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Music Software projects. New york university Adjunct Instructor Scott Burton. Pitch Combinations. Intervals are two note combinations The interval of the octave is special The Harmonic Series exists in nature
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Music Software projects New york university Adjunct Instructor Scott Burton
Pitch Combinations • Intervals are two note combinations • The interval of the octave is special • The Harmonic Series exists in nature • The human ear perceives pitches that are close to the Harmonic series as “consonant” and those that aren’t as “dissonant” • There are other ways to quantify consonance • In the end it’s still somewhat subjective...
Programming Phase • Implement “Harmonic Series” class • Parameterize by “base” frequency • Functions: • Double Hz = interval(int harmonic) • Char* harmonic = ratio(int harmonic degree) • Example: “"4/4”” given param: 4 • Example: “"9/8” given param: 9 • Show() – this should print out the data in the sheet so it can be compared visually with the sheet • Build regression harness using spreadsheet results as test cases.(See harmonic_series.xls) • Submit a program that when run derives all the cells in the sheet using base frequency of 528hz and compares it’s results with expected outputs (saved as a .csvfile)
Next up...The Pythagorean scale • Built on “fifths”: • “This interval, the Fifth, will be found competent to furnish us with the entire scale that the musical feeling and intuition of men have caused them, through-out the western world, at least, to accept as the basis of music an d musical instruments; that is to say, the diatonic scale.” • A “strange twist of human fate” that Pythagoras built a scale on consecutive fifths vs. other intervals in the harmonic series… p. 36 “Tuning in”.
The Pythagorean scale • This scale had a few problems... • A dissonant 3rd degree • Pythagoras expected the following: • But this was not to be– as math-based as he was, this troubled him and supposedly was kept secret in his clan... • This “impurity” in his mathematically driven “invention” was the seed that spawned centuries of music engineering by some of the great physicists, astronomers and mathematicians of their time... • The amount the two terms differ is known as the “Pythagorean Comma” (see pythag_sheet_phase2)...