User:Eliora/How long would it take for music to run out‽

A rather random thought about how long would it take for music to run out in a specific temperament and a specific alien species.

For planet 1 R earth

There were 82 million songs on Spotify in 2022, and the rate is approximately 10 million per year, and it is climbing exponentially. Source for the exponent shape: https://www.gapminder.org/factfulness-book/32-improvements/, Figure "New music".

As such, this could be used as a benchmark for an Earth-like planet composing in a given EDO, to measure.

Music is increasing every year at a rate roughly corresponding to 9/8 equal-step tuning, or if we temper out 531441/524288, about twice every 6 years. However, it is safe to say that as the world population levels, music production rate also levels, so we can expect things to "bend" at a rate of 0.1 song per person and then slow down.

Approach 1: Literally using all combinations in an EDO.

Let's assume that 8 notes or chords, taken from the boolean / power set (2^n), is the benchmark of melody. Any notes or chords, with no regard for consonance.

The formula as such is

6 log2(2^(8EDO)) = 6*8EDO = 54*EDO.

So one EDO has a "step" of 54 years. If we assign the 82 million songs mentioned before to an EDO, we get that right now we are at about 3.28-EDO.

When it comes to human population projection, we assume colonization of all solid surface in the Solar System, and perhaps beyond, which given multiple planets should give a rate of about 100 million people per year, slowed down after demographic transition.

The table as such is the following:

EDO	Progressions (2^EDO)^8 = 2^(8EDO)	Year relative to 2022 (step 54)	Years, realistically based on human population projection
3	16777216	2007	2007
4	4294967296	2061	2061
5	1099511627776	2115	~10000
6		2169	~2.56 million
7		2223	~650 million
8		2277	~160 billion
12		2493	7.205E20 years

As you can see, it would take longer than the age of the universe to run out of all 8-chord permutations in 12edo, even at human composing rate.

But obviously, not all chords in 12edo are consonant, and extrapolating this far is against the rules of science.

Approach 2: restricting to scales and notes

In this case, we define chord progressions as the following: they start with a consonance.

This means using fewer notes, but this approach is much more concrete - 5 limit mixed with fifth as a generator always produces rank two. This is a defining feature of music today (7 & 12), and we will use the ME produced by the rank two as our benchmark. Non-contorted temperaments are chosen.

Since log10(9/8) is approximatly 1/20, we can assume that one note progression here has "step 20" when it comes to years. More ex

Notes in a scale	Some scale names	8-Note progressions Steps^8	Years, realistically (step 19.5)	16-Note progressions Steps^16	Years, realistically based on human population projection
7	Meantone[7]	5764801	1999	7^16	332'000
9	Orwell[9]	43046721	2016	9^16	18 million
12	Pajara[12]	429981696	2044	12^16	1.8 billion
17	Superpyth[17]	6975757441	2061	17^16	486 billion
19	Meantone[19]	16983563041	~2400	19^16	2.88 trillion

As you can see, we already ran out of new 8-note permutations - there's only 5764801 possible combinations of 7 notes when there's 82 million songs on spotify. Using the 16th power, on the other hand, makes the number explode.