There is another useful case for it. You can compute the 'virtual' musical perfect 4th of two notes. If i take the HM of C3 and C4 for example, i get F3. Coincidentally (maybe not?), i get G3 (the perfect 5th) if i take the HM of C3 and C5. 🤔
Very clear video! I do have one question though: why exactly does this work? Is the harmonic mean always equal to the arithmetic mean after factoring in ratios? And does that work for any ratios or is this a specific case where it happens to give the same answer?
the guys who invented this formula are genious, still i cannot get how the hell come out.Only a complex ancient greek text make it a little intuitive to me from Wiki from a student of Pythagoras. "Subcontrary, which we call harmonic, is the mean when they are such that, by whatever part of itself the first term exceeds the second, by that part of the third the middle term exceeds the third. It turns out that in this proportion the interval between the greater terms is greater and that between the lesser terms is less. " - Archytas of Tarentum, To me i translate it simplisticaly like " use it when a measurement devision is subpart of something bigger and its subparts also split further. All follow the parent measurement and its most recent previous subpart in relationship.Like in Music harmonies. The rest are too complex for me to get how and why despite i was pretty good in maths and physics. Again what a complex genius invented this monster measurement
Harmonic mean is how mathematicians do diss tracks.
lmao
Really useful! Helped with my CFA level 1 exam
So this is why there's that weird way to find resistance in parallel circuits.
It's also used to figure out the average fuel economy, if you're using Freedom units
This was amazing! Thank you so much!
Very well explained 😊 Thanks a lot!
Really good explanation Thank you!
Another useful case for it is an evaluation metric in machine learning called f1_score
Great example. Wikipedia gives a good summary: en.wikipedia.org/wiki/F-score
There is another useful case for it.
You can compute the 'virtual' musical perfect 4th of two notes. If i take the HM of C3 and C4 for example, i get F3. Coincidentally (maybe not?), i get G3 (the perfect 5th) if i take the HM of C3 and C5. 🤔
Thank you! ☺
Very clear video! I do have one question though: why exactly does this work? Is the harmonic mean always equal to the arithmetic mean after factoring in ratios? And does that work for any ratios or is this a specific case where it happens to give the same answer?
You might look at the proofs and references in this:
A PROOF OF THE ARITHMETIC MEAN-GEOMETRIC MEAN-HARMONIC ... rgmia.org/papers/v2n1/v2n1-10.pdf
the guys who invented this formula are genious, still i cannot get how the hell come out.Only a complex ancient greek text make it a little intuitive to me from Wiki from a student of Pythagoras.
"Subcontrary, which we call harmonic, is the mean when they are such that, by whatever part of itself the first term exceeds the second, by that part of the third the middle term exceeds the third. It turns out that in this proportion the interval between the greater terms is greater and that between the lesser terms is less.
"
- Archytas of Tarentum,
To me i translate it simplisticaly like " use it when a measurement devision is subpart of something bigger and its subparts also split further. All follow the parent measurement and its most recent previous subpart in relationship.Like in Music harmonies.
The rest are too complex for me to get how and why despite i was pretty good in maths and physics.
Again what a complex genius invented this monster measurement
I am seeing from Bangladesh 🇧🇩