Ptolemy's intense diatonic scale, also known as Ptolemaic Sequence,[1] justly tuned major scale,[2][3][4] or syntonous (or syntonic) diatonic scale, is a tuning for the diatonic scale proposed by Ptolemy,[5] declared by Zarlino to be the only tuning that could be reasonably sung, and corresponding with modern just intonation.[6]
It is produced through a tetrachord consisting of a greater tone (9/8), lesser tone (10/9), and diatonic semitone (16/15).[6] This is called Ptolemy's intense diatonic tetrachord, as opposed to Ptolemy's soft diatonic tetrachord, formed by 21/20, 10/9 and 16/15 intervals.[7]
In comparison to Pythagorean tuning, while both provide just perfect fourths and fifths, the Ptolemaic provides just thirds which are smoother and more easily tuned.[8]
- Note that D-F is a Pythagorean minor third (32/27), D-A is a defective fifth (40/27), F-D is a Pythagorean major sixth (27/16), and A-D is a defective fourth (27/20). All of these differ from their just counterparts by a syntonic comma (81/80).
Sources [edit]
- ^ Partch, Harry (1979). Genesis of a Music, p.165&73. ISBN 978-0-306-80106-8.
- ^ Murray Campbell, Clive Greated (1994). The Musician's Guide to Acoustics, p.172-73. ISBN 978-0-19-816505-7.
- ^ Wright, David (2009). Mathematics and Music, p.140-41. ISBN 978-0-8218-4873-9.
- ^ Johnston, Ben and Gilmore, Bob (2006). "A Notation System for Extended Just Intonation" (2003), "Maximum clarity" and Other Writings on Music, p.78. ISBN 978-0-252-03098-7.
- ^ see Wallis, John (1699). Opera Mathematica, Vol. III. Oxford. p. 39. (Contains Harmonics by Claudius Ptolemy.)
- ^ a b Chisholm, Hugh (1911). The Encyclopædia Britannica, Vol.28, p.961. The Encyclopædia Britannica Company.
- ^ Chalmers, John H. Jr. (1993). Divisions of the Tetrachord. Hanover, NH: Frog Peak Music. ISBN 0-945996-04-7 Chapter 2, Page 8
- ^ Johnston, Ben and Gilmore, Bob (2006). "Maximum clarity" and Other Writings on Music, p.100. ISBN 978-0-252-03098-7.
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