Parman - Activate OP_GFY now!! on Nostr: CAGR (finance) explained for musicians... Compound Annual Growth Rate is analogous to ...
CAGR (finance) explained for musicians...
Compound Annual Growth Rate is analogous to the semitone growth through an octave. How...
All self-respecting musicians already know that the frequency interval of a note grows by the 12th root of 2, which is 1.059463 (ie each semitone "grows" by 5.9463% from one to the next above). The note above A440 is B flat. That is 440*1.059463=466.16 Hertz.
The 12th root of 2 is a number that if you multiply itself 12 times, you get 2.
The upper note in an octave is 2x the frequency of the lower note by definition, and there 12 semitone equal increments from the lower note to the upper note).
Without getting into "equal" temperament vs "well" temperament (a fascinating side topic), the lower note is increased by 5.9563%, through 12 semitones to the upper note, finally resulting in 2x. The A above A440 is A880.
How is this analogous to CAGR?
Well, if you started with $1000, and it doubled in 12 years, the CAGR of your investment is worked out the same way, and is the same value of 5.9563%. The growth rate per interval, in this case the interval is a year.
I overcomplicated it didn't I? It's OK, musicians will get it no, especially piano turners.
Compound Annual Growth Rate is analogous to the semitone growth through an octave. How...
All self-respecting musicians already know that the frequency interval of a note grows by the 12th root of 2, which is 1.059463 (ie each semitone "grows" by 5.9463% from one to the next above). The note above A440 is B flat. That is 440*1.059463=466.16 Hertz.
The 12th root of 2 is a number that if you multiply itself 12 times, you get 2.
The upper note in an octave is 2x the frequency of the lower note by definition, and there 12 semitone equal increments from the lower note to the upper note).
Without getting into "equal" temperament vs "well" temperament (a fascinating side topic), the lower note is increased by 5.9563%, through 12 semitones to the upper note, finally resulting in 2x. The A above A440 is A880.
How is this analogous to CAGR?
Well, if you started with $1000, and it doubled in 12 years, the CAGR of your investment is worked out the same way, and is the same value of 5.9563%. The growth rate per interval, in this case the interval is a year.
I overcomplicated it didn't I? It's OK, musicians will get it no, especially piano turners.