Simply put, musica ficta were notes outside of the diatonic modal system in use for a given piece that would be performed by trained musicians of the period. One common (but not exclusive) use of ficta was to avoid harsh harmonic or melodic intervals (for example the tritone, the 'diabolus in musica'). An example might be the use of a B-flat instead of a B-natural to avoid a tritone against an F in another part. In modern transcriptions of Medieval and Renaissance music, ficta are usually indicated with an accidental engraved above (instead of before) the note. Editors provide these for modern singers who cannot have received the kind of training given to singers several hundred years ago that made such indications unnecessary. Only small portions of that training can be reconstructed from fragmentary and often contradictory sources.
One thing that is well known is that singers were trained to think in hexachords denoted by the names ut-re-mi-fa-sol-la that contained only one half-step: the one between mi and fa. The name musica ficta refers to the elaborate use of hexachorda ficta, these were hexachords other than the three types that were part of the system by Guido of Arrezzo: molle on F, naturale on C and durum on G. The fictive hexachord were notated by indicating that a note, say F had the role of mi in the hexachord (in modern terms: be sharpened) by adding the sign . This created a fictive hexachord on D that would last for a certain (but not indicated) number of notes until the voice mutated into another hexachord. Likewise could indicate that a note was fa in a fictive hexachord, or before B that the hexachord was molle rather than durum. Unfortunately the use of the signs was by no means consistent. It was a assumed that a good singer knew his mi's and fa's, so that the signs were typically only added if the scribe anticipated that singers would otherwise interpret differently.
The exact performance practice of musica ficta, where and when they were used, is a matter of intense investigation and controversy among musicological scholars; it has been controversial, and is likely to remain so, for a long time. Music theorists from Odo of Cluny in the 10th century to Zarlino in the 16th century give highly different rules and situations for application of ficta. The controversy is not only among contemporary musicologists; theorists of the Late Middle Ages were never in agreement on the rules of ficta either. 13th century music theorist Johannes de Garlandia and 14th century theorist Philippe de Vitry both wrote that ficta were essential in singing polyphony, but resisted their use in plainchant, while early 14th century theorist Jacques de Liège insisted that notes in plainchant needed to be altered with judicious application of musica ficta.
The use of ficta originated with the difference between B-flat and B-natural, which was integrated in medieval theory and in practical teaching as part of the system of hexachords. However, rules of cadencing and tritone avoidance could also require other notes to become altered under certain circumstances.
13th century theorists divided the use of ficta into two general categories: causa necessitatis (ficta supplied by necessity, for example to avoid a dissonant interval); and causa pulchritudinis (ficta supplied for reason of beauty). Sometimes a melodic phrase simply sounds better, or sounded better to a trained 13th-century ear, when it is smoothed out by judicious application of ficta.
In particular, contrapuntal treatises of the Renaissance, such as that of Johannes Tinctoris, counseled resolution at cadences through the largest possible sixth into the octave, which in many cases requires the upper voice to use a sharp in order to form the major sixth (see dyadic counterpoint). At such points, accidentals were in fact sometimes notated in the 14th and early 15th centuries.
It was formerly believed that such treatises were addressed to composers; now, by further examination of their Latin texts, many musicologists have concluded that they were in fact speaking to performers, both of notated and improvised polyphony.
As an example of a related contemporary performance practice, Sacred Harp singing contains a situation similar in concept to ficta, involving the non-notated raising of the sixth scale degree in a minor mode (resulting in a Dorian inflection); new singers must be taught to do this by ear.
In effect, any folk singer from different parts of the world could use the same way of thinking, which leads to the interesting fact that musica ficta existed centuries before the principle of temperament.