Objective

Given an input signal and input keyboard notes, manipulate the input signal such that it will sound like the musician is simultaneously singing all of the notes held down on the keyboard.

Spectrograms

Equal Temperament vs. Just Intonation

The figure above shows two spectrograms–an A dominant 7th chord (A, C#, E, G) tuned in equal temperament and just intonation, respectively. Naturally, equal temperament has more deconstructive interference due to its nature of being non-integer multiples of a fundamental frequency. This leads to more beat frequency. As shown in the figure above, just above the 1 kHz mark, the power/frequency of the equal temperament chord has more drastic fluctuation between low power and high power, while just intonation shows a more averaged and smooth power/frequency. This is determined to be part of the beat frequency/instability of an equal temperament chord and gives the ‘wah-wah’ effect. Similarly, the overtones below the 1 kHz mark seem to be more defined, or at least more precise, within the just intonation spectrogram. This is thought to be caused by the just intonation chord having all notes that are integer multiples of each other and therefore have the same overtone series, as opposed to the equal temperament where all four notes in the chord have different overtone series’.

Power Spectral Density

 

The figure above shows the pitch detection algorithm used within the harmonizer. The pitch sang is the peak farthest to the left, and all peaks to the right of that are notes/frequencies within the overtone series.