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# Music Software projects - PowerPoint PPT Presentation

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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## Music Software projects

New york university

Adjunct Instructor Scott Burton

### 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

### “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!

### 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