Jan Swafford’s second recent article on Slate.com concerns the history of tuning and temperament, and it’s an excellent summary of the subject. It’s another enjoyable read–I particularly like the way he describes the impossibility of pure tuning as “the laughter of the gods” and continues the image throughout the article. And again he includes some great musical clips, including Peter Watchorn playing from Bach’s The Well-Tempered Clavier (which, Swafford says, was written “not only to show off this improved system but to help make well-temperament mandatory by writing irreplaceable pieces in every key”) and a side-by-side comparison of a Beethoven sonata movement in modern equal temperament and in a 19th century tuning called Prinz. Can you hear the difference? (Hint: I think it’s a little easier to hear listening to the Prinz first and then the equal temperament, rather than the other way around.)

“The Wolf at Our Heels: The centuries-old struggle to play in tune”



Posted by AJ Harbison at 4:38 pm

The office I work in is about a block down the street from my company’s main office, and I usually walk back and forth between them once or twice a day. I was walking back from the main office this afternoon, and passed a couple of guys with leafblowers cleaning up a parking lot. Each of them had one, and the hum of the two leafblowers was the interval of a fifth apart–in almost-perfect tuning. (A fifth is the distance of, for example, C up to G, or A up to E). They were different sizes, which explained the difference in pitch: the higher one was completely handheld and narrower, while the lower one had a backpack and a bigger tube. Bigger and longer always equals lower in acoustics, whether it’s a string or a column of air–consider how much bigger a cello or double bass is compared to a violin, or a bassoon compared to an oboe.

My first thought was that the “bore” size of the second one must be bigger than the first by a third–because a perfect fifth is created by the ratio of 3:2 to the original note (for example, the rate a string vibrates to produce the tone G is in the ratio of 3:2 to the rate the same string vibrates to produce a C). But I quickly corrected myself when I realized that the hum was created not by the air moving through the tube, of course, but by the motor. (Less interesting that way, but has the virtue of being true). So the fifth was created by some 3:2 ratio between the motors; since I know nothing about mechanics, though, I’m not sure exactly what property it was that created the ratio. But I still found it interesting. Just goes to show that you should always be listening–music (or at least a semblance of it) can be found in the most unexpected places!


“The Drone of the American Continents”

Posted by AJ Harbison at 9:59 am

Last night there was a fearful (and exciting) thunderstorm in Costa Mesa with thunder so loud it made our windows rattle.  The commotion woke my wife and I in the middle of the night, and we looked out our window to catch some views of the lightning and rain before going back to bed. Shortly after we turned back in, our power went out, which (along with everything else) killed the fan that was running in our room. The whole block had lost power, and so everything was very quiet–eerily quiet. We hardly ever, or never, notice it, but there is a constant electric hum that is always running just underneath our perception–we never notice it because it’s always there (just as a fish would never notice that it’s wet because it’s always underwater). But last night, when the power died, the hum disappeared, and it left a notable silence. It was much closer to silence than we ever normally get; my wife loved it, but it made me a little uneasy.

It didn’t last long, and after twenty minutes or so the power came back on. I heard the fan start up again, and faintly, underneath it, I heard the hum begin again; but I couldn’t hold onto it for long, and it soon disappeared again under my level of perception. But it was interesting to experience it unmasked, if only for a short while.

La Monte Young, the father of the musical minimalism movement, explored the concept of drones (a constant tone around which other tones move) quite a bit in his music, and was also one of the primary proponents of just intonation in the last century. He often staged performances and improvisations at his home in New York, and he says in one paper that he chose the 120-cycle hum of his home’s aquarium motor for a drone in order to keep it “in tune with the frequency of the 60 Hz AC power supplied by Con Edison” (basically meaning that the pitch of the hum of the motor was an octave above the hum of the power; 60 Hz is approximately equal to the B-natural two octaves below middle C). He ends that section with this quote, which tends toward the poetic but accurately sums up what I’ve been talking about:

The primary drone on my Original master tape of “April 25, 1965 day of niagra” is 80 Hz, 4/3 above 60 Hz, which is the dominant or the 5th degree. Because the recorder used to make the unauthorized copy that produced the Table of The Elements CD 74 ran at a slightly different speed from the Original, the ToE CD is at a slightly higher frequency and, therefore, has lost the intended effect of its harmonious relationship of a perfect just fourth to the 60 Hz AC power line drone of the American continents.

(P.S. I’m sorry that I haven’t been posting much lately–I’ve still been busy, and I’m still working on putting together my music website at http://www.ajharbison.com. But that’s coming together quite well, and I’m hoping to start posting more often again. We soon return you to your regularly scheduled TLB!)



Posted by AJ Harbison at 9:37 pm

Thanks to my company being so cool, I had the chance to watch part of the inauguration ceremony on Tuesday morning of this week. They set up the big-screen TV in the conference room to stream the video feed; unfortunately it kept hiccuping, the audio and video were out of sync, etc. which was pretty annoying. But I enjoyed the chance to see it regardless.

As you probably know, famed film composer John Williams composed a piece specifically for the inauguration entitled Air and Simple Gifts, based on the famous Appalachian folk melody, and it was performed live by cellist Yo-Yo Ma, violinist Itzhak Perlman, pianist Gabriella Montero and clarinetist Anthony McGill. My first thought upon seeing the performers was “They can’t really be playing, it’s way too cold for the instruments to stay in tune!”

You know, turns out I was right. I saw an article on MSN today making that same point. The musicians were in fact performing live, so the people who were close enough to them could hear them playing; but the instruments were not amplified and the music that was broadcast over the speakers at the event and to the millions watching on TV (myself included) had been recorded several days before.

That’s a reasonable decision–really the only reasonable one, if you think about it. The temperature was about 30 degrees, as the article points out, too cold for any of the instruments to play in tune but especially “play[ing] havoc” on the piano. This happens pretty frequently with classical performances in very cold environments, and even the great tenor Luciano Pavarotti famously lip-synced his final performance. I fully support the decision of the musicians at the inauguration, as I imagine any reasonable person who understands the factors involved would. But I find it amusing that the press wants to make a point of revealing this fact. The article can be found at the link below.

“Their performance was live — but music wasn’t”

When I wrote the first draft of this post, I replaced my original text “I find it amusing that the press wants to make it a big deal” with the text of my penultimate sentence above, thinking the word choice of the former was too strong. But several hours later, the article made it to a more prominent place on MSN’s front page and also added a reader poll, entitled “Vote: Bad Choice?” So now I return to my original thought. It’s ridiculous that the press is making such a big deal out of it. The actual question on the poll is practically incriminating: “Was it wrong to ‘fake’ music at the presidential inauguration?” Fortunately, 68.2% of the people who voted in the poll voted no. But some of the responses (you can comment as well as vote in the poll) are rather amusing in themselves; one person who voted yes commented “Just more smoke & mirrors from the obamamite camp.” The third option in the poll (besides “yes, it was wrong to fool the masses” and “no, who cares, it sounded good”) is “Maybe. If this is how the administration starts out …”, and one of the readers who voted that option also commented “i’m not at all surprise if it was recorded, everything sorrounding the obama campain has been stained with deceitfulness” [sic]. As if Obama or his “obamamite camp” or “campain” had anything to do with the performance (whatever the heck they are). Doesn’t anyone have any common sense anymore?


Electronic Beeps In The Office

Posted by AJ Harbison at 12:48 am

I was sitting at my desk the other day, minding my own billings, when I heard two electronic beeps go off at the same time. The first was the printer in the copy room, beeping to indicate the job it was printing was finished; the second was the microwave in the kitchen down the hall, beeping to indicate the food it was cooking was finished. In any case, they beeped at the same time. The interval between the two beeps was a minor second (e.g. the distance between C and C-sharp), but it was a very small one–the notes were closer together than a half-step. A minor second is defined as 100 cents; I don’t really know, but maybe this was 70 cents. (For prior TLB discussions of tuning and temperament, click here.) It was a very small interval, and a very shrill and displeasing sound.

I wonder who creates the beeps in machines like that. Do the engineers or manufacturers know what note their beep will be? Do they design it with a particular note in mind? Does anyone other than me care?


Beethoven In The Temperaments, Enid Katahn

Posted by AJ Harbison at 2:50 am

While reading back over Kyle Gann’s website about historical tunings in research for my first post about tuning, I came across his recommendation for the CD Beethoven In The Temperaments. (The link is to the Amazon page, but Amazon is currently out of stock and will remain so indefinitely.) The CD is a recording of four Beethoven sonatas–the “Pathétique,” the “Moonlight,” the “Waldstein” and the creatively named “Op. 14 No. 1.” The twist is that they’re performed on a modern concert grand piano (a Steinway D, for those for whom that means something) that’s tuned in two different historical well temperaments common in Beethoven’s time: Prinz temperament and Thomas Young temperament. (The pianist is Enid Katahn, and the piano tuner is Edward Foote.) So, essentially, this is a recording of Beethoven’s sonatas as Beethoven might have heard them. (Had he not been deaf, of course….)

I thought it sounded intriguing (no pun intended), so after failing to find it on iTunes, Amazon, or anywhere else I finally ordered it from ArkivMusic. It arrived on Thursday evening, and I listened to the Pathétique, which is performed in the Prinz temperament. The liner notes said that this temperament was chosen for the great contrasts between keys: pure and consonant for the “home keys” of the piece, and more and more dissonant the further the tonality went from “home.”

(Minor digression: I love Steinways. I’m a huge fan of dark, mellow and rich when it comes to sound, and Steinways are the epitome of that sound in a concert grand. Yamahas, while more popular and much cheaper, tend to be much brighter. If you play guitar, you’ll understand: Steinways are like Martins–sigh–while Yamahas are like Taylors. The latter are good, maybe even really good, but ultimately just can’t compare. For me, at least.)

I have to say that I didn’t notice a world of difference–the difference was certainly there, but it wasn’t nearly as pronounced as I anticipated (or perhaps hoped). In the opening chords of the sonata (click here and push the play button twice–although of course it’s in equal temperament), I could hear slight differences in the resonances of the chords–they were somewhat richer. But the most notable were the dissonances, especially in big chords: they really stood out, almost uncomfortably in places, because of the temperament. It’s interesting, and a foreign concept to those of us raised on equal temperament, that dissonances in other tunings can be dissonant not only because the notes themselves clash (like minor ninths, for example), but also because the notes aren’t quite in tune with one another. As I mentioned, the Prinz temperament showcases differences in keys, and gets more dissonant the further afield the piece roams; so some of the dissonances in the “further afield” keys can get positively crunchy. (Yes, that’s a technical term.)

Overall, it was a rich sound, certainly more colorful and vibrant than an equal-tempered piano. Another interesting temperament experience. It’s no wonder musicians who work in just and well temperaments all the time consider equal temperament so bland.


And… A Little Bit More

Posted by AJ Harbison at 12:05 am

My highly trained professional blogging and SEO consultant Mike (also known as my roommate) has instructed me that responding to comments on my blog is a way to increase interest and also increase commenting, and thus I have decided that I will do so. Therefore, if you leave a comment, I will likely reply to it within a day or so, in the comments section; you can go back to the comments section for that post and there discover my response.

But in the meantime, I thought I would dedicate one more post to tuning before we move on to other things, because Ryan Fleming again brought up an interesting question:

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.

This may get a bit technical, so hang in there with me….

Every pitched note, on any instrument, voice or whatever, actually contains an infinite series of notes within itself. For example, if you play middle C on the piano, there are actually notes sounding above it in addition to middle C: the C an octave higher, the G above that, the C above that, the E above that, etc. etc. ad infinitum. These other notes are an acoustic phenomenon we call “harmonics” or “overtones.” The reason we don’t hear these notes is because they are very weak and diminish as they get higher; but they’re always there, and they’re very influential in the sounds that we hear. When you hear a violin and a flute playing, you can tell that the sounds are being made by different instruments (musicians call this different-sound-quality between instruments timbre pronounced “TAM-bur”]). The reason those instruments sound different is that their overtones are different–various overtones are strengthened or diminished because of the construction and playing method of the instrument, and even though you can’t hear the overtones themselves it’s a big enough difference to allow us to hear very different timbres. Trippy, but true.

Brass instruments, like trumpets for example, are built around this principle. If you take a column of air (like in a garden hose, for example), put a proper mouthpiece on it, and cause the column of air to vibrate (like by blowing through it, for example), it will produce a pitch. And believe it or not, by changing the shape of your mouth (called your embouchure) and the way you blow, you can produce different pitches. The reason for this is that by changing those things, you can access the notes of the overtone series, without the use of any valves, buttons or extra tubes. Also trippy, but also true. The next time you’re around a trumpeter friend who happens to have a mouthpiece and a section of tubing handy, ask him to demonstrate. Here is a diagram of the first 16 harmonics, starting on C and then F (image courtesy of www.usd.edu/~greeves/exercises.htm):

All of the valves, tubes and slides on brass instruments exist for the purpose of making available to the player notes other than these, because with only a tube, these are the only notes that are possible. Valves and slides and such alter the length of tubing, thus making available a different harmonic series. For example, the first valve on a trumpet lowers the pitch by a whole step. If you were playing in the key of C, you would have all of the notes of the C harmonic series (the first one in the diagram) available, and no others. If you played a C note, and then depressed the first valve and “played” the same note (with the shape of your mouth and the way you were blowing air), it would be a B-flat, and you could then use the notes of the B-flat harmonic series, some of which occur in the key of C but not in the C harmonic series or at least not in the same range (for example D; D does occur in the C harmonic series [as the 9th harmonic, as you can see in the diagram above], but if you needed to play the D a whole step above middle C you would need a different series).

This is why brass instruments are said to be in certain keys: “Trumpet in B-flat,” or “Horn in F.” The key is the harmonic series of the instrument without any modifications. Without any valves, the French horn would only be able to play the notes of the F harmonic series detailed in the diagram, because that’s the way the instrument is built.

However, valves and buttons and slides can alter the pitch a little more than intended, and certain combinations have certain tendencies to be off. In addition, many other factors including temperature, playing volume and mouthpiece design can make pitches slightly sharp or flat. A quick glance at this page will give you a much greater appreciation for brass players and the problems they face.

All this to say: Because of the way brass instruments work, depending on the key of the instrument, the key of the piece, what note needs to be played, what valve combination is necessary, the temperature and myriad other variables, some notes need to be altered in order to be “in tune.” (Pitch on a brass instrument can be slightly modified–tuned a little up or down–by changing your embouchure.)

And this, in many cases, includes major thirds.


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.


As I mentioned in my last post, the second event of the concert in Long Beach was a set of guitar pieces by Lou Harrison, performed by John Schneider (of the Partch Ensemble). Harrison (1917-2003) was an American composer who wrote mostly in just intonation, a system of tuning based on pure mathematical ratios, as opposed to the irrational ratios used by the more widespread equal temperament. (As a brief aside: Many hold that just intonation is a purer and more beautiful tuning than equal temperament–the standard in western music from the 19th century to the present day–but the former becomes impractical after a certain harmonic point because some intervals get so out of tune that they become unusable.)

Before Schneider played the pieces (he actually played two suites), he gave a brief talk about Harrison, the tuning he used, and the pieces themselves. The most interesting part of his discussion was his explanation of the guitars he used. Typical guitars use equal-tempered frets, so that they can play with pianos and other equal-tempered instruments, and their fretboards look like this:

However, in order to play just intonation music on a guitar, the fretboard must be modified, to look more like this (the man in this picture, by the way, is Schneider himself):

Remarkably, he showed the bewildered audience that the fretboard was actually a magnet–he slipped it right out from under the strings and held it up to show us. The neck was magnetic, he explained, and the justly-tuned fretboards were put on large magnet boards–just like a kitchen magnet–so they could be interchangeable. The pieces themselves were very good, and held my interest much longer than the other pieces in the concert. I recorded a video of the performance on my cell phone, which you can see below. Neither the video nor the audio quality is too good, but you can hear how the tuning is different from a normal guitar.

Tuning is really a fascinating subject. If you’re interested in learning more, you can find articles and resources at the website of The Just Intonation Network, as well as the excellent Tuning Information page on Kyle Gann’s website.