Terence B Allen

29 Questions 75 Answers 0 Followers

Questions related from Terence B Allen

Does the Gibbs phase rule prove string vibration frequency and amplitude have the same energy source (and are therefore not independent)?

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 6,854 4 View

Isn't it true the guitar tuning by itself proves a Hamiltonian machine? If guitar is Hamiltonian, doesn't this prove the string is too?

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 2,503 5 View

Does a vibrating string stretch (elongate) during vibration or does string length (curvature) remain constant?

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 8,891 10 View

Is musical pitch a real number because it is an arbitrary measure of time?

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 9,384 4 View

Standard guitar tuning has two distinguished vectors (0 5 5 5 4 5) and (0 5 10 15 19 24). What is required to show they are tangent-cotangent bundles?

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 2,972 15 View

Is the sound envelope produced by a plucked musical string a natural experimental that shows how many modes of vibration exist?

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 6,705 4 View

How many steps are required to go from any guitar tuning to the best possible guitar tuning for given music input?

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 4,530 1 View

If the pitch of a string is an algebraic object and the string wave form is a geometric object, does that make a first-order model by itself?

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 6,414 1 View

Since the vibrating string is defined in Z2 by a map S1 on S1, is there a field F2 above Z2?

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 9,837 3 View

How many degrees of freedom does a musical string have? 1, 2, or n?

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 358 7 View

I have two different boundary conditions for a vibrating string. Can you tell me if they are equivalent?

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 644 1 View

Do you agree this video proves the string cannot vibrate in more that one mode at a time?

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 1,212 7 View

Are the overtones for the monochord and the musical string the same series?

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 355 16 View

Is the shape of a vibrating string a sin wave or a concatenation?

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 4,334 4 View

Is there a relation between the set of all sentences closed to implication and detachment and the algebra of subsets of some set?

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 9,913 1 View

Is a metric space where the distance is always 1 also a pseduometric space?

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 3,859 1 View

If H is a 1-dimensional simplicial complex with 6 vertices, each pair of vertices being a 1-simplex, is it possible that H has no realization in R2?

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 3,409 3 View

How is pitch mathematicall defined as a function of frequency?

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 9,376 3 View

Is the guitar a computable device older than the loom and notch card?

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 6,762 6 View

What is the axiomatic basis for music theory?

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 949 7 View

Can you help me design an experiment tesing whether a string has one simultaneous mode or many?

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 1,346 3 View

Is the guitar tuning sufficient by itself to classify tablature mathematically, or is additional information required?

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 1,205 0 View

Why don't Newtonian and Hamiltonian models for string vibration produce the same result?

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 5,376 0 View

In the calculus priority dispute of 1715 between Taylor and Euler, doesn't Euler's principle of superposition violate his principle of least action?

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 5,148 4 View

Physicists/Mathematicians: Can you prove string frequency and amplitude are independent (not determined by the same Hamiltonian wave equation)?

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 4,329 3 View

A challenge to mathematicians and physicists to prove this assertion false: The vibrating string is rigid, not elastic,

Please see the attached document for a summary of my proof of rigidity.

01 January 1970 4,266 3 View

Are the minions at Physics Stack Exchange Kuhnian? Please add to their discussion on string vibation theory.

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 6,665 14 View

Have you read Grinfeld's "Introduction to Tensor Analysis and the Calculus of Moving Surfaces? Want to start a discussion regarding string vibration?

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 4,539 2 View

Is the string open or closed? Can anyone defend the open string in the face of an exact solution?

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 5,792 0 View