### Interpreting Audible Intervals into Visual Learning Tools for Cognitive Brain Training and Musical Advancement

#### Abstract

Accurately identifying audible intervals is a skill that can be polished with training. If it would be paired with the growing cognitive brain-training trend, ear training would easily advance. As intervals are really mathematical ratios, this project attempts to visualize the exponential factors used in determining musical frequencies. Any musician is schooled to better their ear in classes such as sight singing. However standard musical notation upon which many students learn is filled with visual discrepancies. These inconsistencies are not fully understood until the musician has matured in their studies. To train the beginner ear through this notation is to also deceive it. Ear training typically consists of memorizing set intervals that are really simple ratios, multiplied upon the original frequency to produce new tones. Each interval has a unique harmonic relationship. Musicians are not required to know the actual frequency of the note, so the need to multiply by these ratios is naught. Multiplication is harder than addition, to which intervals are more commonly calculated; it is only natural to add. However the better musicians are multiplying anyway. They may not realize when they “add” an octave, they are actually multiplying by 2. Because this ratio produces a different result for every individual note, they cannot add a particular number; it would require a different octave upon each new note. Though the actual frequencies of notes could go by unnoticed by great musicians, it is essential to understand them to devise a system of ear training. In studying the harmonic relationships through which the musical scale was constructed, several possible visual interpretations were constructed in hopes of future gaming use. Ear training is rather tedious and boring, but hopefully when presented as a game, it will not be as painstaking.

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