When you listen to a piece of music you usually don’t think of math, but the two are interlinked and music always involves math even though we don’t always realize it. When musicians play music they are using mathematical formulas to play. There are formulas for making cords, scales and a formula for the what notes they play.
Musical notation also involves math, you use time signatures while playing along to a piece of music which are basically just fractions, 3/4,7/4, and 4/4 are all time signatures. the bottom number in the fraction gives you the type of note to be played and the top gives you the amount of times it is played. There are five basic types of notes to be played in music, the sixteenth note, the eighth note, the quarter note, the half note, and the whole note. For each of these notes you divide the previous note by two. The sixteenth note is divided into two which gives us eight, the eight into four, and so on (see chart). The easiest note to start with is the whole note there is one beat per measure of a song, for the half there is two beats per measure, and so on until there is sixteen beats per measure.
Guitar chords are also made using a formula, first you get the scale of the type of cord you are trying to form, for example lets say c-major the formula for making a major cord would be tone, tone, semi-tone, which would mean the first note in the scale, the fourth, and the seventh. This is how most musicians make a cord. The first note in the scale is always a full tone as is the last this is because this is two octaves apart and they are the root notes.
(guitar player, June 1996)
There are twelve tones in an octave ex. C, C#, D, D#, E, F, F#, G, G#, A, A#, B. A full octave would have another C at the end but it is the same pitch as the first C except an octave higher so it is usually left out. Ancient Greeks came up with this method, they said in an octave each note was an integer multiple of the first. There is not a perfect octave however it is always a couple of numbers off the original frequency. log3/log2= continued fraction[1,1,1,2,2,3,1,5,2,23,…], is the best fraction to get closest to the perfect octave. if we take the notes frequencies, and build fifths we get pretty accurate to a perfect octave. Twelve is by far the easiest number to get closest to a perfect octave which is why there are twelve tones in an octave. A whole tone is usually from one whole note to the other or one # note to the other except on tow occasions: b-c and e-f there is no # note in between those notes so from b-c and e-f is a whole tone but anywhere else it is three notes ex. a-a#-b (www.classic-guitar.com)
Math is also very important while making a guitar. A normal guitar usually contains 21 frets, the spaces in between the frets is usually found by getting the total length of the neck, and then using the rule of 18 which is 17.835. You divide the length of the neck by this number and this gives you the length of the first fret. Then you subtract the length of the first fret from the total neck length and then divide the length by 17.835. You do this until you have the full neck fretted
Bibliography: www.tabcrawler.com, good place for guitar theory
www.classic-guitar.com, good place for time signature
Book: Drum Basics, good source for musical notation]
Guitar Theory, good book for musical theory