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Take a look at real acoustic piano waveforms with an oscilloscope and how they vary on a real piano when different notes are struck simultaneously, it's not straightforward. In reality the variety of sympathetic vibration responses is a very large number. The waveforms that result from sympathetic vibrations are more complex than just calculating mathematical overtones between two notes. The dynamic level, or energy of each note, has an effect on the waveform modulation and piano players usually play far more than two notes at once. Each individual note and its dynamic level have an effect on the overall waveform modulation created by a group of notes. Digital piano makers may call it "string resonance" but its fake. Roland simulates resonance in an artificial way, it's more of a sound effect, it's just a sample sample gets turned on and off when you strike a note. It's a crude simulation and not the same thing as real acoustic resonance. Kawai tries to apply some math programming but it only crudely scratches the surface of the immense number of variations in waveforms that result from the dynamic vibrations of different combinations of notes.

Two observations:

My church has a grand and three uprights. My older model digital is very close to the grand and miles ahead of the best of the uprights. Granted the uprights could be improved with expensive maintenance, this is still my experience most places. I have no trouble moving back and forth to the grand, but moving from the digital to the upright or the upright to the grand takes some adjustment.

Most of the piano listening we do is on CD, through a speaker system. None of us can afford to go to live performances in a concert hall every day. We seem to think digitally recorded piano is acceptable - why not live digital?

Hi, guys,

I’m surprised that my post on technical stuff got heated replies. I’m also amazed by the knowledge of some pianists on electronics. I’m a Chinese. If there is anything offensive in my post, forgive me. That’s my poor English, not my intention.

To be frank, my PhD study has nothing to do with acoustics. My knowledge mainly comes from my wife, who works in Microsoft Research, Asia. The speech engine in Windows Vista is developed by her team. Speech is a sequence of syllables. Music is a sequence of notes. Vista synthesizes speech by concatenating previously recorded syllables, while DP concatenates notes. Following discussion is based on my knowledge of speech, which may not be correct for DP.

1. Single Note
A sound signal s(t) = A * sin(F * t + P) has 3 parameters: amplitude, frequency, and phase. As WhiteBear says, ‘human ears have limitations in terms of frequency and amplitude resolution’. By increasing the sampling frequency (44.1kHz to 192kHz) and bit-width (16 to 24, 32), the amplitude/frequency information of a sound can be accurately captured. The difficulty lies in capturing phase, which carries spatial/directional information. The problem is that MIC array is fixed, but head moves during the play. However, head moves in limited space (within 2 meters from seat, 180 degree rotation). Again, by discretizing the space into regions of different angles, I guess it can be solved. As to rintincop’s worry on dynamic richness, it can be solved by layers. If 4 layers are not enough, let's say 64, 128 layers?

2. Multiple Notes
Next, I suggest solution to rintincop’s worry on ‘hundreds of millions of combinations of notes’. Just like speech is not a sequence of random syllables, music is NOT a sequence of random notes. Here, note includes not only the pitch, but also amplitude, energy, spectrum, etc. By recording the most popular 1000 scores played over the world (enough?), we get repeated patterns of note combination. The total possible combinations are huge, but by recording the most frequently appeared 10% combinations, we may cover 70% of the combinations in the 1000 scores. If the 10% selected combinations are still huge, we can decompose note into lower-level states and study the state combinations (like decomposing molecules into basic atoms). Statistic models, model classification/clustering, etc. are powerful tools to find regularity in disorder. They’ve been successfully used in fields like speech processing and DNA analysis.
As to the 30% non-recorded combinations, how to handle the resonances? As rintincop says, striking one string causes vibrations in the other 87 strings. These vibrations further influence each other. We can measure the intensity of the 87 vibrations caused by 1 string. Altogether we get an 88 by 88 matrix to describe the correlations between any two strings. The easier two strings resonate, the higher the correlation coefficient between them. Of course we need one matrix for each layer. With these matrix, we can calculate the string interaction. After a few iterations, the calculation will converge. Similar method has been used to estimate electric signal interference between wires.

It is a pity that Bill Gates plays Xbox, not the piano. Otherwise he will introduce Moore’s law into digital instruments: in 18 months, price drops by 50% and layers (samples, functions, etc.) double.

I think we have to admit that any string resonance technology has to be a simplification of what happens on an acoustic instrument.

However, perhaps the question lays on whether that simplification is able to capture enough details so that it can not be distinguished by – let’s be ambitious – the above-average ear from the real thing.

On one side we have the number of strings able to resonate. Unless you are using the pedal, only those strings for which you are still holding the key would be able to resonate. I suppose this simplifies things a little bit.

In addition to this, we have the fact that when the string vibrates (in this case due to resonance) the amplitude of the “non-fundamental” (I just made this word up) harmonics go down very quickly as you move away from this fundamental. This means that only a few (I don’t know how many) of the harmonics will be heard and, more importantly, be able to create resonances in other strings.
If we consider that string resonance starts at a very low amplitude compared to the vibration that caused this resonance, then I think we can see that only a few of the harmonics “around” the fundamental (for each string) would be loud enough to be heard or, even less, to create further resonances.

Whether the aspects of the resonance interplay that are “relevant” to our ears can still be properly captured by current technology, I don’t know. However, I’ve always been an advocate of the “blindfolded test”: if you can’t tell the difference, then there’s no difference.
If believe that, as time goes by, more and more people are starting to have problems to really spot the differences. In many cases I’m not able to spot the DP, but then again, I’m not a good benchmark ;-)

Cheers,

I think the ear probably is way overrated: in times when many many people consume mp3s via ipod or even at home (where you can easily spot the difference between 128kbit mp3 and CD), people get so much used to artificial sound (that lacks information), the difference between real and digital piano is barely audible. Go on, make the test: on many recordings of pop music, you hear the cheap keyboards on which piano parts are played. But ask your friends not playing piano what they hear - most of won't even be able to tell the difference between keyboard and stage or real piano. So, in a nutshell, digitals are already very good!
On the other hand, a real upright or grand, that vibrates, makes mechanical noises - it is somehow like a living being. Digital simply cannot capture this. The look is different, watching the hammers hit the strings - it is sheer joy to me and you cannot transfer this to a digital piano. So - digitals can never beat real pianos - live!

Pumucky, thank you for your information. I know nothing about piano. That really simplifies the calculation greatly.

I think vibration caused by striking is NOT fundamentally different from vibration caused by resonance. Energy is just transmitted either by hammer or the common harmonics. So there is no need to analyze the spectrum and harmonics. We just need the correlation like "a striking on string X with (level=53, duration=2s, ...) causes vibration on string Y, which is equivalent to a striking on string Y with (level=3, duration=0.5s, ...)". The correlation table is huge. But based on human ear's resolution, many items in the table will be merged (clustered) and some features (level, duration, etc.) are added or removed. Once the simplified table is obtained, resonance can be calculated accurately. The technology is mature and older than I.

Hi, rintincop
Like you, I really love acoustics. But I never have chance to put hands on a grand. Still, I can imagine the expressiveness of a grand.

Here, I want to further discuss with you on sound (not action). Assume Mozart stroke piano keys 1 million times in his lifetime, which is amazing but still not covering all the notes a grand can generate. Assume an acoustic has a serious 'bug' that it can only generates that 1M kinds of notes, will Mozart notice it? No. So, expressiveness and richness are not decided by individual note, but the note quantity.

You say a still photo is artificial. Yes, a video is more lively. But video is obtained by taking 30 still photos every second. Again, quantity matters. So, it is meaningless to discuss the liveliness and smooth transition on a single photo. We only care whether a photo is accurate or blurred.

Similarly, you cannot attribute the lack of emotions of DP to digital recording. For sound recording, as long as the amplitude, frequency, and phase are accurate, the recording is of high fidelity. This is already achieved. If a DP accurately records all the notes you strike in your lifetime on an acoustic and always picks up the correct note based on your strike force, holding time, etc., will you still complain about the lack of emotions? I believe as the layers and samples increase, DP will express more subtleties.

I like to remember that: video is nothing more than still images that are displayed faster than the the bit rate of your consciousness (see book The User Illusion for more on this).

I think this is a key concept: is the sound from the digital piano good enough to give the brain+ears of the listener the illusion that he is playing either an acoustic or something that is just as good?

Whether or not it duplicates the acoustic is irrelevant. Just as for almost all listeners whether they are listening to just the limited data contained on a CD versus an LP doesn't matter and isn't noticeable; in fact, the CD has benefits for most people over the LP, just as the digital piano is starting to have benefits over the acoustic for many people.

very informative, ge_lw! i really think that it's not even necessary for a DP to match an acoustic grand 100% in accuracy. as long as our ear can no longer distiguish any difference from the 2, then the technology will be is good enough. hopefully, we could have such a DP pretty soon.

Ditto here. I was somewhat surprised to see so many posts comparing the listener's experience of digitals vs. acoustics (i.e., the sound), and much fewer talking about the player's perspective (how it feels). When I play my grand, I feel vibrations in my fingers as the hammer hits the strings. I feel vibrations in my feet when I pedal. I feel vibrations in my.... er, never mind. None of the digitals I have ever tried have captured the sensual experience of playing an acoustic.

I agree with the posters here who say that digitals should be considered a separate instrument, like electric guitars. Not better, not worse: just different, with lots of advantages the acoustic can't beat. But if I could only have one, it would be my acoustic.

Alot of digitals have built in speakers. You can indeed feel the vibration. With a good subwoofer you can feel it there too!

You know, Paul, the digitals I've played I haven't felt any vibration, and I've played some good ones (Clavinova, GEM Genesys, etc.). Maybe I just didn't have the volume high enough (as I was trying these out in stores so wasn't cranking it).

AS the beach Boys used to sing I'm gettin those Good Vibrations...

I think all the effort people put in creating digital pianos that imitates acoustic pianos could be finding ways making concert quality acoustic grand pianos at a much cheaper cost.

rintincop, better resonance handling is becoming more common in software samplers. For instance, a number of NI-format piano libraries are using scripts to add additional harmonic frequencies into the sound dynamically. The Kawai MP8 is a packaged keyboard does it. If there aren't others doing it too, its only a matter of time.

A more exciting and accurate approach is to use convolution and impulse response techniques. I understand piano manufacturers are starting to use this approach in their design stages. Because it can not only generate all the resonances, it can also let them hear how it would change if they used a different string, sound-board, or case material... before going to the expense of building the experimental piano.

I think Monica's right about digital actions. I don't know a one that tries to emulate the jack-action you feel with a real piano action. Except maybe a real piano outfitted for midi.

Howard

We are talking a really new dimension in pianos/DPs at least from a marketing perspective :rolleyes:
(Possibly one of the solution to offer to the thread on stimulating demand for acoustic pianos)

I am a believer in technology, so I can imagine Yamaha ad's lines in few years down the road:
"Clavinova XXX: offering you the sensual feeling of true acoustic vibes and beyond; the instrument to deeply touch your soul and body..."

ge_lw, - a mathematical model can be used to emulate piano string interaction and any speaker can reproduce an as many notes as there are as long as it has the dynamic (amplitude range) and frequency repsonse to the extent audible by humans. You are right about the emulation of the wave front at any and every pointin space by a pair if speakers is not yet possible. That is how you always detect a live performance vs a recording...

Sound pressure emulation in a 3-d space is a still a non-existant specification as far as musical instruments go (requires something other than todays stereo speakers), however surround sound is getting better


Also another problem of emulation is that every acoustic piano is different because of the loosness of construction and it's environmental interaction.

Howard, it is COOL! I never heard about it before! Thank you for your information!

The impulse response technique has beautiful formulation in maths, but requires building complex acoustic models. Compared with human articulation organ (nose, tongue, lips, teeth...) that has evolved and perfected for millions of years, piano is simply pieces of wood & strings. It is possible to build an acoustic model for a piano with certain accuracy. But I'm still conservative that a mathematically computed, purely artificial sound outperforms the careful recording of a genuine grand. In my point of view, it only gives rough estimation of a prototype piano to the designer. If you're sure today's piano model can reflect the nuance between Yamaha C7 and Steinway, please DO tell me.

I think the impulse response technique is more useful in applications that are less sound quality demanding, like speech synthesis. By smoothly changing the lips and tongues in the model, the transition between syllables is more natural than concatenation-based method. But today's human model only has telephone voice quality. That's why Microsoft uses recording-based, concatenative method.

ge_lw, proaudiovault recently released a company-authorized sampled Bluthner Model One. Those samples make extensive use of impulses. Their demos will let you audition how this company uses impulses to change the character of the samples. The site is here.

Also, at the bottom of the home page there's a section, Technical Audio Examples.

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