More On Tuning And Temperament

Posted by AJ Harbison at 4:48 am

Since my last post sparked some interest in tuning, and just intonation in particular, I thought I’d offer a few more thoughts on the subject. My brother Mark asked the following questions:

You said that equal temperament has been the standard since the 19th century . . . was just intonation the norm prior to that? And do the two go beyond guitars (and similar instruments) into music at large, or are they fairly limited?

I thought that the guitar in the video seemed to sound more “classical” (in the layman sense of the word, not the technical musical sense) than I’m used to hearing guitars sound . . . is that because of the music he’s playing, because of the just intonation, or both? (Or is it because I was conditioned by your post to expect such a thing?)

Prior to equal temperament as the norm, there really was no “norm.” It depended on the instrument and the type of music. Singers, for example, since they’re not tied to any specific tuning like pianos or guitars, often would change their tuning as they sang, correcting intervals without fitting into any particular system. Keyboard instruments (including many organs late into the 19th century) were tuned in what was called meantone temperament, in which a very small interval (a few cents, or more specifically, a quarter comma) was chopped off of each note as one went around the circle of fifths. For example, from C, one would tune G, D, A and then E; and because of the quarter comma taken off of each note, the E (major third) would be in tune with the C. (In a tuning and temperament seminar I took at CSUF, I learned how to tune a harpsichord using this temperament. It was a lot of fun.) Just intonation was used as well, along with Pythagorean tuning (which is similar in that it deals with pure mathematical ratios). Stringed instruments such as violins often used Pythagorean tuning, because it complements the pure tuning of their strings (each a fifth apart). So, in short, equal temperament as the tuning standard for virtually all instruments at all times is rather unprecedented in Western musical history.

As far as the guitar performance in the video goes, yes, Lou Harrison was a composer of art music rather than popular music. But notice the energetic rhythm of the piece, and the occasional strummed chords followed by passages of fast single notes; both are examples of the influence of pop music on art music, and art music’s revitalization of rhythm, in the 20th century.

And my most prolific commenter, Ryan Fleming, pointed out how band leaders instruct brass instruments to lower the third. I believe he’s partially right, in identifying the purpose of that lowering as making the third more pure than the equal tempered interval of 400 cents. But in other cases, since brass instruments play in natural tuning, depending on the key sometimes the natural major third is actually very sharp (up to 427 cents, in some cases–remember, as Fleming said, that a pure major third is 386 cents); so the lowering of the third is not just to make it more pure, but to make it more musically usable.

And to Courtney: So tripped out.



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    ryan fleming on 08.12.2008

    Thank you for the reply! I am glad you clarified that issue for me regarding the brass instruments. I was unaware that brass instruments were naturally tuned. Could you expand on that? What is the reason for this type of tuning if it make some notes extremely sharp (as you mentioned some notes can be up to 40 cents sharp from a justly tuned third)? Is it easier to make a brass instrument with that type of tuning? Or is it because of the harmonic nature of a brass instrument (e.g. the same fingering/tuning can produce different pitches by stepping playing in different harmonic registers)? Please enlighten a curious reader of your blog.

    I also wanted to mention something else that I thought was interesting regarding Kyle Gann’s website. He mentioned that piano tuners will measure the beats per second when tuning certain notes. The beats occur because there is dissonance in the interval because the ratio of frequencies are not whole numbers (because of the equal temperament tuning). I thought it was quite humorous that a piano tuner uses dissonance to tell if a piano is “In Tune”.

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