Maths probability: Similar Music chords in Songs?

Question

There are 7 notes in a musical scale.
A great majority of songs use either the Major or Minor variations of these chords.   
So this is a total of 14 possible chords.
On top of this, it is common to play any of these 14 chords as a '7th'.  (ie: E7 or Em7)
So now we have 28 chord possibilities to choose from.

Timing and Rhythm aside, How can I work out the probability of any songs containing the same progression of chords ?

example:
What is the probability of the same 4 chords being in a row ?  and how would I work it out?
Can I easily use this same logic for 5 chords in a row?

Thank you  ;)

? · Accepted Answer

In fact there are 12 notes in a chromatic scale.  And you can create new chords by adding other notes apart from 7ths (e.g. C#m♭9♭3).  So there are actually many hundreds of different chords. But let’s assume that we can only choose from 28 chords.

It is impossible to find the probability because there are too many undefined variables. The ones that spring immediately to mind are:

1.  How do we handle songs of different lengths? Probabilities will be meaningless  comparing a 20 bar song to a 200 bar song for example.

2. How do we handle songs with different numbers of chord changes?

3. Suppose song-1's sequence is  ABCDBAC and song-2’s sequence is FDBACFG
Is this a match?  Both contain DBAC.

I’m sure I could think of other problems!

So the question you pose is unanswerable.  Here’s a question that can be answered:

Two songs have the same number (N-1) of chord changes.  There are 28 allowed chords.  If chords are selected randomly when writing the song, what is the probability that the songs’ chord sequences will be identical​?

For song 1:
There are 28 choices for chord 1
There are 27 choices for chord 2 (can’t use previous chord or it’s not a change)
There are 27 choices for chord 3 (can’t use previous chord or it’s not a change)
.
.
There are 27 choices for chord N (can’ use previous chord or it’s not a change
(That’s N-1 changes.)

Number of possible chord sequences is 28*27ᴺ⁻¹

Song 2 will have 1 of these 28*27ᴺ⁻¹ sequences, so the probability of the songs having the same sequence is 1 in 28*27ᴺ⁻¹

For N=4 this is 1 in 551124
For N=5 this is 1 in 14880348

? · Answer

Given your approach it is just 28 x 28 x 28 x 28 x 28 or 28⁵ as they say in mathland.
  
The joke is tho, in real pop songs the probability of  I, IV, V, vi being used in some order is nearly 100%

Jimmy C · Answer

There are other variations on chords as well, such as 9ths, 13ths, diminished, etc. I am sure a good musical mathematician could add them up and work out the number of possible permutations. 
I have often wondered too about how many ways you can put together 12 notes. 
I am listening to Beethoven at the moment as I type.

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Maths probability: Similar Music chords in Songs?

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