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Aristoxenus was born at Tarentum (in modern-day Apulia, southern Italy) in Magna Graecia, and was the son of a learned musician named Spintharus (otherwise Mnesias). [2] He learned music from his father, and having then been instructed by Lamprus of Erythrae and Xenophilus the Pythagorean, he finally became a pupil of Aristotle, [3] whom he appears to have rivaled in the variety of his studies.
Elementa harmonica (Ἁρμονικὰ στοιχεῖα in Greek; Elements of Harmonics in English) is a treatise on the subject of musical scales by Aristoxenus, of which considerable amounts are extant.
A harmonic motif is a series of chords defined in the abstract, that is, without reference to melody or rhythm. A melodic motif is a melodic formula , established without reference to intervals . A rhythmic motif is the term designating a characteristic rhythmic formula, an abstraction drawn from the rhythmic values of a melody.
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For example, the greater just minor seventh, 9:5 (Play ⓘ) is a 5-limit ratio, the harmonic seventh has the ratio 7:4 and is thus a septimal interval. Similarly, the septimal chromatic semitone, 21:20, is a septimal interval as 21÷7=3. The harmonic seventh is used in the barbershop seventh chord and music.
Percussion bars, such as xylophone, are hung at ≈2/9 and ≈7/9 length, and struck at 1/2 length, to reduce inharmonicity. In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones ) depart from whole multiples of the fundamental frequency ( harmonic series ).
Below the complex spherical harmonics are represented on 2D plots with the azimuthal angle, , on the horizontal axis and the polar angle, , on the vertical axis.The saturation of the color at any point represents the magnitude of the spherical harmonic and the hue represents the phase.
The first four notes are scale degree 3–1–4–2, decimal pi, and fractional pi is hidden in the "two drops of a seventh" following the first 11 notes leading to 2 ⁄ 7 × 11 = 22 ⁄ 7, fractional pi. His "dark saying" is a pun set off by an unexplained double bar after the first 24 notes (all black notes)..."Four and twenty blackbirds ...