7-limit tuning
Musical instrument tuning with a limit of seven / From Wikipedia, the free encyclopedia
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7-limit or septimal tunings and intervals are musical instrument tunings that have a limit of seven: the largest prime factor contained in the interval ratios between pitches is seven. Thus, for example, 50:49 is a 7-limit interval, but 14:11 is not.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Harmonic_seventh_on_C.png/320px-Harmonic_seventh_on_C.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/2/27/Septimal_chromatic_semitone_on_C.png/320px-Septimal_chromatic_semitone_on_C.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Septimal_major_third_on_C.png/320px-Septimal_major_third_on_C.png)
![7 upside-down](http://upload.wikimedia.org/wikipedia/commons/thumb/4/4b/7_upside_down.png/8px-7_upside_down.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Septimal_minor_third_on_C.png/320px-Septimal_minor_third_on_C.png)
For example, the greater just minor seventh, 9:5 (Playⓘ) is a 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. (Playⓘ) Compositions with septimal tunings include La Monte Young's The Well-Tuned Piano, Ben Johnston's String Quartet No. 4, Lou Harrison's Incidental Music for Corneille's Cinna, and Michael Harrison's Revelation: Music in Pure Intonation.
The 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: 21/20, 7/4, 8/7, 7/6, 9/7, 12/7, 7/5, and 10/7.[4] Archytas of Tarantum is the oldest recorded musicologist to calculate 7-limit tuning systems. Those considering 7 to be 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.[4] Those considering 7 to be dissonant include Gioseffo Zarlino, René Descartes, Jean-Philippe Rameau, Hermann von Helmholtz, Arthur von Oettingen, Hugo Riemann, Colin Brown, and Paul Hindemith ("chaos"[6]).[4]