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In music, an octave is two notes such that one is double the fundamental frequency of the other, where we call both notes the same. We use letters between A through G, to denote notes. Within an octave, there are twelve semitones, otherwise known as half-steps. Western music theory defines a key within a given octave, with the first half of the name defining how the scale is determined and the second half defining what is the tonic, or the initial note we wish to start our scale on. For our project, we began first with Major C, which begins on C and proceeds in the following pattern with “W” representing a whole step, or 2 semitones, and “H” representing a semitone: W-W-H-W-W-W-H. Major scales are the easiest to play on piano since it consists primarily of the white keys (C-D-E-F-G-A-B-C ...) and are the most common in popular music.

The next progression in making music is to play more than one note at a time. When you play two notes, you create an interval between the two notes. We name intervals based on the difference between the letters (i.e. C and G are 5ths if counting up from C) as well as the amount of semitones between them. The more important intervals for creating chords are a minor 3rd, which has 3 semitones, and a major 3rd, which has 4 semitones.

A chord is a collection of three or more notes played all at the same time. For our project, we decided to start with Major chords since they are the easiest to hear and pleasant to most people. A major chord can also be called a triad, since it consists of three notes. If within the key of C, a C major chord will consist of C, E, and G. The intervals between C and E is a major third and the interval between E and G is a minor third. However, this logic cannot be applied to all triads within C major. For example, an E chord in the key of C will consist of E-G-B. The interval between E and G is still a minor third but the interval between G and B is a major third, creating a Minor E chord within the key of C. Chords within the key of C fall into the following three categories: Major third-Minor Third (C-E-G, F-A-C, and G-B-D), Minor Third-Major Third (D-F-A,E-G-B, and A-C-E), and Minor Third-Minor Third (B-D-F). You can generalize this by simply changing the tonic and therefore shifting the names of the notes according to the scale. Therefore, if you wish to create a chord within a given key, you must identify the note currently being played and the key you wish to play in.

Mathematically, you can divide an octave up into 12 equal parts. If you take the ratio of two notes an octave apart, you will get a ratio of 2 (or 2 to some power). To have an equidistant scale, you take the logarithm, base 2, of the ratio. If you want 12 equal parts, multiply the ratio times 12 and you will an equal division. Since a musician’s ear is picky and we want more accuracy, you typically times this by 100 to allow for slightly sharp or slightly flat notes to be created. This is equal to “n” cents. Cents is a term used by my musicians to describe tuning. This method can be generalized to find the cents between any two notes, with frequency f1 and f2 and log being of log, base 2:


For our project, n*100 denotes the amount of semitones we wish to g, f2 denotes the frequency of the key (in the correct octave, it must be below the note we are playing) we are currently in, f1 denotes the frequency of the note currently being played. When you apply the formula in this way, you can identify the note being played based on the tonic you prescribe. Knowing this formula, you can now do the reverse where you know the tonic and know how many semitones we wish to move up to compute the frequency of the note and solve for f1.

Questions & Answers

are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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 2015. OpenStax CNX. Jan 04, 2016 Download for free at https://legacy.cnx.org/content/col11950/1.1
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