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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.
A pentatonic scale is a musical scale with five notes per octave, in contrast to heptatonic scales, which have seven notes per octave (such as the major scale and minor scale). Pentatonic scales were developed independently by many ancient civilizations [ 2 ] and are still used in various musical styles to this day.
Octatonic scales can be found in Chopin's Mazurka, Op. 50, No. 3 and in several Liszt piano works: the closing measures of the third Étude de Concert, "Un Sospiro," for example, where (mm. 66–70) the bass contains a complete falling octatonic scale from D-flat to D-flat, in the opening piano cadenzas of Totentanz, in the lower notes between ...
In any meantone or Pythagorean tuning, where a whole tone is composed of one semitone of each kind, a major third is two whole tones and therefore consists of two semitones of each kind, a perfect fifth of meantone contains four diatonic and three chromatic semitones, and an octave seven diatonic and five chromatic semitones, it follows that:
Difference between 12 just perfect fifths and seven octaves. Difference between three Pythagorean ditones (major thirds) and one octave. A just perfect fifth has a frequency ratio of 3:2. It is used in Pythagorean tuning, together with the octave, as a yardstick to define, with respect to a given initial note, the frequency of any other note.
The pattern of whole and half steps characteristic of a major scale. The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees of a major scale are called major. [1] A major scale is a diatonic scale. The sequence of intervals between the notes of a major scale is:
Leichtentritt states that the melodic character resulting from the use of black keys is "based on the pentatonic scale to which the piece owes its strangely playful, attractively primitive tint." [7]: 109 He presents a melodic reduction of the right hand part which, played in octaves by piccolo and flute, resembles a frolicsome Scottish jig.
Pythagorean perfect fifth on C Play ⓘ: C-G (3/2 ÷ 1/1 = 3/2).. In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. [1]
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