Hello everyone,
Thank you all very much for your generous answers to Alan's question on my behalf about inharmonicity, and thanks, Alan, for bring the discussion to this forum!
In answer to the question of how I am bowing the piano, I'm actually using fishing line (not horse hair). I tried using horse hair from an old violin bow at one point, but the length of the hair is shorter than I would like and it necessitates frequent changes of direction, which interrupt the resonance. The horse hair is also not as strong and is more prone to breakage while playing. There is a slight difference in timbre as well between horse hair and fishing line, but despite being a violinist by trade I actually prefer the quality of sound the fishing line produces. Vicki Ray, piano teacher at CalArts, taught me about using small bunches of rosined fishing line, fastened together at the ends by some method (I use a paperclip and electrical tape, and fishing line approximately 3-4 feet long). One end can be fed underneath the string and then pulled back through, and then the string is bowed by holding one end of the fishing line in each hand and drawing it back and forth.
What prompted my curiosity about inharmonicity is that I noticed I could isolate individual upper partials in the spectrum of the piano strings by manipulating the speed, contact point, and intensity of bowing (much like one can do on a violin string with a traditional bow), and that those upper partials seemed to be precisely where I would have expected them in a "just" harmonic series. It's always been a slight source of annoyance for me that piano harmonics are sharp compared to where they would be on a bowed cello or bass, due to the inharmonicity, so I was quite excited about the possibility of composing for piano harmonics that were actually in tune with the fundamental of the string, according to the principles of just intonation.
I knew a little bit about mode-locking from studying string instrument acoustics, and I've been aware for years that string players often tune false fifths by accident when they tune by plucking instead of bowing, presumably due to the inharmonicity of freely vibrating strings, but I wasn't sure of the extent to which the principle of mode-locking still applied to wound piano strings, due to their considerable thickness and stiffness.
I did some experiments recording different high bowed partials (on a 7-foot Bösendorfer, mostly using the bichords) and analyzing the pitch content using Melodyne software. My initial results were that the inharmonicity of the partials was reduced to within 5 cents of the mathematically correct frequencies all the way up to the 15th partial (and in many cases it was less than 1 cent). Beyond that the partials became quite sharp again. The 16th, 17th, 18th, and 19th partials were all 20-30 cents sharp, and that's as high as I measured. I believe the inharmonicity of partials 16 and above is due to the fact that it took a fair amount of force while bowing to get the string to clearly isolate those partials.
Thank you all again for your fascinating responses on this thread! I look forward to reading the many linked articles and learning more.
Wishing all the best,
-Andrew McIntosh
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Andrew McIntosh
Los Angeles CA
775-225-7943
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Original Message:
Sent: 09-23-2020 23:02
From: Steven Rosenthal
Subject: inharmonicity: bowed vs struck
And then there's this: viola organista
https://www.merriammusic.com/school-of-music/da-vincis-piano-cello-combo-a-hit/
https://www.youtube.com/watch?v=gOrn_z9m9lU&feature=emb_rel_pause
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Steven Rosenthal
Honolulu HI
808-521-7129
Original Message:
Sent: 09-23-2020 22:59
From: Steven Rosenthal
Subject: inharmonicity: bowed vs struck
I believe the ebow excites the strings electromagnetically.
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Steven Rosenthal
Honolulu HI
808-521-7129
Original Message:
Sent: 09-23-2020 22:50
From: Mark Schecter
Subject: inharmonicity: bowed vs struck
Without any info on how others may have bowed piano strings, I can say there is (or was) a mechanical device aimed at guitar players, which consists of a rotating wheel/bow that is held in the hand, and placed against the string , acting as a continuous bow. It would be easier to apply than a normal violin-type bow. In case anyone wants to experiment, it is called the Ebow.
Mark Schecter
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Original Message:
Sent: 9/23/2020 10:34:00 PM
From: Alan Eder
Subject: RE: inharmonicity: bowed vs struck
Cindy,
Not sure just how he is bowing the strings. I have invited him to join these lists so he can go through the thread on his own. Perhaps he can explain to everyone without having to go through me.
Alan
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Alan Eder, RPT
Herb Alpert School of Music
California Institute of the Arts
Valencia, CA
661.904.6483
Original Message:
Sent: 09-23-2020 21:58
From: Lucinda Strehlow
Subject: inharmonicity: bowed vs struck
Curious about how he is bowing the piano strings.
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Cindy Strehlow, RPT
Urbana, IL
Original Message:
Sent: 09-22-2020 07:15
From: Alan Eder
Subject: inharmonicity: bowed vs struck
Greetings Lists,
Andrew McIntosh, a composer and violinist on our faculty, writes for bowed piano (among other things). He has observed less inharmonicity in violin strings when they are bowed that when they are plucked, and has floated the notion that piano strings exhibit less inharmonicity when bowed than when struck (possibly due to less displacement/increased tension?). The question is: Is the amount of inharmonicity in piano strings generated, at least in part, by the strings being struck?
Thanks,
Alan
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Alan Eder, RPT
Herb Alpert School of Music
California Institute of the Arts
Valencia, CA
661.904.6483
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