Time Signatures are math organized in rhythm: First of all, to play a piece of music you must know how to count and organize the beats to coincide with the feel of the music or the other instruments you must play with. For example, a form of time signature (which is the most popular) is 4/4 time. The key to this rhythm is emphacizing the 1st and 3rd beats of the measure more than the others. Any musician should be aware of this. Also, a musician should know what types of notes get different types of beats. (quarter note etc.)
Key Signatures are math organized in order. Every musician needs to be aware of all the formulas and order of the sharps (FCGDAEB) and the flats (BEADGCF). For example, the sharp increasing the note by a half step and the flat reduces the note by a half step and every key has a different amount of these sharps and flats. Also, in math, there can be different ways of looking at a formula. This relates to music that in finding the relative minor keys of Major keys. (go down by three half steps is one formula and adding 3 flats in order is another formula)
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Finally, there are intervals. Which is music organized in space. Every musician should be familiar when they hear the words major, minor, dimished or augmented and know the rules for each one and the different types of distances from a note that each interval or chord gets. These words can determine chords and intervals and the type of sound that each of them receive. (Chords: Major third is 4 half steps while minor chords have 3 half steps.)
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