A.) If I start with a note at 439 Hz, what is the frequency of a note a Fifth higher according to the Equal Temper scale? Calculate this to one decimal place.
B.) Start with a note of frequency 512.0 Hz. Go up a Perfect Fifth according to the Just scale to get f1. Start with the original note, but now go up a Perfect Fifth according to the Equal Temper scale to get f2. What is the beat frequency between these f1 and f2? Note, the Perfect Fifth is 7 half steps, and a half step in the Equal Temper scale is 1.0595. Give answer with at least two decimal places.
C.)
1) Using the Pythagorean system for generating notes on a scale, one could add notes endlessly. However, at some point you would no longer be able to hear the difference between the notes. How many notes could you just distinguish in a half-step? (Or, how many just-noticeable-differences make up a half step?) Enter as a whole number with no decimal point.
2) What would be the total number of notes in one octave in this system? (Again, enter as a whole number, no decimal point.)
D.) Suppose you wanted to construct a scale (with pure tones) where no two notes ever had overlapping critical bands so that you could play any two notes without producing dissonant intervals. What is the largest number of notes that could be in this scale? Remember, the CB is 19% of the note's frequency.