hexachordum durum

hexachord, in music, six-note pattern corresponding to the first six tones of the major scale (as, C–D–E–F–G–A). The names of the degrees of the hexachord are ut, re, mi, fa, sol, and la (also called solmization [q.v.] syllables); they were devised by the 11th-century teacher and theorist Guido of Arezzo.

A kindred example is d-b-c[#]-d-c[#]-d-d, which might be sung in the hard hexachord as sol-mi-fa-sol-fa-sol-sol with the semitone b-c and whole-tone c-d "mentally" altered to a whole-tone and semitone respectively; "or a mutation will be made of mi into re," placing us properly in the ficta hexachord of A-F# with c[#]- ...

Colors indicate the three modes of hexachord: durum (hard, equivalent to G major), naturale (natural, equivalent to C major), and molle (soft, equivalent to F major. So the ancient system of solmization includes three base hexachords for each major key.

Hexachordal combinatoriality is a concept in post-tonal theory that describes the combination of hexachords, often used in reference to the music of the Second Viennese school.

Hexachordal complementation is the use of the potential for pairs of hexachords to each contain six different pitch classes and thereby complete an aggregate. Combinatorial tone rows from Moses und Aron by Arnold Schoenberg pairing complementary hexachords from P-0/I-3.

The “hard hexachord” on G contains the “hard” (hard-edged) or square B (i.e., B-natural). The “soft hexachord” on F contains the “soft” (soft-edged) or round B (i.e., B-flat); The “natural” hexachord on C (Guido's original) contains neither hard nor soft B.

How to use hexachord in a sentence. Just as in mediæval times each hexachord commenced with ut, so now every octave of our tonal system commences with do.

seven How many modes are there? The seven main categories of mode have been part of musical notation since the middle ages. So, the list goes: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian. Some of them are major modes, some are minor, and some are ambiguous.

seven There are seven main types of musical mode in Western music: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian.

We can find hexachordally combinatorial pairs without a matrix. For P-combinatoriality, hexachords A and B must map onto each other by transposition. That is, there must be some TnI of hexachord A that produces hexachord B.

aggregate - in music, generally refers to the collection of all twelve pitch classes. The idea may be applicable to both serial and non-serial compositions. aleatoric - making use of chance or indeterminacy, either in the compositional process or during the performance.

In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism.