Music Mathematics Part III. Timeless Music Theory: Musical dimensions and why Noise is the most advanced style

Read Parts 1 and 2 first  

So much for geometry of nation states, but what dimensions describe music? The straightforward answer might surprise you: the vast majority of all music we listen to is recorded and reproduced from a two dimensional grid, like a coastline. The two dimensions are 1) amplitude running up and down and 2) time running left to right. It is just like drawing a pencil line on a roll of chart paper.

These two dimensions record and replay all sound, ranging from a sine wave, which is easily described from a simple formula: this is smooth wave with 440 peaks and troughs per second. When we play this through a speaker, it moves the air in the same pattern, and you'll hear a sin wave tone.

 The waves are far more complex with an orchestra of many instruments and can't be described by any simple formula, but can still be drawn and reproduced extremely well with the pencil on chart paper. For example, here is 1 second from an orchestra playing Thung Kwian Sunrise.
and here is the chart (in mono) of the sound wave of that 1 second: if you play it into a stereo speaker or a telephone, or press it into vinyl or recording tape and then play it, it will play back what you heard the orchestra play

Here is just  10 milliseconds of that sound: see how undulating it is?

Sound is produced by changes in amplitude of air pressure, so for the sin wave above, an air pressure wave similar to waves in the ocean moves from peak to trough 440 times a second. This change in air pressure encounters your ear and your brain interprets it as music.

Sound recording measures the peaks and troughs of that air pressure wave with a pencil line on a chart moving from left to right. Our two dimensional sound recording chart can be stored as changes in the height in the grooves in LP records, or as metal particles on a sound tape, or as bits in a sound file on a computer chip or compact disc. If we replay the chart thorough a speaker, the speaker regenerates the air pressure and sound.

So how do we measure the dimensions of music? The length of the pencil line could be described in only a time dimension with a ruler or stopwatch, which is like using a long ruler for the British coastline (see Part II). But while we measure a line in one dimension, the shape of our music line is like the coastline of Britain: it's not quite 2 dimensional as it doesn't have area, and it obviously isn't a one dimensional line, so should be able to determine it's length more accurately using a partial dimensiona between 1 and 2. A periodic wave like our 440 Hz sine wave has a length that is easily described using a sine wave function. The louder and more irregular the sounds our chart is recording, that is the nosier the sound, the longer our pencil line will be, and the closer to filling an area.

So we can jump now to an easy answer to how to create timeless music: pure noise has infinitely long music line that would fill up our chart paper. In contrast to a sin wave, we can’t accurately describe it, although we can find a dimension that can approximate it's the length of the wave. Now questions of fast or slow are irrelevant, as is the duration We can measure its duration with a stopwatch or ruler, but there is no pattern and no duration of a musical pattern, so the piece doesn't have an ending, you can listen as long as you want.

White noise is this pattern in sound, and is the sonic analog to a coastline of Britain so complex that it is almost two dimensional (this is one second of white noise)

and here is 10 milliseconds of white noise: see how non-regular and complicated it is, compared to either the sin wave (which is still a sin wave no matter how much you stretch it out) or the orchestra sample?

so the country might be described as land, sea or a frothy muck, and so would this extremely complex music, which encompasses virtually every frequency you can hear.
Whenever you are between stations on your radio dial, you are hearing our new timeless music composition, White Noise for Air Columns.