Thursday, August 22, 2019

There Is No Such Thing As "Perfectly In Tune"

Wow, I see I never had a "tuning" tag before. First I do want to just admit a small caveat: yes, given certain stipulations and an entirely digital environment with synthesized instruments, you can have everything perfectly in tune. But it will sound artificial--because it is. With acoustic musical instruments or with a mixture of acoustic and electronic instruments, perfect tuning is impossible.

But we hear things all the time that sound really in tune, don't we? Yes, but that is because our sensitivity to tuning is both conditioned by habitual listening and limited by our sensitivity. Some composers, like Harry Partch or Ben Johnston, seem to have an enormously greater sensitivity to small pitch differences than most people. For this reason they developed tuning systems that use smaller intervals than the usual ones.

The standard, at least since the late 18th century, system of tuning is called "equal temperament" and it divides the octave into twelve equal parts which enables the modulation to every possible key. Prior to this, with the more or less unequal tuning systems, all keys were not equally useable. But the cost of this usability was the loss of the purity of the intervals derived from the overtones of vibrating strings. Systems like Pythagorean tuning used perfect fifths, but this resulted in some very out-of-tune intervals. The meantone system tried to resolve this problem by making all the fifths a bit narrower, but there were still unusable intervals. The adoptation of equal temperament made all intervals equally usable, but the cost was that all intervals are, just slightly, out of tune!

Sometimes you might see a guitarist struggling with tuning the instrument. This comes from an ignorance of how equal temperament works. As your ear improves you start to notice that when you play an E major chord, the third string sounds out of tune. The reason for this is that on the guitar the sixth string overtone series is quite audible and way up there is a G# that is a Pythagorean interval which is flatter than an equal tempered G#. So the third string sounds sharp if you are playing an E major chord. So you adjust the tuning of the third string a bit. But when you play a C major chord the third string open G natural sounds flat! So you go back and forth and typically end up somewhere in the middle, in effect, tempering the tuning a bit. The solution? Never tune with an E major chord, use E minor instead.

But the same problem exists in more complex environments as well. Piano tuners have to ignore the overtones from the lower strings when tuning the higher ones. Bowed instrument players often adjust the tuning of notes to make them more pure (or perhaps sometimes less pure) according to the context. Singers do the same. Wind instruments also make these kinds of adjustments. If you listen just to a certain point of sensitivity it all sounds perfectly in tune, but the closer you listen the more you get the feeling that everything is just slightly out of tune. Which it is.

Here is the Pachelbel Canon three different tuning systems: Just intonation, meantone and equal temperament. Can you hear the difference?


6 comments:

Marc in Eugene said...

And so vanished two hours of my day; thanks. :-)

I tell myself I can hear differences but am willing to admit that that may be due to the influence of the comments over there.

Such a coincidence! Ross Duffin, whose book How Equal Temperament Ruined Harmony I believe you commented on at some point, was just in Portland to give a lecture ('Byrd: Singing True') and conduct a concert at the Byrd Festival; I missed Duffin's lecture, alas.

Wenatchee the Hatchet said...

Johnston died late last month. I've got the Kepler quartet recordings of his string quartet cycle, which I like quite a bit. My favorite 20th century quartet cycles are easily Bartok and Shostakovich but if I had to pick a favorite late 20th century quartet cycle I'm partial to Johnston's. Johnston described what he was doing as extended just intonation, and in other contexts he described what he was doing as proportional tuning. His collected writings in a book called Maximum Clarity get detailed as to how and why he derived pitch relationships the way he did.

What I found interesting about his writing was he proposed that the atonalists who thought tonality was exhausted and embraced serial techniques hyper-extended gesturalism to the point where the old tonal Romantic cliches were replaced by new serialist cliches. He did study with Partsch and Cage and Milhaud but overall he made a case that we should keep tonal systems of organization ... but not feel obligated to stick to any one tuning system; his Quartet No. 4 variations on Amazing Grace has the variations cycling through different ways of tuning for expressive purposes. So at least in Johnston's case he wasn't arguing for there being anything "perfectly in tune" as much as he was exploring ways to think and compose in multiple tuning systems without sticking to equal temperament methods.

It's no surprise he found it easier to do his microtonal experiments with the string quartet than, say, orchestra. Kyle Gann has written a bit about just intonation experiments, equal divisions of the octave beyond 12 and other things like that over the years.

Johnston's polemical version of his argument was that 12-tone technique exhausted the range of options for equal temperament. Schoenberg avoided the cliches of romantic harmony at the price of developing a technique that spent the other options.

If it's a choice between string quartets by Johnston and, say, Elliot Carter, Johnston definitely wins by keeping my interest more.

Wenatchee the Hatchet said...

in case folks hadn't read it already ... as something of an admirer of Johnston's work ... I wrote a bit about him the day after he died.

https://wenatcheethehatchet.blogspot.com/2019/07/ben-johnston-1926-2019.html

Bryan Townsend said...

My pleasure, Marc!

Jesse Read said...

Hello Brian,
I have enjoyed your blog, and recently found the discussion/history and links to Paul Kling, ( 2011) my great friend from
Victoria and later when I was able to hire him to teach violin at UBC when I was Director of the School of Music. I
miss him. The photo of Lanny and Michael Strutt with you and Kling is a delight, I sent it to Lanny and Michael,
and received appropriate comments. Michael was a great inspiration to me as we developed programs and eventually
CD productions. I miss him too!

Keep up the good work, your blog is informative and I often go there as I develop ideas for my classes at SFU.
https://www.sfu.ca/continuing-studies/courses/plus/362-in-harmonys-luminance-music-that-tells-stories.html

Best regards,
J. Read

Bryan Townsend said...

Jesse, how great to hear from you! I miss Paul as well. It was a great priviledge to perform with him.

I might be up in your neck of the woods sometime next year as I am writing a string quartet for the Pro Nova Ensemble and it may be premiered some time next season. I will let you know!

Your course looks great! I had fun teaching a class for non-music majors at McGill when I was a doctoral candidate there.

Kathryn Cernauskas told me recently that Michael had moved to Australia.

Warm regards,

Bryan