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Re: information theory?
Posted:
Nov 4, 2011 6:10 AM
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On Fri, 4 Nov 2011 20:33:48 +1100, "Peter Webb"
<webbfamily@optusnetDIESPAMDIE.com.au> wrote:
>
>
>
>He estimated music contains 40 bits/second entropy.
>How close is MP3 to that?
>
>___________________________________
>I doubt surprised Shannon said that, and if he did its somewhere between
>meaningless and wrong.
>
>CD quality mp3s are roughly equivalent to 178 kbps, over 4,000 times his
>estimate. But then you can encode a lot of sounds that most people would not
>consider music. And it stereo, so you can halve it if Shannon was talking
>about mono.
>
>And how do you define music, except as sound? And random sound waveforms
>cannot be compressed on average at all. To get a smaller figure for music,
>you have to define what subsets of sounds are music. Lots of luck.
>
>The real number probably lies somewhere between 178 kbps and 40 bps. The
>actual number is the base 2 logarithm of the number of different 1 second
>sound bites that the ear can distuingish and would consider as music. I
>doubt even Shannon would have known the answer to that equation.
I expect that if Shannon said something like that, he was considering
music to be more along the lines of a MIDI stream than a digitized
sound file.
Assuming a pianist can make 20 keystroke per second (and there are
scores that require that), 40 bits is a bit light, since you need to
refine the timing a bit, and specify the force of the keystroke, as
well as deal with the releases and the pedals (although those should
need a relatively low bit rate).
But all that together would certainly be less than 1000 bits per
second. That assumes that music is actually random keystrokes at
random times and random forces, at at very high keystroke rate - which
it is, of course, not, no more than English sentences are random
sequences of letters.
Consider that high keystroke rates pretty much require chords, and a
chord is most certainly not three or four random keys, pressed at
different times and forces - rather they're a small subset of the
possible combinations of keys within a hand-span (or two hand-spans in
some cases), hit at the same time, and with the same force (in fact
there are less than about 10,000 chords). And just like English, you
can't really have random sequences, or you'd just have noise.
Still, 40bps intuitively feels a bit light, but not by that much. I
expect that if Shannon said something like that, he was considering
music to be more along the lines of a MIDI stream than a digitized
sound file.
Assuming a pianist can make 20 keystroke per second (and there are
scores that require that), 40 bits is a bit light, since you need to
refine the timing a bit, and specify the force of the keystroke, as
well as deal with the releases and the pedals (although those should
need a relatively low bit rate).
But all that together would certainly be less than 1000 bits per
second. That assumes that music is actually random keystrokes at
random times and random forces, at at very high keystroke rate - which
it is, of course, not, no more than English sentences are random
sequences of letters.
Consider that high keystroke rates pretty much require chords, and a
chord is most certainly not three or four random keys, pressed at
different times and forces - rather they're a small subset of the
possible combinations of keys within a hand-span (or two hand-spans in
some cases), hit at the same time, and with the same force (in fact
there are less than about 10,000 chords). And just like English, you
can't really have random sequences, or you'd just have noise.
Still, 40bps intuitively feels a bit light for some of the busiest
music, but not by that much. For more typical passages, it seems
adequate.
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