His book, " Essays on Musical Intervals, Harmonics, and the Temperament of the Musical Scale, " advocated 19-tone equal temperament and used a division of the octave into 730 parts, now designated as " Woolhouse units ", for measuring musical intervals.
42.
His book, " Essays on Musical Intervals, Harmonics, and the Temperament of the Musical Scale, " advocated 19-tone equal temperament and used a division of the octave into 730 parts, now designated as " Woolhouse units ", for measuring musical intervals.
43.
After criticizing the approaches of his predecessors, Ptolemy argued for basing musical intervals on mathematical ratios ( in contrast to the followers of Aristoxenus ) backed up by empirical observation ( in contrast to the over-theoretical approach of the Pythagoreans ).
44.
Whales are capable of vocalizing over a range of at least seven octaves, yet they tend to proceed through a song in stepwise lilting musical intervals, rather than careering madly from octave to octave; in other words, they sing in key.
45.
Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio ( octave 2 : 1, fourth 4 : 3, fifth 3 : 2, 9 : 8 ) (; ).
46.
There is a row for every possible musical interval, not just fifths, fourths, and octaves but also whole tones, minor thirds, etc . The Array system can be thought of not only as being based on the circle of fifths, but as being based on rows of whole tones.
47.
Music of the Spheres is a term applied to an idea put forth by the Greek scholar Pythagoras ( 6th century BCE ) and his followers, among them Plato and Kepler, that the proportional ratios used to describe musical intervals also refer to those of the physical universe, including the orbiting motion of planets.
48.
For example, articles about musical intervals on Wikipedia currently feature an interval infobox on the top left listing information such as name and size, followed by a picture of music notation of the interval on C . At some point in between cited well known examples of songs or pieces beginning with the interval are given.
49.
In 1618, Robert Fludd devised a "'mundane monochord "'( also "'celestial "'or "'divine monochord "') that linked the Ptolemaic universe to musical intervals . " Was it [ Mersenne's discoveries through use of the monochord ( 1637 ) ] physical intuition or a Pythagorean confidence in the importance of small whole numbers ? . . . It was the latter ."
50.
For instance, the tone from C to D ( in short, C D ) can be decomposed into the two semitones C C and C D by using the note C, which in a chromatic scale lies between C and D . This means that, when a chromatic scale is used, a tritone can be also defined as any musical interval spanning six semitones:
