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Questions related from Terence B Allen
My exploration of the string Euler characteristic made me wonder if the Euler characteristic is related to energy conservation, then why not consider string thermodynamics. Not heat but free...
23 September 2024 6,842 4 View
This is a simple proof the guitar is Hamiltonian. Then by deconstruction so is string vibration because the string is the smallest open set on guitar. The time-independent Hamiltonian has the...
14 September 2024 2,495 5 View
Consider two different theories of string vibration determined by whether the string stretches as it moves. 1) If the string elongates as it bends, then the force acting on a point along the...
03 November 2023 8,880 10 View
If a string vibrates at 256 cycles per seconds then counting 256 cycles is the measure of 1 second. The number is real because it measures time and the number is arbitrary because it does not have...
22 December 2022 9,378 4 View
The pitch value set in music and guitar group in tablature are connected by adjunction of tangent-cotangent bundles. Tuning g is the tangent gradient to the flow of pitch on guitar. It determines...
05 April 2020 2,959 15 View
The sound envelope is observed as a change in sound amplitude over time when a musical string is plucked. The sound envelope has a sharp upswing called the attack followed by exponential volume...
01 April 2018 6,699 4 View
The guitar tuning is the initial state on guitar by which all possible states are known. The guitar tuning is a point in tuning space represented by a 6-digit number such as 0 7 5 3 4 5, commonly...
22 February 2017 4,525 1 View
The string is a real closed field minus finitely many points. If pitch is a continuous function defined on the string interval [0, 1] then there must be a fixed point in the interval. Each mode of...
07 July 2016 6,406 1 View
I think it is clear classic string theory is defined in Z2, if only because waves are 1 and nodes are zero. If we assume the string waves and nodes are defined in Z2 as a deductive system, the...
27 June 2016 9,816 3 View
Daniel Bernoulli established the principle that the number of modes of vibration in a system is equal to the degrees of freedom. In his method of hanging weights on a string, I assume without any...
22 June 2016 349 7 View
The S1 circle is a boundary that classifies pitch in the Z/12Z system as the chromatic circle, which can also be a spiral. The string concatenary is the shape the string returns to when plucked,...
20 June 2016 636 1 View
Check this video: https://search.yahoo.com/yhs/search?p=String+vibration+videos&ei=UTF-8&hspart=mozilla&hsimp=yhs-001 It seems to prove the string modes are finite states that are...
18 June 2016 1,206 7 View
The monochord page in Wikipedia implies that the diatonic scale is determined by the monochord instrument to be ratios defined by the position of a movable fulcrum. However, on musical strings...
05 June 2016 349 16 View
Some books imply the modes of a vibrating string are sin waves but I read that Euler said the string shape is a concatenation. A concatenation is the shape of a rope hanging between two points, so...
24 May 2016 4,327 4 View
In Alfred Tarski's "Logic, Semantics, Metamathemaitcs" the set of all meaningful sentences is described and the ordinary two-valued system of sentential calculus L is shown to be a subset of all...
26 April 2016 9,908 1 View
My terminology here is from "Measure Theory" by JL Doob, Springer Graduate Texts in Mathematics, 1994. Metric and pseudometric spaces are described on pages 3 to 5. My question is what happens if...
22 April 2016 3,854 1 View
The terminology in this question is taken from "Algebraic Topology" by CRF Maunder. See Problem 9 on Page 59. "Let H be the abstract 1-dimensional simplicial complex with vertices a0, a1, a2, a3,...
16 April 2016 3,401 3 View
How is pitch defined mathematically by frequency? Given pitch p and frequency f, what is the mathematic relation that defines pitch. In “Mathematics and Music” by David Wright (2009) we are told...
08 April 2016 9,367 3 View
Some say the loom and notch card are the oldest programmable device. The guitar, or the lute, are probably older than the loom and tablature is at least 400 years old. The guitar is programmed by...
29 March 2016 6,754 6 View
We like to think that music is mathematical but according to Wikipedia there is no axiomatic basis for music. How are musical sets constructed using basic set theoretic tools of union,...
17 March 2016 940 7 View
The Newtonian model of string vibration traces to Euler who asserted the string can have the shape of any curve that can be drawn free hand. The Hamiltonian model traces to Brook Taylor who...
01 January 1970 1,340 3 View
The guitar is a machine operated by a robotic arm. The tuning is the state by which every other state on guitar is known. Therefore, it must be possible to learn the mathematic structure of guitar...
01 January 1970 1,195 0 View
Newtonian and Hamiltonian formalism should produce the same result. But on the string they don't. A clear dichotomy. One is false, the other true. The Newtonian and Hamiltonian equations of...
01 January 1970 5,366 0 View
Taylor described harmonic motion on the string using Newtonian physics as a smooth manifold. This is absolutely unequivocal in Incremental Methods Direct and Indirect. The string field is uniform,...
01 January 1970 5,143 4 View
In trigonometry we know that frequency and amplitude are independent because they have independent variables. Then frequency and amplitude do not have the same equation of motion. But according...
01 January 1970 4,319 3 View
Please see the attached document for a summary of my proof of rigidity.
01 January 1970 4,260 3 View
A minion is a low-level official protecting a bureaucracy form challengers. A Kuhnian minion (after Thomas Kuhn's Structure of Scientific Revolutions) is a low-power scientist who dismisses any...
01 January 1970 6,657 14 View
Introduction to Tensor Analysis and the Calculus of Moving Surfaces, Springer 2013 is a wonderful book that contains everything there is to know about the theory of string vibration under one...
01 January 1970 4,535 2 View
The problem of string vibration boils down to whether the string is open or closed. I say it is closed and everyone else says it is open. Quoting physicist V.I. Arnold: "In formulating the...
01 January 1970 5,784 0 View