Indeed, Marchettus of Padua c

B minor 7 flat 5 notes on dating

This differential can serve as a kind of index of the degree of acoustical tension in thirds and sixths. We will recall that this comma is equal to the difference between a diatonic semitone and an apotome. Having added bb and eb, we now return again to b, at the other end of our chain of fifths, to complete our journey on the sharp side.

We will recall thatThis differential can serve as

In other periods, the tradeoffs between acoustical necessity and musical style may perhaps be somewhat less happy. Renaissance tunings optimize thirds and sixths, accepting the consequence of diatonic semitones considerably wider than cents, typically in fact rather close to the Pythagorean apotome of cents. To find such a difference of intervals, we divide their ratios. As we shall see in the next section, the Pythagorean diminished fifth is slightly smaller than the augmented fourth. To cover this extra distance, each upper voice must move by a not-so-incisive cent apotome rather than a traditional cent diatonic semitone.

For theorists such as Johannes de Grocheio c. As we continue along our chain of fifths, we will generate not only the individual notes of our scale but the various intervals making up the spectrum of concord and discord.

The rule is that the diatonic semitone falls between a flat and the note immediately below e. With an acoustical instrument, this involves adjusting the upper note until no beats can be heard when the two notes are sounded together - a task easiest on a sustained instrument such as an organ. We can demonstrate this point in two ways.