by Erik Zuurbier
[Skip the intro? Lots of music here]
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[Is just intonation good for you? Do the self test]
In the following fragment you can hear the first two tones (C, E) of "Oh when the saints, go marching in", first in succession, then together:
The tuning in this fragment is that of most ordinary keyboard instruments. That tuning is called 12 tone equal temperament. Do you hear the restless/harsh/exciting sound quality when the two tones sound together at the end? That is the effect of beating. Listen very carefully, you can play this more than once.
The following fragment contains the same tones, but now - starting after 6 seconds - the high tone's pitch gradually shifts a tiny bit so that the tone ends up in tune with the lower tone, to form a true consonant:
Do you hear a significant change starting after 6 seconds to a more tranquil/peaceful/dull sound quality? That is the basic idea of just intonation.
The following is a modulation from C major to D♯ major taken from [Re 1903], first in ordinary keyboard tuning (12 tone equal temperament), then in just intonation. It is advised to use quality headphones or speakers.
(Reger, twice)
The difference between just intonation and 12 tone equal temperament could hardly be more evident than in these two Reger-fragments. Here, Reger wrote major and minor triads only: all with fast beating in 12 tone equal temperament and with no beating at all in just intonation. Also, an organ stop of pitch 1 3/5' was used. That emphasises a tone's 5th partial and clearly exposes fast beating in 12 tone equal temperament.
Another example: the closing measures of Trio Sonata BWV526 by J.S. Bach, second movement. Again: in 12 tone equal temperament and in just intonation. Please pay special attention to the sound quality of the long sustained tones in the upper voices over a bass melody, and to the sound quality of the final chord.
(Bach twice)
It will pay off later if you take the time here to compare these Bach fragments until you really grasp the difference. The following fragment may help you with that. It extracts those long sustained tones of the upper voices - each first in 12 tone equal temperament and immediately repeated in just intonation.
The consequences of using just intonation in keyboard music are huge. For instance, you will need many more than the usual 12 pitches per octave. The Reger fragment has 15 different pitches per octave, as opposed to 10 for the 12 tone equal temperament version. The complete works on this website use 17 to 49 different pitches per octave.
On this website the results of over ten years of investigations into just intonation are being published: