Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum About that string coupling theory...

I’ll try to explain.

For RBIs, the more they are tempered the faster they beat and they sound brighter.

For SBIs (including octaves), there is a point where the beats are not obvious and then the color can be heard as something separate from any beating. There is an area between where the beat(s) are not obvious and where the interval is as pure as possible. This is the place to listen for color without being distracted by beats.

If you listen to a temperament 5th, and slowly bring the pitch of the upper note up from well below pitch, you may hear what I mean. But you have to try and ignore any beats. Otherwise you may not see the forest for the trees.

rxd, your comments are precisely in line with Gabriel Weinreich's lecture mentioned by Keith and Mark R:

"It should be clear from this discussion that if we observe the motion of two coupled strings, of which one is left untouched while the other is tuned, we would observe that the untouched string will change its frequency (although it remains at constant tension) as the second string is tuned. This is under condition that the two strings are close to a unison ... What is not so clear - and, in fact, requires considerable mathematical discussion - is precisely what this frequency shift will be. Interestingly, it turns out that it can be in either direction, depending on the impedance of the bridge itself. In particular, there exists a possibility for the two frequencies to "attract" and become locked together, so that slight tuning of either string does not affect the frequency of either but only the decay rates."

I think of it as a contest between the strings and the bridge. When they are within half a beat, or as Weinreich says about 0.3 Hz, the bridge wins and forces the strings to vibrate together. The bridge expends some energy doing this so the decay is greater than in a perfect unison.

The effect certainly helped me to correct an out of tune unison last night; I thought it was beginner's luck.

Hello Jeff

Thank you for your response.

You wrote, "For SBIs (including octaves), there is a point where the beats are not obvious and then the color can be heard as something separate from any beating. There is an area between where the beat(s) are not obvious and where the interval is as pure as possible. This is the place to listen for color without being distracted by beats."

I suppose what you are speaking about in the above few sentences is something similar to unison tuning? No beats (or very,very slow whining)but the question is how clean?

I am not sure I understand exactly what you mean when you use the word colour or why? I suppose that depending on the piano, the area when the SBI intervals are becoming beatless/become beatless may vary in width (if I may use that word)?

However one tunes the SBI intervals, there will always be interval checks that will tell you whether you have tuned a pure, narrow or wide interval and to what degree? So I would think that the interval checks will be the final determining factor according to how one likes to tune.

Regards,

Mark:

Yes it is similar to unison tuning. In fact, I later wished I had included unisons as SBIs like I did with octaves.

By color (colour?) I mean timbre. I think there is more discernment possible when listening to the color of an SBI than by listening to the beat speed, especially if tests are used to determine beat speeds. Much of the color may be due to multiple beats. Like for a 5th, there are both the 3:2 and the 6:4 partial matches.

Jeff,

I am not sure if we should be discussing this on a new thread or privately? I think that I am or we are highjacking this thread. Thoughts?

So in brief, I am not exactly sure of what you are saying in the following few sentences, "By color (colour?) I mean timbre. I think there is more discernment possible when listening to the color of an SBI than by listening to the beat speed, especially if tests are used to determine beat speeds. Much of the color may be due to multiple beats. Like for a 5th, there are both the 3:2 and the 6:4 partial matches."

Are you able to expand on the above? What are you hearing if you are not hearing beats? How are you tuning this timbre/colour in order to get your desired result? Can you be more specific?

All I do when tuning is tune to specific beat speeds, approximations of beat speeds and comprimises of specific beat speeds according to the inharmonicity of the particular piano I am tuning.

I dont know, I am at a loss thinking about this colour/timbre thing!?

Regards,

Mark:

Yes, I think a seperate Topic is in order. I will start one.

I can't speak for Jeff, but my impression is that the differing color exists because of the beats: as the amplitude of some freqs rise and others fall, different constellations of partials become more and less audible, creating differing chords, if you will, of partials.

A related question: Do the strings decouple in the decay? Surely they must, even if very late in the decay on notes played with the pedal pressed down. If so, what determines how quickly they decouple so that their separate freqs\their out-of-tuness becomes audible? The force of the hammer strike? In other words, do hard strikes cause the coupling to last longer?

Have you looked at Weinreich's paper mentioned above? He did not mention uncoupling so perhaps it's not significant; no longer audible when it happens or the music has moved on.

Yes, I've read the Weinreich essay. Just thinking aloud here: The soundboard must be the cause of the delay\non-existence in the detuning? Since it's coupled most directly to the bridge, once the coupled strings excite its nodes, those nodes get transferred back to the strings, too. And the soundboard impedance by definition slows the movement of the vibrations, so even if the strings do decouple, we instead hear the earlier, coupled vibrations moving from the soundboard to the air?

Very interesting subject, in any case--the relationship of beats and phasing and color.