Few people understand how mathematics is connected to music. Music has to do with scales and notes. Mathematics has to do with numbers and symbols. How are they connected? While most people may be surprised, at its core, music can be considered math! In fact, scientists understand musical structure by using math equations! They use what's known as set theory, the branch of math that studies sets of objects, number theory, the branch of math that deals with properties of numbers, and abstract algebra, the branch of math that studies the structures of things to understand music.
The Mozart Effect refers to research that indicates listening to Mozart's vast work of classical music somehow temporarily makes it easier for the human brain to perform what's called "spatial-temporal reasoning" which is the ability to visualize special patterns and then mentally manipulate those patterns. Some areas of mathematics rely heavily on this ability. 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.
In acoustic music and instruments like the acoustic guitar, a 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. 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!
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 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. An octave corresponds to the ratio of 2/1; a fifth corresponds to 3/2. So, when someone is tuning a piano, they use the Pythagorean scale to measure the distance between the notes and adjust them properly. And that's just one example of an instrument that uses math for tuning.