hexachord

• 1.

  A postulated intermediate stage in the expansion from the enharmonic tetrachord to the full octave scale.

  If the pyknon of the lower tetrachord (Hypaton) is split into two microtones while the upper (Meson) one is undivided, a plausible form of the hexachord is produced.

  This process works similarly for the Chromatic and the Diatonic genera assuming that they both were derived from pentatonic precursors of the whole tone and minor third variety. This definition of hexachord is not the same as the one of the medieval theorist Guido D'Arrezzo. (see below)

  [from John Chalmers, Divisions of the Tetrachord]

  
  

• 2.

  As defined by Guido d'Arrezzo, a scale segment consisting of six tones, each tone being assigned a "solfege" syllable, with the syllables, and intervals between "steps", having the following pattern:

  
  
  ut    re     mi      fa     sol     la
     ^       ^      ^       ^      ^
    Tone   Tone  Semitone  Tone   Tone
  
  

  In the system constructed by Guido, hexachords were possible on three pitch-levels, with "ut" on what we would today call "C" (the "natural" hexachord), "F" (the "soft" hexachord), and "G" (the "hard" hexachord). This corresponds to a moveable "ut" centered on the "natural-ut", "natural-fa", and "natural-sol", as follows:

  
  
  ut  re  mi  fa  sol  la
              ut   re  mi  fa  sol   la
                   ut  re  mi   fa  sol  la
  
  

  Notes were generally named by using all applicable syllables, i.e., "G" sol-re-ut.

  I have deliberately left letter-names out of this diagram, to give a sense of the difficulty encountered by ancient and medieval theorists in discussing musical pitches without the use of mathematics or alphabetical ordering.

  see also mutation, gamut, and Margo Schulter's exposition on Hexachords, solmization, and musica ficta

  
  

• 3.

  A development of serial ('12-tone') theory, in which the 12 notes of the row are divided in half, to form two series of 6 notes each, called hexachords.

  Usually, the hexachord pair exhibits similarities of interval structure (i.e., transposition) or other serial properties such as retrograde or inversion, or various combinations of all of them.

  [from JoeMonzo, JustMusic: A New Harmony]

---

(to download a zip file of the entire Dictionary, click here)

For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

I welcome feedback about this webpage: corrections, improvements, good links. Let me know if you don't understand something. return to the Microtonal Dictionary index return to my home page return to the Sonic Arts home page