Does just intonation work for any given key, or is it impractical even for a work in a single key?
According to my understanding any non-chorded instrument, like a string instrument or horn, can use a just intonation, so the problem only arises with chorded instruments like pianos. So, for example, in a symphony that does not have a piano I suppose using just intonation is possible.
On the other hand, let's imagine a piano concerto. As long as the concerto is in a single key, then is it possible to use a just intonation tuning, or will there still be problems?
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Impractical for any key.
C = 1/1
D = 9/8
E = 5/4
F = 4/3
G = 3/2
A = 5/3
B =15/8
C = 2/1
Now check chords; the major chords:
C-E-G 1 : 5/4 : 3/2 or 4:5:6 ratio (multiplying by the LCM)
G-B-D 3/2 :15/8 :18:8 or 4:5:6 ratio
F-A-C 4/3 : 5/3 : 6/3 or 4:5:6 ratio
The minor chords:
D-F-A 9/8 : 4/3 : 5/3 or 27:32:40 ratio <-- !
E-G-B 5/4 : 3/2 :15/8 or 10:12:15 ratio
A-C-E 5/3 : 2/1 :10/4 or 10:12:15 ratio
So the ii chord is already different.
I think it comes down to taste at that point for keyboards. Equal temperament is most common though. A few folk guitar players tune there guitars to just intonnation cause it can give a more pure sound. Coming from a wind band experience and also chior we always try for just intonation as it sounds more in tune and overtones sound nicer, but most of the time the musicians just use their ear and it natrually occurs. Practically and to keep things simpler for piano and mallet players sacrificing being slighty out of tune in every key makes their life simpler and allows you to shift from key to key with out nasty sounding intervals. Hope this helps :)
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