The program possesses the capability to play several historical fixed temperaments, namely Pythagorean, Quarter-Comma Meantone, Werckmeister III, and Equal Temperament. Though this allows every interval between sequentially played notes to be in tune, it does mean that pitches are not fixed, and rather are flexible and changing as a piece progresses. To overcome the impossibility of perfectly consonant temperaments, we have created a computer program that can function as a self-tuning instrument by mathematically calculating the frequency of each pitch played in relation to the pitch preceding it. The difference, then, between notes tuned in terms of different intervals is known as a comma, and the attempts to distribute this comma are called temperaments. For example, an octave in music is the equivalent of three major thirds however, the justly tuned octave (2:1) is not equal to the sum of three major thirds (5:4) 5:4 3=125:64, not 2:1. The nature of the ratios does not allow larger intervals to be explained exactly by the smaller intervals, though they are expected to coexist and be used simultaneously in Western music. a piano), the intervals inherently cannot all be tuned justly, or according to the appropriate proportions.

The problem becomes apparent when the ratios are used to create the Western scale on a fixed instrument. When an interval does not have a small-integer ratio between its notes, it is perceived as “out-of-tune,” and the two frequencies will compete with each other. These small-integer ratios of frequencies represent the consonant (in-tune) harmonic intervals. They follow a proportional pattern of 1:2, 2:3, 3:4, etc. The difficulty in creating such a system of tuning arises from the mathematical paradox of the musical harmonic series, which is the sequence of frequencies that sound naturally as overtones over a fundamental pitch. The premise of this creative Capstone project was to develop a computer instrument that is capable of tuning itself flexibly in such a way as to not require a tempering of the Western scale, as is necessary for fixedly tuned instruments.

Piano tuning software for mac