The undecimal neutral sixth has a ratio of 18:11 between the frequencies of the two tones, or about 852.59 cents. playⓘ
A tridecimal neutral sixth has a ratio of 13:8 between the frequencies of the two tones, or about 840.53 cents.[3] This is the smallest neutral sixth, and occurs infrequently in music, as little music utilizes the 13th harmonic. playⓘ
An equal-tempered neutral sixth is 850 cents, a hair narrower than the 18:11 ratio. It is an equal-tempered quarter tone exactly halfway between the equal-tempered minor and major sixths, and half of an equal-tempered perfect eleventh (octave plus fourth). playⓘ
These intervals are all within about 12 cents of each other and are difficult for most people to distinguish. Neutral sixths are roughly a quarter tone sharp from 12 equal temperament (12-ET) minor sixths and a quarter tone flat from 12-ET major sixths. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together.
A neutral sixth can be formed by subtracting a neutral second from a minor seventh. Based on its positioning in the harmonic series, the undecimal neutral sixth implies a root one minor seventh above the higher of the two notes.
^[1] Jan Haluska, The Mathematical Theory of Tone Systems, CRC (2004).
^Fauvel, John; Flood, Raymond; and Wilson, Robin J. (2006). Music And Mathematics, p.21-22. ISBN9780199298938.
January 01, 1970
neutral, sixth, neutral, sixth, musical, interval, wider, than, minor, sixth, play, narrower, than, major, sixth, play, three, distinct, intervals, termed, neutral, sixths, undecimal, neutral, sixth, ratio, between, frequencies, tones, about, cents, play, trid. A neutral sixth is a musical interval wider than a minor sixth play but narrower than a major sixth play Three distinct intervals may be termed neutral sixths The undecimal neutral sixth has a ratio of 18 11 between the frequencies of the two tones or about 852 59 cents play A tridecimal neutral sixth has a ratio of 13 8 between the frequencies of the two tones or about 840 53 cents 3 This is the smallest neutral sixth and occurs infrequently in music as little music utilizes the 13th harmonic play An equal tempered neutral sixth is 850 cents a hair narrower than the 18 11 ratio It is an equal tempered quarter tone exactly halfway between the equal tempered minor and major sixths and half of an equal tempered perfect eleventh octave plus fourth play Neutral sixthInverseneutral thirdNameOther names Abbreviationn6SizeSemitones 8 Interval class 3 Just interval18 11 1 or 13 8 2 Cents12 Tone equal temperamentN A24 Tone equal temperament850Just intonation853 or 841 Neutral sixth on C Play These intervals are all within about 12 cents of each other and are difficult for most people to distinguish Neutral sixths are roughly a quarter tone sharp from 12 equal temperament 12 ET minor sixths and a quarter tone flat from 12 ET major sixths In just intonation as well as in tunings such as 31 ET 41 ET or 72 ET which more closely approximate just intonation the intervals are closer together A neutral sixth can be formed by subtracting a neutral second from a minor seventh Based on its positioning in the harmonic series the undecimal neutral sixth implies a root one minor seventh above the higher of the two notes Thirteenth harmonic edit nbsp Thirteenth harmonic on C Play The pitch ratio 13 8 840 53 cents is the ratio of the thirteenth harmonic and is notated in Ben Johnston s system as A13 In 24 ET is approximated by A nbsp This note is often corrected to a just or Pythagorean ratio on the natural horn but the pure thirteenth harmonic was used in pieces including Britten s Serenade for tenor horn and strings 4 See also editList of musical intervals List of pitch intervals Microtonal musicReferences edit Haluska Jan 2003 The Mathematical Theory of Tone Systems p xxiv ISBN 0 8247 4714 3 Undecimal neutral sixth Haluska 2003 p xxiii Tridecimal neutral sixth 1 Jan Haluska The Mathematical Theory of Tone Systems CRC 2004 Fauvel John Flood Raymond and Wilson Robin J 2006 Music And Mathematics p 21 22 ISBN 9780199298938 Retrieved from https en wikipedia org w index php title Neutral sixth amp oldid 1146610259, wikipedia, wiki, book, books, library,
