In the Mediaeval world, writing was not the casual matter it is for us; it was worth reducing the amount of writing even by a single sign. In particular, the Middle Ages economised on writing music by means of a system of assumed accidentals known as “musica ficta” – imagined notes.
Unfortunately, while this system was automatic for mediaeval performers, it was lost sight of in the Renaissance, and when interest in mediaeval music revived, at first musica ficta was known as a phrase, but it was simply not understood, since this was long before detailed contemporary accounts of the system were located.
A few fifteenth century references were found quite early which included examples. The explanations of “musica ficta” in these sources were aimed at people who were already immersed in the system, and so were impossible for nineteenth century scholars to understand, but scholars believed they could still use the examples. But this was not in fact the case; the scholars’ preconceptions led them to misinterpret the examples in such a way that by the end of the nineteenth century it was believed that “musica ficta” could justify introducing any accidental that sounded good to nineteenth century ears.
Sadly, this view is still influencing modern editions of mediaeval music – most especially fifteenth century mediaeval and renaissance music. So we find even now sharpened leading notes, flattened high notes and other modern conventions applied as “musica ficta” completely without justification.
It might be worth explaining what modern scholarship has demonstrated on this.
First, “musica ficta” means literally “moulded notes” or “kneaded notes” – notes which have been reshaped like modelling clay from their original form. This process takes a standard note and “moulds” it into something slightly different; and by “standard note” we mean any note on the Guidonian Hand.
Musica ficta takes a note that is ON the Hand and moves it OFF the Hand.
Since all three hexachords are on the Hand, changing to a different hexachord can NOT cause a note to change because of musica ficta.
Second, musica ficta is NOT about horizontal relationships; musica ficta can NOT be used to change a note on the basis of the previous note or the following note in its line. Musica ficta is about vertical relationships, about harmonic relationships.
Musica ficta never changes a note in a monophonic piece
Musica ficta changes vertical intervals; the changes to horizontal lines are a consequence, not a cause, of these changes
Musica ficta can NOT be invoked just because a note is part of a cadence
Third, musica ficta is not usually optional. The only exception, the only element of freedom in the system is where the rules, the “causae”, of musica ficta contradict each other – only then has the performer some freedom to choose which rule to obey and which to ignore.
Every application of musica ficta should be capable of being justified by either of the two “causae” – either by "causa pulchritudinis" or by "causa necessitatis".
Where the two causae collide, in principle causa pulchritudinis should be preferred (rather oddly in view of the names!) but in real life compromises may have to be made.
So, what are the causae?
Well, first, intervals are divided into three groups: complete, which are unisons, fifths and octaves (and their augments and diminishments); incomplete, which are thirds and sixths (major, minor, augmented, diminished); and everything else – seconds and fourths and sevenths. Note in particular that a fourth is NOT complete and therefore nor is a tritone – an augmented fourth, and that complete intervals need not be perfect.
Causa Pulchritudinis (the cause of beauty) deals with an incomplete interval which moves to a complete one: in this case if the movement is upward or widening, then the incomplete interval must be major; if it is downward or narrowing, then the incomplete interval must be minor. Notice that nothing is said about the complete interval!
Causa Necessitatis (the cause of necessity) deals with a complete interval which does not follow an incomplete interval: in this case the complete interval must be perfect; it must not be augmented or diminished.
And Necessitas gives way to Pulchritudo – necessity gives way to beauty.
Finally, let us deal with the oft-quoted “mi contra fa: diabolus in musica”. Ignoring the fact that its earliest attestation is long after the mediaeval period, we can analyse this in the light of musica ficta.
There are seven possibilities:
Notice that musica ficta does NOT ban tritones!