15th harmonic on a piano string

[ricochet]

Hi, bit of a silly question (also wasn't sure where to place this topic), but could anyone assist me with how to generate the 15th harmonic (as a flageolet) on the string a contraoctave D (so effect should be c-sharp from the two-line octave). I'm preparing a contemporary piece in which I have to generate descending flageolets on that particular string, from the 15th to the 9th, and the 15th seems to be the only one to elude me. Any indication or even visual pinpoint on where to trace it on the string would be of great help.

Thanks in advance.

[quantum]

The point is going to differ on every piano, so you will need to practice on the performance instrument.  

There is a contemporary music center in my city where the inside of the piano has been marked up with stickies and labels to aid in performance.  You might want to try those little colored sticky dots.  Of course putting the sticker on the actual string would be a last-resort-only thing.  Using one of the cast iron beams closest to it would be much preferable.  Of course, if it is not your piano you should ask if it is okay to use stickers inside the piano.  

If stickers are too invasive, you could also get a piece of lumber to lie on top of the cast iron frame.  You could then mark up that piece of lumber with your points.  Maybe wrap the contact points between the cast iron frame with felt so it does not rattle.  This method is also very easy to install and remove.  

Are you referring to having difficulty sounding the harmonic on the string?  The node might be under the damper.  You could have an assistant activate the node from the other side of the piano.  You could also try to use a dowel to carefully insert behind the damper and touch the node, however you need to be very cautious not to damage the damper felt.  If at all possible, the assistant is the safer route.  

[ricochet]

Thank you for your reply. It's not an issue of performing on different instruments (I'm already practicing the piece on my home piano, at the faculty and at the philharmonic, where I'll be performing) or marking the harmonics spots (which I have done by knotting twines around the string). Indeed I meant having difficulty in hearing, locating and generating the 15th harmonic.

Never considered the area under the damper, but if it happens to be there it would be really impractical, because of how recurrent generating that harmonic is supposed to be in the piece (the composer conceived it almost as a chaccone-like bass line of descending flageolets); same goes for having an extra aid, which is something the composer never mentioned.

I might just as well get back in touch with the composer, while there's still time to discern this, but I thought of asking others who might be more familiar with generating such effects. Thanks again.

[georgey]

I used to play classical guitar and I have a math background.  I assume you want to generate a harmonic similar to how it is done on a guitar.  In guitar terminology, if you pinch the string at a spot that is exactly 1/15th the distance to the bridge as compared to the total distance from the bridge to the nut, you should in theory generate the 15th harmonic.  You can also generate this at other places on the string.  Example: 2/15 the distance, 4/15 the distance, etc.  (not 3/15,  5/15, etc the distance since 3/15 = 1/5 - the 5th harmonic and 5/15 = 1/3 - the 3rd harmonic, etc).  Your composer should be able to help.  The resultant pitch should be 3 octaves + a major seventh (M7) higher relative to the fundamental tone looking at the Wikipedia article on Harmonics*.   Not sure if this helps any.  Good luck.

* EDIT check:  2^(47/12) = 15.1 which is about 15 – 15th harmonic!  
^ - to the power of