Science topic

# Musical Acoustics - Science topic

Musical acoustics or music acoustics is the branch of acoustics concerned with researching and describing the physics of music — how sounds employed as music work. Examples of areas of study are the function of musical instruments, the human voice (the physics of speech and singing), computer analysis of melody, and in the clinical use of music in music therapy.
Questions related to Musical Acoustics
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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 found on instruments such as the guitar or violin, the string is not a monochord because the detainment of the string allows the fundamental mode to resonate between only two points, and not three.
It follow then that the fundamental of the monochord has a wavelength 2L while the musical string has a fundamental which is 1.
Significantly the musical string does not depend in any way on the length, tension, mass, or composition (within a bound range useful for harmonic oscillations) because the only requirement is the 12th fret is placed at the string midpoint and then one half the string is divided into 12 equal frequency units using the 12th root of 2.  This is the geometric equivalent of the construction of the square root of 2 by the unit square.
My question is whether the monochord and the musical string are in fact the same because it seems the monochord overtones are multiples of 2L and the musical string does not depend on L at all because it is normalized for length.
The string is 1.  It is one thing, always the same, a constant. It is not 1L. Its just 1. It always has the same shape, which is detained in a concatenation.  So the idea that the string is the sum of all the possible modes of vibration is wrong.  There is only one mode and that is the fundamental.  This means the natural overtones are not the defined mutliples of the fundamental.  The multiples are the octave, and any subset of the octave is also a multiple.  You have a ruler and then 12 equal subunits.
The monochord investigates the effect of changing the wavelength and frequency as continiuous variables, but the music string (which is formed by the union of the pitch value and string position sets on the fundamental) are constants that cannot be continuous because the fundamental is a standing wave.
If multiples of the fundamental are defined by the frets that detain the fundamental, then the definition of the overtones is mathematically distinct from the monochord overtones which are degenerate (that is not nondegenerate) forms based on a lower mode of vibration than actually exists.
Doesn't this mean the string under the square root of 2 is always tempered and the problem tempering the piano results because the strings on piano have different lengths?
Terence B Allen, you should not compare pears with apples.
You write: " We have the natural overtone series as the set N = F0, F1, F2, F3, … and the tempered series is the set T = A1, A#1, B1, C1, C#1, …, A2, …n. "
You should realize that while the first series is a series of frequencies (which would better be expressed as N = F, 2F, 3F, 4F, ..., with F being the fundamental frequency), the second is a series of logarithms of frequency ratios.
If units of the tempered series are 21/12, then the logarithmic series that you call the "tempered series" becomes T = 1, 2, 3, 4, etc.
If these two series ressemble each other, it merely is to the extent that a series of whole numbers may ressemble a series of logarithms. However, if you want to express the series of whole numbers in terms of the logarithmic series with basis 21/2, then it becomes, to the approximation dictated by the logarithmic base, log(N) = 0, 12, 19, 24, ... – or, in numeric values of the logarithms, 1, 2, 2.997 (=~3), 4, etc.
This is not high level mathematics, it merely is low level arithmetics. It has nothing to do with the vibration of strings, the arithmetics would remain exactly the same for notes (or frequencies) produced by any other means.
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Dear All,
Please give me your recommendations (or some papers) how I can examine acoustic properties of the titanium printed flute.
How in general acoustic properties in metals are examined and evaluated?
Sincerely yours,
Anastasia
Can you please clarify by "acoustic properties"?
A metal alloy as every solid propagates compressional waves that are "sound waves" with a sound speed of SQR(Young Modulus/Density) with an hysteretic damping generally close to 1E-3; measuring the Young Modulus is a simpler lab test than measuring the hysteretic damping, both can be made on a simple parallelepipedic sample; sound speed and sound absorption ((1-hysteretic damping)*number of wavelengthes) can be also assessed explicitly with an ultrasound probe on a rod (send a short pulse and compare with the echo).
If you manufacture a musical instrument and want to characterize the influence of the alloy on the musical quality of this instrument, this is an absolutely different issue calling for decades of research (the most popular is trying to understand the role of the varnish versus wood selection in Stradivarius violins): I would just ask a good musician to assess it by playing and ranking various instruments manufactured conventionally and by additive printing...
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I saw different examples in 3d-printing of musical instruments from polymers and from wood, but not a lot from metals.
I am looking for examples of additive manufacturing of musical instruments specifically from metals, using not only geometrical capabilities of 3d-printing, but also mechanical and acoustic properties of printed metal.
Can you please provide some papers. Thanks.
Good example -
The Heavy Metal 3D printed Aluminium Guitar https://www.oddguitars.com/heavymetal.html
However from the metallic properties only light-weight of aluminium is used.
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I would like to know about acoustical behaviour of Brass in Brass musical instruments.
As far as I know and in general, it is not the brass in wind instruments like the trumpet that resonates, but rather the wind column within the instrument.
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I need this to calculate further statistics with these results.
Hello, hoping it is still useful 3 years later.
Woodwind sounds are necessarily harmonics (not partials). Because clarinet works as a feedback loop, like for exemple a larsen, solution is periodic (or quasi).
If you mean by calculate to predict the magnitude, a theoretical approximation of the first harmonics  is depicted in Kergomard Acustica Vol86 (2000) 685-703.
Then, if you have an idea of the impedance spectrum of your instrument you should use some numerical simulation tools like this one in python: https://hal.archives-ouvertes.fr/hal-00770238v2
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I have the records of hydrophone deployed in a river I would like to find such a method to separate the water turbulence from other signals.
My understanding is that the signals of sound intensity Sound to Noise Ratio (SNR) comprises both water turbulence and bedload noises in addition to some cases the noise which comes from human activities like (transportation, etc.).
I am interested to find  a way to decompose those signals. Is there any direction!
It may be helpful to have a look on the following paper:
Denoising and Despiking ADV Velocity and Salinity Concentration Data in Turbulent Stratified Flows: Kourosh Hejazi · Roger A. Falconer · Ehsan Seifi
Oct 2016 · Flow Measurement and Instrumentation.
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I would like to investigate the sound characteristics of traditional musical instrument with the skin goat as the membrane, like percussion. I need some references and publications related to the sound characteristics of traditional musical instruments using membrane. Any suggestions will be appreciated.
Hi Waluyo,
There is information on a particular string instrument that is made with goat skin, which you might find interesting. The whole website is very cool as well, there is information on instruments from many parts of the world.
Also check out this two part video on the making of a goat skin drum:
I hope you find these sources interesting and helpful!
Let me know what you think!
~Jonathan
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Since our study of the Baschet acoustical system to analyze the functional element of every possible sound device, we noticed some inconsistencies on the notion of "Idiophones", as it was set by HornBostel and Sachs nearly a century ago.The idea of an Idiophone is that it produces the vibrations and radiates them as a result of its own body properties (tension and radiating surface). This is clear for bells, cymbals, gongs, etc. But probably because of the western lack of familiarity with other organologic principles, many instruments had been also clasified as Idiophones, just because their activation is done by stricking or plucking.
The definition of Idiophone seemend to be acurated in its principle, but then we lack a taxonomical family for lamelophones and other similar structures using rods, tines, and other clamped elements.
The confusion on this subject is missleading not just for classificatory purposes, but specially because it creates an intellectual misunderstanding for the acoustical research and disclosure on both idiophones and the other instruments classified as it by mistake (suck as Kalimbas, Zanzas, Toy-Pianos, Daxophones, Baschet Sound Sculptures, etc... wich all need to have added radiators and some tensioning devices to the oscillators)
The building processes, and the real-time manipulations during onthe performance are completely different, and so are the reseaches on their acoustical behaviour. We are preparing a paper on the subject, while reading Margaret Kartomi's book "On concepts and classifications of musical instruments", but we would like to know if there is any particular study on the organology of idiophones, discerning the real ones from those other structures, that deserve to have a taxa on their own.
About the Baschet instruments, and although my own experience with them in the Brussels Museum dates more than twenty years ago, my memory is that the tuning is done on the metal structures supporting the glass rods; we had several broken rods, but their being broken did not affect the sound. I'd conclude that the "primary vibrators" ain't the glass rods, which act as mere bows, but their supporting metal structures. These of course are quite unable to radiate sound in the air, hence the piano strings attached, and the inflatable soundboxes.
The objection that one migh have against their classification as idiophones is that the classification takes account of only a tiny part of the whole instrument. And, indeed, a "post modern" classification might want to take other aspects in account, among others the visual aspect of these structures (and other social aspects). But this was not the purpose of the Hornbostel-Sachs classification, which hardly can be faulted in its own terms and its own purpose.
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I need to know how music processing can be carried out using Java. Please suggest any references or sites if any.
You can try out jaudio. It is for audio processing not specifically for music but we can use it for music.
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I want to know a PDE of the special strings of violin for example (A string) at the special frequency for example (440 Hz). Could anyone help me?
Just to add some further complication, the oscillations of the string are coupled to the oscillation of the corpus of the violin, since the latter are induced and leave the violin, leading to an energy loss of the vibrating string. The coupling is presumably mainly induced by the additional point mentioned by Peter Spellucci, that is mounted on the oscillating wooden corpus of the string. But the other points on the  violin where the string is fixed are also oscillating.
One should also keep in mind that the oscillations of the string are induced by the hairs of the bow, in a so-called "Rutschkupplung" (a friction clutch ?) which is said to be rather complicated but very important for the violin players.  Although the movement of the bow seems to steady and continuous, the string sticks to the bow for a short period until the tension gets to large, and it snaps free. Probably, this was meant bei Thomas I Seidmann ("the question of bowing").
I thus would guess that a single PDF will probably not be sufficient, and one has to use several ones for these various parts of the system, each being quite elaborate. Not to mention the nonlinearities ...
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I am looking for some new materials, which can be fabricated and applied as a tweeter membrane. Any tips ?
Hi Krzysztof, might you be more precise about the technical performance you need from this component? For instance: cut-off frequency, range, impedance, applied power...
Will it work in a system? What kind of?
Let me know, thanks!
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I am looking at the positive effects of low frequencies in music, predominantly below 50Hz. This involves aural as well as mechanosensations. I am interested in seeing if reinforcing the low frequency content below 50Hz can help produce a more immersive listening experience at lower overall sound pressure levels (particularly when measured using the A weighting scale). Trouser flapping bass.
Please be aware that, historically, religious chants have used low frequencies for production of alpha wave states. In particular I would suggest examining Tibetan Buddhist chant e.g. the Gyoto Monks.
or then there's Charlie Watts and Bill Wyman :-) same thing however.
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an approach for aggregation along frames.
I would use a two-side approach: frequency spectra snapshots and amplitude envelope on one side, plus a net of semantic correlations (i.e. connotations) on the other. The latter to be considered as a shared feature among a pre-defined group of listeners.
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For instance, any research about how to use the different tuning systems and/or the equal temperament when there is a guitar in the ensemble.
The composer Stephen Goss said in an interview (I can get you the text if you're interested): "Many composers fall into the trap of thinking of the guitar as first and foremost a harmonic instrument. I think of the guitar as a melody instrument, more a violin or a cello with extra possibilities of resonance, than as a piano with debilitating limitations."  He mentions the "learning curve" and the challenge that the instrument represents to the composer. The view from the "composer's side" is quite interesting.
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I exploit this phenomenon in several compositions but do not fully understand it. Assume here that I have a single stringed guitar, and ignore microphonic feedback from the pickups.
When a string vibrates and the gain is high enough to cause feedback, the pitch of the feedback is a harmonic of the vibrating string. If I then change the angle or position of the guitar relative to the amplifier, the pitch changes to another harmonic of the string. What's happening here? is it the phase relationship changing as I move?
Example here:
I would say that the distance between the speaker and the guitar has a lot to do with the harmonic that's going to be excited in a direct relation with the wavelength.
Also, for a guitar, I would say that the strings interfere with each other, causing different pitches for the feedback.
This is all speculation, I hope someone with more knowledge on this subject answers with better information, as this seems quite interesting.
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