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Encyclopedia of Microtonal Music Theory

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[Joe Monzo]

In musical tuning theory, within the finite boundaries of the lattice, there is a fluidity of factoral interpretation possible, which allows categorical perception of intervals and interchangeability between various different rational designations of particular categorical intervals.

This is made possible by means of small intervals, such as various schismas, which Margo Schulter has named "xenharmonic bridges". According to Monzo's theory, these bridges allow interpretation of a ratio's factors to change from one set of primes to another, without affecting the prime-affect experienced by the listener. Monzo calls this fluidity of prime-affect "bridging".

In Monzo's notation, the bridge is indicated by writing the prime-limit of the lower-limit system on the left, followed by two 'equal signs', with the prime-limit of the higher-limit system on the right; for example: the interval which Fokker considered to be a bridge between the 5- and 7-limit systems, 224:225 [= 2571:3252 = 2,3,5,7-monzo [ 5 -2, -2 1 > = 0.07 Semitone = ~ 7.712 cents], would be notated by Monzo as a "5==7 bridge".

A designation as a particular bridge is in itself still a categorical designation, since there is an infinite number of small intervals which could be perceived as being any one particular bridge.

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