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: using 5-limit consonance
In this case, we define chord progressions as the following: they start with a consonance.