The math behind the circle of fifths
Polychoron Productions・6 minutes read
The circle of fifths organizes notes in Western music in a sequence of successive fifths, crucial for note organization, with step size and item number sharing prime factors creating star-like shapes in reverse patterns, while the chromatic scale's intervals must not share factors with 12 to create various musical structures.
Insights
- The circle of fifths in Western music organizes notes in a sequence of fifths, starting and ending on the same note, crucial for note organization.
- Different musical structures like whole tone scales and diminished seventh chords are represented by geometric shapes in the chromatic scale, based on the number of semitones in intervals that do not share factors with 12.
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Recent questions
What is the circle of fifths in music theory?
The circle of fifths organizes notes in a sequence of successive fifths, crucial for note organization in Western music.
How does the circle of fifths create a star-like shape?
To visit every item in a circle by moving a certain number of spaces, the step size must not share prime factors with the number of items in the circle, creating a star-like shape.
What happens when moving by the total number of items minus the step length in a circle?
Moving by the total number of items minus the step length will produce the same pattern in reverse, as seen in the example of moving by 13 spaces in a circle with 20 items.
How does the chromatic scale relate to musical structures?
In the chromatic scale, to visit every note once by jumping a constant interval, the number of semitones in that interval can't share any factors with 12, leading to various geometric shapes representing different musical structures like whole tone scales and diminished seventh chords.
What is the significance of the circle of fifths in music composition?
The circle of fifths is crucial in music composition as it helps in organizing notes, understanding key relationships, and creating harmonic progressions in Western music.
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Summary
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Circle of Fifths and Musical Geometric Patterns
- The circle of fifths is a fundamental concept in Western music, organizing notes in a sequence of successive fifths starting and ending on the same note, crucial for note organization.
- To visit every item in a circle by moving a certain number of spaces, the step size must not share prime factors with the number of items in the circle, creating a star-like shape.
- Moving by the total number of items minus the step length will produce the same pattern in reverse, as seen in the example of moving by 13 spaces in a circle with 20 items.
- In the chromatic scale, to visit every note once by jumping a constant interval, the number of semitones in that interval can't share any factors with 12, leading to various geometric shapes representing different musical structures like whole tone scales and diminished seventh chords.
