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Sunday
Nov152009

Well-Tempered Instruments

[Ancient Faith Radio; Sept 9, 2009]

 

F: I’m sitting at my kitchen table on a Thursday morning, talking to my son Stephen Mathewes, who is going away tomorrow. He’s going to drive up to Holy Cross Seminary in Brookline, Massachusetts, and begin classes as a seminarian, and, hopefully, in three years graduate and be ordained a priest. Dad and I are very, very proud of you, son.

 

S: Thank you.

 

F: [laughs] But he also has a sideline. He was a Musicology major in college, and during the course of that time, to pick up a little extra cash, he became a piano tuner. Now, some years ago, when you all were small, I read an article in a magazine or a newspaper, assessing, “What is the very best possible job?” Of all the jobs, of all the professions. And they ranked them by different categories, like how much flexibility do you have? How stressful is it? Are you exposed to the elements? Are you out in the rain? And when they combined all of that, the best job in the world was piano tuner. Because you’re self-employed, it’s low-stress, it’s never an emergency, you can take time off and go see your kid’s play and then tune the piano after that. The hang-up was that you had to have perfect pitch, or very close to perfect pitch. Things have improved, so now there are electronic piano tuners that, though they don’t substitute for an exquisite sense of pitch, sort of help it along. So, the piano tuning field is more crowded. When you get up there to Brookline, I know you’re going to try and establish yourself as a piano tuner there. And you were saying that, who knows why, but that it is one of the most crowded markets in the country, that there were 109 piano tuners in the local association, and in all of New York only 77.

 

S: Yeah, somewhere around 75, or so. Which just seems so ridiculous.

 

F: Imagine that; with all the live music venues there are in New York. So who knows why? A lot of pianos in Boston, I guess, or I hope so!

 

S: Right. I don’t know the population difference between Boston and Baltimore. I’m sure Boston is at least a little bit bigger. But Baltimore has about 40 or so tuners.

 

F: Huh.

 

S: And even that is fairly well-saturated.

 

F: Huh.

 

S: So I’m not really sure what to expect when we get to Boston [laughs]. Because that’s one of the things that I had always heard about piano tuning as I was getting into it: that there is always such a demand, it’s so easy to find work. And that’s certainly been true for friends of mine who have gone into piano teaching

 

F: Oh, yes.

 

S: But, for me, in the Baltimore area, it’s been a little on the tough side. I mean, I’ve had to be a little more aggressive and proactive than usual to try and gain clients. And it seems to me that Boston is just going to be that much worse. And in fact, I was speaking with the [Piano Technicians] Guild [Boston chapter] president, and she mentioned to me that Boston is quite possibly the most saturated, or overly-saturated, tuning market in all of the country.

 

F: Oh my goodness.

 

S: So yeah, it’s going to be tough.

 

F: A lot of people who start out in piano tuning have the advantage that they can go right to the churches of their denomination. And of course we don’t have pianos in Orthodox churches. [laughs]

 

S: Right. But there are still markets that hopefully I can tap there; through Holy Cross hopefully, and people from the church that we will be attending, St. George in Norwood. Hopefully I’ll be able to meet some good people, and get the name out there, and let God…

 

F: …open those doors for you.

 

S: Yeah, exactly.

 

F: The whole question of tuning, tuning pianos or tuning stringed instruments, is something I don’t understand. It’s called “temperament”, isn’t it? What does temperament mean? And I know that Bach composed a series of exercises for the, quote, The Well-Tempered Clavier?

 

S: Preludes and Fugues. There was a prelude and a fugue each for all of the 24 keys.

 

F: Only 24 keys on a clavier?

 

S: [laughs] No, no, harmonic keys.

 

F: Harmonic keys. Like, in the key of ‘C’.

 

S: Exactly. Key of ‘C’, key of ‘C minor’, then ‘C-sharp’, then ‘C-[sharp] minor’. All the way up.

 

F: Oh, that reminds me of something I read. [laughs] I was reading a book about animals growing and developing in the womb, and it was talking about a dog’s hearing. It said that if you went all the way to the high end of the piano scale, for the highest note a human can hear, you would add 28 keys to the piano. But for the highest note a dog could hear, you would add four octaves.

 

S: Wow.

 

F: Yeah, it’s kind of imposing.

 

S: I believe it. Very cool.

 

F: So what did it mean in Bach’s time for an instrument to be tempered?

 

S: Temperament by definition just means that every interval in the Western scale, or what they call the diatonic scale, which if you’re looking at a piano keyboard, starting at ‘C’ it would be all the white notes up to ‘C’ [an octave higher].

 

F: And the distance between the white notes, that’s called an “interval”?

 

S: Yes. An interval would be the distance between any two given notes.

 

F: Alright. And if I understand this correctly, a piano keyboard is digital. That is, you have ‘C’, then you have ‘D’ next to it, and they are defined keys. But, in reality, there is an infinite number of notes.

 

S: There is.

 

F: As if you were playing a violin string.

 

S: That’s true, there is an infinite number. Because all notes are frequencies. Sound travels in wavelengths. The faster or closer together the wavelengths are— how many wavelengths travel in a second— determines the frequency, or the pitch of a note. So when people refer to “A 440”, they mean that there are 440 wavelengths traveling from the sound source to your ear in one second.

 

F: And is that ‘A’?

 

S: That would be ‘A’. And that’s a standardized note. It’s all arbitrary really, but it’s been standardized. I mean, it had been standardized for a while, but it actually was changed. 432 was the standard for a long time.

 

F: Of ‘A’?

 

S: Yeah. And then 440, I think became the standard around 1930 or so.

 

F: Huh.

 

S: And ‘A’ 442 is actually the standard in Europe. So even still, to say it’s “standard” is very loose and rather inaccurate.

 

F: This is just an odd historical tidbit. I read this years ago; I hope it’s true. The inventor of the foghorn was walking home one night in London, I think, in a fog, and he could hear what he thought sounded like somebody pressing the same piano key over and over at random intervals. And as he got closer and closer he began to hear other notes, but for a long time he only heard one note. “Bong”, and then there would be a pause, and then, “bong”, and a pause. Very random-sounding. The note that he could hear at a distance was ‘A’. And so he realized that there was something about it, or about human ears, that it penetrates farther than other notes do, if a sound volume is controlled for. So that’s why a foghorn is in ‘A’. You think that’s just something I made up, I can tell from your expression! [laughs]

 

S: No, no! I believe that you read that somewhere. But, where you read it… [both laugh]

 

F: The question is, am I recalling it accurately, even if I did read it?

 

S: Was this in Mad Magazine? Because they’re not the most trustful resource. [both laugh]

 

F: I read it on the Internet, it has to be true! [both laugh] There was a picture of a cat playing a keyboard. [both laugh]

 

S: Yeah, to my knowledge there hasn’t been any scientific study that shows that any certain note, within an octave or even outside of octaves, has different properties in that sense. But, timbre can make a huge difference: the difference between playing a note on a trumpet, and playing the exact same note— the same frequency, same pitch— on a violin. And how the human ear can tell, “That’s a trumpet, that’s a violin.” That’s timbre, it’s the, uh…

 

F: Texture, sort of.

 

S: Yeah, texture. Color, as people often like to refer to it.

 

F: Color.

 

S: And that has to do with… well, it gets very complicated, in terms of the acoustics, but, when a wavelength of sound occurs, like a plucked string on a guitar, for instance, that could vibrate at 440 oscillations a second, and that would be your ‘A’. But the vibrations start to interact with one another, and kind of end up cutting the string into fractions, and then those fractions vibrate on their own, in addition to the whole string vibrating. And it’s a really complicated action, which results in all these little fractions of the string oscillating in their own time. And they create what people call “harmonics”, or “overtones” of the original note. So, any note created in the real world will have overtones involved in it. And there is a natural overtone series, so again if it’s a bird call, or a guitar string, or a trumpet, or anything that’s making a noticeable pitch, the harmonic [or overtone] series, the harmonics that are created on top of the original note are always the same. So, timbre isn’t that the harmonics are different necessarily, but it’s actually an issue of which ones are quieter and which ones are louder that changes from one instrument to another, and that’s what gives them different tonal qualities, the different timbre.

 

Anyway, so I have heard that— for instance, drum and fife bands. The reason that marching bands are primarily brass is because brass has the timbre to travel very far. As, obviously, do drums.

 

F: It doesn’t just mean that it’s louder. It means that there’s something about the quality of it?

 

S: Well, I think that one could certainly say that a trumpet is usually louder than a violin, so that’s true as well. But, yeah, it’s mostly—

 

F: Even if you control for volume…

 

S: Yeah, it’s mostly the timbre. And I couldn’t rattle off what the difference is between those two instruments, but I know that the composition, or make-up, of the timbre of a brass instrument operates such that it can travel much further, you know, cut through wooded areas and stuff. So, it works for drum and fife bands.

 

F: And you don’t really play a cello in a marching band, I guess.

 

S: Well…

 

F: Only if you’re Woody Allen.

 

S: Woody Allen, yeah! [both laugh]

 

F: A very funny scene in… what was the title?

 

S: “Take the Money and Run.”

 

F: “Take the Money and Run”, a terrific movie. Talking about temperament and tuning, and about the differences between the notes, isn’t it true that one of the things that makes Byzantine, Greek or Arabic music difficult for us to understand is that they have more notes? Am I right about that?

 

S: Yes. Earlier when I was talking about the diatonic scale, I made sure to refer to it as the Western diatonic scale, because we have our tradition from the Renaissance, the Gothic Era, and then up through the Baroque Era, and all of that is informed with the same musical scale. But in the East, the many different cultures in the East— pretty much cultures in the West all use the same scale, we all have the same ancestry. But in the East… it’s something I don’t know a whole lot about, but in Middle Eastern cultures you can find lots of different alternate scales, and same with India, and China, and other Asian countries.

 

F: And in the scales, there can just be more there?

 

S: Yes.

 

F: Because it is analog, not digital, in reality.

 

S: The Western scale is one of the more barebones scales. I hesitate to say anything that I may be wrong about [both laugh], from some of the things that I remember learning…

 

F: I never hesitate, you should learn from me. [both laugh]

 

S: Well, I had heard, in a Byzantine chanting class at one point, that the scale used in Byzantine chanting by the native Lebanese and so forth… the rough way of saying it would be that, while we have, in one whole note— and again, I’m talking about an interval, not a rhythmic thing— in a whole tone, say, between ‘C’ and ‘D’, we have one step there, we have a ‘C sharp’ (or ‘D flat’). But in the common scale used in Byzantine chanting, in Arab cultures, there are six steps there.

 

F: Wow!

 

S: Yeah.

 

F: Instead of one?

 

S: Instead of one. And so, for Western ears, growing up hearing just one step, it’s very difficult to hear six steps.

 

F: Wow, and difficult to produce. It must be very hard to learn that.

 

S: It’s completely foreign to us. And vice versa.

 

F: Yeah, I guess to simplify it would be difficult. Huh. Well, you’ve just finished reading a book. I’m looking at this very striking-looking cover here. The author is Ross W. Duffin, and the title is “How Equal Temperament Ruined Harmony (And Why You Should Care).” What is equal temperament, and why was it a bad thing?

 

S: The thesis of the book (he doesn’t really get into it until the final chapter) essentially says that equal temperament isn’t bad in and of itself, but the fact that there became a universal adoption of equal temperament is what ruined harmony. That’s because equal temperament isn’t the best harmonic choice in all types of music.

 

F: Does equal temperament mean, “We all agree that ‘A’ is 440”?

 

S: Not exactly. So, there is a standard decision for how many wavelengths there need to be in a given tone, and… [baby crying] Let me grab him.

 

F: Do you need to pick up the baby? This is little Lucas! He’s exactly one week old today. And he has that “new baby” cry. Only new babies have that [mimics cry] kind of cry. Yeah. There, he’s holding his head up so nice! Look at that. And you can really see the blond hair coming in underneath. It’s like his blond roots are showing. [laughs]

 

S: Again, so temperament— I hadn’t gotten a chance to define that earlier— what I started to say was, sound travels in wavelengths, and what that mean is, if you have two different two different sounds at two different pitches, there is going to be a ratio between how many wavelengths in a second one of the sounds has versus the other [sound]. The very basic ratios are equivalent to the intervals that we have in our Western scale. So obviously, if you have a 1:1 ratio, that would be a unison, the same note from two different sounds.

 

F: Is that “unison” or “monotone”? Oh, I guess I’m bringing in a wholly irrelevant term.

 

S: Yeah, monotone is something else. And a 2:1 ratio would be an octave, like ‘C’ and then ‘C’ one octave up, on the keyboard. Then a 3:2 ratio of the wavelengths— [baby cries] Hey! Are you OK?

 

F: [to baby] Do you need your mama? Hey, Jocelyn, can you take him?

 

S: A 3:2 is a fifth, and a 4:3 is a fourth, and it goes on like that; the ratios get slightly more complicated up and up and up. And again, these refer to a kind-of Pythagorean ideal, I guess you could say.

 

F: Huh. There’s math in music.

 

S: Exactly. There is tons of math in music. But the funny this is that this is almost like the theoretical existence of music because the problem is that these intervals don’t actually work together in real life, and in practice (if you’re playing an instrument and you’re trying to tune it to those numbers). One way of looking at it is what is called the “circle of fifths”: starting at a given note, usually C, and then you go up from there to its fifth, which would be G, and then from that note up to its fifth, which would be D, and you keep going up, from D to A, A to E, E to B, B to F sharp, and you can go all the way around through all twelve notes of the scale, and then you will end up at F going to C. And if you do the math, multiplying all those 3:2 ratios together, in theory we should end up with a 1:1.

 

F: Yeah?

 

S: But we don’t.

 

F: Ah!

 

S: We end up with a note that is slightly higher. This is just one of the many mathematical indications—

 

F: Puzzles.

 

S: Yeah, that the ratios that we have, that occur naturally, don’t quite fit. And that is where temperament comes in. Obviously temperament is the idea that the notes need to be tempered slightly so that they can agree.

 

F: Just to make sure: temperament and being tempered has nothing to do with timbre.

 

S: Right. So, with early music, that was usually monotonous, just a single melody with at most a single counterpoint melody, it didn’t matter so much if the harmonies got to be a little off, or if the math didn’t quite work. So they kept to those simple ratios and they kept everything as pure as possible. Which is good: that’s the good thing about those simple ratios is that they do sound the best to the human ear.

 

F: Uh-huh.

 

S: But as music in the pre-Baroque era became more complex, something needed to be done about [these musical/mathematical inconsistencies]. One of the interesting things in this book, How Equal Temperament Ruined Harmony, that was revealed to me is that it is a misconception that Bach, because he wrote “The Well-Tempered Clavier”, meant— and I had always assumed this, as people often do— that he was an early proponent of equal temperament. I had always held that assumption. But apparently that wasn’t true; he didn’t actually care for equal temperament, which, by the way, was just starting to develop at that time.

 

F: Huh.

 

S: And equal temperament is essentially just slight adjustments in all of those intervals so that all twelve notes fit within an octave, and that the distance between each half-step is exactly the same.

 

F: Hmm, OK.

 

S: Hence the “equal” in equal temperament.

 

F: So you’re compressing it, forcing it to meet a certain pattern that, in nature, it really wouldn’t.

 

S: Yeah. So things here or there are being slightly flattened, slightly sharpened. And some have to be stretched or squished more than others. The most noticeable ones are the fifth, which is a bit narrower than 3:2, and the major third, which is much wider than its normal 5:4 ratio. And for people like Ross Duffin, the author of this book, that makes a huge difference; to make the third so wide just kills the music. It sounds terrible.

 

F: Yeah. I guess the move exquisite your sense of hearing or sense of pitch, the more something like that would grate on you, because it isn’t exactly mathematically correct.

 

S: Mm-hmm.

 

F: So, has this changed how people write music? People are now writing, as Bach did originally, for equal temperament.

 

S: Oh, yes. Again, the book spends a lot of time going through the history of how [equal temperament] went from being just one of many ideas about, How we can solve this problem that the numbers don’t quite gel? And, how can we create a scale that is useable that still sounds nice? You know, something that is practical but still aesthetic. So equal temperament was just one of many [temperaments], and no one is quite sure where it came from, or who invented it. But, how did it come to beat out all of the others, and even over pure tuning (or what people nowadays usually call “just intonation”)?

 

F: Just intonation?

 

S: Which would mean tuning an instrument so that all the intervals are perfect. And again, to say that makes it sound like, “Well, why don’t you just do that?” But that’s a very rough description, because, again, it doesn’t actually work practically.

 

F: Is that the just intonation so that you end up with the circle of fifths where you are still a little bit high?

 

S: Exactly.

 

F: OK.

 

S: Which means that, if you have a keyboard in just intonation, you can get all the white notes to sound great with each other, but when you get into the black notes, that is when they sound very bad. If you have to move from one key to another, if you have to have any type of chromaticization in the music, that’s when you really hear it.

 

F: You’d have to stay in ‘C major’ all the time and just ignore those black notes.

 

S: Right. So equal temperament became universally adopted right around the turn of the 20th century. You can see people like [Arnold] Schöenberg, who was crazy about writing “twelve-tone” music (which is atonal, there’s not key to it, but also it has to follow a specific patter of using all twelve notes before it can start again using all twelve notes again), and people in Schöenberg’s camp that used equal temperament as a new frontier for music. And that is all well and good, because equal temperament can do things that other tunings or temperaments can’t. But again, if you’re talking about playing a Mozart string quartet, harmonically it’s going to sound terrible, because it’s not necessarily what should be used in that type of music.

 

F: And it isn’t what Mozart thought it should sound like, because he wasn’t using tempered instruments.

 

S: Right.

 

F: So did you end up being convinced by [Duffin’s] argument? Do you think that equal temperament ruined harmony? And is the only alternative Schöenberg? [laughs] Is there something else that we would… wait, am I getting that backwards? How equal temperament is different from just intonation. What is it called, even temperament?

 

S: Equal temperament and just intonation.

 

F: Just intonation, yeah. [Little girl yelling] Do you want to come in, Ruthie? You look so cute with your face pressed against the screen door. [laughs] Come on in, darling.

 

S: I was convinced, but only because, in the end, his thesis was really just a matter of being good for what it does, but that it’s not ideal in all situations, and it shouldn’t be used as ubiquitously as it is. People should consider using other tuning systems, other temperaments. It should be a case-by-case thing: what type of music are you playing, and what’s the most important thing to consider? Is it the melody, or is it more of a kind of vertical stacking of the harmonies in the instruments, which can really inform what one should be working for. What is comes down to is: there are strengths and harmonic sonority to be found in all of the types of temperaments, but they are strong in different places. So, where do you need to be strong in the particular music that you’re playing? And I think that’s really what it comes down to.

 

Again, equal temperament is now so ubiquitous that no one use anything else. It is an absolute afterthought to use anything but equal temperament in any music outside of classical music. To use it in rock, or blues, or country, or jazz… anything like that. But maybe [something else] would work! Maybe it would work better for various types of popular music. So, I think he’s right that it’s worth at least re-thinking.

 

F: It’s worth exploring.

 

S: Yeah, giving equal attention to all of the temperaments.

 

F: And, in theory, it could sound better than Schöenberg does to somebody like me? And is it just that I’m used to equal temperament, and that just intonation sound strange? Or is it that objectively it doesn’t sound as good? [laughs] I guess you can’t even say that?

 

S: I think it’s a bit of both, actually. On one hand, we are used to what we’ve grown up hearing, and people in the 20th century have grown up hearing equal temperament. Hardly ever do you hear anything that is not in equal temperament. So in one sense you’re used to hearing that, and it’s hard to appreciate anything outside of that. And often it’s hard to hear the difference. I’ll be honest: as much as I’d like to think that I have a great ear, with my piano tuning and stuff, when I’ve heard music in just intonation, it’s very difficult for me to hear the difference. But, with that said, it’s been proven that people generally do like the sonorous sound of the simple, pure intervals that come in just intonation. If you are going to play a Bach cello piece, people would greatly prefer hearing that with those pure intervals than to hear it in equal temperament.

 

F: It’s more sonorous.

 

S: Yeah, even though that’s not what they are used to hearing. So there is an objective aspect.

 

F: An objective beauty to it. Which corresponds to mathematics and to nature. I mean, it is just true to life, in a sense.

 

S: Yeah.

 

F: I think I’ve understood about, uh, maybe 80% of what you’ve been saying. [laughs, Ruth talks] How about you, Ruthie, what do you want to say? Yes, nodding your head? You like the recorder, don’t you? You know what, I’m going to turn it off now. Thanks so much, Steve.

 

S: Sure! Goodbye.


 

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