Suomeksi | In English

Hexachords

Since the concepts of major and minor scale have existed for hundreds of years, it is hard to imagine a scale with only four or six consecutive steps and a limited number of notes.

From the Middle Ages to the Renaissance, music theorists and composers thought about music in six-note hexachords. If the range of a melody was larger than a sixth, they just switched to another hexachord. Hexachords always involved the same diatonic scale structure: T T S T T; a symmetrical figure, the same from the end to the beginning. This feature was utilised, for example, in polyphonic music.

Monk Guido d'Arezzo (approx. 995-1050) is usually considered to be the father of the hexachord theory; his ideas probably led to the development of the hexachord system, although not before the 13th century. Guido connected the syllables ut, re, mi, and so on (from the hymn Ut queant laxis) to note names so that it was easier for his students to perceive the location of semitones. Originally there were three different hexachords: h durum, h molle, and h naturale:

Hexachords

Hexachords

  1. The same hexachord is repeated at octave intervals
  2. The Greek letter gamma (capitalized) was used under A to complete the hexachord. Its full name was Gamma Ut.. The next one was A re, then B mi, and so on. Note names are listed in the table below.
  3. The note C (today small C) was named C fa ut. Thereafter, note names had several syllables (D sol re, E la mi, F fa ut, and so on).
  4. Hexachordum molle had bflat (b fa), but hexachordum durum had bnatural (b mi). The symbol resembling H was the basis for the note name H (used for B in Germanic languages) and the chromatic signs natural and #.

An essential point in the hexachord system was the location of the semitone (mi-fa). Hexachordum molle has a "b" (b rotundum, a round and soft b); hexachordum durum has an "h" (b quadrum, square and hard). For a choral singer, the quality of a hexachord was a matter of judgement; for example in the progression F-G-A-H, whether to sing the last note as a durum on the "mi" or as a molle on the "fa". Transferring from one hexachord to another was called a mutation. The syllable "mi" often led to a cadence, as seen in the example:

Hexachord example

When works of music began to show signs of chromaticism, other than the mere alteration between H and B, more hexachords were needed. It was possible to join the syllables mi and fa with other notes. For example, a hexachord starting from D renders the "mi" F sharp. It is worth noting that chromaticism was originally an extension of diatonicity. As late as the 16th century, it was extremely rare to have chromatically altered notes in a piece of music other than F sharp, C sharp, G sharp, E flat, and B flat. The hexachord system was gradually given up during the 17th century.

Guido's note names listed in a table:


Note name
Syllable
ee             la
dd           la sol
cc           sol fa
bbnatural             mi
bbflat           fa  
aa         la mi re
gg         sol re ut
f         fa ut  
e       la mi    
d     la sol re    
c     sol fa ut    
bnatural       mi      
bflat     fa        
a   la mi re      
g   sol re ut      
F   fa ut        
E la mi          
D sol re          
C fa ut          
B mi            
A re            
ut ut            

The term hexachord is today used in a wider sense to denote any group of six notes (for example, in set theory).