Why Logarithmic? - Page 1
Forum section: electronics / beginners

author: olsenn
author_rank: Frequent Contributor
timestamp: October 16, 2012, 09:22:50 pm
content: Logarithms have always been a weakness of mine; I understand the math just fine, but I can't picture things on a logarithmic scale. For instance, when I use my spectrum analyzer, I always have it set to display voltage/power linearly. I like to see things in proportion to each other.My question is a bit specific though: I would like to know why frequency response for speakers/headphones are given with a logarithmic vertical timebase? I understand (never actually bothered testing it) that volume appears changes logarithmically, but not frequency! I'm looking for a pair of headphones that is maximally flat, and all the graphs show the first 1KHz as the first two thirds of the graph, and the remaining 19KHz in the audio spectrum to be only a third of the horizontal space.This annoys the hell out of me because my origonal thought is that a headphone is very flat with only a small frequency dip in it, but then I realize that that means that it isn't flat at all over the majority of the audio spectrum!

author: JuiceKing
author_rank: Regular Contributor
timestamp: October 16, 2012, 09:56:19 pm
content: Quote from: olsenn on October 16, 2012, 09:22:50 pmActually, audio frequency response curves often use logarithmic scales for frequency. The reason for this is so that you can see detail in the lower octaves where the ear is sensitive while at the same time seeing the general response in the upper octaves where the ear isn't so selective and you can make due with less detail in the graph. Same is true for volume...the ear is exquisitely sensitive to small differences in volume at low levels, but exponentially less so as volume goes up.

author: ejeffrey
author_rank: Super Contributor
timestamp: October 16, 2012, 09:59:44 pm
content: Many physical quantities are perceived logarithmically (or roughly so). For instance, a sound that is twice as powerful (3 dB more) will sound considerably louder but not overwhelmingly so whether the original sound is faint hard drive spinning or a crowded bar during a football game.For pitch, the answer is particularly clear. The important relations that make tones sound melodic or dissonant are spaced logarithmically. For instance, octaves are a factor of two apart, fifths are 1.5:1, and so on. This means that lower pitch notes are spaced by fewer Hz and higher pitch notes are spaced by more. If you look on a response plot on a log frequency axis, each octave gets an equal portion of the plot. 10-20 kHz may be half the audible spectrum, but it certainly isn't half in terms of your perception. Finally, as a matter of practice, the upper two to three octaves of the audible spectrum are of much smaller importance. Your hearing is much less sensitive there, and few instruments make much noise there. Mostly only synthesizers are capable of playing notes above a few kHz. Pianos top out at just over 4 kHz, and IIRC piccolos can play up to 7 kHz, but almost never do. You still have harmonic content that contributes to the timbre so you need the upper registers, but they are just less important.it is definitely possible to use logarithmic plots deceptively, but linear plots can be just as deceptive. It is all about using what is most appropriate for the measurement at hand. Often that is the log plot.

author: JuKu
author_rank: Frequent Contributor
timestamp: October 17, 2012, 07:31:27 am
content: Quote from: olsenn on October 16, 2012, 09:22:50 pmYou understand wrong. The ear perceives frequency logarithmically.