In a practical sense, the violin has the perfect termination. Both ends of the string are terminated on a single narrow point and their duplexes are free to vibrate equally in the X and Y vector. The piano has one single point, the capo or agraffe, and the opposite end, a flat bridge; the flat bridge poses special termination issues by restricting the freedom of movement in the X vector, although both ends of piano wire pose additional angular stress tensions in both the X and Y vectors because of the stiffness of the wire. These stresses can be reduced or eliminated with proper bending techniques.
Another way of explaining the false beat issue is: The pitch of a wire is 99% determined by the length, diameter and tension. The remaining 1or 2% is dictated by the stiffness of the termination in either the X and/or Y vector. That 1 or 2% bps (beats per second) is largely influenced by the mass; large mass equals slower bps, and lighter mass equals faster bps.
P.S. I hope the findings illustrated in the "False Beats – Understanding through Critical Thinking", lays to rest the age-long myth that loose bridge pins cause false beats.
Original Message:
Sent: 08-04-2026 19:40
From: William Truitt
Subject: strange false beats
Hi Roger:
I too admit that my responses may lack clarity. :-)
What I was referring to was the pattern of beating that one can hear in multiple notes at certain times. It can coexist with false beats, but is not the same thing. Its pattern and regularity are visually distinct and sound like the pattern I am seeing. My two cents tells me that the source is bridge roll. Why bridge roll? Bridge roll originates from the collectively enormous torsion that comes from the front bridge pin tops leaning toward the bass at an angle of 70 to 75 degrees to horizontal, and the rear pins leaning towards the treble at 70 to 75 degrees. With a span of say 18 mm, this means that all the front pins are pulling towards the treble side, and all the rear pins are pulling towards the bass side, they work to twist the bridge. The bridge is restrained, so that, along with string tension works to roll the bridge forward and down. This can distort the soundboard panel into a sine curve, down in the front and up in the back. When sounding, the bridge is rocking forward and down in a regular pattern, the pitch rises and falls.
X and Y vectors most commonly denote the horizontal and vertical vectors.
As best I understand what you are saying is that the mass of a string dictates how fast the beats can be in a string. Of course, there is a strong connection between mass and inertia. So I think what you are saying is correct.
I would be grateful if you could define what a nearly perfect balanced termination would be. It is not a flippant or demanding question. There is a lot going on in that simple string rounding a corner on a pin set at an asymmetrical angle.
Stiffness can have two distinct meanings. One is material - such as Modulus of Elasticity. If made from the same steel, F3 and C8 would have the same MOE. The other is structural. F3 has a larger diameter pin (perhaps .086"), and C8 might be .076". F3 would have a higher bending stiffness than C8.
I read your articles a couple of times and enjoyed them, and shared a couple of emails with you.
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William Truitt RPT
Bridgewater NH
(603) 744-2277
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Original Message:
Sent: 08-04-2026 11:35
From: Roger Gable
Subject: strange false beats
William,
Sorry for the delay, I had difficulty signing in to myptg.org.
Yes, I admit my response may lack clarity. I try to keep my responses short. Short text draws more readers.
Your statement, "Listening to them while looking at my Tunelab display, I can separate the false beats from this pattern.
What," this" are you referring to?
Your statement, "What exactly constitutes the X and Y vectors for you?
The X vector is the movement of the string parallel to the soundboard and the Y vector is the movement of the string perpendicular to the soundboard. The false beat is created by a dipropionate stiffness of the termination in the X and Y vector
Your statement, "I am also not clear as to what you perceive the role of inertia that creates the slightly out of phase beating that we hear.
The inertia does not create a slightly out of phase beating "per se". The inertia dictates boundaries of the speed of the false beat. A nearly perfect balanced termination will create a slow false beat within the boundaries of the inertia of a given string. The inertia in a long heavy gauge wire lies outside the boundaries of a fast-beating false beat, whereas a short light weight string will not beat at slow rate. To give you an example; a string with a distorted termination vibrating at 100 cps (hertz's) can only produce a distortion rate in the X and Y vectors of about 2 cps. The inertia is too great to vibrate much higher. The opposite if true in the short higher frequency strings.
Your statement." F3 will be much stiffer also. "Your F3 reference to C8. You need to restate or rethink that.
Your statement," But the fact that C8 is physically so distant and clearly in its own unique setting robs me of the opportunity to make a meaningful connection between the two that is descriptive of real phenomena.
You lost me on that.
P.S. I would encourage you to read the articles, False Beats Understanding through Critical Thinking, in the February and March 2025 PTG Journal
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Roger Gable RPT
Gable Piano
Everett WA
(425) 252-5000
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Original Message:
Sent: 08-02-2026 06:16
From: William Truitt
Subject: strange false beats
Roger, while I agree with you and Peter that the same beat rate spanning many notes is likely a tell that the root cause of the beating is not false beats, I think your description lacks clarity. When I hear the beating we are talking about here, it is by way of contrast an orderly and consistent pattern to my ears, whereas false beats are more random and chaotic. Listening to them while looking at my Tunelab display, I can separate the false beats from this pattern. Interestingly, the pitch is rising and falling in that pattern, and I can hear the changes in pitch.
I know what X and Y vectors are, but it is not clear in your explanation what you are referencing in terms of string behavior (if that is what you are talking about). What exactly constitutes the X and Y vectors for you?
I am also not clear as to what you perceive the role of inertia that creates the slightly out of phase beating that we hear. The F3 string will have more inertia than the C8 string because the F3 string has more mass because the string is much thicker and far longer. F3 will be much stiffer also. But the fact that C8 is physically so distant and clearly in its own unique setting robs me of the opportunity to make a meaningful connection between the two that is descriptive of real phenomena.
Wherein lies the causal link that bridges inertia and the beat rates?
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William Truitt RPT
Bridgewater NH
(603) 744-2277
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Original Message:
Sent: 07-31-2026 16:49
From: Roger Gable
Subject: strange false beats
Timothy,
After reading your original post stating the false beats situation on a Wurlitzer spinet, you are not hearing false beats. It is physically impossible for all plain wire strings to produce the same false beat rate. Consider what a false beat is. It is the beat produced by the differential termination stiffness in the "X" and "Y" vector. That differential will create only a slight frequency variance between the two vectors. The rate of the beat is determined by the inertia in the wire. The plain string at the F3 has more inertia than C8. It is impossible for the inertia in the F3 string to have a 5-beat rate or the C8 string to have a 1-beat rate.
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Roger Gable RPT
Gable Piano
Everett WA
(425) 252-5000
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