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Key of examples
Not that there's anything wrong with it, but is there any reason for the examples being changed from C major to F major? Just curious. --Camembert (22 August 2003)
My proposed outline:
- introduction: Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. Another way of considering just intonation is as being based on lower members of the harmonic series. Any interval tuned in this way is called a just interval. Intervals used are then capable of greater consonance and greater dissonance, however ratios of extrodinarily large numbers, such as 1024:927, are rarely purposefully included just tunings.
- Why JI, Why ET
- JI is good
- "A fifth isn't a fifth unless its just"-Lou Harrison
- Why isn't just intonation used much?
- Circle of fifths: Loking at the Circle of fifths, it appears that if one where to stack enough perfect fifths, one would eventually (after twelve fifths) reach an octave of the original pitch, and this is true of equal tempered fifths. However, no matter how just perfect fifths are stacked, one never repeats a pitch, and modulation through the circle of fifths is impossible. The distance between the seventh octave and the twelfth fifth is called a pythagorean comma.
- Wolf tone: When one composes music, of course, one rarely uses an infinite set of pitches, in what Lou Harrison calls the Free Style or extended just intonation. Rather one selects a finite set of pitches or a scale with a finite number, such as the diatonic scale below. Even if one creates a just "chromatic" scale with all the usual twelve tones, one is not able to modulate because of wolf intervals. The diatonic scale below allows a minor tone to occur next to a semitone which produces the awkward ratio 32/27 for Bb/G.
- Just tunings
- Limit: Composers often impose a limit on how complex the ratios used are: for example, a composer may write in "7-limit JI", meaning that no prime number larger than 7 features in the ratios they use. Under this scheme, the ratio 10:7, for example, would be permitted, but 11:7 would not be, as all non-prime numbers are octaves of, or mathematically and tonally related to, lower primes (example: 12 is an octave of 6, while 9 is a multiple of 3).
- Diatonic Scale: It is possible to tune the familiar diatonic scale or chromatic scale in just intonation but many other justly tuned scales have also been used.
- JI Composers: include Glenn Branca, Arnold Dreyblatt, Kyle Gann, Lou Harrison, Ben Johnston, Harry Partch, Terry Riley, LaMonte Young, James Tenney, Pauline Oliveros, Stuart Dempster, and Elodie Lauten.
Hyacinth (30 January 2004)
History needs fixing
I added a section on "terminology" which might help inexperienced readers. But I can't really fix the "history" section because I don't know much about it. The article Pythagorean tuning attributes it to Pythagoras, but a footnote on this page says it's Babylonian. The history section includes a bunch of unnecessary mathematical detail, but I'm loth to take it out without having some real history to include instead, especially history from non-Western cultures. Who can help on this? —Wahoofive (talk) 23:12, 7 November 2019 (UTC)
There seems to be a lot here that isn't to do with Just Intonation itself. Why is Phythagorian tuning here? Why is there 20th Century stuff? This might be helpful *context* for Just Intonation, but this isn't explained and is frankly confusing.
I don't see any mention of Mersenne, Zarlino and so on who discussed these things quite a long time ago and should presumably be definitive sources...
A look in Groves' (at Just Intonation, and Temperament) might help quite a lot here. Sorry I don't have time to take this on myself. -- Preceding unsigned comment added by 220.127.116.11 (talk) 14:39, 7 March 2020 (UTC)