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We can't eliminate ALL the MIDI values within the noise component (my original quoted statement above), only those below a level we consider has negligible effects on the player noise and subsequently on the loudness/timbre.


That's what our MIDI keyboard already does. It samples/digitizes the human velocity which includes whatever human noise there is. So I'm not quite sure what else you are saying there? Can you clarify?


I'm not sure about using dithering in this manner. When we dither audio or video signals we dither frequencies below the Nyquist sampling rate, but here we are taking discrete samples of singular events (once for each key press or note). For instance, in the limit, when we play a single note we can dither the resulting audio sound over 1000's of samples during the second or so that sound is produced from the single key hit. But we can only apply dither to a single MIDI velocity value for that key hit, which accomplishes nothing but introducing a singular error in that particular MIDI velocity. I'm not sure adding dither noise to a succession of "widely-time-spaced" key hit values does anything more than increase the amplitude of the player noise, which isn't an positive effect. Can you expand on what your thinking is for this case?

@Macy:
Let's assume that after careful testing, it is determined that humans can only reliably strike a key at about 16 different velocities. If we ask them to strike with any more precision than that (say, 32 velocities), we find that they're just as likely to strike at velocity value 1 as they are velocity value 2. They will always strike 1 or 2, but they can't strike either of those two velocities with statistical significance. Same goes for 16 & 17, etc etc. Given this, we decide to quantise the velocity to 4 bits, to make our design as efficient as possible.

So, we now feed this 16 step MIDI signal to our nice Disklavier piano, and see how it sounds. We may find that certain tone shades which were sometimes invoked by the player before are simply NEVER produced, and this IS noticable. The player can't produce these tone shades on demand, but they notice that now, they can NEVER produce them, and it bothers them.

To solve this problem, I'm asserting that it is entirely valid to superimpose a random signal (with an amplitude of +/- half a step), so that the player is once again able to produce those intermediate tonal shades, in a random fashion, because they were only ever able to produce them in a random fashion to begin with. The required resolution of this new velocity signal will depend on the characteristics of the instrument. This process of adding random noise is called dithering.

The brute force approach, though, is of course simply to increase the sampling resolution, so that the human noise is in fact sampled as well. (and the required resolution again depends on the characteristics of the instrument)

Greg.
p.s I realise that a 4-bit MIDI velocity can in fact only represent 15 velocities, because velocity 0 (zero) cannot be used - 0 means the same as a Note Off. (and this is why a 7-bit velocity has 127 values rather than 128).

This will tell you only about the listener's experience. It will say nothing about how a performer is affected by the change in quantization. If a performer feels that a piano is somehow not performing as s/he wishes, it will disturb their equilibrium and make it very difficult for them to perform at their best. This is a far more important aspect to this question than the playing back of MIDI files. This is why I said that this argument misses the point. It's not about sound, it's about playability.

Greg,

Thanks for the further explanation. That isn't what we normally think of as dithering and not what I thought you were describing earlier.

What you are describing here is a case where the MIDI quantization would be more coarse (fewer bits) than the the internal sound generator quantization. i.e. in your example the MIDI interface has 4-bits, while the internal samples or other sound generator mechanism might have 7-bits. So by adding random noise to the MIDI velocity values we randomly excite the additional available sound generator bits. I got it now, but that's not usually how dithering is used, which is why I wasn't sure what you were describing earlier.

Dithering is normally used in audio and video when reducing the bit-depth of signals. In other words, instead of having more bits available for the output (as in your example) we have fewer bits in the output than in the input. To avoid the coarseness (and correlation) of the output quantization error (which leads to "harsh" forms of distortion), dither adds noise but makes the output average out to a higher resolution result than the quantization error would otherwise allow. To put it another way, dither allows us to represent an input value with more resolution than the available output bits would normally allow by averaging the output, at the expense of added random noise. Conversely, in your case, a lower resolution number is being randomly converted to a larger set of output values, not to make the output more accurate, but to make it more "interesting". (Of course that means the "feedback" to the player is less accurate as well, but I will leave that for you to debate with voxpops.)

I'm trying to understand why you think you need more MIDI steps for playability.

Please correct me but what I think you are saying is:

1) The player plays a note (or perhaps has played a succession of notes) and has received audio feedback (and maybe tactile feedback) from the note(s) he just played.

2) The player processes the feedback (somehow - consciously or subconsciously) and as a result of that feedback produces some velocity for the next note he plays based on the previous feedback.

3) The 127 MIDI steps are too coarse to allow the player to produce a velocity that results in the sound output he wants to produce in step (2). The errors between the sound output the player wanted to produce in step (2) and the sound output actually produced will "disturb their equilibrium and make it very difficult for them to perform at their best". Therefore, the 127 MIDI steps creates a playability problem.

Is that your reasoning for why 127 MIDI steps creates playability problems?

Macy, this idea has been explained ad nauseum by myself and Vox. It's actually very straightforward. This will affect more skilled players (aurally and technically) than the less skilled because the skilled are much more attuned to the input/output balance. If a person is not a skilled player, they would have no real feeling for how this problem manifests and probably doubt its existence as a result.

@Macy:
Thanks! I agree and understand. The process I described is not dithering.

In our case, the human velocity signal is already "dithered" naturally, because of the naturally occurring human noise. So, taking my example, simply quantising the velocity to 15 (16-1) steps is good enough - we don't need to add noise to the velocity signal before we sample it (@4-bits), because we do that naturally.

If the musical instrument we are playing can make audible (interesting/desirable) differences with a step size that is less than our 15 step MIDI velocity, I'm suggesting that simply superimposing a random signal will produce a result that will be indistinguishable to the player and listener. We are synthesizing the non deterministic component of the human velocity.

Perhaps the process I am describing is simply humanization



I don't agree with this. The feedback will be just as accurate, because we have sampled the person's desired velocity with sufficient precision. The random part has been added back in, and no-one is any wiser.

Greg.

OK. So did I describe your reasoning right or wrong?

That's a very good summary of what I'm saying. With my very mediocre playing ability, I'm able to detect a difference in the way a real acoustic responds to the way a digital does. I can play a (well-maintained) grand with a higher degree of sensitivity than a digital. It's certainly something that I notice less with my FP-7F than with other digitals, so it probably has to do with more than just MIDI velocity steps, but it's still there nonetheless.

Now amplify my skill level to that of a concert pianist of world-class stature (I wish!), at the peak of their performing career. Because their whole system is attuned to the way their instrument responds - their livelihood depends on it - they can detect the most subtle changes in tuning and response, and they are notoriously picky. So far, as far as I know, none has chosen a digital to take on stage with them. What is the reason for that? My conjecture - and it is only conjecture - is that the digital instrument cannot respond sufficiently well to meet their needs. I don't say that it's just velocity resolution - in fact it's more likely to be timbre with sampled pianos - but I really think it's time for a leap forward with all aspects of digitals, and that includes refining the whole system, and making full use of today's computing power. The V-Piano is much more responsive than the average sampled device, and that must be down to the fact that the timbre changes across the whole spectrum of available velocity levels. I believe that it makes use of more than 127 internally, but I cannot be sure, and I may be wrong. Either way, even the mighty V is only seen in the hands of concert pianists paid to endorse this product.

My proposition is this: don't hold back any aspect of DP development in the belief that it's currently good enough. While we may or may not ever see digitals being used for Chopin and Rachmaninoff in Carnegie Hall, it would be a wonderful testament to the designers and engineers if they could be.

I suspect the difference between acoustic and digital is all to do with factors other than the number of MIDI velocities. Or what I should say is that with the current state of the art the MIDI standard is not a significant limiting factor - it's everything else. The difference between a good DP and a bad one can be absolutely night and day - but they are still both using 127 velocities.

When the other DP inadequacies have been successfully addressed, THEN a limiting factor MIGHT be the number of MIDI velocities. I think R&D resources would be better spent by addressing the more obvious DP shortcomings before an overhaul of MIDI specifications needs looking at. Just my thoughts...

+1000 to EssBrace.

I guess we have to take this a step at a time for me to understand. Blame it on me for being slow

What do you mean by "good enough". Good enough for what? You are quantizing the players analog velocity input. There is always quantizing error (noise) that also contributes to the players noise. Unless you make the quantizing noise significantly less than the human noise it adds additional error to whatever the player was trying to play. (The error is not "dithered" out, there is no averaging of multiple key presses into a single key press.)


What do you mean by "indistinguishable"? Do you mean the signal you created by adding random digital noise to the digitized velocity signal is indistinguishable from digitizing the human signal plus human noise with more MIDI resolution? If so, that isn't true even if the added digital noise is equal to the human noise. The signal you created also includes a much larger quantization error because you reduced the MIDI resolution from 7-bits to 4-bits. You may have "simulated" the human noise part but you increased the quantization noise by using less bits too.


I'm afraid not. You digitized the analog signal (with the human noise) using less resolution and therefore increased the quantization error too. Then you added your simulated human noise back in again. The result is not the same as digitizing the original analog velocity (with the human noise) using more quantization steps.

Of course the quantisation adds noise. We simply have to sample with sufficient resolution such that this noise is negligible.

Take an extreme example. Let's say a player plays a MIDI keyboard, and they're absolutely hopeless. After careful statistical analysis, we determine that his attempts at hitting any velocity result in white noise. (a random number 1 to 127) Do we need to sample this white noise in order to reproduce the same impression of that player? Of course not. We do not need to send ANY velocity information to our piano whatsoever, and instead, we can simply send a synthesized white noise signal that is created by generating a random number between 1 & 127. (at whatever resolution we think is appropriate)

If we are in fact interested in the precise detail of any given performance of this strange performer, then of course we then need to sample that white noise with whatever precision we deem necessary.

Do you at least agree with me thus far?

Greg.

By the way, does anyone around here actually own a VAX77 and PianoTeq? It sort of gets mentioned a lot as a possibility but I haven't heard anyone talking about theirs, so I'm not sure it's possible for us (meaning the people involved in this discussion...I'm really on the periphery, but I still count myself).

Ok, so we will make you a piano with twice as many MIDI steps, so that it has steps 1/2 the size as now. Then in step (2), from the feedback you received in step (1), you will have to be able to precisely produce a velocity for each note that is within 1/2 of the current 127 MIDI step size that you intend to produce for that note, else you will not get the sound from the piano that you intended to produce. Any errors between what you want to produce and what you really produce in step (2) will be more than a 1/2 step and just as coarse (or more coarse) than what you get with 127 MIDI steps. Any errors, will as described in step (3), disturb your equilibrium and you will have the same playability problems described in step (3).

So do you think you can play from note to note with that precision, consciously, subconsciously, or supernaturally? Otherwise, adding more MIDI steps won't solve that playability problem.



I think we can all tell the difference between the way an acoustic piano and a digital piano responds. I suspect I can think of a dozen better reasons than only having 127 MIDI steps.

Let's take your reasoning and apply it in the opposite direction. That would imply that the fewer the steps available the more likely I am to be able to play accurately, because I am much more likely to be able to strike at a particular velocity and therefore meet my feedback/restrike criteria. I think 10 steps should do it.

Again, that is not the way we play. It would suggest that an acoustic with an "infinite" number of steps available would be impossible to play! The feedback would overwhelm the player because they would become unable to strike anything at the desired level.

No, a player almost subconsciously molds his playing to the input he is receiving. The finer the resolution available, the better he is able to play.

Ok, well I thought that is about where we are today. I can't see reducing MIDI to 6-bits, let alone 4-bits, because I think it would add too much quantization noise. There are certainly people here that would like to increase it to 8-bits or more, which would be fine too if the virtual/digital piano designers would use the extra resolution advantageously. Right now, I see too many examples of not doing 127 levels very well. But suppose they produce some really good sound generation with 8-bit or 9-bit velocity input, then it might be interesting to see what adding some noise bits as you suggest would do with the current MIDI 127 levels.

@Macy:
I was simply giving an extreme example, to try and make my point clearer. I don't know how precise humans are at playing a keyboard and generating a velocity signal. It would require very careful testing with many different playing techniques. The feedback to the player should also be very good - perhaps much stronger than a piano - for example, allowing the player to observe the MIDI velocities displayed by a MIDI monitor. This would then cater for a wide range of instruments.

Greg.

True the fewer the steps the more likely that you could hit the steps you intend out of the available steps. The problem is that too few steps will sound awful. Try 3 steps for instance. You won't have much expression because you have so few loudness/timbre choices to play for each note. So we increase the steps to give you more choices and your playing can sound better. Do we continue to 10,000 steps just because we could? At some point, the steps get so small we can no longer control our motor skills well enough to reliably play the steps we would like to play, even assuming we can somehow (consciously or sub-consciously) process the feedback from our playing with enough resolution to intend to play in those smaller steps. We simply can't do it.

Even a machine will have some resolution and tolerance limits. Once we reach the limit of what we control we are simply creating additional randomness (noise) to our performance if we add more steps. Is that good? It might be if we are a mechanical machine that only produces 8 steps, but produces them so precisely we never get anything but those 8 steps. Adding another bit or two (16 or 32 steps) with 1 or 2 steps of noise might make the machines playing seem less mechanical.

Do humans need more steps of randomness than what we have now? We have 127 steps. How many of those can the best pianist use reliably and how many become his noise? I don't know. I've never claimed to know that answer. I just know what I can do. Mac3 postulates, I think, that just adding some more steps of velocity input noise to a higher resolution sound generator might improve a performance. I wonder how the best concert pianist would react to that? We are going to add a little randomness to the existing randomness of your playing to improve it? Not real well, I would guess.


You can't get away with that any more. I asked you how you played, and then described my understanding of your process, and you agreed it was a very good summary of what you were saying. So let's stick to that process.


It suggests no such thing. You can't process the feedback with infinite resolution. You don't blow a mental transistor because your mind or muscle memory can no longer distinguish one small change in volume or timbre from another. You simply process things to the level you are capable, and then use that feedback to drive your motor skills to the level they are capable.


No, none of us have infinite feedback sensor resolution or infinite motor skills resolution. Once you abandon that concept I think this entire subject becomes easier to analyze.

@Macy,
With respect, after having read your reply to Voxpops, I still don't think you have fully understood what I have been trying to say.

Adding the noise to the MIDI velocity is simply to restore the randomness that the quantisation has removed. For example, in your example where you have quantised the player's velocity to 10000 steps, it may be that the steps which you have thrown away that fall inbetween those 10000 steps are important. There is no way to invoke those intermediate steps any more - they have been stolen away from the instrument. The player cannot play any given one of those intermediate steps on demand, however the player may notice the complete absence of those steps.

There are two issues here:
1. How many steps does it take to sample a human's intended velocity with sufficient accuracy?
2. How many usable/interesting steps is the instrument able to reproduce?

These two issues must be treated seperately.

Greg.