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Topic: information theory?
Replies: 83   Last Post: Dec 22, 2011 5:14 AM

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 Androcles Posts: 43 Registered: 10/9/11
Re: information theory?
Posted: Nov 4, 2011 7:35 AM

"Robert Wessel" <robertwessel2@yahoo.com> wrote in message
news:r6d7b7l6nt23kcu3n0cisoe85j0d6go5no@4ax.com...
| 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
| >
| >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

The difference between MIDI and audio compression is the
synthesizer. The same pianist can play 20 notes a second on
a church organ or harpsichord and it will sound bloody awful,
the pipes don't have the same percussive attack that a hammer
on a string has. Same with speech, it is the explosive attack of
the consonant that makes the word, not the drawn out vowel
which is often changed by accent. Orz-dry-lee-uns still write
"Australians" but change the sound of the vowels as we all do.
Much of the spoken word is cliché, "it's like" "know what I
mean". The first four notes of Beethoven's 5th are a cliché,
it wouldn't matter what instrument they were played on, you'd
still recognise the phrase. Audio compression carries more
information than MIDI, it has to.

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