Tuesday, March 20, 2007
Reading too many blogs
So, when I finally do settle down to practice, it's too late to get everything done before Z is awake and hanging around, "hinting" that he wants the computer (where I play). It's my own fault, though. We don't want him sleeping through the entire spring break, so Y has been waking him relatively early - 9 am. Today he showed up as I was working on my newest and toughest pieces. I don't even think about it when he and Y are in other rooms while I'm practicing on weekends, but if they come into the room where I am playing, I start doubting myself and end up stopping.
This week, I've been really pleased with my cello's sound. I started working on intervals last week, which made me start thinking about the different tunings. Until now, I've tuned each string to its piano frequency - equal temperament. But I've been curious about tuning to fifths, so my teacher suggested I look at Violin Masterclass. I started experimenting with this "other" tuning. I'm not sure I have it right yet, but: I tuned A to exactly 220.0, and then tuned each adjacent string exactly one-fifth lower using the calculated frequencies; e.g. 2/3 of 220 Hz is 146.67 Hz (instead of the equal tempered 146.8 Hz). This is too subtle of a difference for my uneducated ear. I'm still confused, though; I read somewhere that the human ear can only distinguish sounds 1 Hz apart, so what's the big deal? Yet, can hear that my strings are flat or sharp by even three or four tenths of a Hertz. Now I'm wondering if I should be trying to educate my ear another way. I saw a link today in gweipo for EarMaster, an ear-training program. Maybe I should consider it.
Well, anyway, I started playing double-stopped intervals on all the strings. It has already helped me with my bowing - just trying to bow each string with equal emphasis. I can't yet say if it has helped my intonation, but I sure am more keenly aware when I do miss a note. Handel's Bourree has been coming along nicely, but I've still got a long way to go with Ashokan Farewell.
I came across this chair somewhere today. Disturbing.
1) I learned to hear the beats by playing unison double stops, open D with 4th position D on the G string, for instance. Do some experimenting until you have a sensation of feeling the pulsations with your eardrums.
2) Tune the A string comparing with tuner. The beats are more subtle when tuning against the A440-ish note than against A220.
3) Check the A string tuning with the gauge. If off, don't just tune to the needle. Repeat step 2 until step 3 is where you want it.
4) Tune each pair of strings as double stops. Use either the lower string peg or the fine tuner while continuously playing the notes (not back and forth.) Tune the lower string down until it's definitely flat, then bring it up slowly while both listening and feeling the sound. Start by going past what you think is right until it is definitely too sharp. You will start hearing how the sound "opens up" when the lower note is a perfect fifth.
5) Check the lower note tuning against the gauge. Repeat step 4 as many times as necessary to get step 5 where you want it.
Initially this takes some time, but training your ears to tune this way is worth it. The whole instrument comes alive when it's well in tune.
Yup ... reading too many blogs. But still more productive than watching TV.
Tuning by ear in perfect fifths can be problematic for string players because the result of tuning justly (by the 2/3 calculation) does not fit the equal temperament system. If each string is tuned to 2/3 the frequency of the upper string, starting with A at 220 Hz, then the result will be a C string which is too flat compared to the piano, and which most people will think is too flat compared to the cello open A. That's why most string players consciously or subconsciously tighten their open fifths, like on the piano. The result is usually very close to what you'd get using a tuner on your metronome.
Its true that the human ear can only distinguish sounds 1 Hz apart, but only at high frequencies! Due to the logarithmic nature of sound perception, 1 Hz is a big difference at lower frequencies, such as the open strings of a cello. In terms of frequencies, each pitch one octave up is twice as big as the one below it, so as you compare intervals in higher octaves, you get bigger numbers. (The difference between C2 and G2 on the piano is about 33 Hz, and between C5 and G5 is about 261 Hz, so a difference of 1 Hz matters more at the lower octave.) Its more accurate to speak in terms of cents, which are the same for intervals in any octave.
An example: The open C string tuned by just (2/3) perfect fifths is 65.1851 Hz. The equal tempered pitch on the piano is 65.4064 Hz. The difference is only 0.2213 in Hz, so no big deal, right? Wrong! In cents, that difference is 5.87, which is actually pretty big.
I've read that the average person can hear a difference of 5 cents. I'm sure that trained listeners and musicians can hear smaller differences. I've found that I can hear differences lat least as small as 2.5 cents, which is the highest resolution I get on my electronic tuner.
So, for most purposes, I'd say that you should tune by ear using the fifths, but try and get the fifths to be as tight as possible while still sounding good. Then compare the open strings to the piano and see if you're happy. Of course, if this takes too long I say just tune with the electronic tuner and practice more.
Hope that helps!
I can always tell when my cello is "off" by two or three "cents". But since I've been tuning to equal temperament until now, if I start tuning to fifths, I'm going to have to retrain my ear.
My recent experimentation with intervals has been helpful in starting to appreciate these subtle differences.
You got the theory down, so now it's a matter of practice, practice, practice.
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