Best notation for 'out of tune' natural harmonics?

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David Ward
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Best notation for 'out of tune' natural harmonics?

Post by David Ward »

I'm writing a piece for a virtuoso cellist that includes passages of very high natural harmonics. Some of these are between the notes of equal temperament, but attempting to notate them as 1/4 tones (which they aren't) would miss the point.

Might using the most usual text book notation for the harmonic series with an asterisk * placed over the severely 'out of tune' notes be a sensible approach? Actually, even the 3rd (perfect 12th) harmonic is very marginally out from equal temperament, but harmonics 7, 11, 13 & 14 are way different from the notes in any of our usual diatonic/chromatic scales.

I will need to confirm with the cellist just how high he can go while playing natural harmonics. Experimenting with a friend on a cello with gut strings we managed the 16th harmonic, which on the C string was a week, 'breathy', but atmospheric sound, while it was strong and clear on the A string. The cellist for whom I'm writing uses metal strings and has a super-secure technique, so …
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OCTO
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Re: Best notation for 'out of tune' natural harmonics?

Post by OCTO »

If they go more toward the ponticello, maybe even more harmonics can be produced.
I would use just circles, and approximate notation (regular). Maybe also accidentals in parenthesis as narrow down or narrow up. How much - no need to make it so in detal, anyway you cannot play other harmonics between no 15 and no 16. There is no harmonic at 15,5. So, playing just harmonic no 15 is this tone. No more no less.
So, the best would be, just notate harmonics and circles, and approximate accidentals. Eventually inform the player that these are out of tune.

Maybe you can drop us a screenshot of your solution?
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MJCube
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Re: Best notation for 'out of tune' natural harmonics?

Post by MJCube »

My friend Toby Twining wrote a cello piece called 9:11 Blues (2002) that uses the same very high natural harmonics. But he writes in extended J.I. throughout, using Ben Johnston’s notation. If your piece otherwise assumes E.T., you’ll have to just choose a notation system for the just intervals. Have a look at Sagittal. (By the way, Dorico and SMuFL support all of the commonly used microtonal notation systems.)

When you’re up that high on the fingerboard it’s very hard to find your location by feel; you have to do it by ear anyway. So I wouldn’t worry too much about e.g. quarter-tone notation being imprecise. What I find helpful in the score is the harmonic number over notes which are harmonics. Perhaps you’d want just a footnote somewhere explaining that the 7th and 14th harmonics are 31 cents flat to E.T., the 11th is a ‘real’ quarter-tone (–49 cents) and the 13th is 41 cents sharp.

P.S. I was so eager to post this reply that I didn’t read OCTO’s excellent suggestions first. Better than mine.
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David Ward
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Re: Best notation for 'out of tune' natural harmonics?

Post by David Ward »

Thank you both for the comments and suggestions. I'll give it thought and report back later.

The cellist who'll play the piece, Rohan de Saram http://rohandesaram.co.uk/ has been experimenting recently with very high harmonics in improvisations, which is what gave me the idea to exploit them in my own piece (which is also to be partly improvised as it accompanies projections by an artist). First performance is due in just under a year from now.
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qanunji
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Re: Best notation for 'out of tune' natural harmonics?

Post by qanunji »

I would write them as usual.
the deviation from the equal temperament is natural, and you can't choose an accidental.
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