A02. Minimal Information Content

Written by peterkienle on August 11, 2020

There is not a whole lot to say about this chromatic scale. 

– There are 12 steps (of theoretically, but not practically equal distance)

– After 12 steps the scale repeats, with every step doubling in frequency (this is called an octave)

Alternatively, this could also just be expressed as a string of consecutive numbers: 

1 2 3 4 5 6 7 8 9 10 11 12 (octave 1)

13 14 15 16 17 18 19 20 21 22 23 24 (octave 2)


A little more practical visualization would be to imagine a piano keyboard – but one with white keys only. Let’s say we have about three octaves of chromatic scale – each octave repeats the same notes but at double the frequency. We usually perceive an octave as ‘the same note just higher’. On this imaginary (white keys only) keyboard we now have 36 (plus two extra) white keys with no markings. Unless we use the lowest (left-most) or highest (right-most) key and count keys there is no good way to find a specific note. 

Imagine yourself the size of an ant, standing on one of these white keys somewhere in the middle. Looking forward, toward the higher pitches, or behind you, toward the lower pitches everything looks uniform, no matter on which white key you stand. This arrangement clearly doesn’t contain (or encode, or produce) a lot of information.

A01. The Chromatic Substrate

Written by peterkienle on July 11, 2020

We are using the 12 note chromatic scale as the basic substrate for our exploration of music theory and its possible parallels with the fabric of reality. Above the twelve steps with sound frequencies above each step (or “station”).

The Chromatic Scale normally used in modern Western music has a pretty clear definition. 

“Our” chromatic scale has 12 pitches of increasing frequency. For now we call these pitches 1, 2, 3,…..12. After step 12 the scale repeats, but every pitch/note will have a doubled frequency. This frequency doubling happens every 12 steps. This makes the pitches NOT equidistant from each other in frequency. In other words, the difference in frequency from step 2 to step 3 is smaller than from step 3 to 4. However, this doesn’t concern us here – we say that every step in a chromatic scale is one step away from its two neighbors.

This simple substrate will provide the building material for our “Music Theory”

A. Only A Music Theory

Written by peterkienle on

When I started playing guitar at age 14 or so, I was concentrating on the sheer awkwardness of getting to make my fingers hold down the right string in the right position. Only after the physical aspect got a little easier and more second nature, did music theory come in the mix. At first it was learning about various chords that somehow belong together. At some point the need to improvise a melody arose. You use a scale, or two, or three. Then musical keys. Major/minor relationships. And, yes, I am leaving rhythm out, because that was possible without a theory.

Things got interesting when I developed an interest in writing my own music. Although, to be honest, that was for a very long time more the process of picking out segments or sections from existing music that gave me goosebumps, rewriting it and somehow making it my own. But that’s no disgrace; in art, most output seems to be some sort of imitation – occasionally improving on the original.

You can take whole university semesters learning about highly advanced and refined aspects of music theory. Oftentimes (to me at least), compositions coming out of that sound like case studies, and unless one knows the theory behind a certain piece it it can sound pretty random. For the “everyday working” musician, theory is more like a tool to find the right chords and scales – with the final judge being if it sounds “good”.

I want to start this philosophical trip with music. Mostly because I know some stuff about it. 

Rounding Errors

Written by peterkienle on June 3, 2020

For as long as I can remember one of my most favorite pastimes has been thinking about god, the universe and everything. Half of the books I read deal with this subject one way or another (the other half is Science Fiction, which often deals with the very same topics). In the past few years there has been a quickening of ideas on various subjects. Probably helped along by the fact that we have a little dog in the house since 2014, who loves to take hikes – and nobody else will take her. Without me noticing at first, many of the seemingly unrelated topics and ideas started getting connected while taking long hikes around our nearby lake.

As an example, as a musician I deal with and practice scales and chords – or, in other terms, the organization of the twelve notes of the chromatic scale into larger structures. In this example it means taking seven of the twelve notes to make more “melodic” sounding scales or tone-rows. The asymmetry of picking seven notes out of 12 equally spaced ones leads to interesting and rich structures by necessity. 

Another fruitful playground are the basic workings of a digital computer. In this very idealized example the whole layer cake of operating systems, various level programming languages and interfaces, GUIs, apps etc. creates an intricate tower of increasing structured abstraction leading to interesting philosophical ruminations.

I finally decided to write this stuff down. But I am not a book author and this is not anything that would be of interest to a serious scientist or a religious person. Somehow I still feel it should be a little more out in the open rather than just fade away in a forgotten Google Doc. And since I don’t think anybody ever comes to this blog it’s perfectly safe….

Copyright © by Peter Kienle