# Motivation and background information

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This module explains our motivation for undertaking the task of piano note detection, and background information on the mathematics of music that is relevant to our project.

Reading a song on sheet music and then playing it on an instrument is a completable task for any musician. This century, computer software has also been designed to do just this. Programs can create audio files (music we can hear) from sheet music very effectively for a whole range of instruments.

A major problem is that the reverse task, listening to or recording audible music and then generating the sheet music for that piece, is much more difficult to complete for both computers and the talented musician alike. Our goal is to take a recording of a piano and translate it into some form of sheet music with high accuracy.

This program could prove very useful for composers in particular. A composer I once knew would sit down at a piano and begin playing completely improvisationally, writing the song as he went. However, when he finished, he could never remember what he had just played. With this program, he could take a recording of himself, and generate the sheet music of his new composition. It is with composers such as him in mind that we undertake this project.

## Background information

All sounds, including music, that we hear are actually vibrations in the air that propagate through as a wave. This wave can be represented as a signal transmitted to the ear over time. Through Fourier analysis, this signal can be represented as a sum of different frequency waves each weighted with its own "strength". These different frequencies cause one noise to sound "higher" or "lower" than another. In fact, the pitch of a noise, or how high or low it sounds, is determined entirely by its frequencies and their strengths.

Every musical note is a noise that is concentrated at a particular frequency. In typical musical formats, all musical notes are divided up into octaves, or repeating sets of notes that sound like a higher or lower version of the octaves around it. Each octave contains 12 different notes denoted C, C#, D, D#, E, F, F#, G, G#, A, A#, and B, in increasing order. The notes denoted with a sharp (#) symbol are so denoted because they are slightly higher than the note sharing the same letter. However, the same set of notes can be denoted using flats (b). This indicates that a note is slightly lower than the note that shares the same letter. Thus F# and Gb are the same note, and because they sound the same, they are indistinguishable by sound alone. These notes will be denoted as F#/Gb for the rest of this project. On a piano, the white keys are the unaltered letter notes, while the black keys are the notes with sharps or flats. Finally, every note has a number on the end denoting which octave it is in, with higher numbers meaning higher pitch. For example, middle C is C4.

Mathematically, the frequency of each note is exactly $\sqrt[\mathrm{12}]{2}$ times larger than that of the note immediately below it. Since there are 12 notes in an octave, the frequency of a note is exactly twice the frequency of the note an octave below it. For example, the frequency of A5 is 880 Hz, while the frequency of A4 is 440 Hz. In fact, the set of all frequencies that are a multiple of a note's frequency are called its harmonics . So the harmonics of A4 are 880 Hz, 1320 Hz, 1760 Hz, and so on. In this example, A4, or 440 Hz, is called the fundamental frequency , or fundamental for short. Harmonics are important because they are the only frequencies where an integral number of wavelengths can fit into one wavelength of the fundamental. Thus, in any instrument that is tuned to play a certain note, all of that note's harmonics will also be created. What makes instruments sound different is the relative strengths of their harmonics.

Every song has a tempo , or a speed at which the music is to be played. Tempo is defined as beats per minute, where a beat is usually defined to be a particular length of note. All notes lengths are then given a value, such as a quarter or a half. This value determines how many beats that note should last. Interestingly enough, a beat is usually defined to be one quarter note, and thus a quarter note is 1 beat, a half note is 2 beats, and an eighth note is half a beat. Additionally, a dot can be added to a note to add half its length to it. So a dotted quarter note is 1.5 beats, a dotted eighth note is .75 beats, and a dotted half note is 3 beats.

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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Berger describes sociologists as concerned with
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