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Music Software projects

Music Software projects. New york university Adjunct Instructor Scott Burton. The Pythagorean Scale Adjusted to One Octave. Pythagorean vs. Harmonic S eries. Built on successive 3/2 ratios only vs. taken directly from upper ratios in the naturally occurring harmonic series

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Music Software projects

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  1. Music Software projects New york university Adjunct Instructor Scott Burton

  2. The Pythagorean ScaleAdjusted to One Octave

  3. Pythagorean vs. Harmonic Series • Built on successive 3/2 ratios only vs. taken directly from upper ratios in the naturally occurring harmonic series • The next unique interval in the harmonic series after 3/2 is 5/4 • This step in our modern scale is known as the “major third” (E in a C scale which we will see more of later). • “Unstable” interval of 81/64 • Slightly higher than the closest interval of 5/4 which is present in harmonic series • Difference is 81/80 • 81/80 = 81/64 ÷ 5/4 • “Perfect Intervals” • Fourth • Fifth

  4. “Pure” or “Just” Intervals sound good but… • C 1/1 x 528 = 528 Hz • D 9/8 x 528 = 594 Hz • E 5/4 x 528 = 660 Hz Now build off of the "D" note: • D 1/1 x 594 = 594 cycles per second • E 9/8 x 594 = 668.25 cycles per second Should the "E" be tuned to 660 or 668.25 Hz??? Not a problem for singers, string players (non-fixed pitch instruments) Problem for pianos or other fixed pitch instruments!

  5. Some Terminology • “Pythagorean” • Built from the 3rd harmonic in the harmonic series (3/2) • The 3/2 ratio is also known as the “fifth” since it is the 5thdegree in the Pythagorean 7 note scale • All scale degrees/intervals are derived from by multiplying by successive fifths • “Just” • Usually synonymous with “Natural” or “Pythagorean” or other scales that use integer ratios to build their scale degrees • “Natural” • Taken from harmonic series integer ratios occurring in nature (e.g, the vibrating string) • Also used to refer to a scale without sharps and flats (more on this later) • “Equal-tempered” or “Even-tempered” • Octave is divided into equal steps • Makes all keys sound the same • Can be 12 or more intervals ( more than 12 is considered “microtonal” ) • “Well-tempered” • Some intervals are more usable than others • “Mean-tone” is primary example • Optimize the thirds and and fifths in selected keys at expense of the rest

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