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In tunings such as 1:1, 9:8, 5:4, 3:2, 7:4, 2:1, all the pitches are chosen from the harmonic series (divided by powers of 2 to reduce them to the same octave), so all the intervals are related to each other by simple numeric ratios. Pythagorean tuning Prelude No. 1, C major, BWV 846, from the Well-Tempered Clavier by Johann Sebastian Bach.
Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory.
And the problem of how to tune complex chords such as C 6 add 9 (C→E→G→A→D), in typical 5 limit just intonation, is left unresolved (for instance, A could be 4:3 below D (making it 9:8, if G is 1) or 4:3 above E (making it 10:9, if G is 1) but not both at the same time, so one of the fourths in the chord will have to be an out-of-tune ...
10 17: 100 PHz: 10 18: 1 exahertz (EHz) 10 19: 10 EHz: 10 20: 100 EHz: 300 EHz + Electromagnetic – gamma rays: 10 21: 1 zettahertz (ZHz) 36 ZHz: Resonance width of the rho meson: 10 24: 1 yottahertz (YHz) 10 27: 1 ronnahertz (RHz) 3.9 RHz: Highest energy (16 TeV) gamma ray detected, from Markarian 501: 10 30: 1 quettahertz (QHz) 10 43: 10 ...
Most time signatures consist of two numerals, one stacked above the other: The lower numeral indicates the note value that the signature is counting. This number is always a power of 2 (unless the time signature is irrational), usually 2, 4 or 8, but less often 16 is also used, usually in Baroque music. 2 corresponds to the half note (minim), 4 to the quarter note (crotchet), 8 to the eighth ...
to signify the notes of the two-octave range that was in use at the time [10] and in modern scientific pitch notation are represented as A 2 B 2 C 3 D 3 E 3 F 3 G 3 A 3 B 3 C 4 D 4 E 4 F 4 G 4. Though it is not known whether this was his devising or common usage at the time, this is nonetheless called Boethian notation.
The Pythagorean scale is any scale which can be constructed from only pure perfect fifths (3:2) and octaves (2:1). [5] In Greek music it was used to tune tetrachords, which were composed into scales spanning an octave. [6] A distinction can be made between extended Pythagorean tuning and a 12-tone Pythagorean temperament.
Félix Savart (1791-1841) took over Sauveur's system, without limiting the number of decimals of the logarithm of 2, so that the value of his unit varies according to sources. With five decimals, the base-10 logarithm of 2 is 0.30103, giving 301.03 savarts in the octave. [33] This value often is rounded to 1/301 or to 1/300 octave. [34] [35]