Originally posted by DoctorScribbles
Wasn't it once the Church's position that the tritone was evil?
I also recently learned that to this day, the Mormon church still considers the guitar an evil instrument and forbids its use in worship.
Well, it was called the 'Devil's interval.' The reason for this is because, mathematically, you
can't have a 'perfect tritone.' You can easily have perfect fourths and fifths (which are
simple mathematical ratios of 4:3 and 3:2 respectively); that is, if an A = 440 mHz, then a
perfect E will = 660 mHz and D will = 586 2/3 mHz. Pythagoras figured this out. A tritone
doesn't really have a 'perfect' state because even if you try to make the ratios reasonable,
it still sounds unstable. This was noticed by Zarlino and Guido di Arezzo (two of the earliest
music theorists). Further, if you make the ratios reasonable, they only sound good in one or
two keys. Thus, practically, the ratio between the two notes in a tritone do not tend to have
nice, neat numbers on instruments that don't offer direct pitch control (like a violin) so that
the tritone can serve different musical functions. There's some funny Latin limerick about
tritones...something like 'Diabolos in musica,' but I can't remember it.
Despite this instablity, it was routinely sung, because the oscillation between unstable sonorities
to stable ones is what makes music interesting. However, it was just not written out. That is,
the tradition of 'Musica ficta' (that is, the altering of musical tones to create certain melodic
relationships) is pretty well established. Consider this example:
http://www.cpdl.org/wiki/images/d/d3/Josquin-Ave_Maria_a_4.pdf
On page 2, in the Tenor (third line down), in m. 24, on the second beat (half-note gets the beat),
you see that Josquin has written an 'F.' Against the Bassus (bottom line) which has a 'C,' this
is merely a perfect fourth. But you'll notice that the editor (not the composer!!!) has indicated
a sharp
over the note (as opposed to next to the note, as I'm sure a musician is used to
seeing). This is because there is an implicit understanding that when you have two melodies
approaching a unison/octave in conjunct motion (opposite directions) by step, one will be a
half-step. So, you see that the Contratenor has an 'A' moving to a 'G.' So, the performer
singing Tenor will alter the pitch up a halfstep in order to give better musical closure at that
arrival. Simply, in performace:
Contra----A-->G
Tenor-----F-->G
becomes:
Contra----A-->G
Tenor-----F#->G
This, of course, creates a tritone with the Bassus. So, for a period of time, composers simply
didn't write these alterations down, largely because the composers themselves were either in
or conducting the choirs themselves. When music publishing with moveable-type printing became
economically feasible, composers began to take greater care with accidentals (because they
weren't there to supervise the performances). And, so, the dislike at 'seeing' tritones kind of
disappeared as a concern.
A comment about 'Musica ficta:' It's kinda subjective and often retrospective. For example,
in the same piece, on p. 6, in the Bassus, in mm. 125-6, you see that the F# is indicated even
though there is not movement to the G in the Tenor. That's because the arrival is in m. 127,
and to only sing the last F as F# is musically quite awkward. So, sometimes you work your
way backwards in figuring out which should be.
The subjectivity can be heard in recordings; some people are very spare about using Musica ficta,
only altering tones at major arrivals. Other are very liberal: whenever they see a sixth expanding
out to a unison (or a third/tenth expanding inward), they alter a tone. Both extremes tend to
make for idiosynctratic performance. I, myself, lean towards using more rather than less, but
I don't force odd harmonies. And, sometimes, you try some and decide it sounds better
without them, and just stick with the more modal sounding resolution.
Nemesio
P.S., Rereading this, I'm guessing that maybe the example might be cryptic. If you need a
better one, I can find one tomorrow. This was the best I could do on the fly.