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Wouldn't the same kind of resolution limits also apply to an acoustic mechanical system like a piano?

You're leaving out all the levels between them, which are also notated in classical music, i.e. crescendos.

- MIDI has 128 velocities
- MIDI XP has 1024 velocities. This is the format used by the Disklavier
- Hi-Res/CC88 MIDI has 16.384 velocities

As DazedAndConfused stated, these quantized velocity values are used when sending or receiving MIDI data. The actual
velocity values measured by the sensors and then sent to and used by the sound engine may use the same resolution as MIDI or may use a higher resolution.

For example, the Casio PX-560 (and other PX models) support Hi-Res MIDI and that wider velocity range can be used with PianoTeq, which also supports Hi-Res MIDI (the effects are not noticeable, IMO). Anyway, this means that these DPs have sensors that are able to read more than 128 velocity values. Which is not surprising at all because DPs calculate the velocity of a key by measuring the time difference between the activation of its two or three sensors. So, the measured velocity is probably a high resolution value (e.g. 16 bits). One question is whether the sound engine makes use of that high resolution value or quantizes it first. The other question is if it is possible to hear the differences..

But that is not the point of this thread. The OP specifically states that a person can achieve 10 dynamic levels on an acoustic piano. It is to that statement I am responding.

If you have read this thread carefully, you will also note that I explicitly state that the number of dynamic levels on an acoustic piano is, in theory, infinite. I use thousands of them every day, but I don’t tell people that I am doing it. Nor am I even aware that I am soing it. I make music. I let people listen for themselves. Chances are they will hear 4 or 5 different levels averaged from the 1000s I use.

Remember, between any two values in the analogue domain (not quantum), there are an infinite number of intermediate values, and between each of those values, and infinite number of intermediate values, ...

Also, OT, there are different size infinities,

Aleph Null - the infinity of countable numbers

Aleph One - the infinity of uncountable numbers.

Don’t get me started.

Actually, you and I are both wrong.

By definition, a level is ‘level’, that is, a specific, finite length time quantifiable value.

By definition, a crescendo or decrescendo is not level. It is constantly changing and can be measured only through a differential calculus as an instantaneous value. Therefore, a crescendo is not a level.

But each individual note in a crescendo (say, between f and ff) is at some fixed strike level. So that crescendo include strikes at f, ff, and a variety of other levels in between.

For the purposes of this discussion, you are correct. (In reality, this is not the case. A struck note on the piano never, ever maintains an amplitude level.)

I suppose we could assign levels to a two octave scale that is marked with a crescendo. In that case, we clearly have 25 distinct levels which will likely be incrementally larger as the run progresses. If we perform a crescendo on a scale from C1 to C8, we would have 85 distinct levels. I think that knocks the OP’s claim of only 10 levels out of the ballpark.

Cheers.

My understanding is that [pp, p, mp, mf, f, ff] are relative musical values. They are not tied to the absolute physical velocity/volume levels of the keys.

For example, if a piano's keys have 1000 velocity/volume levels, then I might play a smokey blues in the range of around 200-500 or to put some punch into a toccata or gigue, I might play in the range of around 400-700. I may also change the velocity/volume range depending on the room/audience; using a lower range for an intimate setting or a higher range for a large crowded hall.

But within each those absolute ranges, I can musically use the values of [pp, p, mp, mf, f, ff]. And it's the combination of velocity/volume level plus [pp, p, mp, mf, f, ff] that contributes to my Interpretation of the score.

I'm not 100% sure of what I'm saying here---I'm paraphrasing from another conversation I had on another thread, so bear with me. From what I remember, on digital pianos that are sampled, there maybe a limited number of velocity levels e.g., on the Korg Grandstage, the number is 10 (in the diagram, the example keyboard has 4). However, it seems that modern sampling software interpolates so that different velocities available when playing a note are mapped within a velocity level (e.g., 4 in the below eg). This in practice means that there are many more volume levels available than velocity levels. When playing a VST via midi, there are 127 volume levels (128 if you count silent) mapped across how ever many discrete velocity levels there are (in the eg below, 4). If a hardware digital piano like the Kawai ES8 had a lot more than 127 volume levels for it's on board sounds, then those volume levels would be mapped across however many velocity levels the instrument has. Someone will probably correct me if I'm wrong, hopefully.

Velocity levels are the same thing as volume levels - or rather, 128 velocity levels (the input) correspond to 128 levels of output volume.

The block levels (4 in your diagram) are different samples (per note). They might be better referred to as 'sample levels' than velocity levels, since, as far as I know, there are always at least 128 velocity levels. Newer VST s typically have a lot of samples per note (often called velocity levels). Around 18 seems fairly common. But good dynamic effects can be achieved with far fewer samples, using DSP to alter the tone across the note's dynamic range.

Yes, sort of what I imagined (discrete samples for each volume level); however, am I right to say that the term 'velocity level' refers to the mapping of discrete volume levels in the diagram to a range of key velocities; such that, if the velocity of a keystroke is between a and b, then X volume level is triggered. However, as I understand it---or putting it thusly---the transition between discrete volume levels is smoothed out somehow by the sampling software (seamless layer interpolation), such that in practice, there is no sudden discrete change of volume. Am I understanding this correctly?

The sampled VSTs I've read about do use about 18 levels. I think there are some with 20 or more. Seems to be a factor that is creeping up with each year.

You don't trigger volume levels, you trigger samples. So if the velocity of a keystroke is between a and b, then sample X is triggered, at a volume level determined by the velocity.


No... the technique you're describing is not smoothing transitions between volume levels, rather it's smoothing transitions between samples. The audible result is a smoothing of the difference in tone (not volume) of lower velocity strikes vs. higher velocity strikes. It is typically called crossfading, you can think of it as one sample is "fading out" in its usage as velocity increases, while another is fading in. It is not an attribute of all sampled pianos... many (most, I think, at least among hardware DPs) simply play different samples at the different velocities, without crossfading, but this is a technique that is sometimes used.


There would never be a sudden discrete change of volume, even if there were only a single sample used for the entire velocity range (and there have been pianos designed that way). Again, the number of samples affects tone, not volume (remember that real pianos change, not just in volume, but also in tone as you strike their keys with different amounts of force). If a DP plays the same sample at all velocity levels, you would say its samples have a single velocity layer. If it chooses from 4 different samples on a key depending on how hard you hit the key, you would say it has four velocity layers. Either way, there is no difference in the ability to generate different volumes at soft and hard velocities. What's changing is the amount/character of tonal variation between strikes of different velocities.

Mortensen's 10 levels is fine within the context of what he is saying and his series of videos. The whole point of that particular one was to point out to starters that

a) hammer speed is the sole control over tone and the idea that certain ways of playing the key can produce different sounds is rubbish - those ways can help make getting different speeds easier and more natural but they are a means, not the end.

b) realistically, most people won't be able to play, to order, at more than around 10 'areas' of volume. Obviously when crescendoing/diminuendoing the transition is fairly smooth and hits many different levels but as an intentional 'zone' of volume to play in, particularly for a series of notes rather than an individual one were you have a little more control/force to spare for super loud or super soft, 10 is pretty good going and this is largely reflected in the way that notation tends to specify a maximum of 8 broad levels (10 if you go for the 4x pppp/ffff that some of the romantic composers brought out)

Now context is important here. That does not mean the piano is only capable of 10 levels, or that, on a note to note basis you will only play at 10, it's just trying to get people to understand the fundamental limitation of the control we have on a piano.

Similarly, one cannot take that 10 and use it to say '10 will do' for digitals, it will not, a digital piano only capable of 10 volumes will sound unnaturally 'flat' and 'lifeless' and probably also sound weird should you end up playing on the boundary between two volume levels when notes fall either side. Crescendos etc will also sound distinctly weird.

Regarding what is sufficient for a digital piano, the 128 for midi certainly seems sufficient, even a very good player trying to play at a consistent level will show plus or minus a few from note to note and the human ear would struggle to pick out the difference of one as well.

Also the vast majority of current digital piano engines will either blend or otherwise recreate a smooth change in tone as volume changes rather than using distinct velocity layers that only change in volume within them.

Thankyou very much for that clarification---the way you explained it, I think I've got a better idea now:

So checking, what you're saying is that for any velocity layer, the volume level is determined by the velocity of the key strike. Each velocity layer (which is a sample of an acoustic triggered at that key stroke velocity) there is a different tone, so with varying velocity of a key stroke, a different tone is played as well as a different volume. Also, to prevent big tone differences between notes played at quite similar velocities---which just happens to map to the boundary of two velocity layers---the total output of that note becomes a mixture of two velocity layers (samples) played at different volumes depending. Am I close to understanding?

Kind regards,

Doug.

Yup. Though again, that "mixture of two velocity layers (samples) played at different volumes" is not something every DP does, often they just do a hard switch. And for those that do some kind of "smoothing" at transition points, there's more than one way to do it. But your basic understanding is right.

Ah so only some DPs (perhaps meaning the more expensive models in a range) use cross fading; but also, some manufacturers achieve the result using a different method.

Thanks again for the explanation!

Yes. That is the idea! DPs have a fixed number of velocity layers, each with a number of samples. Ideally there should be a minimum of 88 samples per velocity layer, one for each note. There can be more samples per note on the same velocity layer, e.g. with/without una corda, with/without sustain pedal, with different mic positions, etc. But some DPs actually do not sample each of the 88 notes. Instead, they store just a few samples and then "stretch" them to change the frequency and produce the missing notes. This is why some DPs state in the specs things like "Full 88 Key Sampling".

Most sample-based DPs and VSTs have less than 127 velocity layers. So, they may need to "mix" several layers in order to artificially produce a velocity level that was not sampled. To do this, the DP/VST will fetch the layers with the samples that best match the velocity that was played. Then the DP mixes these samples together to produce a new (i.e. not sampled) sound wave with a timbre/tone that is a function of the original samples according to an acoustic model. Finally, the overall volume of the mix is normalized to fit the 1-127 velocity level. If this process is done properly, then the sound should seem continuous across the whole velocity range, without sudden "jumps" in timbre/tone and volume. In this sense, a sampled-based DP/VST is also model-based because it is synthesizing sounds that were not sampled. Note that this model.based sound-synthesis is different than the "models" used for resonance and other effects. Also note that many DPs do not do this "mixing" properly and some do not mix the layers at all and do have sudden "jumps" between the layers..

That's why I said "strike" level. After the strike, of course, each note decays.


Not most. All. The most I've seen is about 18.


There's a lot of stuff in there that is kinda right, kinda wrong. Without getting into every bit of it, I'll just say, again, the purpose of providing samples of different velocities is not to produce different volumes (you can get the full range of volume out of a single sample), but to provide the different tonal characteristics you get on a real piano at different volumes. Most hardware based pianos (digital pianos or other keyboards that have piano sounds) have used "hard" transitions, some use some kind of smoothing/crossfading (I don't know how common the different methods are in VSTs). When "mixing" of layers is done, it would be a mixing of two (adjacent) layers, not a mixing of "several." A mix of two waves is not modeling, but modeling approaches can also be used to generate non-sampled tones (e.g. Roland SuperNatural).

There are some virtual pianos with more than 18 layers : 26 on Bechstein Digital Grand, 32 on Keyspace, 100 (yes, 100) on VSL Vienna Imperial.

I don’t think blending samples from two layers is common. I haven’t seen blending on Kontakt piano : the full software can edit each Kontakt based pianos (excepted scripts which are password protected). I don’t remember to gave seen 2 samples in the same layers to permit such a blend. The issue with Bechstein sampled by EWQL shows that there is a gap between two layers. I don’t think layers ate blended there.

Good to know!


I think it is the exception rather than rule, But that's one of the things the DPBSD evals tried to suss out.