7-limit tuning

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.

Harmonic seventh Play , septimal seventh.

Septimal chromatic semitone on C Play .

9/7 major third from C to E [1] Play . This, "extremely large third," may resemble a neutral third or blue note.[2]

Septimal minor third on C Play .

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: 7/4, 8/7, 7/6, 12/7, 7/5, and 10/7.[4] 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, A. J. von Öttingen, Hugo Riemann, Colin Brown, and Paul Hindemith ("chaos"[6]).[4]