1505 words

Music theory 2

In my last entry I wrote about creating interesting patterns that sounds difficult to predict. For example the pattern x:

1,2,1,3,1,4,1,2,1,3,1,4,1,2..

A pattern alone might not make a song interesting enough, to make it more interesting we can create multiple patterns and add them on top of each other, if we have pattern y:

4,5,4,5,6,4,5,4,5,6,4,5...

and play it while playing pattern x:

--4,5,4,5,6,4,5,4,5,6,4,5
1,2,1,3,1,4,1,2,1,3,1,4,1,2

You might have been able to tell that pattern y started a while after x, and ended before x ended. If we add another pattern z to this pyramid of sounds:

----6,7,7,6,7,7,6,7,7,6
--4,5,4,5,6,4,5,4,5,6,4,5
1,2,1,3,1,4,1,2,1,3,1,4,1,2

Now this is a song alright. Let's add two peaks to this shape with the t pattern:

--------8,3-----8,3
----6,7,7,6,7,7,6,7,7,6
--4,5,4,5,6,4,5,4,5,6,4,5
1,2,1,3,1,4,1,2,1,3,1,4,1,2

What is cool is that we can create patterns of patterns. If we abstract the numbers with the character representing the patterns, that is:

x = 1,2,1,3,1,4,1,2,1,3,1,4,1,2
y = 4,5,4,5,6,4,5,4,5,6,4,5
z = 6,7,7,6,7,7,6,7,7,6
t = 8,3

We can write the song as:

----t---t
--z-------z
-y---------y
x-----------x

Music theory 1

I was talking to a couple of friends about what makes music interesting and or good. We came to the subject of patterns in music. That is, each piece of music is built using some form of pattern. In its most basic form, this pattern can for example be a repeated list of drum beats. Let's try to represent this repeated list of drum beats with numbers. Imagine each number as a unique sound.

1,2,1,2,...

Can you guess what comes next? Both visually, and auditory guessing what comes next is intuitive. 1,2 of course. We can make this repetition of numbers more interesting by making the pattern harder to predict, what if we add a new sound:

1,3,2,1,1,3,2,1,...

This is still too easy, what about:

1,2,1,3,1,4,1,2,...

We can make this harder and harder to predict. My theory is that our mind is being stimulated by finding repetitions, it being audio or visual repetitions. But only up to a limit. What if I gave you this string of beats:

1,3,2,4,1,2,2,4,3,4,2,...

This was made by a random number generator. I don't think we'd enjoy this piece.

I think different beat complexity is nice for different purposes. If your sole activity is to listen to the music, you probably want some more complex repetitions. However, if you are listening to music while driving, gaming, studying or anything that requires focus, you probably want to listen to less 'complex' music. The complexity of the music is the difficulty of finding the pattern of notes in the music.

Each song is 'built' using strings of notes. Each string contains a pattern of notes and each string has different patterns. That is, we can call the following pattern string a:

1,2,1,2,1,2,1,2,1,2,1,2...

If it is too difficult to understand the pattern of a string in the time it is played, perhaps the string can be replayed multiple times over the course of the song. This would give the listener more time to understand the string. Maybe a simpler string can be used to allow the listener to 'rest' in between more complex patterns. Perhaps a pattern can be made of strings. That is if there exists three strings a,b and c, all containing different patterns of beats, the strings can be played in a repetitive order. E.x.

a, b, c, a, b, c...

This is all speculatory, but I believe the song you enjoy the most makes you understand the beat pattern just before the song changes beat pattern. That is, once you have understood the pattern of a string, the next string should be played. Parts of one string can be a sub-string of another string to make the other string easier to recognize.

This might also be the reason for why we get tired of listening to the same song. It becomes too repetitive. That is if we are not emotionally attached to the song. Perhaps that is also why we can start out disliking a chaotic song, but start liking it once we have listened to it multiple times. The pattern is becomes easier to predict once we've heard it multiple times.

Time

I had a discussion with a couple of friends about the new Nolan movie Tenet. We came to a point where we were trying to explain what entropy and time is. (slight spoilers) The main idea of the movie is that objects and people can enter a reversed-entropy state. In this state, the 'entropy' of their existence is moving in the opposite direction of what we view as the normal entropy direction. When trying to how this worked in the movie we came to a point where we thought of time as two lines.

Measure of entropy, right = more entropy, left = less entropy.
-------------------------------------------1----------------------------------------------------
-------------------------------------------2----------------------------------------------------
Image 1 being a person, Amy, and 2 being another person named John. As Amy's and John's entropy changes, their respective position on this timeline moves as well. If both of their entropy changes normally they continue moving on this timeline. However, when Amy and John are having opposite entropy, they first move towards each other and then pass each other.

John & Amy have the same entropy change:

  • Starting position for Amy & John in our timeline.

-------------------------------------------1----------------------------------------------------
-------------------------------------------2----------------------------------------------------

  • Something changed with Amy and John

---------------------------------------------------1--------------------------------------------
---------------------------------------------------2--------------------------------------------

  • Something changed with Amy and John again

---------------------------------------------------------------1--------------------------------
---------------------------------------------------------------2--------------------------------

John & Amy have opposite entropy change:

  • Starting position for Amy & John in our timeline

-------------------------1----------------------------------------------------------------------
-----------------------------------------------------------------2------------------------------

  • Something changed with Amy and John

---------------------------------------------1--------------------------------------------------
---------------------------------------------2--------------------------------------------------

  • Something changed with Amy and John again

-----------------------------------------------------------------1------------------------------
-------------------------2----------------------------------------------------------------------

You might have already come to the same conclusion that we did. What does it mean to Amy and John to be at different places in the same timeline? Does Amy & John disappear when not on the same entropy 'level' (timeline position)?

Before I try to answer these questions I'd like to introduce another model for representing time: Observed change. Imagine a simple universe. This universe consists of two particles whose only properties are its x, and y position in a 2-dimensional grid.

Time step 1:

1 * *
* * *
* 2 *

Oddly enough, these particles are also named Amy & John (1 = Amy, 2 = John). If Amy & John does not change positions, time does not move either. If Amy moves one step to the right, like so:

Time step 2:

* 1 *
* * *
* 2 *

Time has officially moved! What happens if Amy moves back to her original position? I'd argue Amy goes back in time.

Time step 3:

1 * *
* * *
* 2 *

Can we represent this model with a timeline as well? You betcha'.

1-----------------------------------------------------------------------------------------------
Amy is at position 1,1 (top left corner in our universe). We can write this as U(1) (The state of the universe as shown at time step 1.).

-1----------------------------------------------------------------------------------------------
Amy(2) is the exact state of the world when Amy has moved to position 2,1 in our model universe.

If we increase the size of the universe, the number of moving objects or the complexity of the moving objects, it becomes more and more difficult to move 'back' in time.

Also, using this world model shows why the 'double' timeline model does not work when trying to explain Tenet. Only one timeline can exist at once, and a tick in the timeline can be seen as the state of all objects in a universe. If Amy is having her entropy reversed, while Johns entropy is moving as normal, it just means that their states are changing differently. They still exist simultaneously in the universe at all points in the timeline.

Some odd things do occur in our small universe, if the timeline is supposed to represent change of state. If Amy moves one step to the right, one step down, one step to the left and then one step up she ends up in the same state as she started in. This means that the timeline is not as intuitive as we'd like it to be.

1 * *

* * * 1----

* 2 *


* 1 *

* * * -1----

* 2 *


* * *

* 1 * --1---

* 2 *


* * *

1 * * ---1--

* 2 *


1 * *

* * * 1-----

* 2 *

The timeline model doesn't make much sense.

What is interesting with this state model of time, is that it shows why it's close to impossible to travel back in time. To be able to travel back in time, you would need the entire observable universe to 'reverse entropy'. That is, everything in the world would have to change back to the state that they were in, at the moment you want to travel 'back' to. It also shows how traveling forwards in time is much simpler. Traveling forwards in time simply requires you to stop changing, while everything else changes.