Tuning

[joe grimm]

James Tenney wrote a lot on this topic. One of my favorite essays of his is "John Cage and the Theory of Harmony." Among other things, he talks in this essay about just intonation and "tolerance". I think his account is pragmatic and balanced.

He considers the just (fractionally-related) intervals to be centers of gravity in pitch-space. But obviously on an instrument we can never be 100% in tune (the perfect interval is more like a mathematical ideal that generally doesn't exist in the real world). Even though the intervals we hear are almost never perfect, in a syntactical sense we hear them *as* those just intervals -- this is because of what he calls tolerance: the listener's willingness to accept a certain amount of deviation from the interval. The pitch can be close enough to a just interval for us to accept it. This is why in a practical sense, the chromatic scale works for many purposes -- though the intervals are all out of tune, they fall within the tolerance range.

The just intervals are mathematical realities, but tolerance is variable from one listener to the next, and variable in different cultural contexts.

[7/4]

James Tenney wrote a lot on this topic. One of my favorite essays of his is "John Cage and the Theory of Harmony." Among other things, he talks in this essay about just intonation and "tolerance". I think his account is pragmatic and balanced.

He considers the just (fractionally-related) intervals to be centers of gravity in pitch-space. But obviously on an instrument we can never be 100% in tune (the perfect interval is more like a mathematical ideal that generally doesn't exist in the real world). Even though the intervals we hear are almost never perfect, in a syntactical sense we hear them *as* those just intervals -- this is because of what he calls tolerance: the listener's willingness to accept a certain amount of deviation from the interval. The pitch can be close enough to a just interval for us to accept it. This is why in a practical sense, the chromatic scale works for many purposes -- though the intervals are all out of tune, they fall within the tolerance range.

The just intervals are mathematical realities, but tolerance is variable from one listener to the next, and variable in different cultural contexts.

A nice theory, but not very relevant in practice (for me). This kind of thing is not a reason to not use JI. No one ever seems to discuss how any of the equal temperaments are never really in tune or how accurate they are on acoustic instruments.

[snailed]

James Tenney wrote a lot on this topic. One of my favorite essays of his is "John Cage and the Theory of Harmony." Among other things, he talks in this essay about just intonation and "tolerance". I think his account is pragmatic and balanced.

He considers the just (fractionally-related) intervals to be centers of gravity in pitch-space. But obviously on an instrument we can never be 100% in tune (the perfect interval is more like a mathematical ideal that generally doesn't exist in the real world). Even though the intervals we hear are almost never perfect, in a syntactical sense we hear them *as* those just intervals -- this is because of what he calls tolerance: the listener's willingness to accept a certain amount of deviation from the interval. The pitch can be close enough to a just interval for us to accept it. This is why in a practical sense, the chromatic scale works for many purposes -- though the intervals are all out of tune, they fall within the tolerance range.

The just intervals are mathematical realities, but tolerance is variable from one listener to the next, and variable in different cultural contexts.

A nice theory, but not very relevant in practice (for me). This kind of thing is not a reason to not use JI. No one ever seems to discuss how any of the equal temperaments are never really in tune or how accurate they are on acoustic instruments.

How is it not relevant in practice? If anything, the perfect mathematical ideals of just intonation are not relevant in practice, for the reasons Joe mentions above (an instrument never being able to be completely 100% in tune, inharmonicity, etc etc). They are ideals, and in practice / real life, they do not always conform to those ideals. A tolerance that allows our ears to accept deviations from these mathematically perfect intervals makes using JI a much, much more reasonable and practical way to understand pitch relations. If it had to be perfect, JI music would be unbearable to listen to as there would so rarely (maybe never, unless done via computer) be completely perfect realizations of the music. This is not a theory, but a reality in how listeners actually perceive the sounds.

I don't think Tenney (or Joe, for that matter - but correct me if I'm wrong there) is saying that this tolerance for imperfection is a reason to NOT use JI. Rather, it is a reason TO use JI. With our ability to accept imperfections in intonation, it is far less stifling a prospect to compose in just intonation. This creates an acceptance for imperfect acoustic instruments, or imperfect human performers. This allows JI ideas to be used while not completely invalidating their worth if they are not "perfect". If absolute perfection was necessary, THAT would be a reason not to use just intonation. Only the most virtuostic performers and the most exact, perfect instruments would be acceptable. Instead, to me, it gives one every reason to use just intonation - an art where mistakes and imperfections are not allowed would be stifling. Because there is a tolerance of getting "close", it makes using just intonation as a way of framing or describing pitch relations a much more practical tool.

An intolerance for these imperfections would leave out many works of the genre. Just as an example, Tony Conrad's "Four Violins" is constantly wavering between hitting the perfect just intervals, and finding the way back to them via the cracks in between. That's why that piece works for me, if it was only the perfect just intervals it would be a far less interesting piece. This tolerance for imperfection makes JI less of a science and more of an art, as it should be (all IMO of course).

No one ever seems to discuss how any of the equal temperaments are never really in tune or how accurate they are on acoustic instruments.

As far as everything being perfectly, equally beating, we don't hear complaints as much because people expect imperfections in a tempered scale, since that is one of its defining features - temperament is measured imperfection. I think people should expect some imperfection in JI music, too, for the reasons I stated above. As far as people being down on ET, I hear it all the time. I just got an Amazon.com recommendation for a book that's called "How Equal Temperament Destroyed Music". It's very popular to be down on equal temperament these days, at least within certain groups of the new music community.

[joe grimm]

I don't think Tenney (or Joe, for that matter - but correct me if I'm wrong there) is saying that this tolerance for imperfection is a reason to NOT use JI. Rather, it is a reason TO use JI. With our ability to accept imperfections in intonation, it is far less stifling a prospect to compose in just intonation.

Exactly. Tenney did tons of work using various tuning schemes, including extended just intonation. Obviously he wasn't interested in promoting the hegemony of the chromatic scale. His writings I referenced above are valuable because they keep ideas about intonation in perspective, taking our perceptual tendencies into account. (He also addresses why, despite being out of tune, so much equal-tempered music sounds awesome).

Without this sense of balance, an interest in tuning can lead to a painfully anal search for purity and perfection, which closes off avenues of experimentation rather than opening them up.

[7/4]

A nice theory, but not very relevant in practice (for me).

How is it not relevant in practice?

I don't tune pianos.

[mudd]

presumably somebody does. maybe it would be best if the thread remained generalized, and we didn't dwell on what does or does not work (for you).

m

[7/4]

presumably somebody does. maybe it would be best if the thread remained generalized, and we didn't dwell on what does or does not work (for you).

m

Then people with practical experience should be able to comment without someone else attacking them or editing their comments.

[mudd]

nobody should be attacking you. but i do think you should take a step back from this thread for a bit. practical experience is handy, i'm sure, but it doesn't give permission to make obnoxious posts.

m

[bryan]

...Tony Conrad's "Four Violins" is constantly wavering between hitting the perfect just intervals, and finding the way back to them via the cracks in between. That's why that piece works for me, if it was only the perfect just intervals it would be a far less interesting piece.

Totally. I was going to cite the same piece here. Both "Four Violins" and messing around with Lissajous patterns lead to how I feel about temperament: approaching perfection is more perfect to me than perfection itself.

In the notes to the Early Minimalism Vol 1 box Conrad mentions his intonation slipping on the last violin pass on "Four Violins", and that the newly recorded material sounded really good. For my money, "Four Violins" trumps all the other stuff by a long shot precisely because it's got a thrilling energy to it... it's raw and immediate sounding with all these quavering beat frequencies between notes that are sliding around a bit (thanks bow strokes and intonation slippage).

I like Just Intonation very much, but Equal Temperament does its thing and neither can replace the other. No matter how "perfect" an instrument is tuned, you've got (for example) the individual strings with varying degrees of inharmonicity. We're not just dealing with the fundamentals, the pitches, it's also the competing overtone series between the notes within an interval.. what about those? Not to mention how the pitch changes within a single sounding of a note, from the attack to the decay, the note rises and falls. You gotta draw the line somewhere when it comes to "absolute" note relationships... but the ear's already done that, it's pretty forgiving.

[snailed]

Bryan, those videos are really cool - I didn't see you had embedded a link until just now!

There's an incredible book out there called "Tuning the Historical Temperaments by Ear" by Owen Jorgensen which will teach you how to tune non equal temprered tunings by ear. A lot of this can be applied to other tuning systems plus a lot of the historical temperaments are plenty cool in and of themselves. The book is super rare and expensive to own but libraries and inter-library loan is a viable option.

Hey, I found this book in my local university library today! Along with another (thicker) book by Jorgensen called Tuning. Thanks for the rec, hatta! Looks great. Not only did they have these, but a ton of scores that I had been looking for (Partch, Tenney, all of Ben Johnston's string quartets, except the first- and not so relevant to our topic, but tons of Feldman, Cardew's Treatise... I was very impressed).

[hatta]

Nice! I need to trawl through my local libraries sometime. What with online search I tend to see if they have something specific, then finding they don't never go. Anyway let me know how you find that book, I've been wanting to check it out for ages.

[bryan]

Bryan, those videos are really cool - I didn't see you had embedded a link until just now!

glad you dug it!


BTW, I did a bit more reading with a translation of Ptolemy's Harmonics and the title The Science of Harmonics in Classical Greece. The ancient modes of Greek music came about by playing one note after the other as opposed to choosing note relationships because of how they sounded simultaneously. "Harmonics" was the study of these inherited (from tribal music, etc.) tunings and scales, analyzing and transcribing them.

Pythagoras, more mystic cult leader than scientist, appears to get a heap of undeserved credit via his rediscovery and deepening of the legend by Boethius. His "harmonious blacksmith" is fake, for starters.

[Stephen]

Is there such a thing as a tuner which can tell you the frequency in Hz of a note played into it? Or is it only bulky lab-oscilloscope-type gear that can do that?

[mudd]

you can do an fft in a microprocessor, i don't imagine it would be very difficult to add a microphone, a2d, and and an lcd to the same assembly. so you certainly wouldn't need an oscilloscope.

i think the guy who tuned my piano has just that sort of thing, actually. though of course you realize that you're going to get a pretty broad band from most instruments, so you will get the dominant frequency from a simple readout, not the full spectrum. spectral analysis is pretty easy too, i guess. got any access to matlab?

m

[kp*]

Is there such a thing as a tuner which can tell you the frequency in Hz of a note played into it? Or is it only bulky lab-oscilloscope-type gear that can do that?

Pitch tracking is a notoriously knotty problem. Of course there have been pitch trackers for decades, with many of the early crude ones just tracking zero crossings in the time domain. Not real reliable. As you can imagine a little DC offset and you are up the creek without a paddle. Modern approaches do all kind of different things and results are better. You can do some reasonably good pitch tracking in max/msp using fiddle~, but the results will still occasionally seem highly caffeinated, but folks have had success massaging the data and tweaking fiddle to get it to give you something useful.

I've had luck using Miller Puckett's ancient "pt~" object instead of fiddle~. I've found it's is a bit more responsive, although it does have octave errors, which can be overlooked by "detonate" with the right settings. You'll have to ask around the max/msp list for better answers than i can give you, but if you have a computron and you have access to msp (or pd?) you can download fiddle~ which is free.

cheers,

kevin

[Stephen]

Thanks for the suggestions guys. The dominant frequency would really be plenty for my purposes. I have got a copy of pd that I have never got round to using but that sounds like a practicable solution and certainly preferable to building my own.