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f ( t ) = a 0 + n = 1 a n cos ( n 2 π f 0 t ) + b n sin ( n 2 π f 0 t ) MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWG0bGaaiykaiabg2da9iaadggadaWgaaWcbaGaaGimaaqabaGccqGHRaWkdaaeWbqaaiaadggadaWgaaWcbaGaamOBaaqabaGcciGGJbGaai4BaiaacohacaGGOaGaamOBaiaaikdacqaHapaCcaWGMbWaaSbaaSqaaiaaicdaaeqaaOGaamiDaiaacMcacqGHRaWkaSqaaiaad6gacqGH9aqpcaaIXaaabaGaeyOhIukaniabggHiLdGccaWGIbWaaSbaaSqaaiaad6gaaeqaaOGaci4CaiaacMgacaGGUbGaaiikaiaad6gacaaIYaGaeqiWdaNaamOzamaaBaaaleaacaaIWaaabeaakiaadshacaGGPaaaaa@5C86@

where f 0 is the fundamental frequency (in Hz), n denotes the harmonic number, and a 0 is the DC (constant) offset.

When an instrument produces overtones whose frequencies are essentially integer multiples of the fundamental, you do not perceive all of the overtones as distinct frequencies. Instead, you perceive a single tone; the harmonics fuse together into a single sound. When the overtones follow some other arrangement, you perceive multiple tones. Consider the screencast video in which explains why physical instruments tend to produce overtones at approximately integer multiples of a fundamental frequency.

[video] Why musical instruments produce overtones at approximately integer multiples of a fundamental frequency

Musicians broadly categorize combinations of tones as either harmonious (also called consonant ) or inharmonious (also called dissonant ). Harmonious combinations seem to "fit well" together, while inharmonious combinations can sound "rough" and exhibit beating . The screencast video in demonstrates these concepts using sinusoidal tones played by a synthesizer.

[video] Illustration of harmonious and inharmonious sounds using sinusoidal tones

Please refer to the documents Consonance and Dissonance and Harmony for more information.

Tuning systems

A tuning system defines a relatively small number of pitches that can be combined into a wide variety of harmonic combinations; see Tuning Systems for an excellent treatment of this subject.

The vast majority of Western music is based on the tuning system called equal temperament in which the octave interval (a 2:1 ratio in frequency) is equally subdivided into 12 subintervals called semitones .

Consider the 88-key piano keyboard below. Each adjacent pair of keys is one semitone apart (you perhaps are more familiar with the equivalent term half step ). Select some pitches and octave numbers and view the corresponding frequency. In particular, try pitches that are an octave apart (e.g., A3, A4, and A5) and note how the frequency doubles as you go towards the higher-frequency side of the keyboard. Also try some single semitone intervals like A0 and A#0, and A7 and A#7.

The frequency values themselves may seem rather mysterious. For example, "middle C" (C4) is 261.6 Hz. Why "261.6" exactly? Would "262" work just as well? Humans can actually perceive differences in the sub-Hz range, so 0.6 Hz is actually noticeable. Fortunately an elegantly simple equation exists to calculate any frequency you like. The screencast video of explains how to derive this equation that you can use in your own music synthesis algorithms. Watch the video, then try the exercises to confirm that you understand how to use the equation.

[video] Derivation of equation to convert semitones to frequencies

What is the frequency seven semitones above concert A (440 Hz)?

659.3 Hz (n=7)

What is the frequency six semitones below concert A (440 Hz)?

311.1 Hz (n=-6)

1 kHz is approximately how many semitones away from concert A (440 Hz)? Hint: log 2 ( x ) = log a ( x ) log a ( 2 ) . In other words, the base-2 log of a value can be calculated using another base (your calculator has log base 10 and natural log).

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, Musical signal processing with labview -- introduction to audio and musical signals. OpenStax CNX. Nov 07, 2007 Download for free at http://cnx.org/content/col10481/1.1
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