords on A and D (Micrologus). The lowest note of the system was the note below A, indicated by the Greek letter Γ (gamma); the hexachordal ranges were from Γ (G) to E and from C to A. In his Epistola de ignoto cantu he defined the abstract tonal relationships between different six-note groups, showing how their intervallic similarities meant that they could be defined by the same group of six syllables, introducing for the purpose the syllables from Ut queant laxis (see Theory, theorists, fig.2). Thus mi-fa, the only semitone in such a group, became a central point of reference, and any note could be defined in relation to those around it by the use of the note-name with the ‘solmization’ syllable (vox) – hence ‘d re’, ‘a re’ and also ‘g re’. This enabled the singer to conceptualize intervallic relationships within any melody. Such practice was related to the wide-ranging use of the hand for the demonstration of melodic intervals, traditionally attributed to Guido but probably not introduced by him, by which each degree was assigned to one of the joints of the hand and fingers.
Johannes Cotto in his De Musica attested the rapid dissemination in other parts of Europe of the practice of learning melodies by syllables; alternative sets of syllables were also used (see Solmization, §I, 1). Johannes suggested that the student use his hand to ‘test, correct or compose’ a melody, thus expanding its use to encompass all the needs of the music practitioner. Guido's contemporaries continued to work in the tetrachordal system (using the syllables ut–fa), although Crocker has argued that the major 6th as discussed by Hermannus Contractus was identical to the hexachord. In any case, the hexachord system developed in the 11th century from the traditional tetrachordal structure.
Melodies
that exceeded the range of a 6th required an expansion to another hexachord by
means of mutation. The hexachord on C became the point of reference and was
named hexachordum naturale. A progression by semitone above A was marked
by the ‘soft’ or rounded letter B (), and the ensuing hexachord on F ut, with A–B solmized mi–fa, was
named the hexachordum molle. A progression by a tone above A required
the ‘hard’ or square B (), with B–C solmized mi–fa, using the hexachordum
durum. The entire gamut was covered by seven hexachords, with each note
named by the solmization syllables of the hexachord or hexachords to which it
belonged (for a table of the hexachords see Solmization,
§I, table 2). This tri-hexachordal system was fully described in
13th-century treatises. Engelbert of Admont (De musica) delineated both
the process of stepwise mutations beyond la as well as the solmization
of leaps by 7ths (GerbertS, ii, 324–5), and there are also descriptions
by Elias Salomo and Hieronymus de Moravia.
In
the 14th century the hexachordal system was expanded in response to an
increased use of signed accidentals (the and 
signs are later derivations of the square B sign);
from the beginning of the 14th century music using such notes was called Musica
ficta. Petrus
frater dictus Palma ociosa stated in his Compendium de discantu mensurabili
(1336) that the introduction of a ficta degree involves a mutation into
a ficta hexachord (ex.1). The anonymous author of the
Berkeley treatise (Ellsworth anonymi, US-BEm 744; c1375) expanded
the gamut to F below Γ, thus forming an eighth hexachord which is
not ‘in usu’ but ‘in arte’: that is, not part of the Greek system but
artificially formed. In this way the low B (gravis) became a recta
degree. The Berkeley treatise also introduced the term coniuncta for the
note that is common to two conjunct hexachords, and this term also came to
delineate the expansion of the hexachordal system, whereby, for instance, B fa of the hexachordum
molle could become ut-fa of a new conjunct hexachord, leading to a
new note fa above D mi, which we would today call E. Furthermore, the Berkeley treatise
discusses ‘disjunct’ movement from one hexachord to another, ‘without whatever
mutation of syllables might be possible there’ (Ellsworth, pp.48–9).
Although
Prosdocimus de Beldemandis (early 15th century) discussed notes of musica
ficta as separate degrees with no reference to hexachords (Herlinger), the
basic tri-hexachord system remained as standard in the 15th century, with
dependence on the sign (either
as a staff signature or before a particular note or passage) to determine
whether the hexachordum molle should be used (otherwise the hexachordum
naturale and hexachordum durum were assumed), a practice dating from
at least the mid-13th century. On the other hand, a or sign could be used without a change of hexachord,
as described in a number of sources from the 14th to 16th centuries – a note
prefixed with either of these signs was never solmized as mi, but may be
either ut, fa or sol temporarily raised by a semitone.
This system was in use well into the 16th century, but there were signs of
simplification in the second half of the 15th century when it became acceptable
for the sign to be
solmized as fa without a change of hexachord being necessary. Further
simplifications led ultimately to systems of Solmization still in use today.
From the end of the 15th century the hexachord was used as the thematic basis for compositions, the mass and the instrumental fantasia being the two forms for which the hexachord was most frequently used. The earliest hexachord mass is Brumel's Missa ‘Ut re mi fa sol la’ (1503); later masses with the same title were composed by Morales and Palestrina, among others. The hexachordal instrumental fantasia was a slightly later development, one of the most extreme examples being the work Ut re mi fa sol la by Alfonso Ferrabosco (ii), based on a series of hexachords, ascending in the first section and descending in the second, that are transposed on each repetition by a semitone. This composition was one in a line of similar works by composers from Bull to Sweelinck; Frescobaldi also composed a number of Capricci on a hexachordal theme (see also Inganno (i)).
The hexachord retained its status even when its relevance was increasingly questioned. Mattheson's request to dispense with both hexachords and modes (Das neu-eröffnete Orchestre, 1713) was angrily challenged by Fux, leading to Mattheson's mocking riposte of 1717, Das beschützte Orchestre (J. Lester, CMc, xxiv, 1977, pp.37–62).
For the use of the term hexachord in connection with twelve-note music, see Serialism and Twelve-note composition.
Guido of Arezzo: Micrologus, GerbertS, ii, 2; also ed. J. Smits van Waesberghe, CSM, iv (1955); Eng. trans. in Hucbald, Guido, and John on Music: Three Medieval Treatises, ed. C.V. Palisca (New Haven, CT, 1978)
Guido of Arezzo: Epistola de ignoto cantu, GerbertS, ii, 43–50; partial Eng. trans. in StrunkSR; ed. and trans. in D. Pesce: Guido D’Arezzo’s Regule rithmice, Prologus in antiphonarium, and Epistola and michahelem (Ottowa, 1999)
Hermannus Contractus: Musica, ed. and trans. L. Ellinwood (Rochester, NY, 1936)
E. Salomo: Scientia artis musice, GerbertS, iii, 16–64
Hieronymus de Moravia: Summa, CoussemakerS, i, 1–155; also ed. S.M. Cserba (Regensburg, 1935)
W. Odington: Summa de speculatione musice, ed. F.F. Hammond, CSM, xiv (1970)
Engelbert of Admont: De musica, GerbertS, ii, 323b–8a
Ellsworth anonymi, ed. and trans. O. Ellsworth, GLMT, ii (1984)
Tractatus de musica plana, anon., CoussemakerS, ii, 434–83
Prosdocimus de Beldemandis: Contrapunctus, CoussemakerS, iii, 193–9; ed. and trans. J. Herlinger, GLMT, i (1984)
Ugolino of Orvieto: Declaratio musicae disciplinae, ed. A. Seay, CSM, vii (1959–62), partial Eng. trans. in A. Hughes: Manuscript Accidentals: Ficta in Focus 1350–1450, MSD, xxvii (1972), 29–40
J. Tinctoris: Expositio manus, CoussemakerS, iv; trans. A. Seay, JMT, ix (1965), 194–232; ed. A. Seay, CSM, xxii/1 (1975), 31–57
Adam von Fulda: De musica, GerbertS, iii, 329
F. Gaffurius: Practica musicae (Milan, 1496/R), Eng. trans, MSD, xx (1969); ed. and trans. I. Young (Madison, WI, 1969)
MGG2 (C. Berger, J.J. Dean)
StrohmR
H. Oesch: Guido von Arezzo: Biographisches und Theoretisches unter besonderer Berücksichtigung der sogenannten odonischen Traktate (Berne, 1954)
J. Smits van Waesberghe: Musikerziehung, Musikgeschichte in Bildern, iii/3 (Leipzig, 1969)
G. Allaire: The Theory of Hexachords, Solmization and the Modal System: a Practical Application, MSD, xxiv (1972)
R. Crocker: ‘Hermann's Major Sixth’, JAMS, xxv (1972), 17–37
J. Hirshberg: ‘Hexachordal and Modal Structure in Machaut's Polyphonic Chansons’, Studies in Musicology in Honor of Otto E. Albrecht, ed. J.W. Hill (Kassel, 1980), 19–42
B.J. Harden: Sharps, Flats and Scribes: ‘Musica ficta’ in the Machaut Manuscripts (diss., Cornell, U., 1983)
D. Leech-Wilkinson: ‘Machaut's Rose, lis and the Problem of Early Music Analysis’, MAn, iii (1984), 9–28
M. Bent: ‘Diatonic Ficta’, EMH, iv (1984), 9–48
D. Pesce: ‘B-Flat Transposition or Transformation’, JM, iv (1985–6), 330–49
K. Berger: Musica ficta: Theories of Accidental Inflection in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino (Cambridge, 1987)
B.R. Carvell: ‘Notes on “una nota super la”’, Music from the Middle Ages through the Twentieth Century: Essays in Honor of Gwynn S. McPeek, ed. C.P. Comberiati and M.C. Steel (New York, 1988), 94–111
M. Bernhard: ‘Das musikalische Fachschrifttum im lateinischen Mittelalter’, Rezeption des antiken Fachs im Mittelalter, Geschichte der Musiktheorie, ed. F. Zaminer, iii (Darmstadt, 1990), 37–103
K.J. Sachs: ‘Musikalische Elementarlehre im Mittelalter’, ibid., 105–62
B. Sydow-Saak: ‘Musica falsa/musica ficta’ (1990), HMT
K.W. Niemöller: ‘Deutsche Hexachordkompositionen im Lichte der Musiktheorie und in ihrem europäischen Kontext’, Von Isaac bis Bach: Festschrift Martin Just, ed. F. Heidlberger, W. Osthoff and R. Wiesend (Kassel, 1991), 127–37
C. Page, ed. and trans: The Summa musice: a Thirteenth-Century Manual for Singers (Cambridge, 1991)
C. Berger: Hexachord, Mensur und Tonstruktur: Studien zum französichen Lied des 14. Jahrhunderts (Stuttgart, 1992)
J. Lester: Compositional Theory in the 18th Century (Cambridge, MA, 1992)
R. Toft: Aural Images of Lost Traditions: Sharps and Flats in the Sixteenth Century (Toronto, 1992)
P. Lefferts: ‘Signature Systems and Tonal Types in the Fourteenth-Century French Chanson’, PMM, iv (1995), 117–47
J. Hirshberg: ‘The Exceptional as an Indicator of the Norm’, Modalität in der Musik des 14. und 15. Jahrhunderts/Modality in the Music of the Fourteenth and Fifteenth Centuries, ed. U. Günther and J. Dean, MSD, xlix (1996), 53–64
M. Bent: ‘Diatonic Ficta Revisited: Josquin's Ave Maria in Context’, Music Theory Online, ii/6 (1996)
Y. Plumley: The Grammar of 14th Century Melody: Tonal Organization and Compositional Process in the Chansons of Guillaume de Machaut and the Ars Subtilior (New York, 1996)
JEHOASH HIRSHBERG/R