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Since I commented last time on temperament I thought another tidbit on the subject might be of interest. When using tuning systems before equal temperament some notes were very out of tune when playing is certain keys. This was a big problem on instruments having fixed pitches like the harpsichord.

There were several approaches taken to get out of this difficulty. The most common was not to write music in the "bad" keys.

A second was to retune the instrument when changing keys, but this was slow and annoying.

The most creative approach was to squeeze in extra keys to handle the worst notes. I haven't been able to find a photo of an actual instrument, but this diagram from Wikipedia gives the idea:

The illustration shows what is called a short octave, which was used to save creating a few notes at the bottom of the scale which would never be played as the lowest note in a chord, but the use of the accidentals split in th a front and back half is the technique I'm referring to.

The most common notes to be split were D#/Eb and G#/Ab. These notes have the same pitch under modern tuning but where noticeably different under older systems like meantone.

There is still some discussion as to whether modern violinists and singers adjust the pitch as they perform so as to be closer to the natural harmonic series.


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by rdf (robert.feinman@gmail.com) on Wed Apr 23rd, 2008 at 05:09:59 PM EST
Isn't one of the points of using vibrato when singing or playing, to make sure to hit the harmonic pitch along the others ?

Also, pitch adjustment is very important when playing in an orchestra. Reed and string instrument players constantly adjust their pitch while playing, to make sure all the pitches are the same, and to make the harmonies sound good.

Indeed, pitch adjustment is also important harmonically, especially if the instrument is tuned with an equal temperament : when playing A on a guitar, you don't get a pure 440 Hz vibration, but also bits of 439 Hz and 441 Hz, etc..., so that when playing a chord, there will be perfect harmonies between the various notes...

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by linca (antonin POINT lucas AROBASE gmail.com) on Thu Apr 24th, 2008 at 04:41:39 AM EST
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linca:
Isn't one of the points of using vibrato when singing or playing, to make sure to hit the harmonic pitch along the others ?

No, it's more because vibrato sounds nice. I suppose it could work as a disguise for not-quite-in tune sounds, but almost every culture seems to have invented it, including the ones that are harmonically exotic. (By Western standards.)

linca:

Indeed, pitch adjustment is also important harmonically, especially if the instrument is tuned with an equal temperament : when playing A on a guitar, you don't get a pure 440 Hz vibration, but also bits of 439 Hz and 441 Hz, etc..., so that when playing a chord, there will be perfect harmonies between the various notes...

Not quite. Open strings play a fixed pitch - if there elements of pitches either side of the fundamental, you'd get obvious beat effects.

What guitars do is kind of complicated, and depends on the kind of guitar and how it's being played. But usually the pluck starts very slightly sharp because the string has to be stretched to make the note. There's a wide mix of overtones in the pluck, and they're not all harmonic.

During the sustain part the overtones become harmonic, with some phase cancellation created by sympathetic resonances in the other strings, which are never perfectly in tune. So you get a moving overtone structure even from a single string. Pianos do this even more. Play a chord and hold it and the sound keeps changing.

But what you don't get on fretted instruments is perfect harmonies. Guitars have to be detuned slightly to sound their best, which is why you can use a digital tuner and still find the sound is not right.

I have a fretted dulcimer which can't be tuned perfectly. You have a choice between a good fifth on on open strings, or a good unison when the middle string is fretted. So the middle string has to be tuned between those extremes, and it never quite sounds right.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Fri Apr 25th, 2008 at 05:41:49 AM EST
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