Posted by: New Class Traitor | April 29, 2017

Making sense of Byzantine scales

A friend who had just returned from a trip to Greece played back some clips of Byzantine church music on her cell phone. I became intrigued by the peculiar scales I heard, so I did some digging. A lot became clearer from this academic paper in the Journal of the Acoustical Society of America, where a trio of Greek researchers discuss their findings recording and analyzing the singing of a number of well-known Greek Orthodox psaltes (cantors).
They note that in actual practice, cantors deviate from the prescriptive standards laid out by the Patriarchal Music Committee (1883), depending on musical context. (One can see similar phenomena in unaccompanied singing or solo violin playing.) But let me give you the “Cliff Notes” version on Byzantine church singing.
All Byzantine scales are based on four “genera” (plural of genus):
  • Diatonic
  • Chromatic mild
  • Chromatic strong
  • Enharmonic
[Note that, in context, these terms do not have the same meanings as in Western music theory.]
All four genera have the following in common:
  • scales span an octave (2/1)
  • scales are heptatonic, i.e., they have seven notes, the “eighth” note being the first note raised by one octave (just like the Western major and minor scales)
  • scales are made up of two identical tetrachords [rows of four notes] a perfect fifth (3/2) apart
  • each tetrachord spans a perfect fourth (4/3)
  • this leaves the two middle notes in each tetrachord movable
Unlike Arabic music (which is monophonic or heterophonic, and hence has no harmonic exigencies), Eastern Orthodox Church music has two or sometimes three voices. Hence harmony does enter the picture: Greek music theorists going back to Pythagoras, Didymos, Ptolemaeus,… have used rational fractions to define/describe musical intervals. (There is actually deep physics behind this idea: frequency ratios between overtones of a common fundamental.) In the case of Byzantine music, said ratios get, well… Byzantine.
So in 1883, the Patriarchal Music Committee (PMC) decided to create some order in the chaos by looking for an equal-temperament approximation to the clutter of micro-intervals. The closest fit they could find was 72-tone equal temperament (ET72): that is, dividing the octave into seventy-two equal steps called moria  (plural of “morio”, Greek for mote, trifle, molecule). One morio equals 2^(1/72)=1.009673533.
Note that ET72 contains as subsets both
  • ET12 (twelve-tone equal temperament, the Western standard for keyboard and fretted instruments): each semitone on the keyboard is six moria
  • ET24 (quarter-tone equal temperament, often used to describe Arabic maqamat [scales]): each quarter-tone is three moria
The PMC took the intervals of Byzantine vocal music and rounded them to the nearest integer number of moria. A perfect fifth then becomes 42 moria (seven ET12 semitones), a perfect fourth 30 moria (five ET12 semitones). The four Byzantine genera were then standardized to the following tetrachords (number of moria for each step given):
  • diatonic genus: 12-10-8
  • chromatic mild genus: 8-14-8
  • chromatic strong genus: 6-20-4
  • enharmonic genus: 12-12-6
Note that — unlike in ancient Greek music — the enharmonic genus is (after rounding) equivalent to the major scale in ET12! For comparison, let’s put up the tetrachords of some Western scales and modes that feature repeated tetrachords:
  • the major scale (a.k.a. Ionian mode):  in ET12 corresponds to 12-12-6, in just intonation: 12-11-7. So the Byzantine diatonic genus is like the major scale in [5-limit Ptolemaic] just intonation — except that the major third has been flattened one morio.
  • Dorian mode: 12-6-12 in ET12, approx. 11-7-12 in just intonation[For non-musicians: this mode is commonly heard in “minor”-sounding Anglo folk tunes and in rock/pop music deriving from it, as well as in modal jazz.]
  • Phrygian mode: 6-12-12 in ET12,7-12-11 in just intonation[For non-musicians: this very dark mode is fairly commonly heard in heavy metal, and its use in battle scenes in film music is something of a cliché.]
  • Double-harmonic (“Byzantine”) scale: 6-18-6 in ET12, approximately 7-16-7 in just intonation. Note how this looks a but similar to the “chromatic sharp” 6-20-4 genus of Byzantine music.
The “minor scale” (technically, the Aeolian or natural-minor mode) is absent here, as it has two different tetrachords — so does the mixolydian mode.  In my next post, I will explore how two different tetrachords can be used to construct many different musical scales and modes in the Western tradition, and how their “bright” or “dark” character can be rationalized through the tetrachords.

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