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Diatonic scale on C, equal tempered Play ⓘ and Ptolemy's intense or just Play ⓘ.. Ptolemy's intense diatonic scale, also known as the Ptolemaic sequence, [1] justly tuned major scale, [2] [3] [4] Ptolemy's tense diatonic scale, or the syntonous (or syntonic) diatonic scale, is a tuning for the diatonic scale proposed by Ptolemy, [5] and corresponding with modern 5-limit just intonation. [6]
This scale is known as the Pythagorean diatonic and is the scale that Plato adopted in the construction of the world soul in the Timaeus (36a-b). [12] The next notable Pythagorean theorist known today is Archytas, contemporary and friend of Plato, who explained the use of arithmetic, geometric and harmonic means in tuning musical instruments.
Ptolemy substituted a diatonic sequence of seven transpositions pitched either a whole tone or a semitone apart. The entire double-octave scale system was then transposed onto each of these relative pitch levels, requiring (in modern terms) a different key signature in each case, and therefore a different sequence of whole and half steps in the ...
Claudius Ptolemy of Alexandria described several 7-limit tuning systems for the diatonic and chromatic genera. He describes several "soft" (μαλακός) diatonic tunings which all use 7-limit intervals. [7] One, called by Ptolemy the "tonic diatonic," is ascribed to the Pythagorean philosopher and statesman Archytas of Tarentum.
In music theory a diatonic scale is a heptatonic (seven-note) scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps. In other words, the half steps are maximally separated from each other.
This is known as Ptolemy's intense diatonic scale. Here the row headed "Natural" expresses all these ratios using a common list of natural numbers (by multiplying the row above by the lcm of its denominators). In other words, the lowest occurrence of this one-octave scale shape within the harmonic series is as a subset of 7 of the 24 harmonics ...
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.
Unlike divisions of the octave into 19, 31 or 53 steps, which can be considered as being derived from ancient Greek intervals (the greater and lesser diesis and the syntonic comma), division into 34 steps did not arise 'naturally' out of older music theory, although Cyriakus Schneegass proposed a meantone system with 34 divisions based in effect on half a chromatic semitone (the difference ...