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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 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.
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.
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.
Ptolemy, in his Harmonics, ii.3–11, construed the tonoi differently, presenting all seven octave species within a fixed octave, through chromatic inflection of the scale degrees (comparable to the modern conception of building all seven modal scales on a single tonic). In Ptolemy's system, therefore there are only seven tonoi.
Notice that this scale is an extension of the diatonic scale shown in the previous table. Only five notes have been added: C ♯ , E ♭ , F ♯ , G ♯ and B ♭ (a pentatonic scale ). As explained above, an identical scale was originally defined and produced by using a sequence of tempered fifths, ranging from E ♭ (five fifths below D) to G ...
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 ...