What is Equal Temperament tuning?

Equal Temperament tuning is a system of tuning in which every note is placed in equidistant intervals.  In the western system of music, the fundamental interval is the octave, which are two notes where one’s frequency is double that of the other.  Western music uses a 12-note scale, which means that to preserve the equal temperament condition, the ratio of any two adjacent notes must be 21/12.

What is just-intonation tuning?

Just intonation is the tuning of chords where the goal is to adjust to frequencies so that the ratios between notes are whole numbers.  Typically in practice, a group playing or singing a chord will listen to the musician playing or signing the lowest note in relation to their note, and tune with respect to them.

What is a beat frequency?

Beat Frequencies are caused by the interaction between two or more frequencies.  When frequencies are not in phase with each other, they can create patterns that are noticeable to the human ear.  Particularly, it sounds like the volume of the overall sound is fluctuating.


Overtone Series (Harmonic Series)

The harmonic series is a collection of pure tones (sinusoidal waves) in which the frequencies are integer multiples of the lowest frequency, the fundamental frequency. All of these frequencies are inherently in tune with each other. 

Image result for overtone series

The left side of the figure below shows the distance relationship between a fundamental frequency (in this case, called the ‘tonic’) and the subsequent overtones based on integer multiples of the fundamental frequency. The right side of the figure shows the distance relationship of each overtone with respect to the preceding overtone. 

Although all the overtones of a frequency are inherently in tune with each other, the frequencies generated by multiples of a fundamental do not converge to the same frequencies heard in the equal temperament system. This means that if a piano were out of tune for one key’s overtone series, it would be badly out of tune for other keys.


Vocoder/Harmonizer History

What is a vocoder?

A vocoder is a device that takes in human speech and disassembles the signal into a series of smaller digital signals. The initial design of the vocoder (then called the “Voder”) was created by Homer Dudley and was intended to create fewer bits in the signal (slower speed signal) that you can then transmit better over long distances. It would save bandwidth and copper costs by compressing phone conversations/speech and transmitting only the necessary frequencies characteristic of human speech. However, due to the high costs of developing models of the vocoders and their lowquality outputted signals, the communication aspect of the vocoder was not very successful.

How did that lead to a harmonizer?

Although there were problems with the original idea and implementation, it was determined that it was possible to manipulate a signal enough, while keeping enough artifact to sound like a distorted voice. This piqued interest in many different people across many different disciplines but became most prominent within the music industry. Artists started using this new technology to create different and new music, where the voice can be manipulated to desired pitches and allow an individual to harmonize with themselves. This new application has led to a change from vocoder (voice manipulation) to harmonizer (specific musical voice manipulation), and the progress and innovation have yet to slow down. Especially with technology becoming cheaper and more accessible, the harmonizer is becoming more and more prevalent within the music industry.