Haven’t heard of the harmonic mean before! That’s pretty cool Harmonic mean 500/1 = 500hz 500/3 =166.667 hz 500/5 =100 hz Arithmetic mean 500hz 300hz 100hz Geometric mean (logarithmic or equal division) 500hz 223.61hz 100hz
Geometric mean happens to sound pretty decent even though it's a seemingly ugly ratio of square root of 5 (2.236:1). It's very close to the just tempered major ninth (9/4 or 2.25:1) and even closer to the equal tempered major ninth (2^(14/12) = 2.245:1).
You can also check harmonic and arithmetic means of 1 and X by dividing X into an isoharmonic chord of three notes, that is a chord consisting of harmonics M, M + N, M + 2N where M, N are integers. Here we have such a chord as 1:3:5. Now, harmonic and arithmetic means here are just two intervals with the middle note: 5/3 and 3/1. I don’t remember which is which but that’s honestly not an issue because you can always check later; and if you’re certain that one is the arithmetic mean then the other should be the harmonic mean.
Love a mannfish interval
thank you, these are great teaching resources
missed chance for 1/5/25 yesterday 😔
hi five, lo five
Haven’t heard of the harmonic mean before! That’s pretty cool
Harmonic mean
500/1 = 500hz
500/3 =166.667 hz
500/5 =100 hz
Arithmetic mean
500hz
300hz
100hz
Geometric mean (logarithmic or equal division)
500hz
223.61hz
100hz
Geometric mean happens to sound pretty decent even though it's a seemingly ugly ratio of square root of 5 (2.236:1). It's very close to the just tempered major ninth (9/4 or 2.25:1) and even closer to the equal tempered major ninth (2^(14/12) = 2.245:1).
nice
5️⃣
wouldnt harmonic mean be 5/2
my understand is it would be 2 / (1/5 + 1)
That's arithmetic mean
You can also check harmonic and arithmetic means of 1 and X by dividing X into an isoharmonic chord of three notes, that is a chord consisting of harmonics M, M + N, M + 2N where M, N are integers. Here we have such a chord as 1:3:5. Now, harmonic and arithmetic means here are just two intervals with the middle note: 5/3 and 3/1. I don’t remember which is which but that’s honestly not an issue because you can always check later; and if you’re certain that one is the arithmetic mean then the other should be the harmonic mean.
what
what is this normie stuf tbh smh fr