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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 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.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elec 301 projects fall 2006. OpenStax CNX. Sep 27, 2007 Download for free at http://cnx.org/content/col10462/1.2
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