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Pythagorean Vs. Equally Tempered Tuning Is A Paper Discussing The Differences, Pros, And Cons Of The Two Systems Of Tuning Musical Instruments. Complete With 6 Source Bibliography

1278 words - 6 pages

Pythagorean vs. Equally TemperedIn the western world of music, there is a commonly used system of tuning for an instrument, called equally tempered tuning. However, this was not always the system in use. Before equal tempered tuning, there was the Pythagoras scale, developed about 2,500 years ago by Pythagoras. Although Pythagoras' scale sounded very natural, it had a flaw. Over time, more complex instruments were created that could reach higher octaves, where the flaw became too obvious to ignore. While equal tempered tuning fixed the error, some qualities were also lost. To understand both of these systems and their differences, we must first have a basic understanding of sound.Sound is ...view middle of the document...

The sound frequencies that sound good together became the basis of his scale. He first discovered that an octave starts with one frequency and the octave above begins with twice that frequency.In each octave, Pythagoras determined that two notes sound good together. These were the root and the 5th. The root is the first note and base note of any given scale. The "fifth" is fifth note of that scale, and is still used for basic harmony and power chords. This root-five discovery was the beginning of the scales Pythagoras developed. After following the cycle of fifths (playing fifth after fifth, etc.) and developing a full scale, Pythagoras determined there are eight notes in a scale, and that there are different intervals, or spaces, between the eight notes in the scale. Going through the spacing between the notes of the scale, the steps are whole tone, whole tone, semitone, whole tone, whole tone, whole tone, semitone, which brings you back to the root note, but an octave higher, which has a frequency ratio of 2:1 from the original note, and a string length ratio of 1:2. Pythagoras discovered many other ratios, for example, the frequency ratio for whole steps is 9:8. There is a total of 1200 cents in an octave. A cent is a unit with which intervals between notes are measured. There are 204 cents in a whole step. Semitones, or half notes, are where the scale becomes confusing, because there are two kinds. There are diatonic and chromatic semitones. Chromatic semitones are used when a sharp or flat of any note in the scale is needed. A chromatic semitone has 114 cents. A diatonic semitone has a smaller value. This is the semitone that is used in the scale, when a semitone is required. Diatonic semitones have 90 cents. This is why, on a piano, there is no black key between B and C, and E and F. These are the two semitones in the key of C, the key pianos are created in. A diatonic semitone and a chromatic semitone make up a whole tone. However, when two chromatic semitones are next to each other, there is an overlap of 24 cents. It is like trying to fit two boxes worth 114 into a box worth 204.If you follow the cycle of fifths (playing fifth after fifth, etc.) around 12 times, you should get back to the original starting note, but seven octaves higher. To find the frequency of this note, you must use the fifth ratio (3/2) and multiply it by itself 12 times to get 129.74....

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