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Musica ficta
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==Historical sense and relation to hexachords== Throughout the period that incorporated ''musica ficta'', singers sight read melodies through a series of interlocked hexachords that formed the backbone of the [[solmization]] systemβa method that eventually became the modern system of [[tonic sol-fa]]. To sing notes outside the ''recta'' pitches of the [[Diatonic and chromatic#Diatonic scales|gamut]] (the range generally available to composers and performers, i.e., from G at the bottom of the modern bass clef to E at the top of the treble clef), performers had to invoke "fictive" hexachords to sing pitches such as F{{Music|sharp}} or E{{Music|flat}}. Hexachords normally were formed only on C, F, and G, and the interval pattern within each of these hexachords was always tone-tone-semitone-tone-tone, which was sung as ''ut re mi fa sol la''. Hence, if singers needed to sing the pitch F{{Music|sharp}}, they had to think of the half step between F{{Music|sharp}} and G as the solmization syllables ''mi'' and ''fa'', for ''mi-fa'' always represented the half step within a hexachord. When they did this, they invoked a nominal hexachord starting on the note D, and this hexachord was considered fictive because it contained a false or fictitious F{{Music|sharp}} (that is, a pitch that did not belong to the ''recta'' notes of the gamut). Moreover, since the hexachord built on F naturally contained a B{{Music|flat}}, music based on a scale involving the soft or F hexachord had the pitch B{{Music|flat}} as part of the ''recta'' notes of the scale.<ref>{{harvnb|Toft|2014|loc=267β269}}. For a fuller explanation of these procedures, see {{harvnb|Toft|2014|loc=259β261}}.</ref> However, in the 16th century, the signs used to represent these fictive notes (the signs for ''b mollis'' [{{Music|flat}}] and ''b durum'' [{{Music|sharp}}]) came to acquire their modern meanings of raising or lowering notes by a half step.{{sfn|Toft|1992|loc=13β14}} Adrian Le Roy wrote that "b sharpe doeth holde up the tune halfe a note higher, and b flatte, contrarywise doeth lette it fall halfe a note lower".{{sfn|Le Roy|1574|loc=fol. 6r}} But as early as 1524, theorists also had this understanding of these signs.{{sfn|Toft|1992|loc=13β14}} Moreover, near the beginning of the 17th century, Michael Praetorius employed the words ''signa chromatica'' (chromatic signs) to refer to sharps and flats.{{sfn|Praetorius|1619|loc=31}} Hence, musicians of the later Middle Ages and Renaissance did not all share a uniform interpretation of this concept.
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