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Lesson 126: Creative Composition - Numbers and Music: The Fibonacci Sequence, Pi, Aleatoricism and Fractals

The Fibonacci Sequence

The Fibonacci sequence of numbers is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers.

Let us use a 7-note scale, for example the C major scale. From the table below you get the corresponding note for every number. This is called modular arithmetic or clock arithmetic - using a 7-hour clock. Note that it corresponds exactly to the musical intervals: for example 3=e, 5=g, 7=b, 9=d, 11=f, 13=a...

 c	 1	 8	15	22	29	36	43	50
 d	 2	 9	16	23	30	37	44	51
 e	 3	10	17	24	31	38	45	52
 f	 4	11	18	25	32	39	46	53
 g	 5	12	19	26	33	40	47	54
 a	 6	13	20	27	34	41	48	55
 b	 7	14	21	28	35	42	49	56

Below we have a melody where the pitches come from the Fibonacci sequence. You can listen to it here.

You can also use the Fibonacci sequence for rhythms. Below we have a template where the rhythms come from the Fibonacci sequence. You can listen to it here.

Pi

Pi is approximately 3,14159265358979. If you decide that 1=a, 2=b, 3=c, 4=d, 5=e, 6=f, 7=g, 8=a and 9= break, you get the melody below. You can listen to it here.

I chose to let the number 9 be a break because that gave the melody a nice rhythmic twist. You could also decide that 9=b and 0 would quite naturally be c.

More Fun with Numbers

You can do this with any number and any scale of your choice.

Below is a melody where the pitches come from my phone number. The scale is the C major scale, so 1=c, 2=d, 3=e, 4=f, 5=g, 6=a, 7=b, 8=c, 9=d and 0=e. You can listen to it here.

Aleatoricism

Aleatoricism is the incorporation of chance into the process of creation. The word derives from the Latin word alea, which means the rolling of dice.

So, we could literally take a dice and either

  • a 6-note scale
  • 6 chords
and let the dice determine the order of the notes or the chords.

The melody below was generated by rolling a dice. I decided that 1=c, 2=d, 3=e, 4=f, 5=g and 6=a. You can listen to it here.

I decided to do one more melody. I now chose a C blues scale, so 1=c, 2=eb, 3=f, 4=f#, 5=g and 6=bb. I also wanted different note values, so I used a second dice for the note values. For the note values, I decided that 1= whole note, 2= dotted half note, 3= half note, 4= dotted fourth note, 5= fourth note and 6= eighth note. One more decision I made was to use 8 notes in the first phrase and 9 notes in the second and third phrase. You can listen to it here.

The chords below were also generated by rolling a dice. I decided that 1=Cmaj7, 2=Dm7, 3=Em7, 4=Fmaj7, 5=G7 and 6=Am7. You can listen to it here.

You can choose any 6 chords. For the next try I decided to use a constant structure, all maj7 chords, and that 1=Cmaj7, 2=Dbmaj7, 3=Ebmaj7, 4=Fmaj7, 5=Bbmaj7 and 6=Abmaj7. I also wrote a melody to it and called it Scary Tune. You can listen to it here.

2014 Tomas Karlsson. All rights reserved.