Music Software Projects New York University Adjunct Instructor Scott Burton

Now that we have implemented to collection types Harmonic Series 2. Pythagorean Scale (first seven intervals) Our scale engineering should evolve via inheriting, containing and re-using functions There is common behavior shared by the two collections built so far. As you implement new methodologies you will have the opportunity to improve what you have built prior...

Using the Pythagorean Scale How can we achieve variety or interest using a scale? “Modes” are constructed using the same set of notes but starting place is a different scale degree Even though we constrain ourselves to the same interval set, starting on a different scale degree produces a unique sound Using software we can play them in close succession to easily hear how they different they sound Using different modes is a tool every improviser has in their toolbox! Before “modulation”/changing key, musicians used modes to create variety

The Pythagorean Collection Initialized with 528Hz We will establish a note naming convention of C = 528hz Name each of the first 7 “natural” degrees (add this attribute to your collectable): “C” “D” “E” “F” “G” “A” “B” “C” (refer to spreadsheet) Play the sequence of notes successively: D E F G A B C D E F G A B C D E F G A B C D E F … B C D E F G A B C D E F G A B C (1 octave up) These are the “modes” of the scale

Modes Visualized Ionian Dorian Phrygian etc Notice where the white keys are adjacent to each other...

Modes - Phase 3 Requirements We can now derive intervals in two ways: 1. New living spec “pythag_sheet_phase3.xlsx”. With this method we simply raise each scale degree (in a starting scale) successively by an octave. 2. Prior living spec “pythag_sheet_phase2.xlsx”. Builds a new scale on each scale degree using successive multiplication by 3/2. The two methods produces different frequencies for the same notes. As usual this programming phase will use the living spec for this week. Mode names are shown in pythag_sheet_phase3.xlsx (e.g., “Aeolian”, “Locrian”...)

Modes - Phase 3 Reqs... Sort by frequency ascending after adjusting down to first octave Play each mode starting with Ionian with 2 seconds in between each mode You can use your pure sine wave tone or another more interesting one Initialize with the base frequency of 540Hz. Play each note 1 second No silence between notes Play 8 tones to end on an octave Run the regression test by default. Test against expected results (cells in spreadsheet). Note the sheet was built with a different base frequency – you will use a different one (next slide) IN ADDITION TO ABOVE: Display the mode name and frequencies while you play the modes starting with “Ionian” Happy coding!