7-limit or septimal tunings and intervals are musical instrument tunings that have a limit of seven: the largest number contained in the interval ratios between pitches is a multiple of seven.
For example, the greater just
minor seventh, 9:5 is a Play ( · help ) info 5-limit ratio, the harmonic seventh has the ratio 7:4 and is thus a septimal interval. Similarly, the septimal chromatic semitone, 21:20, is a septimal interval as 21÷7=3. The harmonic seventh is used in the barbershop seventh chord and music. ( ) Compositions with septimal tunings include Play ( · help ) info La Monte Young's , The Well-Tuned Piano Ben Johnston's String Quartet No. 4, and Lou Harrison's Incidental Music for Corneille's Cinna.
Great Highland Bagpipe is tuned to a ten-note seven-limit scale: [3 ] 1:1, 9:8, 5:4, 4:3, , 27:20 3:2, 5:3, , 7:4 16:9, 9:5.
In the 2nd century
Ptolemy described the septimal intervals: 7/4, 8/7, 7/6, 12/7, 7/5, and 10/7. Those considering 7 to be [4 ] consonant include Marin Mersenne, [5 ] Giuseppe Tartini, Leonhard Euler, François-Joseph Fétis, J. A. Serre, Moritz Hauptmann, Alexander John Ellis, Wilfred Perrett, Max Friedrich Meyer. Those considering 7 to be dissonant include [4 ] Gioseffo Zarlino, René Descartes, Jean-Philippe Rameau, Hermann von Helmholtz, A. J. von Öttingen, Hugo Riemann, Colin Brown, and Paul Hindemith ("chaos" ). [6 ] [4 ]
Lattice and tonality diamond [ edit ]
7-limit tonality diamond:
This diamond contains four
identities (1, 3, 5, 7 [P8, P5, M3, H7]). Similarly, the 2,3,5,7 pitch lattice contains four identities and thus 3-4 axises, but a potentially infinite number of pitches. LaMonte Young created a lattice containing only identities 3 and 7, thus requiring only two axises, for The Well-Tuned Piano.
See also [ edit ]
Sources [ edit ]
^ Fonville, John. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.112, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137.
^ Fonville (1991), p.128.
^ Benson, Dave (2007). Music: A Mathematical Offering, p.212. ISBN 9780521853873.
^ a b c Partch, Harry (2009). , p.90-1. Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments ISBN 9780786751006.
^ Shirlaw, Matthew (1900). Theory of Harmony, p.32. ISBN 978-1-4510-1534-8.
^ Hindemith, Paul (1942). Craft of Musical Composition, v.1, p.38. ISBN 0901938300.