By Ross W. Duffin
When composers first began writing polyphony with the new cadence types in the early 14th century, they tended to specify fairly completely the accidentals they wanted performers to use. For some reason, however, it became conventional for composers not to notate many accidentals, and the choice of accidentals became a matter for performers to decide. In many cases, these accidentals are crucial to the music, so there is a certain irony that necessary instructions as to the required pitches were not always supplied by the composers. This practice became universal, however, and performers had the right and the obligation to interpret the counterpoint and harmony in order to add accidentals that were not notated in the score.
In many cases, these accidentals were not found among the notes in the gamut, the system of usable notes first devised by Guido of Arezzo ca.1025 and used through the rest of the middle ages and Renaissance. The gamut stretched from the G, an 11th below middle C, to the E a 10th above middle C, and included both Bb and B natural. The notes of the gamut could be described as constituents of overlapping groups of six notes — hexachords — starting on any of three pitches: G, C, or F (like a movable Do system but with only three basic possibilities). The hexachords all had exactly the same pattern of tones and semitones — Ut (like Do) Re Mi Fa Sol La — tone-tone-semitone-tone-tone. So the hexachord on F required a Bb (Fa) in order to put its single semitone in the right place. Any notes that were not part of the gamut, like F#, C#, Eb, etc. were said to belong to fictitious hexachords, so they were referred to as musica ficta or musica falsa. An F#, for instance, would normally be a Mi in a fictitious hexachord built on D (although it could alternatively be a Re in a fictitious hexachord built on E if there is also a G#).
Thus, most of the un-notated accidentals added by performers can accurately be referred to as music ficta. In “Musica Recta and Musica Ficta,” a seminal 1972 article, Margaret Bent pointed out that Bb is actually part of the gamut. So, although Bb might often be among the accidentals supplied by performers, it doesn’t qualify as ficta because it’s part of the gamut, or, in other words, Bb may be an accidental added by performers, but it’s musica recta (correct music) because it’s in the gamut. That’s why I equivocate in using the term musica ficta and refer more generally to “un-notated accidentals.” Peter Urquhart, who has also written a great deal about this issue, refers to un-notated accidentals as “performers’ accidentals.” One question about recta/ficta usage, however, is whether the presence of a Bb in the signature causes the transposition of the gamut, so that Eb becomes recta. The reason this is an issue is because theorists state that performers should choose recta over ficta whenever possible, and this leads to a proliferation of flats once flats occur in the signature.
But why are these accidentals necessary?
The very first accidentals were added in the 11th century in order to avoid imperfect simultaneous pure intervals. In organum, moving in parallel 4ths or 5ths would eventually encounter a problem when an F occurred with a B-natural, or an E occurred with a Bb. The tritone (i.e., three consecutive whole tones) was considered to be a forbidden interval. There is a Latin jingle that represents that sentiment although it’s not clear how early it dates: Mi contra Fa est diabolus in musica — Mi against Fa is the devil in music. B-natural was always Mi and F was Fa, so B-F was to be avoided, typically by adding a flat to the B. Similarly, Bb and E-natural conflict in the same way, so either the B would need to be raised or a flat added to the E. This is generally done for both tritones and diminished 5ths, although it was the tritone that got most of the bad press. It can also be used for imperfect octaves, like Bb and B-natural, since the former is always Fa and the latter always Mi. Correction of dissonance in the music is referred to as the application of accidentals “for the sake of necessity” — causa necessitatis.
These vertical dissonance rules were also applied to clearly outlined horizontal passages, where Mi and Fa occurred at the extremes of a melodic figure, as shown below. According to the usual modern editorial practice, the added accidentals are shown above the note, rather than on the staff. In modern scores, they apply only to the note above which they sit (although the accidentals themselves are usually taken to last for as long as the passage remains in the same hexachord).
It seems that such correction almost never involved adding a sharp to avoid the tritone (as might have been possible for the third note of the first example above, for example), unless a cadence was also involved and the sharp satisfied the requirements for that, as outlined below.
Related to Mi contra Fa is another rule which has yet another Latin jingle: Una nota sopra La semper est canendum Fa — One note above La is always sung Fa (or “is always singing Fa” as its bad Latin says). This states that when you are in a certain hexachord and ascend one note above the top of it, then return to the original hexachord, the one note above the La is lowered to be a momentary Fa, as follows:
This is often because the Fa in any hexachord makes a prominent melodic tritone with a whole tone above La, so both Latin rules sometimes work together. These examples also show how singers needed to master “mutation” — changing from one hexachord to an adjacent one — if they wanted to use the syllables (the voci) to help them sight-sing. The process of applying the hexachord syllables to a passage of music is called solmization, meaning the application of Sol and Mi, etc. to the notes.
The other main category of accidental addition is “for the sake of beauty” — causa pulchritudinis. This sounds less important because it seems like it’s just to make the music “prettier,” but in fact cadential fictafalls under this category, so it’s just as important — some would say more important — than cause necessitatis. This is because the requirement to make cadences was so strong. Basically, any 6th expanding to an 8ve was required to be be a major 6th, and any 3rd contracting to a unison was to be a minor 3rd. In the earlier polyphonic era, any 3rd expanding to a 5th needed to be a major 3rd, although this seems not to have been sustained for long. In practice, to require ficta, the 6th-8ve progression needed to be at the end of a phrase, or to include things like a suspension of the leading note. The 6th resolving to the 8ve remained the essence of the cadence right through the Renaissance, even after bass parts started doing something like V-I at cadences, so it was extremely important.
One thing you no doubt noticed about these cadences is that one of them does not need any accidentals to make the cadence. This is true of cadences to E, F, and C (assuming no flats in the signature). Two of the cadences above also have the semitone leading downward at the bottom of the progression rather than leading up. This kind of cadence is called a Phrygian cadence, after the Phrygian mode which uses E as its final note, and therefore is approached by semitone from above. Phrygian cadences are thus most likely to occur on E or on A, where the use of Bb — musica recta, remember — frequently indicates its use. The choice of G# or Bb depends on the context, as the sample problem passages will show.
Three-voice cadences can be made simply by adding an inner part that exactly parallels the top part a 4th below. This is called a double-leading-tone cadence and was widely used in the 14th and 15th centuries in three-voice music. While this practice was still current in the early 15th century, the third part (the contratenor) sometimes took a note a 5th below the penultimate note of the tenor then resolved by leaping up the 8ve. This is called an 8ve-leap cadence. The addition of a fourth voice in the later 15th century allowed the typical V-I bass “perfect” cadence style to emerge. Phrygian cadences in four voices were different, however, with the bass moving from a 3rd below the tenor to a 5th (or occasionally another 3rd) below on the resolution.
A question that arises frequently in English Renaissance music and also in some Franco-Flemish music of the late 15th and early 16th centuries, is the extent to which cross-relations were intended or tolerated. A cross-relation is the simultaneous or close consecutive juxtaposition of two different chromatic forms of the same note, like F-natural and F# for example, or Bb and B-natural. Typically, these occur — or can occur — where the linear direction of two different voice parts, using the melodic rules outlined above, favor the singing of conflicting notes, as shown here.
The F and F# here make a cross-relation, sounding a brief but simultaneous augmented 8ve. One solution, of course, would be to avoid the cadence (and the conflict) by choosing not to inflect the leading note (i.e., omitting the #). But in some cases, both notes are signed, so we know a cross-relation was intended. Also, the strength of causa pulchritudinis often suggests that the cadence needs to be made, even if the result is a cross-relation. Using the historical concept of a performer making ficta decisions based on a single line of music (i.e., not a score), Peter Urquhart opines that cross-relations probably occurred much more frequently in performance than most people realize. In fact, it’s possible to acquire an appreciation for the sound of the cross-relation, so that its pungency is enjoyed and contributes to the effect of the music.
Occasionally, there is no obvious solution to a ficta problem. The theorist Johannes Tinctoris, in fact, gives a few passages with apparently insoluble ficta problems and basically blames the composers for writing so inelegantly. In other cases, there is more than one acceptable ficta solution, as may be seen in the sample problem passages.
There are many well-reasoned opinions on the application of un-notated accidentals in the middle ages and Renaissance. My own short guide to the Renaissance practice, based on thirty years of performing and editing, is given here.