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Math in relation to music by Spencer Houghton TEMPO – The tempo is set at the beginning of the piece and this tempo is held by the percussion or in an orchestra, by the conductor. Tempo involves patterning. The way tempo involves patterning is that the tempo is the pattern of how many beats per minute (BPM) there are. A change in tempo affects the speed of the entire piece. For instance, if a song had a really low BPM it would be very slow, whereas if it had a high BPM, it would be very fast. A very fast BPM would be a song like, “M+M’s” by Blink 182 and a very slow BPM would be something like, “Waiting for my Ruca” by Sublime. Both these pieces sound very different and both have a completely different feel all because of their respective tempos. The pattern that the tempo follows controls the sound of the entire group and without it, music would be confusing and everyone would be playing at different speeds. This is a reason math is necessary in music. TIME SIGNATURE – The time signature in a piece assigns a value to each Quarter Notes
bar, as an example in a piece that uses 4/4 time there are four beats in Fig.1 each bar which means at the end of each bar the collective note value must add up to four. The type of mathematics this uses are patterns and in a way fractions, because halfway through the bar the note value could be two out of the four notes played. 1 2 3 4 There can be variations on notes in the bar, such as playing a triplet groove. It is ok for these notes to be split up into different grooves which most of the time Eighth Notes
are variations on the 4/4 beat. They can do anything in a bar as long as they add up to the bar value at the Fig.2 end. In the above figures, the note value is demonstrated with quarter notes (fig.1) compared to eighth notes (fig.2). Both figures contain the same value of notes even though it may seem that figure 2 contains a longer groove. Below you can see a chart of note values. In this case the whole note would be equal to 4 beats and the quarter notes are equal to 1 beat. This process involves division because each note is divided by 2 to create a smaller note value. A larger time signature such as 6/8 could be used with tempo to extend the piece. Note Structure BEYOND MUSIC ‐ Digital music has replaced an entire form of music and has changed the record industry forever. This is all thanks to math; math has allowed the conversion of music from analog to digital. Over the past few decades, the way that music has been recorded has changed. This is all due to computers being able to break musical notes down in to binary information Sample Rate known as samples. The higher the sample rate the better the playback quality. As the music industry progressed so did the playback, as time went on it became possible to use a higher sample rate. Forty years ago before music went digital, the way music was played back through vinyl records had to do with the vibrations and the grooves on the record; this is an example of analog recording. The vibration would create sound which would provide the play back. The change over from analog to digital first happened with CD’s which had a Sample Rate of 0–22,050 Hz. The way this works is through frequency, which is measured in hertz (Hz), describes the number of cycles per second. (For example, a 1000‐Hz waveform has 1000 cycles per second.) The higher the frequency, the higher the musical pitch as well as a better playback quality. As the music industry progressed from CDs to something like blue ray which is 0–48,000 Hz the quality improved. Using the analog to digital conversion we can take musical notes and convert them to binary. Without the math involved in binary or the patterning involved in hertz (Hz) this wouldn’t be possible. In conclusion, math must be used in music otherwise a piece would never come together properly. Without math the music industry wouldn’t be at the same level it has achieved today. The two mathematical factors I found had a big part in the creation of music were patterning and division. Without these two elements a musical piece could never be composed. Math controls the speed and the groove of the music as well as the way it is recorded and distributed.