Intonation IV: Our Partner in Crime

By Partner in Crime I mean our most common collaborator in the traditional repertoire: the piano (or harpsichord). Here is some information I've gleaned from reading Fundamentals of Musical Acoustics by Arthur H. Benade (standing left in photo, playing homemade flute). To know the acoustical properties of the piano is to be able to deal with its intonational quirks. The burden of this lies with us, the flutists. The piano is not able to adjust to our intonational quirks.

Pianos and harpsichords have what are called inharmonic partials as opposed to a flute's regular harmonic partials.

A flute sound will be comprised of its fundamental and its more weakly-heard upper partials: an octave (2 x the frequency of the fundamental), 12th (3 x the frequency of the fundamental), octave again (4 x the frequency), and so on. Everything is all laid out and predictable. What an orderly instrument!

Pianos and harpsichords have inharmonic partials due to string stiffness and effects of the sound board. Their partials are spread, that is, the first partial will be slightly more than 2 x the fundamental. This is important for us to know: given the same note, the upper partials of a piano have a higher frequency (are sharper) than the flute's. Just how sharp these partials are will depend on the quality of piano: an expensive concert grand will have less deviation - an upright with a too-short sound board will have more deviation.

Here is an example of a typical deviation for a decent instrument, based on the frequency of C4=261.63hz
Fundamental Flute:261.63 Piano:261.63
2nd partial Flute: 523.26 Piano:523.51
3rd partial Flute:784.89 Piano:785.91
etc. You can see that the higher you go, the farther apart the frequencies will be between the two instruments.

The piano's "spread" inharmonic spectrum explains why its attack sounds sharper (higher in pitch) than its immediate decay. Initially a great number of partials are excited, including the higher ones that display spread inharmonicity. As the sound dies away, we are left with the lower few partials, which are more or less "normal", that is, less inharmonic.

What else does this inharmonicity mean for us flutists?

I need to back up and explain another acoustical lesson from Benade. Sometimes, there is a difference between matching a pitch between alternately presented sounds and simultaneous sounds (p. 268). Why? Because sometimes the ear is matching overall pitch rather than frequency. What?

Overall pitch is what the ears interpret, given any sound with a harmonic spectrum. We infer the fundamental from that sound. That fundamental, which we infer from its upper partials, may not actually match the frequency of the fundamental. (Really! It's a case of the mind inferring its own reality. Maybe like an optical illusion?)

How does that affect a flutist who plays the same note in alteration with a piano? Given the example above for C=261.63 hz, and "assuming the first six partials [only the first 3 listed here] to be equally important in determining the pitch, one finds that the normal [flute] tone must have its pitch raised about 4 cents...if the two are to agree when presented alternately." (p. 318)

He gives a further example on page 323:

"Suppose for example that a flutist plays a mezzo-forte G4, maintaining it accurately in tune with the G4 produced by a single harpsichord string (whose inharmonicity is very similar to that of the strings we have been discussing all along). The flute is sounded steadily, and the corresponding harpsichord key is struck repetitively at the rate of about 2 per second, so that the tone is restored quickly after each dying away. (...)If, however, the harpsichordist sounds one more note after the flutist has shut off his well-tuned tone, this last note sounds a trifle sharp to our ears..."

Well, I beg to differ... the harpsichordist will not sound sharp: the flutist will sound flat!

There are a couple of other things that are interesting to know about the piano.
On page 319 Benade describes what he calls "the piano tuner's octave". Octaves on the piano are not completely pure, it seems. They are also tuned a few cents too wide. Funny, I would have thought that would be the one interval that could have a 2/1 ratio (the upper note having exactly 2 x the frequency of the lower). But, if you think about that spread inharmonicity, it does make sense.

Furthermore, not even unisons are pure on pianos! (p. 334) This is what blew me away. Most piano notes are produced by multiple strings, which may have as many as 1 - 8 cents difference between them. This is deliberately done to enhance the decay time.

Given the shimmering effect of de-tuned unisons, together with the spread inharmonicity of each individual string, the piano creates a vibrant, pulsing sound. This is one reason I think it doesn't make sense to play non-vibrato with piano. Of course, there are musical contexts where non-vibrato is appropriate. However, as a general rule, I think the flute should go with the piano's flow of vibrations!

Photo credit: AIP Emilio Segre Visual Archives

Practice Motto: Amongst Our Weaponry Are....

Surprise, fear, ruthless efficiency and a fanatical devotion to the--- wait a minute ----- that's not my practice motto, that's The Spanish Inquisition skit from Monty Python!

Hmm, well, surprise and fear do come into play now and then. It's the term ruthless efficiency that's been running through my head recently. Ruthlessness seems to be the rule, given minimal practice time these days in which to prepare for May's difficult ensemble concert and July's solo concert. It's a tough juggle, my husband is working almost round-the-clock to make a deadline, and my 7-month-old son could care less about my piddling artistic/flutey problems. So practice moments need to be cunningly snatched. Linked with my policy of brutal honesty, which involves keeping the tuner by my side, I seem to have a very pugnacious attitude in the practice room these days. It's a place where "no one expects the Spanish Inquisition!" But guess what? It's paying off!

I will share some of my weaponry that inflicts ruthless efficiency:

• a daily task list and
  
• a projected schedule of when I will practice each piece

Since it is impossible to practice every piece every day, I take what is difficult from each piece and work it into my daily practice. Some things on my list now are: the multiphonics found in Berio Sequenza and Takemitsu Voice, double tonguing as fast as possible....

The projected schedule is something I make when it seems there are too many pieces and too little time. I start from the first day and project up to the concert day(s). I figure out how much practice each piece will need, and assign one or more pieces to practice in detail each day. That way, I don't have to worry about practicing each piece every day. It keeps me from panicking, and importantly, from procrastinating. If it's my day to practice that difficult trio I was dreading, just do it. Put the other pieces aside - the items on the daily task list will keep me up-to-date, in shape and on top of them.

I do seem to be making headway, and watching Monty Python for a laugh now and then does help!

Intonation I : Flutonation

Practicing intonation, I've noticed a few funny quirks of mine which I know are shared by many other flutists, so I think it is worthwhile confessing and hanging them out to dry.
(By the way, barring any live musicians I can scare up to do my nerdy exercises, my partner in intonation practice is my Korg OT-12. It's a bit chunky and pricey, but it offers decent range of sound output. It is also recommended by orchestral piccoloists for its good registration of high pitches.)

But first I need to get another pet peeve off my chest: flutonation. It's the natural intonation of the flute. I often hear it when a flutist is playing a solo piece without accompaniment, esp. a contemporary (atonal) piece that they think doesn't need to be in tune. Oh boy....eyes rolling.....
I admit that I have flutonation in spades: C# too sharp, low and mid Eb too flat, but the high Eb too sharp. This is why I hate hearing it in other players :-)

Now for those other quirks:
When tuning unisons, I notice I tend to tune just a few cents sharp. I realized why after awhile: when perfectly in tune with my OT-12, the sound of the OT-12 disappears completely! The harmonic structures are so interlocked that they are indistinguishable. If I'm a little sharp though, I can still hear the tuner. And in my quest to always listen, to play so I can hear my partner (even if mechanical), I play so that both can be heard. Funny, huh? A case where overdoing one aspect can mess you up in another area. Sort of opposite the way pitch rises in orchestra - where you play sharp so you can hear yourself.

Another thing is octaves. I can tune vertical octaves without any silliness, but melodic (horizontal) octaves are another story. They are almost always too wide. I don't know why, maybe I have played the flute too long and have a severe case of octave flutonation. Then there is picctonation. I hear octaves on the piccolo too narrow. That's probably because I like to play with the cork rather close to the embouchure hole - but still, I should know better. I really have to re-train my ears with a fixed pitch instrument or my korg. I've developed some exercises for octaves with my korg that involve listening, not looking at the blinking lights.

In general, I've got several exercises for tuning with a tuner that involve listening to combination tones, complete with explanations. They are no longer publicly on my site because I am considering publication, but- if someone is really interested I can send them pdf.

Intonation II: "Gimme That Ol' Time Religion"

Here's a still from the TV broadcast of us playing Henza's Requiem
in the Cathedral of Cologne, April 2009

Our latest concert presented quite a challenge! The Cathedral of Cologne has an evening temperature (this time of year) of 15.3˚ C (59.4˚ F). That was with spotlights and extra spots from the television crew.

As we bundled up to play Hans Werner Henza's Requiem, we took great care in tuning. Actually, it wasn't too bad, all things considered.

Here's what we had to consider:

From one equal-tempered semitone to the next there is a 6% increase in frequency.

A 10˚C change in temperature is equal to a 2% change in pitch frequency. That's a whole third of a semitone!
[From "The Musician's Guide to Acoustics" by Murray Campbell, p. 201]

The Cathedral air was not a whole 10 degrees below room temperature (22˚C) but it was enough to make things really tricky.

So what was it like playing in one of the world's tallest cathedrals? The acoustics of the choir area (on the east end, behind the altar) are not bad. The choir of Cologne Cathedral, measured between the piers, holds the distinction of having the largest height to width ratio of any Medieval church, 3.6:1. [info from Wiki] The whole cathedral is so large and so high that it is almost like playing outdoors, you don't get that "churchy" acoustic. The nave is 43.35 meters high (144.22 feet) - the 4th highest in the world. Only when you stop playing, do you hear a long, long, decay of the sound.

When I stepped into the interior of the Cathedral for the first time in the summer of 1995 I almost cried, it was that moving and impressive. I am used to tall buildings, I've even been up the Sears tower in Chicago, but being inside such a vast structure is awe-inspiring. Imagine the impression it made on the pre-modern psyche!

Back to our intonation question:
How to stay on top of these extreme situations, hot or cold?
*keep flexible by practicing note bends - both ways. I find this absolutely crucial in piccolo playing.
*know alternate fingerings
*know the tendencies of other instruments under these extremes (strings go sharp in the cold, not like us!)

Intonation III : the Spectre of Spectralism

Some days ago I got the score for G. F. Haas' new work „ … wie Stille brannte das Licht“. (What is it with German-speaking composers and their titles with elipses?). It got me thinking about how different composers notate microtonality. I like what Haas has done, it is explicit in placing the note within a frame of reference.

The notated C quarter-sharp in bar 241 is the 11th partial of G, and the A-flat in bar 245 is the 21st partial of E-flat (along with the indication that you are in a perfect fifth with the clarinet). I like having this kind of information in the score, but if he had notated the exact deviation in cents, that would have been even more helpful. This is easy enough to find out in Wiki

That 11th partial should a C# 49 cents flat, and the 21st partial should be an A-flat 29 cents flat. Like I said, easy enough for find out, but it would have been nice if the composer had provided this information.

We haven't had rehearsal yet, so I can't say how this will sound or how easy this will be to hear. [ed. read my follow up at the bottom of this post]
So now the question arises: How does one practice this stuff?

First of all, I get my tuner. Trying the A-flat first, I make sure that our Eb's are in tune. Then I play an A-flat ca. 29 cents flat. Then I keep that tone while putting the sound on to Eb and I hear a Bb combination tone. This is a clue that I am on the right track, or within the correct overtone spectrum. Your combination tone (it may be a true difference tone or not, depending on the timbre and register of instrument) should lie in close relationship to the fundamental - say an octave, fifth or major third (which is the 5th partial, you don't want to go much farther than that). Put in simpler terms, it should be part of the major triad formed by the fundamental.

Now to try the C# against the G. Again I tune the G's, then test my C3 so the needle goes about 49 cents flat, then put the sound on G. My difference tone is B natural this time, still close enough (a major third - the 5th partial) in relation to G to be correct.

Again, I have no idea how this will work in the context of the piece, or if it will be heard. But now I know, theoretically, how much adjustment is "correct".


Whether this works in context or not, I love working with combination tones. Scientists are still not in agreement as to what they are - but it is a wonderful example of how our brains work - how they "fill in the blanks" of the overtone spectrum. I wonder if this is the same phenomenon that allows transistor radios to work? Only the upper partials are projected, the brain fills in the rest.

Also, I've noticed that I'm one of those people who can read things like this, hence my spelling problems, most likely. (Thanks to my like-minded Uncle T for this text):
fi yuo cna raed tihs, yuo hvae a sgtrane mnid too
Cna yuo raed tihs? Olny 55 plepoe out of 100 can.
i cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the hmuan mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervti sy, it dseno't mtaetr in waht oerdr the ltteres in a wrod are, the olny iproamtnt tihng is taht the frsit and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it whotuit a pboerlm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Azanmig huh? yaeh and I awlyas tghuhot slpeling was ipmorantt!

[Follow-up added May 5, 2009]
The passage in question was acually not so difficult to hear! You are a part of this "lump" of sounds that are related to the fundamental. It is tricky that he has two harmonic spectrums going at once: those of G and E-flat.

When considering dynamics in this piece we realized that there was a lot more going on than just playing loudly or softly. It helped to think of crescendo/decrescendo passages as adding/subtracting harmonics to your individual sound rather than just making the sound louder or softer. This made for a much more interesting color. Also, the very quiet passages must be played with focus and good attack. Even the quietest notes need some harmonics in the sound, none of this fluffy airy stuff! It just didn't match the color system.

I do admit the 11th partial gave me the most trouble in this piece. Tricky to hear! It must be 49 cents flat. I must make some exercises.

Speaking of which, I asked the composer and my colleagues how one can study and practice this music. The answer is always the same, learn the overtone series, horizontally, note by note, by ear. How can one do this? Programming a synthesizer seems to be the most popular idea. However you do it, once the sounds are in your head, you have to find a way to play them (of course, in a comfortable range of your instrument. I'm thinking middle octave) by using a combination of alternate fingerings and lip bending. Another project for me!