# Music and math relationship triangles

### Music & Geometry

Music theory has no axiomatic foundation in modern mathematics, yet the basis of musical . Because we are often interested in the relations or ratios between the pitches (known as intervals) rather than the precise pitches themselves in. The Story of Mathematics - Greek Mathematics - Pythagoras. justice; five, marriage; six, creation; seven, the seven planets or “wandering stars”; etc. The holiest number of all was "tetractys" or ten, a triangular number composed of . that the intervals between harmonious musical notes always have whole number ratios. In music education, we rely on an equilateral triangle. symbiotic relationship in the music lesson process, but also because math and music.

### Mathematics and Music | zZounds

This is what scientists are referring to when they insist that listening to Mozart make you smarter, especially when you are very young. It's presumed to have some kind of effect on mental development.

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Beat Frequencies In acoustic music and instruments like the acoustic guitara beat is the interference you hear when two separate sounds waves of different frequencies hit your ear at the same time.

Trigonometry is the study of the triangles and their planes.

## Triangular Numbers

So how do those two intersect? A beat frequency is an example of what's known as a "product to sum" identity and that is what is used to identify triangles aka trigonometry.

In other words, scientists were able to define beat frequency into an equation! Pathways between Math and the Arts Interestingly, it's actually easier to understand music if you've first mastered math.

Music and math both use basic concepts or rules that remain constant no matter what action is being performed; music and math both use shapes, patterns, and numbers. A good example of a pathway between the two is a musician assigning musical notes to a particular sequence. That musician is measuring those notes and fitting them into the sequence where they belong and mathematicians do the same thing when figuring out equations.

Tuning and Tones Tuning an instrument also uses math!

The easiest example would be a piano. The interval between one piano note and the next should always be an octave. When it becomes out of tune, the octaves are no longer the proper length apart. There is also a set distance between notes like C and G and D and A; it should be a fifth.

So, when someone is tuning a piano, they use the Pythagorean scale to measure the distance between the notes and adjust them properly. These scales cannot be constructed with "simple mathematical ratios.

### Harmony and Proportion: Pythagoras: Music and Space

The numbers themselves, by which the tones can be expressed, have insoluable irrationalities. Payne translation, Dover Publications,p.

The connection between maths and music - Pythagoras Comma (Longer version)

To be sure, music can be played using the intervals derived from adding fifths, or even using the original ratios, and the ear may not object -- despite using notes created by systems that are ultimately inconsistent.

The differences are, after all, rather small, even for the original and traditional ratios.

But it is annoying. There is a sort of Pythagorean itch that keeps us thinking that there should be a proper mathematical solution to the matter. This is not going to be as simple as what Pythagoras expected, but the belief continues that the fundamental ratio, the octave, 2: Although Schopenhauer, with his characteristic pessimism, does not seem to have appreciated it, something can be done about the problem.

The solution, or at least one solution, is to adjust the ratio of the fifth so that it is commensurable with seven octaves. Seven octaves is