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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.
[3] Octaves are given in scientific pitch notation, with Middle C written as "C 4". (The 'A' above Middle C would then be written as "A 4"; the next higher octave begins on "C 5"; the next lower octave on "C 3"; etc.) [4] Because stringed instruments are easily re-tuned, the concept of a "standard tuning" is somewhat flexible. Some instruments:
In music, an octave (Latin: octavus: eighth) or perfect octave (sometimes called the diapason) [2] is a series of eight notes occupying the interval between (and including) two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music ...
The rest of the combination tones are octaves of 100 Hz so the 7:5 interval actually contains four notes: 100 Hz (and its octaves), 300 Hz, 500 Hz and 700 Hz. The lowest combination tone (100 Hz) is a seventeenth (two octaves and a major third) below the lower (actual sounding) note of the tritone.
Violin – G 3 D 4 A 4 E 5 (ascending perfect fifths, starting from G below middle C) Viola – C 3 G 3 D 4 A 4 (a perfect fifth below a violin's standard tuning) Cello – C 2 G 2 D 3 A 3 (an octave lower than the viola) Double bass – E 1 A 1 D 2 G 2 (ascending perfect fourths, where the highest sounding open string coincides with the G on a ...
5 / 6 × 2 / 1 = 10 / 6 = 5 / 3 . A 12 tone scale is obtained by removing one note for each couple of enharmonic notes. This can be done in four ways that have in common the removal of G ♭, according to a convention which was valid even for C-based Pythagorean and quarter-comma meantone scales.