I get 1 000 000 = 2^19.9 so a 20 bit dynamic range. I don't think A/D/A hardware ever gets better than about 110 dB dtnamic range though.
cheers Miller On Thu, Apr 23, 2015 at 05:20:51PM +0200, Cyrille Henry wrote: > > > Le 23/04/2015 16:41, Alexandre Torres Porres a écrit : > >Yep, nice indeed, I guess I learned - in short and in layman's undetailed > >terms - that audio output is ~24bits (a bit higher, but much higher for > >smaller numbers). > > > >Moreover, digital audio cards won't likely have more than 24 bit precision > >for many years to come, so it's just way more than enough. > The human ear is usually consider to be sensible from 0dB to 120dB, so a > range of 10^(12/2) between the smallest and biggest amplitude. > i.e from 1 to 1 000 000, or from 1 to 2^13.8 > so, the human ear sensitivity can be considered to be about 14 bits. > 16 bits diffusion should be enough. > 24 bits diffusion is already overkill. > > cheers > c > > > > >thanks > > > > > >2015-04-23 6:43 GMT-03:00 Julian Brooks <jbee...@gmail.com > ><mailto:jbee...@gmail.com>>: > > > > Nice. Thanks Chuck, I learnt something. > > > > On 22 April 2015 at 23:45, Charles Z Henry <czhe...@gmail.com > > <mailto:czhe...@gmail.com>> wrote: > > > > On Wed, Apr 22, 2015 at 5:11 PM, Alexandre Torres Porres > > <por...@gmail.com <mailto:por...@gmail.com>> wrote: > > > > > So I start with this idea that the audio (values from -1 to 1) > > can't be in > > > full 32 bit float resolution, it's less. I don't see why that is > > "wrong". > > > And then, from it, my first question here was: "what is the audio > > resolution > > > then?". I'm still clueless here about this answer. > > > > > > Moreover, is it more or less than what 24 bit audio cards handle? > > > > Let me try: > > > > 32-bit floating point numbers have 24 bits of precision. Always. > > The > > remaining 8 bits are just for the sign and exponent. When the > > amplitude of the signals decrease, you don't lose any precision in > > floating-point. The value of the least significant bit (LSB) gets > > proportionally smaller. > > > > However, the output of a 24-bit soundcard always has a fixed > > quantization. The LSB is always the same size. Smaller numbers have > > less precision. > > > > The mismatch occurs when converting from the 32-bit floats to the > > 24-bit fixed point numbers. Now, the smaller numbers aren't as > > precise anymore. They get rounded to the nearest number in the > > 24-bit > > fixed point system. > > > > So, yes, the resolution (of small numbers) in floating point > > (internal > > to Pd) is finer than the resolution of those numbers when output > > (driver/DAC). > > > > Also, the 24-bit fixed point format is for values between -1 and 1. > > That means that numbers between 0 and 1 have just 23 bits. In 32-bit > > math, the numbers between 0.5 and 1 still have 24 bits of precision > > (the sign is held elsewhere). That means that Pd's internal > > resolution is finer than the soundcard resolution for all numbers > > between -1 and 1. > > > > Chuck > > > > _______________________________________________ > > Pd-list@lists.iem.at <mailto:Pd-list@lists.iem.at> mailing list > > UNSUBSCRIBE and account-management -> > > http://lists.puredata.info/listinfo/pd-list > > > > > > > > > > > >_______________________________________________ > >Pd-list@lists.iem.at mailing list > >UNSUBSCRIBE and account-management -> > >http://lists.puredata.info/listinfo/pd-list > > > > _______________________________________________ > Pd-list@lists.iem.at mailing list > UNSUBSCRIBE and account-management -> > http://lists.puredata.info/listinfo/pd-list _______________________________________________ Pd-list@lists.iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list