It was ever thus, wrestling with the gods.

April 21, 2010 9:53 AM

The Wolf At Our Heels. The centuries-old struggle to play in tune, and the battle between equal temperaments and historical tunings.
posted by The Card Cheat (35 comments total)

Metafilter: do I care about all this meshugas?
posted by jquinby at 10:09 AM on April 21, 2010

Great article, and a nice complement to cortex's recent primer on chords in pop music.

I've never really understood what a key is, or what a tuning is. I know the math, including unusual tunings, and I fully understand the linked article. But I can't begin to explain conceptually why things sound like they do. I don't really understand why people find Schoenberg or Webern alienating. I can't even tell you why Shostakovich's 24 Preludes and Fugues are really any different from the Well Tempered Clavier. I mean if you sit me down in front of a score and point at harmonies, I can see the math of it. But I don't understand the music.

Fortunately my ignorance makes it easy for me to enjoy all sorts of music. I've pretty much given up trying to really understand music theory, just like I don't really understand why Bordeaux is better with steak and Burgundy is better with duck.
posted by Nelson at 10:33 AM on April 21, 2010

Fascinating post. I've never thought about music this way before.
posted by The Lurkers Support Me in Email at 10:35 AM on April 21, 2010

What a great article.
It seems like I'm learning all kinds of stuff like this lately, after playing music for most of my life. I posted a question of Metafilter Music Talk a year or so ago about this very issue, not understanding why it was so hard to tune the B string on my guitar.
posted by chococat at 10:46 AM on April 21, 2010 [1 favorite]

Good article- seems like a book to check out... I have an MA in flute performance and I play quartertone flutes made by Dutch maker Eva Kingma

I play all kinds of music and have had to tune in many ways- jazz and rock instruments are usually flatter than the classical groups I've played with. Then baroque music is another story altogether! Each city had a different tuning...
posted by cherryflute at 11:03 AM on April 21, 2010

"This book was written by a madman. Or is he?"

Those sentences were constructed by a college graduate! Or is he?

sorry, this is making me two tense
posted by Devils Rancher at 11:13 AM on April 21, 2010 [7 favorites]

I know just enough about music to be a menace to society, but tuning systems have fascinated me for years. Trouble is, I can never hear a convincing difference that I couldn't just as easily attribute to different recording conditions, intrinsic differences from one instrument to another, etc. I've never heard live performances in different temperaments, the same instrument played with different tunings, etc.

Does anybody have any audio clips of "the wolf"? I'd love to hear a good howling wolf chord compared to the same chord in equal temperament.

It seems like electronic keyboards could be programmed to provide a variety of temperaments at the push of a button (right? or is there something fundamental about producing electronic sounds that would prevent this?) It would be very cool to have an instrument that could play baroque and modern music in its intended tuning. I wonder how many people would be able to hear the difference, especially in the keys that were favored because they were sweet and tractable.

Lastly, do people with perfect pitch find "fudged" temperaments unpleasant? How perfect is perfect pitch, really?
posted by Quietgal at 11:18 AM on April 21, 2010

That's good writing. I thought my ignorance about music theory would prevent me from enjoying this, but no. Writers who make me interested in stuff I only half-understand have my respect.
posted by The Mouthchew at 11:19 AM on April 21, 2010

I thought this was an interesting book on the subject. Even Newton came up with hundreds of tuning schemes. If you're really interested in this sort of thing, a lot of 20th century music has been written with 'just intonation.' Harry Parch was probably the biggest pioneer in this realm.
posted by Lutoslawski at 11:22 AM on April 21, 2010 [1 favorite]

Quietgal, check out "Bach Meets Cape Breton", an album recorded some years ago by Puirt a Baroque. The fiddler is versed in both classical and traditional Cape Breton fiddling styles, and on one track, proceeds to play a baroque piece with his instrument tuned to the "folk" tuning of A=400 as opposed to the "classical" A=440. The difference in the character of the piece and the sound of the instrument is mind-blowing.
posted by LN at 11:35 AM on April 21, 2010

Trouble is, I can never hear a convincing difference that I couldn't just as easily attribute to different recording conditions, intrinsic differences from one instrument to another, etc. I've never heard live performances in different temperaments, the same instrument played with different tunings, etc.

One thing you can listen for is 'beating'. With out of tune notes, the soundwaves will drift in and out of phase with each other, which causes the volume to increase and decrease as the waves either enhance or cancel each other out. It's part of the reason people find out of tune notes unpleasant.

PS: Wave interference is also how scientists proved that light acts as a wave.
posted by empath at 11:37 AM on April 21, 2010

Some decent synth modules can allow you to play in different tuning systems (at least my old proteus 2000 can). I didn't really appreciate why the tritone/wolf tone was forbidden until I heard it in just intonation- it's truly ugly (not devilish so much as ghoulish I'd say).

Meanwhile I'm all for music in different tuning systems, but a lot of this reeks of the need to sell more CDs-'authenticity' is a big market-and endless refinements to what is essentially a ritual (wonderful profound rituals though they are) rather than live music making.
posted by leibniz at 11:41 AM on April 21, 2010

For anyone interested in the possibilities to be found in music that falls out of the equal tempered mainstream, I'd suggest you get a copy of the tragically-neglected masterwork Beauty in the Beast, by Wendy Carlos (and be sure to read all the related material on her site, which lays out a really fascinating inside look at the process of getting away from 300 years of equal temperament). The piece "Just Imaginings" alone still makes my hair stand on end and shoots a million volts up my spine after all these years and literally thousands of listenings. Wendy has been a tireless advocate for the landscape of intervals outside of twelve even steps for a long, long time now, and BitB really takes the theory and makes it breathe. I lament the fact that she's not done another piece like that since, with the exception of the excellent, but more traditional, Switched-On Bach 2000, which renders Bach in the original period tunings.

There's just so much there, once you open up and let the intervals start working in your head.

One of the things I love about my sumptuously-unreliable (but extraordinary for its time) Ensoniq EPS sampling keyboard is the ease with which you can build alternate tuning maps. Being able to work in golden pentatonic, pelog, and slendro tunings with unlimited instruments is just…well, it's just…soul-opening, for want of a less wibbly-wobbly expression. I've been sad to find that instrument manufacturers since the eighties and nineties are increasingly unlikely to include user-accessible tuning tables in their hardware and software (my kingdom for tuning tables in Reason, dammit!).

One day, the last custom chip or floppy drive for my EPS will die, and then I'll be S.O.L., alas, unless I'm able to finally master Csound by then (and I'm not getting any smarter as the years brush by, it seems). The irony is that I'm really not even clever or informed enough to even use these tunings properly, within their cultural context, but you can do a lot by feel.
posted by sonascope at 11:57 AM on April 21, 2010 [8 favorites]

Is this why A flat is my favorite key somehow?
posted by cmoj at 12:09 PM on April 21, 2010 [1 favorite]

Once, when I was young, I bought a small book called How to Tune a Piano. I mean, how hard could it be, really? The answer, of course, is really really hard. To simplify this whole business for non-piano-tuners, you have to stretch out the upper half of the keyboard so the notes are slightly higher and likewise, lower with the bottom half. (If this oversimplification is wrong, I'm sure someone will correct me!) You do this by tuning in fifths and purposely make them imperfect, by, say, counting seven "beats" (wavering to the ear) in 10 seconds. Or you can use a computer program. In fact, I've always wanted to have my tuner use his computer to tune my piano the way they did before equal temperament, but I'm too chicken. I sure would like to hear a "wolf," though.
posted by kozad at 12:10 PM on April 21, 2010

|snip| proceeds to play a baroque piece with his instrument tuned to the "folk" tuning of A=400 as opposed to the "classical" A=440. The difference in the character of the piece and the sound of the instrument is mind-blowing.

Most of the thread is dealing with the character of the intervals between notes and not the absolute tuning of any note in the scale. One can play tuned to A440 or A400, in either equal temperament or any other method of forming intervals.

But the choice of frequency to tune a single note to (regardless of what way you're going to tune the rest of the notes relative to it) is still an interesting one. An instrument like the violin has a source (a bowed string) that's spitting out all manner of frequencies, sending energy to a radiator (the body of the violin), which radiates those frequencies with widely varying efficiencies. So when you're tuned to A440, then when you play that A, maybe the violin's body emphasizes the 10th harmonic of that note, but when you play an A tuned to 400, the violin would emphasize the 11th harmonic. Same frequency (4400 Hz) but different contributions to the song, given the context of the rest of the notes played.

Also, like all instruments but especially so, violins radiate different frequencies preferentially in different directions; the different character of the song may have been a function of how he was positioned or moving as he played.
posted by Jpfed at 12:56 PM on April 21, 2010 [2 favorites]

This is why I love Metafilter. Great article.

For those having trouble hearing the difference in those compared clips, The last two clips, listen to the second chord (the one right around the 5 second mark). You can hear that one sounds quite whole, without any dissonance, and on the other, the chord has a harsher, less full sound.

Can you tell I don't really know what I'm talking about?
posted by toekneebullard at 12:57 PM on April 21, 2010

Jpfed, sorry for the derail, but I was responding specifically to Quietgal's comment:
I've never heard live performances in different temperaments, the same instrument played with different tunings, etc.

It was the only exmple I could think of from my own experience that shows the same instrument on the same recording with two separate tunings. But your point about intervals versus absolute tuning is well-taken.
posted by LN at 1:11 PM on April 21, 2010

LN, a different tuning isn't just a different hertz value for A. It's about the way the intervals are tuned on the instrument; if you walk perfect fifths all the way around the circle, you don't quite, exactly, come back to the original note, so in order to have your octaves in tune, you have the cheat the fifths. Which fifths you cheat, and how, can have a profound effect on the feeling of the music.
posted by KathrynT at 1:16 PM on April 21, 2010 [2 favorites]

And that, among many other reasons, is why I (full disclosure: I'm a classical singer) love a capella choral music so very much. The infinite tuning possibilities of the human voice can allow for microintonation adjustments from note to note, beat to beat, resulting in the closest thing possible to truly in-tune music.
posted by KathrynT at 1:18 PM on April 21, 2010 [1 favorite]

The Wolf tone article on Wikipedia has an audio sample of a cello. Listening to it makes the long-buried musician in me gargle with confusion and rage...I wonder what it sounds like on a piano/harpsichord/etc?
posted by The Lurkers Support Me in Email at 2:08 PM on April 21, 2010

The Lurkers Support Me in Email, that recording seems to be of a different phenomenon with a coincidentally similar name. That sound is, according to the article, "produced when a played note matches the natural resonating frequency of the body of a musical instrument."

So it's an acousticophysical artifact of the instrument itself, audible when a single note is played, and unrelated to the wolf interval which occurs between two notes in historical temperaments.
posted by magnificent frigatebird at 2:40 PM on April 21, 2010

Wow, lots of good suggestions to check out here - thanks, LN, sonascope et al.

Lurkers, I think the "wolf tone" is different from a "wolf chord", since the former is caused by resonance with the body of the instrument (and sounds horrible, to be sure). The wiki article on the latter had an audio sample, and to me the wolf sounds like a completely different interval, I'd guess an augmented fifth (instead of, say, C-G it sounds more like C-G# to me). I didn't hear howling or ugliness, just a different chord. Although I could see how that could be a problem if it occurred unexpectedly where you didn't want an augmented fifth...

I've always had trouble hearing beats, though - does anybody else hear a howl? Maybe synthesized notes are less prone to howling/beating, having fewer overtones and other frills? Or maybe my ears/brain are just rubbish at this.
posted by Quietgal at 2:42 PM on April 21, 2010

Stupendous! I'd just harassed a few people via MeMail from this recent post to learn more about tuning and harmonies, and was slowly working through the many great links I was sent. Now this? Huzzah- it's a banner week for music theory at Metafilter!
posted by hincandenza at 3:25 PM on April 21, 2010

And that, among many other reasons, is why I (full disclosure: I'm a classical singer) love a capella choral music so very much. The infinite tuning possibilities of the human voice can allow for microintonation adjustments from note to note, beat to beat, resulting in the closest thing possible to truly in-tune music.

To be fair, any ensemble of instruments can make the same sort of microtonal adjustments, provided they aren't fixed-tuning instruments like the piano, which is why the piano specifically is such an interesting and problematic case. In fact, microtones are pretty ubiquitous in even orchestral music from the past sixty years, even orchestral music that isn't specifically 'microtonal' (c.f. Ligeti, Penderecki, Crumb). It's a common misconception amongst non-musicians (not saying you aren't a good one, KT) that playing the violin or the saxophone or what have you is a matter of pressing the right 'buttons' at the right time. On the contrary, you make the same conscious, minute adjustments the entire time you're playing - with your fingers or your embouchure or what have you.
posted by Lutoslawski at 3:57 PM on April 21, 2010

It seems like electronic keyboards could be programmed to provide a variety of temperaments at the push of a button (right? or is there something fundamental about producing electronic sounds that would prevent this?)

Various electronic and even acoustic microtonal pianos exist. When I was studying for a brief time at NEC, they had an 800-note microtone piano. Pretty sweet. (Check out the Boston Micro Tonal Society, probably the most active group in the art form).

Another sweet listening example is perhaps the Bad Plus's cover of Iron Man - Ethan plays two pianos tuned a quarter tone apart. Makes the difference oh-so-clear (tough a quartertone is admittedly large given the scale we're talking here).
posted by Lutoslawski at 4:06 PM on April 21, 2010

Fascinating stuff. Of course there are composers whose whole aesthetic is based on the rhythm of beating patterns, which takes this whole idea to a new level.
posted by ob at 4:11 PM on April 21, 2010

in order to have your octaves in tune, you have the cheat the fifths. Which fifths you cheat, and how, can have a profound effect on the feeling of the music.

Your cheatin' fifths
Will keep you tuned
You'll strum and strum
Fretboard festooned
But friend, your song
Is just plain crap
Your cheatin' fifths
Can't fill that gap

You'll play and plaaaaayy
With har-mo-neeeeee
Your band still suuuuucks
Oh can't you seeeeeee?
List'ning to you
Just ain't no fun
Your cheatin' fifths
Can't help you none

apologies to one of my alltime favorites and recent posthumous Pulitzer winner Hank Williams. Let's listen to ol' Hank now, shall we?
posted by flapjax at midnite at 4:12 PM on April 21, 2010 [3 favorites]

What's sort of interesting is that Steve Reich's early pieces "It's Gonna Rain" and "Come Out" illustrate beating and "wolf notes" in a very slow, macroscopic metaphor, with the dissonance between slightly out of tune lines being manifest as a gradual cycle through rhythmic variations instead of a warble or "beat."

Translate that off-syncness (i.e. out of tuneness) to measures, say a loop of 11 measures against one of 13, and it'll generate constant novel counterpoint for 143 measures before repeating.

Ah, this mathematical wonderland, music.
posted by sonascope at 4:43 PM on April 21, 2010 [1 favorite]

ob: Fascinating stuff. Of course there are composers whose whole aesthetic is based on the rhythm of beating patterns, which takes this whole idea to a new level.

It's interesting you mention that: after reading some of this, I had a similar thought as what Jpfed had here, in that the frequency itself is another relation to consider.

Since frequency and interval ratio relate to define a number of beats per second- whether you're perfectly in tune or slightly out of tune as in equal temperament- my thought was along the lines of "If my tunings are a little off by the nature of equal temperament, then surely there'll be a subconscious 'beat' to the discrepancy... and maybe there's an aesthetic element to tempo in a piece of music based on the beat found inherently". Or to put it another way, that perhaps the ear can detect even on a subconscious level if you lift your hands from a chord on the piano too 'early' because you cut it off before the right number of beats had occurred or too soon before/too long after the beats finally coincided again with their least common multiple.
posted by hincandenza at 5:20 PM on April 21, 2010

...a loop of 11 measures against one of 13, and it'll generate constant novel counterpoint for 143 measures before repeating.

i made a loop of a thousand measures
against another of a thousand and three
made all kindsa crazy patterns
for the next coupla months, y'see
by the time it all came back 'round to the one
i had left on the midnight train
gone to mississippi and come back again
with those beats poundin' in my brain
with those beats poundin' in my brain

they crissed and they crossed
and they shimmered and weaved
and they kept all the neighbors awake
they flammed and they diddled
and rattled and popped
and made all the teacups shake
they pittered and pattered
and dribbled and drabbed
like a old tin roof in the rain
gonna let 'em go on foreever, you know
those beats poundin' in my brain
those beats poundin' in my brain
posted by flapjax at midnite at 5:25 PM on April 21, 2010 [3 favorites]

Quietgal, I have perfect pitch (in my case this means you play a note I tell you what it is. If its some funky chord I don't know the name id I'll still know what its between) and I can definitely hear the difference between different kinds of tunings. I don't mind dissonant music at all as long as I'm actively listening to it but can't stand it as background noise.

Over the years I've come to realise that I hear/feel/visualize music quite differently from most people. Some singers I've always described as "singing on chords" but didn't know why. This article is tsuper interesting to me. Thanks for posting it!
posted by fshgrl at 10:47 PM on April 21, 2010

Huh. I was at the Y this morning and The Sadies song Wolf Tones came on the iPod.
posted by chococat at 8:40 AM on April 22, 2010

It's taken me a while to get back to this thread and finally write in it, but here goes if anyone is still interested:

This area of tuning and temperament is what I will endeavor to research if I ever get into a musicology program. I am more interested in the use of it in the 18th and 19th centuries, however.

I have read the book by Duffin. It is a great, compact read that would clarify many misconceptions to people who haven't studied music, however, it gets denser in the math and music as it goes on. It is very short, though, and is definitely rewarding to get through.

When the octaves don't match up using the 5th ratio (3:2), 4th ratio (4:3), or 3rd ratio (5:4), it's best to think of it as more of a spiral because that is in essence what it is doing.

Finally, there is this portion of the article which I absolutely disagree with, and shows, that the writer should have read Duffin's book more closely:

Still, nobody can reasonably claim that piano works after the early 19th century should be played in other than the equal temperament they were written in. Says my Boston Conservatory colleague Jim Dalton, himself more equal-tempered than many aficionados, "Equal temperament is the price we pay for all the marvelous modulations and exotic scales" from Schumann through Debussy to the present.

Except for the fact that they were still functioning in meantone temperament. They had moved closer and closer to the ideal of equal temperament but it wasn't until 1917 because we didn't have the technological tools to accurately tune pianos. In fact, they were all using an extreme form of meantone temperament which explains why late into the 19th century they were still speaking of keys having character and mood. They don't have it in equal temperament and they never will. It is something that has always bothered me ever since I started learning music and here is the answer: they don't.


Also, Bradley Lehman, THE researcher of the Bach curlicue tuning if I remember correctly, wrote in the article:

There were at least two harpsichord recordings of the WTC in that 1681/91 Werckmeister temperament, long before Pechefsky's: Blandine Verlet's from 1993, and Edward Parmentier's also from the early 1990s (but released 2004).

To learn about the temperament used in Watchorn's recording, see http://www.larips.com . "Cabalistic"? Straightforward diagram!

There is a lot more to the performance and composition of music, and to theory of tuning, than the incidence of fifths and major thirds. The WTC is at least as much about linear motion, diatonic scales, and modulation as about playing decently-tuned but isolated triads. Almost all the preludes and fugues in the WTC go beyond 12 differently-named notes (such as needing both G# and Ab installed on the keyboard at the same time), and *that* is the problem the book sets up: how to tune so compositions can do that enharmonic overlapping, freely, through all major and minor scales.

The assertions about HIP ("To date there are few recordings in period tunings...") would be more nearly true if they had been written in c1965, not 2010.

The assertion about meantone ("most of the accumulated fudges were dumped onto two notes, usually G# (aka A flat) and E flat...") is simply preposterous. In meantone, all of the fifths are reduced by a constant amount, geometrically. The point is that G# *is not* the same thing as A-flat, and the interval of G# to Eb is *not* a fifth; it's a diminished sixth at the place where things don't close, having worked around to it from both sides. That's why it doesn't sound like a fifth. There are other "wolves" in there, as well, such as C# to F, and F# to Bb: they are diminished fourths, not major thirds, and that's why they sound different. F to G# is a wolf: an augmented second, instead of a minor third from F to Ab. Wolves in meantone are the two-note intervals where both notes don't belong to the same diatonic scale.

I suppose I've just labeled myself as a "geek" by knowing these things.... :)

Anyway, it is nice to see the enthusiasm about Dr Duffin's fine book!

It is well-worth posting here as well. Also, in addition, before G#/Ab became the same note, it is interesting to point out that Ab was actually higher in pitch than G#. G-G#-Ab-A is the order it would have gone and therefore when playing an Ab performers would have automatically chosen a higher pitch or a smaller interval from A.
posted by lizarrd at 1:50 PM on April 24, 2010

Forgot to add:

Here is Professor Duffin's Letter to Readers of the Book.

And a site of his with more tuning examples:
Baroque Temperament. Introduction to Exercises and examples.
posted by lizarrd at 1:55 PM on April 24, 2010