[pinnahertz]

   
1. We can't assume uncorrelated signals though, particularly when mixing music and, they're not at the same level. Nevertheless, even though the "law of uncorrelated summing" is extremely imprecise in practice (the real world of mixing real acoustic sound signal), as we increase the channel count we would build level. 

Actually, you can assume uncorrelated. Correlated summing, and the resulting 6dB voltage increase when the number of summed channels doubles, only happens when you sum perfectly identical waveforms, in phase, and at an identical level.  As you increase the total number of channels, the rare possibility of that happening gets buried in the huge number of uncorrelated channels being summed.  Designing for correlated summing would only become necessary if you planned to identical signals to the majority of channels. Not something that would happen in music or film.  Uncorrelated summing is also a worst-case scenario because it too assumes identical levels, but of completely different signals, to build at the rate of 3dB/channel count doubling. Reality is usually below that, often by quite a bit. 
 
Headroom is simply the ratio of a nominal (and somewhat arbitrary) reference level to 0dBFS.  16 bit puts that somewhere around -15 to -20dBFS,  usually.  24 bit lets you fudge that around without taking a noise hit.  We're saying the same thing in different reference frames.  If you look at a gain-structure diagram of an analog mixer you'll see reference levels moving all over the place depending on the specific need for headroom at that point in the design.  That's how I look at 24 bit, you get more room to adjust your gain structure during the original recording because you're not fighting with the noise floor as much. Where I think a lot of location sound guys mess up is they record lower, but don't match the overload points of the entire system, so shouted dialog still gets crunched by a clipped preamp even though it's below 0dBFS.   Just a guess, but easy to confirm.

 

[lantian]

  I'll let those who didn't stop using math the day school ended

, explain in detail if they feel like it .but basically it's the same mistake as the great classic "humans have 140db of dynamic range so of course 16bit isn't enough!". the values come from something real but specific, and are then abused out of context to try and make a point.
get me loud iterated ripple noises and square waves as the only sounds in your favorite song, and then we can discuss some 5 to 10µs delays audible to humans in "music".
 
for the "sample rate to period" thing, it doesn't mean what you seem to think it means. the actual signals in music are sine waves, the actual resolution will depend on the bit depth and loudness of the signal, and most certainly does better than 20µs. to degrade to any not even significant values, we'd need to go look at very low levels, which of course negates the 5µs of the paper anyway as nobody would ever pass the test at very low volume levels.
so it's pretty safe to say that you are wrong on this. the results of a specific test are valid for the specific conditions of the test.

Thank you

 

[spruce music]

Higher sampling rates are simply producing more life like resolution of your music.  Human ear is perfectly capable of hearing the difference between higher sample rates. The so called auditory resolution of human hearing is about 5-7us, a 44.1khz audio has each slice of 20us, 96khz has something like 10us, and only 192khz can offer time resolution of 5us. That would seem perfectly smooth to our auditory systems/brain. Go ahead and correct me If I am wrong on this.

Old myth hard to kill. Time resolution of digitally sampled audio is not the time between samples. It is 1 divided by time between samples x 2pi x number of levels. For 44/16 that's about 56 picoseconds. Dither actually lowers that number further. So this is about 100,000 times smaller than your 5 microseconds.

 

[gzubeck]

This video will answer all your questions concerning audio from 16bit to 24bit audio...Lot of laughs starting at 20 minute mark.
 

 

[TheoS53]

  This video will answer all your questions concerning audio from 16bit to 24bit audio...Lot of laughs starting at 20 minute mark.
 

Very good vid, well worth the watch. Thanks for sharing

 

[StanD]

  Ring modulation would be a kind of analog synthesis effect, and as such, I doubt high precision is even desired.  Remember, early FM  synths were 12 bit, then 15 bit.  With today's interest in vintage instruments you probably want that 12 bit grit. 

Early synthesizers were analog computers and ring modulators were four quadrant multipliers. I have an ARP 2600 somewhere in my attic.

 

[StanD]

   
1. I'm not sure I understand what you're asking. In general, 16bit is enough when multiplying two different 16bit numbers (for whatever sound effect). The problem starts to arise when taking that result and multiplying it with something else and gets worse if you then take that result and multiply it with something else again, and then keep repeating that procedure.  Certainly, 48bit or 64bit float is more than enough for any conceivable, realistic number of such processes/procedures and btw, a 48bit fixed virtual mixing environment is not a new thing, it was introduced about 20 years ago and was pretty much ubiquitous by about 15 years ago.

In a strict 16 bit integer system, multiplying two 16 bit numbers would cause an overflow of more than what just a flag could contend with, hence clipping.
Floating point is not perfect enough for audiophile applications.

 

[gregorio]

  [1] Actually, you can assume uncorrelated. Correlated summing, and the resulting 6dB voltage increase when the number of summed channels doubles, only happens when you sum perfectly identical waveforms, in phase, and at an identical level.   .... Uncorrelated summing is also a worst-case scenario because it too assumes identical levels, but of completely different signals, to build at the rate of 3dB/channel count doubling. Reality is usually below that, often by quite a bit. 
 
[2] Headroom is simply the ratio of a nominal (and somewhat arbitrary) reference level to 0dBFS.  16 bit puts that somewhere around -15 to -20dBFS,  usually.  24 bit lets you fudge that around without taking a noise hit.  We're saying the same thing in different reference frames.  
 
[3] Where I think a lot of location sound guys mess up is they record lower, but don't match the overload points of the entire system, so shouted dialog still gets crunched by a clipped preamp even though it's below 0dBFS.   Just a guess, but easy to confirm.

 
1. I did not say that we can't assume uncorrelated summing and therefore we must assume correlated summing. In reality when doubling the track count we don't generally get either exactly +3dB or +6dB but some variable amount.
 
2. I think we're saying the same thing. Although, the point I was trying to get across is that no matter what the nominal reference level to 0dBFS is set to (on a particular ADC or DAC), it's the same nominal level for both 16 and 24bit. In lay speak, 24bit does provide more loudness, it provides more quietness.
 
3. OK, this is way off topic but generally they tend not to "record lower". Location sound guys are usually taught to try and get a peak level of -6dBFS, they could/should easily go much lower still and not affect the noise floor. The mic-pres on industry standard location kit (Sound Devices) are very good but at the standard film reference level (-20dBFS = 0VU) there is no benefit in trying to peak at -6dBFS, -12dB would be better.
 
Quote:

  [1] In a strict 16 bit integer system, multiplying two 16 bit numbers would cause an overflow of more than what just a flag could contend with, hence clipping.
[2] Floating point is not perfect enough for audiophile applications.

 
1. I'm still not sure I understand, I'm not deliberately trying to be obtuse btw. Assuming two full-scale or near full-scale 16bit numbers/signals, then yes multiplying them together would result in clipping but if we take exactly the same two signals (same amplitude/level) in 24bit instead of 16bit, we still get exactly the same clipping. IE. There's no difference/advantage to 24bit vs 16bit. We would also get exactly the same amount of clipping with floating point. The difference with floating point is that instead of simply loosing any data which exceeds full-scale (0dBFS), we can recover it by lowering the output.
 
2. Not sure if this is sarcasm (aimed at audiophiles)? If so, I wouldn't be surprised if that's what they think, regardless of the fact that there's in effect no difference (between 32bit float and 24bit fixed) and that virtually all PCM mixes are floating point at least in places if not in their entirety (until they get printed to a distribution format).
 
G

 

[watchnerd]

 
Floating point is not perfect enough for audiophile applications.

 
Well in that case, you're screwed, because all the DAW software uses floating point.

 

[castleofargh]

floating points make the music flow and sound smooth, but it works only with wav files.

 

[limpidglitch]

  I have an ARP 2600 somewhere in my attic.

 
One of those pieces of junk, eh? I'll be kind and pay for shipping if you want to get rid of it 

 

[sterling1]

I remember when CDs were introduced the slogan for the medium was perfect sound, forever perfect. Now, if that statement was true, then how can todays hi-res be more perfect? I know that I can't distinguish 16/44 from 24/96 so all of these bigger files seem to do nothing more than fill up library space. I remember when digital was just an idea and the idea was that 16/44 was all that was necessary to assure the best possible outcome.

 

[StanD]

  Early synthesizers were analog computers and ring modulators were four quadrant multipliers. I have an ARP 2600 somewhere in my attic.

 
 

   
One of those pieces of junk, eh? I'll be kind and pay for shipping if you want to get rid of it 

I probably have some spare parts like matched pairs of complementary transistors for the exponential voltage to current converter for the VCOs. When I was in college (EE) I was the Warranty Service guy for Arp and Moog in NYC. The first to do this outside of either company. I used to modify synths for all sorts of well known musicians. I met Robert Moog and spoke with him many times. His transistor ladder VCF was a stroke of genius.

 

[StanD]

  floating points make the music flow and sound smooth, but it works only with wav files.

You must be smooth operator.

 

[pinnahertz]

  Early synthesizers were analog computers and ring modulators were four quadrant multipliers. I have an ARP 2600 somewhere in my attic.

Of course they were.  But we're talking digits here aren't we?  So, the digital realization of a ring modulator.