Talk:Just intonation

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)

Outline

My proposed outline:

1. 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.
2. Why JI, Why ET
   1. JI is good
   2. 1. "A fifth isn't a fifth unless its just"-Lou Harrison
   3. Why isn't just intonation used much?
      1. 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.
      2. 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.
3. Just tunings
   1. 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).
   2. 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.
4. 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.
5. conclusion

http://www.musicmavericks.org/features/essay_justintonation.html

Hyacinth (30 January 2004)

Limitations oh Human Hearing Range

Consideration of the various tuning methods such as Just Intonation vs. balanced intonation puts a demand on the skill of the musician, or else the use of something like an oscilloscope. Most humans can hear as tones down to approximately 40 hertz; below that the sound may be interpreted as beats rather than a tone. Depending on age, humans initially may hear as high as 20,000 hertz but a lifetime of loud noise exposure reduces the sensitivity to higher frequencies first. But human hearing has two additional components besides raw upper and lower frequencies: the ability to discriminate small differences in volume and the ability to discriminate small differences in pitch (frequencies). "Perfect Pitch" is the ability to hear smaller differences in frequencies and remember accurately the desired frequency even without a reference note. The corresponding properties in vision would be someone with excellent color vision, who can correctly identify the exact shade or color from memory without reference to a "paint swatch", even when the color is present at low saturation (a pale pastel or a very dark shade approaching black). Individuals who can hear perfect pitch are often pressured to consider a career in music, as they will have a much easier time performing music that is pleasing to the average person's ear compared to someone who is less aware of when they (or their instrument) is not in tune. This ability can be lost due to anything that can lead to hearing loss, just as color vision can be degraded or lost by exposure to light such as a welding arc or harsh chemicals. The definition of who has perfect pitch is subjective, based on someone noticing that the individual is well above average in perception of very small differences in pitch. There is not an objective reference such as the label can only be applied if one can hear a 440 hertz note plus or minus 0.01 hertz and identify that it isn't exactly 440 hertz. 206.206.162.198 (talk) 04:01, 19 May 2025 (UTC)

Just intonation = whole number ratios ?

The article begins with this: "just intonation or pure intonation is a tuning system in which the space between [...] intervals is a whole number ratio." The French article defines [Intonation juste] as a system in which all intervals are "just," and adds that this could only concern octaves, fifths and major thirds, as represented in the Tonnetz. Murray Barbour, in Tuning and Temperament (p. x), defines just intonation as "A system of tuning based on the octave (2:1), the pure fifth (3:2), and the pure major third (5:4)," which corresponds to the definition in the French article. With the more general definition of the English article, Pythagorean tuning (with pure fifths) and meantone temperament (with pure thirds) also belong to just intonation, as do all tuning systems, including Arabic descriptions of "Zalzalian" intervals (neutral thirds) and other non-Occidental descriptions, before the invention of logarithms. The French article says that the name "just intonation" is from 1707, in Sauveur's Méthode générale pour former les systèmes tempérés de musique.

Shouldn't something be done about this? — Hucbald.SaintAmand (talk) 09:50, 9 June 2025 (UTC)

In meantone (with true major thirds) each factor of 3 is replaced by the fourth root of 80, so it is not fully just. —Tamfang (talk) 04:27, 12 June 2025 (UTC)