Talk:Just intonation

Update external link to JIN

you have a link on this page to the Just Intonation Network

effective immediately, the URL for the Just Intonation Network has moved

Old URL: www.dnai.com/~jinetwk

New URL: www.justintonation.net

Please update you link.

thank you.

--DBD (David B. Doty--Just Intonation Network)

Done - incidentally David, if you're still around here - you could have edited the page yourself. Wikipedia can be edited by anyone. See Wikipedia:Welcome, newcomers if you're interested. --Camembert (24 November 2004)

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)

Just tuning

I was going to merge the content below from Just tuning, but which "one possible scheme of implementing just intonation frequencies" does the table show? Hyacinth 10:29, 1 Apr 2005 (UTC)

It shows the normally used just intonation scale - I don't think that it has a special name. It can be constructed by 3 triads of 4:5:6 ratio that link to each other, e.g. F-A-C, C-E-G, G-B-D will make the scale of C. Yes, this should definitely be included. (3 April 2005)

Please Wikipedia:Sign your posts on talk pages. Thanks. Hyacinth 22:03, 3 Apr 2005 (UTC)

content for merge:

Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. This table shows one possible scheme of implementing just intonation frequencies.

Just tuning frequencies of all notes in each key based on A = 440 Hz when in the key of C. The just intonation scale ratios of 24:27:30:32:36:40:45 are used and each key note has the same frequency in the scales with +/- 1 sharp or flat.

Note that the 6th note in a key changes frequency by a ratio of 81/80 when it becomes the 2nd of the key with one more sharp or one less flat. All other notes retain the same frequency. In C all frequencies are an exact number of Hertz.

In just intonation incidentals tuning must be worked out on a case by case basis. Often the minor third and minor seventh take the ratios 28 and 42 when the tonic is taken as 24, so that in C the tuning for Eb and Bb would be 308 Hz and 462 Hz. These frequencies allow dominant seventh chords with frequency ratios of 4:5:6:7.

For frequencies in other octaves repeatedly double or halve the tabulated figures.

There is a difference between Gb and F# which amounts to a ratio of ${3^{12}}/{2^{19}}$ = 1.0136433 as discovered by Pythagoras.

Key \ Note	C	Db	D	Eb	E	F	Gb	G	Ab	A	Bb	B
Gb (6b)		278.123		309.026		347.654	370.831		417.185		463.539	494.442
Db (5b)	260.741	278.123		312.889		347.654	370.831		417.185		463.539
Ab (4b)	260.741	278.123		312.889		347.654		391.111	417.185		469.333
Eb (3b)	260.741		293.333	312.889		352		391.111	417.185		469.333
Bb (2b)	264		293.333	312.889		352		391.111		440	469.333
F (1b)	264		293.333		330	352		396		440	469.333
C (0)	264		297		330	352		396		440		495
G (1#)	264		297		330		371.25	396		445.5		495
D (2#)		278.438	297		334.125		371.25	396		445.5		495
A (3#)		278.438	297		334.125		371.25		417.656	445.5		501.188
E (4#)		278.438		313.242	334.125		375.891		417.656	445.5		501.188
B (5#)		281.918		313.242	334.125		375.891		417.656		469.863	501.188
F# (6#)		281.918		313.242		352.397	375.891		422.877		469.863	501.188
Key / Note	C	C#	D	D#	E	F	F#	G	G#	A	A#	B
Equitempered	261.626	277.183	293.665	311.127	329.628	349.228	369.994	391.995	415.305	440.000	466.164	493.883

JI/ horn deletion

Hello, you noted that natural horns play far from just intonation, but the lead from the article says

In music, Just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series.

If natural horn players always modify pitches other than the key note, the deletion makes sense (my small exposure to them suggests they use the natural notes) but if it is because the 7th and 11th harmonics don't fit in the diatonic pattern it doesn't because these are rational intervals and members of the same harmonic series, and the same notes played from the trumpet marine. --Mireut 23:37, 4 February 2006 (UTC)

Actually, I think the whole section (as it was) is rather silly (especially given that there are only two instruments, one of which is rather bizarre). There are thousands of instruments capable of just intonation not mentioned here, many quite conventional. The question is more whether or not they are ever asked to.

However, on the Natural Horn specifically, I think I'd have to argue with you. It produces a harmonic series quite easily, and quite naturally. To produce other notes, yes, there is a stopping technique that is used to flatten pitches. The seventh harmonic is actually used a fair bit, though you're right that the 11th is hardly ever used (Benjamin Britten's Serenade is a fun exception). However, in its standard technique, the harmonic tones which are used (1,2,3,4,5,6,(7),8,9,10,12,(14),15,16) are indeed just.

You might argue that if this is true, the natural horn can only be played just in one key then. This is also true. A quick study of natural-horn writing will attest to this. They were only asked to play in one key at a time, and the out of key notes were expected to be dull and out of tune. I don't think you can rightly argue that the Natural Horn is not a just-intonation instrument. Rainwarrior 00:08, 5 February 2006 (UTC)

According to my understanding just intonation means that each note is in a perfect ratio with the preceding note. In the natural horn, each note is in a perfect ratio with the fundamental of the horn itself, not with each other note. This is not very clearly stated in the article, I agree, but it's rather complicated and I'm not sure how to re-word it. The natural horn is a little more like Pythagorean intonation, although it's not quite that either. I hope this helps. Makemi 00:02, 5 February 2006 (UTC)

Pythagorean tuning is a tuning system of a series of fiths. This is quite different from what the horn does. If you compared a pythagorean diatonic scale to the natural horn's you'd get quite a few differences. On C: C (same: 1/1), D (same: 9/8), E (different: 81/64 vs 5/4), F (different: 4/3 vs irrational), G (same: 3/2), A (different: 27/16 vs irrational), B (different: 243/128 vs 15/8), C' (same: 2/1). Rainwarrior 00:24, 5 February 2006 (UTC)

Actually, I think the whole section (as it was) is rather silly (especially given that there are only two instruments, one of which is rather bizarre)

Sure but then why favor bagpipes? --Mireut 00:22, 5 February 2006 (UTC)

I think this is also silly. That information probably belongs on the bagpipes page. Rainwarrior 00:24, 5 February 2006 (UTC)

Oops, sorry, I reverted without looking at the talk page. My bad. —Keenan Pepper 02:45, 5 February 2006 (UTC)