The floating point portion has to do with variable processing. The DAW program has recorded (or imported) your audio in whatever it's source format was-either 16 bit or 24 bit. Now, while the audio is being processed in regards summing or VST plugs, the DAW may decide to process those segments at 32 bit to better handle the procedure in question. Just like 24 bit increases headroom and processing power of 24 bit, 32 bit is incrementally better than 24 bit. Why then don't we just work from A-Z with 32 bit? Because the size of the files. These files would be quite a bit larger.

Someone else will have a better explanation I'm sure.

Mathematically, 32-bit float increases the number pool available to describe the audio waveform. The more numbers, the more subtlety can be encoded in the output.

IOW, more detail in the sound, like the subtle pluck of an acoustic guitar or a quiver in a voice. Not the best examples, but sufficient here.

A single 24-bit track on it's own can sound great, but when, for example, 24 tracks are mixed together in 24 bit, some numbers may have to be "thrown out", thus omitting parts of the sound. With 32-bit float, there are more numbers and more decimal places available to counteract that. Add in plug-ins and it gets even more complicated.

Someday it will all be 256-bit float from A-Z! And "real life" will have an undo function, as well. :)

Simple explanation, anybody want to elaborate?

32 bit math in audio algorithms also creates better dynamic range something on the order of 140-150db and that's probably with truncation.
I've read that 32 bits can actually produce somewhere around 300db of dynamic range...and if the engine is using 64 bit processing that number can grow exponentially to over a 1000....of course not sure how practical that would be...that is strictly binary math being done within the CPU and software routines and then converted back to 24bit....I suppose if you had converters and amplifiers that could faithfully reproduce those kinds of ranges it might be pretty interesting...in fact it's very possible that will be the direction in the future...but the weak link and limiting factors would be the D/A conversion and then the actual amplifiers and speakers....
Dynamic range tends to be the thing that most peoples ears detect as "better" sounding....dynamic range has always been the primary factor in sound improvement over the years, most older people here will remember how different 70-80db sounded compared to 90-100db...which is almost common today...even 16bit CD players are around 90db and if you grew up listening to records or cassette's you know how astounding that changed things!
Doing digital math in 32bit FLOP just gives you way more precision than 24...the permutations of 24 bits is 16777216 and 16 bit is 65536 and 32 is 8 bits longer than 24 so the math there is well beyond what is needed or can be used...technologically were at the mercy of the analog converter chip guys to come up with faster more precise converters...when that moves to the next level of cheap viable processes...the current 110-115db should move up a notch!

Excellent thread!

I so remember Vinyl, 8 track, Cassette, CD, DAT, Beta and to date ... All those stages have been incredible level improvements and you are right, a big part of how I have measured gear in the past has been by the SNR specs.

Do you all have a 32-bit floating point option with your DAW and do you have it active?

I see school is back in session. This is why I love this site so much. Always something new to learn.

Most modern DAW's are already floating 32bit whether they tell you that or not. Maybe some of the LE versions or other restricted versions are not but I would be surprised any full featured DAW was NOT 32 bit float or even the option (Audition does) of working completely in 32 bit.

Oh, and expect floating 64 bit in the not distant future.

TheJackAttack, post: 355182 wrote: Oh, and expect floating 64 bit in the not distant future.

Sonar Producer 8.5 already has 64 bit float as an option.

I'm still using Cubase 4.5.2 set at 24bit in the project setup with my meager WinXP AMD FX-60 and the RME FF800 at 44.1 sample rate and to me that sounds pretty amazing to my old ears...I did try a test of piano recorded at 192khz with the 32bit selected in Cubase. Of course listening to that back through the headphone output of the RME with ATH-M50's....it was better....very open and airy, but it was a very subtle difference to me....that was the only test I've done.....to me it was the two extremes to see if there was a discernible difference.
I usually listen to MP3's these days with WMP which sounds as good as CD (well maybe not quite as good as my Pioneer) but pretty darn good...I tend to compare sound quality to music I know very well with all the little ambiance and nuances etc...so these days that's how I judge my electronics and setup...and I tend to pick up the headphones a lot.
I think we all strive to get better and better sound from the electronics which is where it's at....always....I'm still able to hear a difference today and then I'm happy with that new quality....the next time the electronics changes something in audio I hope I can (will) still be able to hear that improvement....BTW to all you younger children of sound out there....always protect your hearing...I always did over the years but still had a couple serious level blasts to my eardrums....so always think before your ears start ringing...or if you find yourself screaming to be heard in a concert or club...that's a sign.....always plug your ears and always be careful with your controls.....

I had heard that 1 bit recording was actually the next big thing. At extremely high sample rates, it's supposed to be able to capture up to 100KHz. Or something like that. Must be massive files? How exactly it works is a mystery to me.

apstrong:
The 1 bit is basically this: The digital "wave" starts at zero. A 1 determines if the wave should go up, and a 0 means it should go down. So, 100,000 times per second it's either going up from the previous value or down from it. So it isn't 1 bit as in quantization like we are used too, it's a totally "new" way of using bits; it is driving an analog-like output section. It's reminiscent of SACD.

audiokid:
I'm using Cubase LE 4.something, and a PreSonus Firepod. The 'pod does 96K@24bit, but Cubase does 32bit float internally for mixing/FX. I render mixdowns at 96Khz@32bit-float and master that file in Wavelab 6.

Leaving 1-bit DSD aside for the moment (since we have covered it in previous threads), many of these posts are confusing 32-bit fixed point with 32-bit floating-point.

With 32-bit fixed point you can sum 256 24-bit fixed point numbers and not lose accuracy or risk overflow.

With 32-bit floating-point, you still have only 24 bits of precision (the mantissa), but the remaining 8 bits form an exponent that says where the 24 bits sit in the whole representable range. This is fine until you start to sum floating-point values that have different exponents. One of the two operands has to be shifted until its exponent matches the other, and then 24-bit summation can happen. It means that for every operation, precision is irretrievably lost by the bits being shifted out.

Many high-quality digital mixing desks use 32,40 or 48 bit fixed point arithmetic, as the summation process is always accurate. Least significant bits may be discarded in the sum signal when converting and rounding back to 24-bits for output.

The higher-quality DAW packages use either 64-bit fixed point or 64-bit floating point to minimize the effects due to data loss when summing channels. 64-bit (double precision) floating point uses 53 bits in the mantissa.

ah...

So the next question is, why do they give us the option to activate it or not? when would you say... ah, time to select 32-bit floating point?

In Sequoia 11 it says this:

An outstanding strength of Samplitude and Sequoia the absolute sound neutrality featured. Highly developed digital algorithms, absolute phase stability, and continuous application of floating point calculations ensure that the sound maintains its special nuances during even the most intense digital processing. This results in transparency, neutrality, maintenance of transients, and space. Different audio formats from 16-bit to 32-bit floating point and sample rates up to 384 kHz are possible in the same arrangement.

Ah, found this from Benjamin Maas.

The 32 bit float option is pretty much a legacy setting from the days before they could record a 24 bit fixed file. Use 32 bit float only if you are going to be doing destructive effects and saving the settings. Otherwise, use 24 bits.

So there are debates whether to use it or not in a mix down or final project to 32bit float for mastering and/or with vst plugins?

And then whether the AD DA can actually deal with this anyway.

I'm thinking, when in doubt, stay at 24 bit .

audiokid, post: 355207 wrote: ah...

So the next question is, why do they give us the option to activate it or not? when would you say... ah, time to select 32-bit floating point?

It all depends on the DAW and your computer. Under all conditions, 64-bit representation of data takes twice the space of 32-bit representation, so you either need more addressable memory, or you put up with fitting less data at a time in the memory you have. Arithmetic on 64-bit data takes longer to compute than 32-bit, although usually not twice the time in a 64-bit program environment. However, if you are running a 32-bit version of the DAW, using 64-bit data can take more than twice the time, as the double data fetch and store times become the dominant part of the time to operate on the data.

If you are running a 32-bit DAW under either a 32-bit or 64-bit operating environment, it's probably not worth selecting 64-bit data representation for a particular job, unless you have only a few tracks with huge dynamic range. In a genuine 64-bit OS and DAW environment, there is no point in selecting 32-bit data representation unless you are really short of memory (in which case, fit some more).

Regarding Sequoia, Magix are particularly coy about whether the version that runs under a 64-bit OS is a 32-bit or 64-bit build. They spec it as needing twice the amount of installed memory when running under Vista64, and that might indicate that it is a 64-bit build, but I have my doubts. They may be simply indicating that the 64-bit OS consumes so much memory that there is little left for user programs.

Bos, I wish you lived next door to me:) but this is definitely the next best thing isn't it!

32 bit floats & beyond

Hey ya'll, great info....I am a firm believer in using 32 bit float 1st-ly, as a 1TB HDD is (higher end) about $120-150 so drive space shouldn't an issue. I'm using Cubase 5.5 & even "True Tape" 32 bit feature in VST 5.0, was created with good reasons according to Steinberg's Mr Warner... & as I use Cubase 5.5 now, I still always select 32. The headroom gained in audio will be captured for all-time & may have even greater advantages, as ad/da units go in that direction. Despite obvious comparison issues....the taking more density of frames per second on film, is pretty much self-evident example of why it's the best choice.

Yes, we have to re-convert back to 24 bit & once it's captured, 32 bit is still a good choice, whether or not new standards will bring sound converter ad/da's to better use this extra "frames". I'm not a math expert by far but an increase in bit rates from 12 to 16 were hailed as revolutionary; the move forward is ongoing & once you've recorded at 16 or 24, you stuck with this into the future, should you wish to re-work a track with higher bit hardware. 64 bit is already here, & elsewhere on it's way....

My Delta 1010, employs a 36 bit float...though it's 24/96. I will bet, in 2 years, this debate will be over. I'm more than happy to hear what the math experts have to say about extra headroom, but it is recommended by some of the best mix & mastering engineers. Trevor Horn's advice & MO is good enough for moi!

This is a truly great forum....thx to those who greater understand algorithms, though in the end, it's my ears I listen to....awesome explanations pro & con...

Ditto....audiokid...

Hi Boss...1 thing...isn't my quadcore i7 CPU, MSi P55-GD65 mb Superpipe w/OC Genie, Asus GeForce 9400gt graphix & ripjaw RAM a consideration in being able to deal with saving power to handle this slowdown in 64 bit usage? Not newbie but eager to know more...

Maybe I mistook the thrust of this thread and people are actually arguing about 16/24/32 bit representation of audio data and not whether they should choose between 32-bit and 64-bit floating-point for their DAW operations. All computers are capable of processing 64-bit FP, whether as native instructions or as low-level written-out 32-bit procedures, but there will be a wide spread of times needed to perform frequent operations such as 64-bit add, normalize and multiply. Even with a genuine 64-bit computer (as studioshaman has), 32-bit DAW builds may not make use of native 64-bit arithmetic processing.

As the wordlength of (fixed-point) audio samples is increased from 12-bit through 16, 20 and 24, it becomes increasingly difficult to hear differences above 20 bits, but with good conversion hardware and good listening conditions, 24 bits is about as far as one needs to go for audio samples. That implies that the mixes that make up those 24 bits should all be better than that level if the mechanics of the mix are not to intrude in the final result. It is with that in mind that I said in a previous post that 32-bit FP is not the ultimate, as the mantissa is only 24/25 bits, and that can get shifted to a lower representation during summation. For the point of view of summing, 32-bit fixed point is better than 32-bit floating point, since samples are not truncated prior to being summed. In audio, the range of the numbers is relatively restricted compared with the overall range that FP can represent, so much of the exponent range is unused.

Those of you who have had the experience of live studio (analog) sound in comparison with various digital representaions of it may well have formed an opinion that there is little audible difference between the direct analog sound and digital, but only once you get to 96KHz 24-bit digital, with the digital being either direct-to-digital (with analog mixing) or via 32+ bits of integer or 64-bit FP digital mixing. These mixes can sound better than 32-bit FP mixes, irrespective of sampling rate. Some of the best (16-bit) CDs I have heard have been recorded direct-to-disc via an analog mixer and then two-track 44.1KHz/24-bit digitization with careful rounding to 16-bit. In many cases, I prefer the sound of these to the 24-bit analog conversion of 32-bit FP digital mixes that are so prevalent from today's studios.

One thing that has not yet been pointed out is that modern processors (since the 486!) all have an integrated floating point processor which, even with 32 bit processors have double precision capability (i.e. they can do 64 bit floats). Many years ago Pro tools led the field by using fixed point 48 bit processing, however this is not only slower (as fixed point routines have to be programmed and use CPU power) than floating point calculations which are offloaded to the floating point coprocessor.

This means that it is now more efficient to create code using either 32 or 64 bit floating point maths rather than custom fixed point routines. The actual resolution of 32 floating point is 25 bits although the mantissa is only 24 bit. This is due to the nature of how floating point operations are defined. Hence we have 150 dB dynamic range with 32 bit floats as opposed to 144 dB with 24 bit integers (which is what we get nowadays from our soundcards). As Boswell pointed out, this is far more than the 96 dB of the 16 bit CD format and usually we will be introducing noise above this level when we dither down to 16 bit.

So why does anybody bother with 64 bit floats with absolutely enormous dynamic range? Well the argument is that we do some very complex mixes and at every calculation there will be rounding errors. After several calculations, these errors build up (surprisingly quickly) and will certainly affect 24 bit output files as used with DVD's.

With 64 bit floats, such errors are way below what could ever be significant to even 24 bit mix outputs. All this effectively for nothing with 64 bit CPU's. If the errors can be reduced to absolute insignificance without cost, then why not! Note that this does not affect recorded file sizes on your hard disks as these will still be saved as 24 bit integers. Of course if you wish you can export your mix as 64 bit floats for subsequent processing with different software (say for mastering) and these will naturally be larger files but you only need a few files, one for each stem.

In the end, the choice is yours. Use what you feel happy with!

This thread appears to be initially & primarily of the thrust you implied, Bos...but indeed, in humility, I was speaking in a practical sense what DAW res is a benefit or not to use, so yes an under tow of comment of 16/24/32 res choices, (if just to provoke how much I don't know). You’ve helped me understand/explore with excellent overview, the theory of sampling & system bit conversion & such….I’m just learning the math, so thx for bearing with me. The comments on this thread blow my mind & sparked great interest in understanding the fundimentals....thx again.

I believe that recording in 32 bit preserves options for all time without a negative. Error rate correction has come up, with the full use of highest rates re: 64 bit's time to re-calculate, yet I stick to there’s no down side, the (my) hardware can perform this without loss of notable efficiency .…but there are upsides. Also, advances in pro gear & delivery to *consumers may spur new thought on the 24 bit best question…(ya, many of *whom are fine with MP3!).

I was producing a mastering session, with a very very good engineer, & when asked he said, their simply wasn't a need to use 32 bit res. at recording even with it's known advantage of headroom, exactly as you state: it's going back to 24 bit then 16. Then I saw him fudge a bit....or 8.

As side point: I worked on DVD production liners & saw Blu-ray plastic polymers being developed (received a used liner from GE Polymers if I recall right, with all these dark sprues stuck in crannies as we set it up-circa 2000).... Blu-ray made multi-layer DVD dead in the water...from "our" view (both in production & usage) & changed what was able to be delivered with both audio & video... This of course says little about bit rates & conversions but lots about what's next. It changes the ability of delivery to the consumer, whether or not they all can appreciate it. In turn makes new industry standards & studio protocols as with 5.1 to 7.1.

It was a much clearer set of questions about sound & ears, when tape was still totally superior, outside digital "conveniences" ( & cost per getting decent studio/sound result for the smaller ops/$'s). Of course it's not in MP3's, ear buds or prosumer conditions that these finer details make their mark, it's in a theatre/home theatre & studio of now to the future. I never know, what I've scored for movie licensing that may benefit from these decisions down the road, be they however small. Also meaning that people (some I know) have utterly lavish pro systems for their entertainment that includes acoustically correct room & pro gear that rivals many bigger studios!. I've slid way off topic...My Bad!

Coming from a session player's background, when Studer & Otari ruled, to various my home studios, & have seen & heard each rung up the ladder. Also, I have CD's made on twin Otari's then sent to be mastered in 16 bit; the older ones sound so cold compared to the last 10 years...Tech debates aside… I've come to the point that if it's there, use it. I suppose even as analog was pried out of some die hards ears, digital technologies grew & became, well, at least equivalent, we're are now just reaching the point where DSP & VST is starting to replace the warmth they knew wasn't present early on...we loved from analog. I will love & likely use my Urei & Focusrite’s for years, no doubt...Please excuse my massive liberty to stray wildly...Thx to you experts, for you bright light helping me understand digital audio...

Hi Mr E....Thx for your comments...I'm on a deliberately sharp learning curve by joining this forum, building a better understanding of the math of of this topic: combining factors so I can optimize my system's configurations thru full understanding of the math...I'm under few (lol) illusions of the great level of sampling & system rap here, is where I'm at....I just don't want to disrupt it. It's helped me focus my study & my appreciation is huge, as I know my help to others on other forums where I can help someone with Nuendo/Cubase 5, Delta 1010 operational questions; the quirky things that I am solidly grounded in. So, know that I know, I'm dealing with some well versed experts on the math & considerations for DAW system optimization. Thx much....SS

Welcome to recording.org,

Once you get this sorted, take a hit of this:
http://recording.org/showthread.php?45012-What-is-clock-jitter

Thx much Boswell...I really appreciate being able to post & receive such great info & commentary...I'm on a steep curve, but am on my way to understanding the math of sampling & better system config's...Hope I'm not dumbing down the discussion...This is my weak spot...thx for taking an interest...u r already a great help....thx much SS

Shaman,

As you are just learning all this, it is worthwhile to put some real world figures with all the theory. With Human hearing we have defined a threshold of hearing which is statistically the quitest sound that humans can detect. This is referred to a 0 dBSPL (Sound Pressure Level). Most adults have a slightly worse threshold of hearing. We also have something defined as the threshold of pain, this is somewhat more variable and taking the average is somewhere around +130 dBSPL (results vary from +120 to +140 dBSPL). What this means is that the maximum dynamic range anyone can perceive is around 140 dB. What it does not mean is that when you are standing by a Saturn V rocket taking off at the Kennedy space centre you will be able to hear some very nervous wildlife twitching about at the same time!

24 bit converters offer up to 144 dB dynamic range so there is absolutely no point in having more bits as we could never hear the difference. Sadly, due to the laws of nature (electronic noise) we cannot hope to realise the full capability of 24 bits anyway (unless we start running our converters at very low impedance and near absolute zero!), so we get an effective range from current state of the art converters in the order of 120 dB (unweighted). Thus when recording there is absolutely no point in going to 32 bit unless it gives some advantage in processing speed which is very unlikely.

Also it is important to realise that even the best soundproofed studios are unlikely to get the background noise below +20 dBSPL and we are unlikely to have studio levels that will cause pain (thus losing another 30 -40 dB of possible dynamic range), so the current crop of top notch converters are not going to be contributing any significant noise to our recordings anyway. The bottom line is that current technology is matching the performance of our environment and perception of audio such that further improvement is unlikely to offer any perceivable sonic benefit. Recording 32 bit files will offer no more meaningful data than 24 bit files.

Of course it is a different question with all the maths involved in mixing and maintaining that accuracy - which I have already alluded to in this thread.

Hope that all helps!

To re-interate the point made above: don't bother recording files with any more than 24 bits, as they will just end up larger than they needed to be.

When you render your mix you should also use 24 bits IMO: a 32 bit float file will only be better if your audio exceeds 0dBFS, so just mix with a sensible amount of headroom instead.

As mentioned above: there are theoretical reasons why summing mulitple tracks should be done with extra resolution. I'm not convinced I have ever been able to hear any real difference, but I turn it on anyway if given the option. :biggrin:

However, there is one area where the extra resolution really is critical, and I'm not sure that has been mentioned yet: most digital filters use Infinite Impulse Response algorithms (IIRs :wink:) which is another way of saying that they have internal feedback loops. You only need very tiny errors in these feedback loops to create large errors in the resulting sound: some filters won't even work at all if the resolution is too low, as the errors become large enough to make the filter unstable.

To put all that another way, an equaliser plug (of the non-linear phase variety) that uses 64bit resolution internally is likely to significantly out-perform an equivalent plug using 32 bit floats. And IIR based filters will crop up in other places as well, such as the gain smoothing in compressor plugs for example

To sum up the summary:
1. Record 24 bit audio
2. Mix with plugs that use 64 bit internal processing if possible
3. If your DAW offers a choice, turn on 64 bit mixing. Otherwise don't worry about it.
4. Render 24 bit mixes with plenty of headroom for the ME to work with