7-limit or septimal tunings and intervals are musical instrument tunings that have a

limit Limit or Limits may refer to: Arts and media * ''Limit'' (manga), a manga by Keiko Suenobu * ''Limit'' (film), a South Korean film * Limit (music), a way to characterize harmony * "Limit" (song), a 2016 single by Luna Sea * "Limits", a 2019 ...

of seven: the largest

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only way ...

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. For example, the greater just

minor seventh In music theory, a minor seventh is one of two musical intervals that span seven staff positions. It is ''minor'' because it is the smaller of the two sevenths, spanning ten semitones. The major seventh spans eleven. For example, the interval fro ...

, 9:5 () is a

5-limit Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note ...

ratio, the

harmonic seventh The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cent (music), cents). This is somewhat narrower than and is, "particularly sweet", "sweeter in quality" tha ...

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 Music is generally defined as the The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...

. () Compositions with septimal tunings include La Monte Young's '' The Well-Tuned Piano'', Ben Johnston's String Quartet No. 4,

Lou Harrison Lou Silver Harrison (May 14, 1917 – February 2, 2003) was an American composer, music critic, music theorist, painter, and creator of unique musical instruments. Harrison initially wrote in a dissonant, ultramodernist style similar to his ...

's ''Incidental Music for Corneille's Cinna'', and Michael Harrison's ''Revelation: Music in Pure Intonation''. The

Great Highland bagpipe The Great Highland bagpipe ( gd, a' phìob mhòr "the great pipe") is a type of bagpipe native to Scotland, and the Scottish analogue to the Great Irish Warpipes. It has acquired widespread recognition through its usage in the British mil ...

is tuned to a ten-note seven-limit

scale Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number ...

: 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 Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of import ...

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'', pp. 90–91. . Those considering 7 to be

consonant In articulatory phonetics, a consonant is a speech sound that is articulated with complete or partial closure of the vocal tract. Examples are and pronounced with the lips; and pronounced with the front of the tongue; and pronounced ...

include

Marin Mersenne Marin Mersenne, OM (also known as Marinus Mersennus or ''le Père'' Mersenne; ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for ...

Giuseppe Tartini Giuseppe Tartini (8 April 1692 – 26 February 1770) was an Italian composer and violinist of the Baroque era born in the Republic of Venice. Tartini was a prolific composer, composing over a hundred of pieces for the violin with the majority of ...

Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

François-Joseph Fétis François-Joseph Fétis (; 25 March 1784 – 26 March 1871) was a Belgian musicologist, composer, teacher, and one of the most influential music critics of the 19th century. His enormous compilation of biographical data in the ''Biographie univ ...

, J. A. Serre, Moritz Hauptmann, Alexander John Ellis, Wilfred Perrett, Max Friedrich Meyer. Those considering 7 to be dissonant include

Gioseffo Zarlino Gioseffo Zarlino (31 January or 22 March 1517 – 4 February 1590) was an Italian music theorist and composer of the Renaissance. He made a large contribution to the theory of counterpoint as well as to musical tuning. Life and career Zarlino w ...

René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathe ...

Jean-Philippe Rameau Jean-Philippe Rameau (; – ) was a French composer and music theorist. Regarded as one of the most important French composers and music theorists of the 18th century, he replaced Jean-Baptiste Lully as the dominant composer of French opera ...

Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Associatio ...

, Arthur von Oettingen,

Hugo Riemann Karl Wilhelm Julius Hugo Riemann (18 July 1849 – 10 July 1919) was a German musicologist and composer who was among the founders of modern musicology. The leading European music scholar of his time, he was active and influential as both a mu ...

, Colin Brown, and

Paul Hindemith Paul Hindemith (; 16 November 189528 December 1963) was a German composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advocate of the '' ...

("chaos" Hindemith, Paul (1942). ''Craft of Musical Composition'', vol. 1, p. 38. .).

Lattice and tonality diamond

The 7-limit tonality diamond: This diamond contains four identities (1, 3, 5, 7 8, 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''.

Approximation using equal temperament

It is possible to approximate 7-limit music using equal temperament, for example 31-ET.

References

External links

Centaur a 7 limit tuning
shows Centaur tuning plus other related 7 tone tunings by others {{Musical tuning

Lattice and tonality diamond

Approximation using equal temperament

See also

References

External links