If more of us valued food and cheer and song above hoarded gold, it would be a merrier world.  J.R.R. Tolkien 
Circle of FifthsIt is suggested that Pythagoras of Samos (~582 BC  ~507 BC) is attributed with being the first to discover the ratiometric nature of musical notes and intervals, specifically the octave, the fourth and the perfect fifth. The Perfect Fifth is the lowest ratio harmonic you hear and is mathematically calculated by multiplying a frequency by the ratio 3/2 or 1.5. For example, in the note of C, the perfect fifth would be a G. You can continue to go up the scale by fifths and you will eventually arrive back at the note of C. Here's the pattern: C > G > D > A > E > B > F# > C# > G# > D# > A# > F > C. Pythagoras first used the idea of tuning an instrument up and down by fifths and, in fact, the slight error that occurs when you tune using this method is called the Pythagorean comma. Click to read details on the Pythogorean comma. Johann David Heinichen published the Circle of Fifths in his book, Der Generalbass in 1728. By placing each note in a slice of the wheel, you can see that the relationship of a fifth is one past the note opposite. Looking at the pattern produced when the notes are placed on a wheel clearly shows the repeating pattern of the notes.


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