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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 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 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''. The Great Highland Bagpipe is tuned to a ten-note seven-limit scale:〔Benson, Dave (2007). ''Music: A Mathematical Offering'', p.212. ISBN 9780521853873.〕 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.〔Partch, Harry (2009). ''Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments'', p.90-1. ISBN 9780786751006.〕 Those considering 7 to be consonant include Marin Mersenne,〔Shirlaw, Matthew (1900). ''Theory of Harmony'', p.32. ISBN 978-1-4510-1534-8.〕 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 Gioseffo Zarlino, René Descartes, Jean-Philippe Rameau, Hermann von Helmholtz, A. J. von Öttingen, Hugo Riemann, Colin Brown, and Paul Hindemith ("chaos"〔Hindemith, Paul (1942). ''Craft of Musical Composition'', v.1, p.38. ISBN 0901938300.〕).〔 ==Lattice and tonality diamond== The 7-limit tonality diamond: This diamond contains four identities (1, 3, 5, 7 (P5, M3, H7 )). Similarly, the 2,3,5,7 pitch lattice contains four identities and thus 3-4 axes, but a potentially infinite number of pitches. LaMonte Young created a lattice containing only identities 3 and 7, thus requiring only two axes, for ''The Well-Tuned Piano''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「7-limit tuning」の詳細全文を読む スポンサード リンク
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