Absolute pitch

The short story is, I don't have it.

Absolute pitch, formerly called perfect pitch, is the ability to name a pitch after hearing it. It's to be distinguished from relative pitch, which is the ability to name intervals after hearing two notes in succession, or at the same time; or copy melodies etc. There's different kinds: some people can do it in some contexts and not others. It's said to be rare: possessing "perfect pitch" is often included in the litany of inborn genius characteristics of the young prodigies, "one in ten thousand". People are studying it, though, and it's a little more complicated than just being a God-given gift to the chosen few. Learning music when being young helps, speaking a tonal language helps. Nearly everyone has some aspect: eg if you ask musically untrained members of the general public to sing a currently popular song, they start in the right key much more often than you would expect from chance. I've known people who had it, in a useful sense: my junior high orchestra director, for instance, would hear an airplane flying overhead, and announce that it was an E, but somewhat flat. And my son's AP is pretty good. I've never had the sense of having perfect pitch, but I feel like I do have some aspects of it. I can imagine playing any note of the bassoon, for instance, hearing the pitch and the timbre in my head, and imagining what my fingers and air column are doing. I'd be surprised if the pitches I'm imagining were that far off. And once when I was trying to learn intervals, with my wife playing them at the piano, she noted that I was always getting major and minor wrong, but was quite accurately calling white notes major and black notes minor. It's wrong, sure, but your brain can't make that kind of mistake without knowing, in some sense, what the absolute pitches are.

So I was intrigued when I read about an online study of AP. Here it is, out of UCSF. They are interested in the genetics, so there are survey questions about family background, musical training, and languages, before they hit you with an online pitch recognition test. I found the pace pretty quick, you get maybe one second for each tone, and I didn't feel like I was doing any better than guessing. About halfway through it switched from pure sine wave tones to piano notes, and I felt like I was doing even worse. I didn't care, I just wanted to finish. The results reflect that: I scored 14.75 on pure tones, and a 3 on piano tones; this is out of a best possible of 36. The average score in their test-taking population is a touch over 17, and random guessing would give you 7.5. Their cutoff for having AP is 24.5. There's a plot of where I fit in:

A couple of interesting things here: the responses cluster in two places: top right, where you mostly get them right, but with some errors; and middle lower left, around random guessing. So it does mostly look like a "you have it or you don't" binary proposition, though there are lots of intermediate people as well. There's a pretty good correlation between the scores for most participants: if you can do it for one type of tone, you can do it for the other. There are outliers, sure. Mostly these are above the line: people whose AP is pretty good when you play piano notes, not so good for sine waves. This could be a practice effect, people who get better at taking the survey during the survey itself (since the piano notes come second), but I think it's more likely people who grew up playing piano and can just recognize the notes better when they are played by a piano. People like me, who are better at the sine waves, are rarer. I'm not the furthest outlier in this direction, there's a dot way off in the lower right for someone who actually has perfect pitch on sine waves but was as bad as me at piano notes. He or she might have unusual characteristics, or perhaps they just didn't take the second part seriously. My personal results do look pretty funny: definitely better than guessing for sine waves, but worse than guessing for piano notes. Huh. I feel like if the survey had been bassoon notes, or if it has at least been notes in the bassoon range or my singing range, I would have done better. There were a lot of high notes, and I just feel totally lost up in the treble.

The fastest possible trill

For the trilly bits in Mozart, starting at the pickup to 51 and again at 120, I long ago decided I wanted to do 32nd notes, something like this:

Three turns, starting from the bottom. The advantage of straight 32nd notes over something like a 7-tuplet is that it's easier to practice slowly with a subdivided beat. When I crank up the metronome, I don't always manage to get all three turns in, or maybe there will be two clean ones plus a little bounce near the end, but this is the plan anyway.

There are lots of ways to play these, of course. My teacher I think told me he played 5 turns, which seems like a lot to me. And of course, when he demonstrated, they went too fast for me to count. With recordings, we can slow things down. Here's that section from Klaus Thunemann's recording, which has pretty fast trills:

  Kt-normal by TFox17

It's too fast for me to count, unless I slow it down:
  Kt slowed by TFox17

From that, it's pretty easy to write out what he is doing:

I count four turns, starting from the top, for straight 32nd notes all the way through. So not, on paper, any faster than my plan, although faster in practice, since he both takes a faster tempo, and is able to execute the whole thing beautifully.

Now, how fast can a trill go? It turns out that there are limits in principle, not just practice. First of all, there are limits as to how fast fingers can move. Kochevitsky's book on piano technique goes through some of the studies.   Apparently the 2nd and 3rd fingers can make 5-6 movements per second, 4-5 with the other fingers. Training doesn't help peak speed: great pianists and members of the general public were about the same, with some untrained participants able to make 7 per second, which some pianists were only able to do 5. For a trill on piano, you can alternate two fingers, so 6 movements per second can give you 12 notes per second. On a wind instrument, you can only move one finger, but each full movement cycle, up and down, gives you two notes. So it's more or less the same, 12 notes per second. It turns out that there's a limit to what the ear will perceive of as distinct notes. Passages played faster than this will blur together. This makes sense: after all, every note is just a cyclical progression of pressures, and A0, reachable by a contra with an extension, has a frequency of about 22 Hz. The limit of hearing notes depends on several things: the pitch of the notes (low notes get muddier faster), the complexity of the passage (scales, trills and tremolos are easier to perceive than more complex passages), and the listener. This limit is typically around 12 notes per second, sextuplets at 120 BPM, which interestingly corresponds to about the limit of what's possible to produce. For a trill, the limit quoted is more like 15 notes per second, which is around what Klaus Thunemann is performing his trill. We can test this ourselves, though, by shifting the tempo on the recording, and seeing what happens.

Here's the tempo shifted to about 150 bpm, which gives us about 20 notes per second:

  Kt 151 by TFox17

And again, to about 180, which gives us 24 notes per second:
  Kt 182 by TFox17

For me, at 150 it still sounds like a trill, though I certainly can't count the notes. At 180, it's degenerated into a sort of fluttery effect on a sustained tone. At 240, the 16ths become indistinct.

From this I think we can conclude that Klaus Thunemann's trills are, not just fast, but essentially at or near the limit of being the fastest possible, either to perform or to hear.

Pop tunes for whales

This is fascinating:  humpback whales sing to each other, not uncommon in the animal world. But all the males in a population sing basically the same song at the same time, which is not so different from hit radio. What's more, the songs change from year to year: they get bored, I guess, and switch to a new tunes. The new tunes are transmitted, culturally (!), from group to group, as the latest hits spread across the oceans. That's just amazing to me. The link has recordings of the latest hits in whale songs. It reminds me a bit of the Gubaidulina Concerto for Bassoon and Low Strings that I've been listening to recently. A lot of extended techniques: microtones, multiphonics and slides, but very much an integrated piece. Here are various YouTube versions, and the great album on iTunes from Rino Vernizzi.