### The Connection Between Music and Mathematics | Kent State Online Master of Music in Music Education

About geometry in music, math, geometrical shapes (polygons) of intervals, scales, For example: the geometric relationship C Major and G♭ Major is the same as the . which is the geometrical representation of the fourth triangular number. condition for a causal relationship between music and math. Five experi- . shapes (e.g., blocks or triangles) would fit into a larger shape. In the two studies by. It is known that many mathematicians play some instrument. Also there are books about music which use a lot of mathematics in order to express music.

Odd numbers were thought of as female and even numbers as male. The Pythagorean Tetractys The holiest number of all was "tetractys" or ten, a triangular number composed of the sum of one, two, three and four.

### How a little mathematics can help create some beautiful music

It is a great tribute to the Pythagoreans' intellectual achievements that they deduced the special place of the number 10 from an abstract mathematical argument rather than from something as mundane as counting the fingers on two hands.

However, Pythagoras and his school - as well as a handful of other mathematicians of ancient Greece - was largely responsible for introducing a more rigorous mathematics than what had gone before, building from first principles using axioms and logic.

Before Pythagoras, for example, geometry had been merely a collection of rules derived by empirical measurement. Pythagoras discovered that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth.

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Written as an equation: What Pythagoras and his followers did not realize is that this also works for any shape: One of the simplest proofs comes from ancient Chinaand probably dates from well before Pythagoras' birth.

It was Pythagoras, though, who gave the theorem its definitive form, although it is not clear whether Pythagoras himself definitively proved it or merely described it. Either way, it has become one of the best-known of all mathematical theorems, and as many as different proofs now exist, some geometrical, some algebraic, some involving advanced differential equations, etc.

This discovery rather shattered the elegant mathematical world built up by Pythagoras and his followers, and the existence of a number that could not be expressed as the ratio of two of God's creations which is how they thought of the integers jeopardized the cult's entire belief system. Poor Hippasus was apparently drowned by the secretive Pythagoreans for broadcasting this important discovery to the outside world. But the replacement of the idea of the divinity of the integers by the richer concept of the continuum, was an essential development in mathematics.

It marked the real birth of Greek geometry, which deals with lines and planes and angles, all of which are continuous and not discrete. He enjoys it so much if somebody tells him that his color is yellow, or green, or that his note is C, D, or F on the piano.

He does not care to find out why. It is like telling somebody: Part of a conversation which forms the basis of this subchapter: There are many problems with "transposing color into sound". The common approach is to divide the frequencies of the color spectrum by 2 again and again about 40 times in total until the numbers fall into "complementary" frequencies of the audible range.

This is arbitrary and based on the assumption that any tone whose frequency gets halved or doubled is the same tone. This is "the very most" fundamental mistake of music: A tone whose frequency gets halved or doubled is NOT the same tone, period.

Here's what I mean by that: This is a single frequency, just like that of a simple "sine wave". But this "transposed" frequency is actually the fundamental of a complex tone as opposed to a single harmonic of sound or lighthaving its own series of harmonics which are perfect integer number multipliers of it: Or, it could be the fundamental of an inharmonic tone, meaning a musical sound whose harmonics deviate from perfect numbers due to physical properties of the oscillator like rigidness.

The "correct" way of interpreting this is taking the fundamental harmonicHz and realizing it is part of a complex tone who has many other harmonics we can hear, and a whole lot more we can't hear, but we experience differently — for example, we can see its 1. But at this height of "pitch", harmonics are so close to one another that we can safely say all the color spectrum is in fact harmonics of a single fundamental frequency, no matter what that audible frequency might be. All these a, b and c processes can be different from individual to individual.

Actually, this is also misleading since I was using the colors of my LCD screen to determine it, instead of passing natural sunlight through a prism and setting for a value like Helmholtz did yea, he's also famous for light. The main thing is, and I'm sure you noticed this too, we perceive different colors at different light-intensities.

Modular Arithmetic and the hour Clock This section is under preparation. The indig of the series. Marko Rodin uses numbers in Base 10 - Mod 9. There is no surprise once you limit all conceivable numbers to Modulo 9, that patterns begin to repeat every 9 numbers. This in itself is no special, aside from the fact that 9 is a multiple of 3.

You could use any Base n - Mod n-1 and still get nice patterns for doublings, Fibonacci, and so on. Try Base 7 - Mod 6 and map the numbers on a circle; a more difficult arbitrary one is Base 12 - Mod 11 both presented below. Patterns appear wherever you create them. To help calculate, use the following formula in an Excel spreadsheet: Example for the number in Base 3 Mod 2: