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Re: The DPBSD Project! [Re: dewster] #1898876
05/17/12 09:52 PM
05/17/12 09:52 PM
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Chapel Hill, NC
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Originally Posted by dewster

When you play a note on a piano, except for the lowest bass notes, the hammer hits more than one string. Most notes in fact have three strings. These strings are tuned almost exactly the same, but the slight difference produces a slow moderate phasing sound.

Another thing that might cause this phasing is the direction the strings are vibrating. On a grand piano the hammer hits the strings vertically, but during the decay I think the vibrations can slowly rotate around to horizontal and back again to vertical.


Dewster,

I think what you are referring to as a "phasing sound" might be more appropriately called a "detuned sound", according to your description of the effect as a by-product of slight detuning of the three strings.

To an audio engineer, phasing is technically something slightly different. As you probably already know, a phase shifter takes the dry sound and mixes it with a wet sound that is in a constant state of time shift (induced by speeding up and slowing down the sound slightly), at a certain modulation speed. As the shifted signal comes into phase with the dry signal there is a notch where certain frequencies go away almost completely, and it feels like your head is collapsing in on itself. The key here is that there is modulation involved. The wet signal is slowing down (getting very slightly flatter), then speeding up (getting very slightly sharper), but in reality with a phase shifter sound, the detuning isn't usually enough to to be perceived as pitch shifting. If you play with these parameters on a time delay program, widening the modulation and amount of time delay will take you from phasing into chorusing.

But in any case, the piano strings are not modulating - they are each staying in tune as they know it, and the beautiful sound produced by all three together is what an audio engineer would call detuning.

But I know what you're getting at, and for street lingo, "phasy" is not too bad of a description.

Really enjoyed reading all of your DPBSD stuff, by the way - extremely informative. Nice work.

-Wes


Wes Lachot Design Group
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Re: The DPBSD Project! [Re: Wes Lachot] #1901714
05/23/12 08:44 AM
05/23/12 08:44 AM
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In re-reading the various posts on "panning/phasing" etc.

I think it is as much that a) the string excites the board b) then the board gets out of phase with the string c) the board feeds back to the string and excites it d) the board gets back in phase with the string again (repeat loop).
Bearing in mind that the strings themselves are NOT producing much sound and that there are (as dewster has said) more than one string per note - and more than one note sounding at a time.
A dozen, two dozen strings, all quasi randomly exciting then suppressing the soundboard by being in and out of phase with it.... Yeah, I think my head wraps around that as a model
Now if I could just wrap the math around that model, perhaps Viscount would employ me on the physis project ? (-:
(perhaps, but VERY unlikely)

Re: The DPBSD Project! [Re: Wes Lachot] #1901724
05/23/12 09:01 AM
05/23/12 09:01 AM
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dewster Offline OP
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Originally Posted by Wes Lachot
I think what you are referring to as a "phasing sound" might be more appropriately called a "detuned sound", according to your description of the effect as a by-product of slight detuning of the three strings.

Yeah, "phasing" is a term that means something very specific to an audio engineer, and I don't mean to abuse it. But I'm not sure how else to describe the sort of gentle swirling sound in the decay of a real (i.e. fully sampled) piano note. "Detuned" is more accurate as to the root cause, but perhaps has a negative connotation?

I'm glad you've found something of use in the DPBSD testing Wes!

Re: The DPBSD Project! [Re: R_B] #1901729
05/23/12 09:09 AM
05/23/12 09:09 AM
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Originally Posted by R_B
A dozen, two dozen strings, all quasi randomly exciting then suppressing the soundboard by being in and out of phase with it.... Yeah, I think my head wraps around that as a model
Now if I could just wrap the math around that model...

Heck, if someone could just sufficiently sample the thing I'd be pretty much out of a job on this thread. We have the equivalent of severed, crawling hands posing as full healthy bodies in most DPs.

Re: The DPBSD Project! [Re: dewster] #1902011
05/23/12 06:48 PM
05/23/12 06:48 PM
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Re: "phasey", I think we're really splitting hairs here. I would have used exactly the same word in this context. The "phaser" effect could also be called a "detuner" too, because whenever the delay time of the delayed versions of the input signal are changing, the pitch of those delayed signals is necessarily different to the input. wink

Greg.

Re: The DPBSD Project! [Re: dewster] #1902267
05/24/12 08:37 AM
05/24/12 08:37 AM
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I think the phaser effect is similar to, but not the same as 'detune'. In practice, they usually overlap, as effects:

The 'phaser' effect usually means two or more versions of the same signal but beginning at a slightly different phase of the wave (signal one: zeroº and signal two, 70º or 90º, etc etc). This causes a 'band reject' effect as the waves' sum: sometimes = x2 but at others, about zero (the one cancels the other out at certain points of the phase).

However, 'phasers' as musical effects are almost always dynamic, in that the distance between the two (or more) signals is constantly changing (with a LFO (low frequency oscillator), usually). That does not, as far as I can think, involve actual detuning.

However, a similar 'phasey' effect is obtained by having two (identical or similar) signals playing very slightly out of tune - simply because the phase length (frequency) of one is going to be shorter than the other, so the 'phase' of each finishes at a slightly different time, and so on until both get to start at zero again. In other words, 'detune' gives you a kind of automatic phasing.

Indeed, the early 'Harmonisers' in the 70's and early 80's worked by having two or more coordinated 'phasers' to give the impression that the input signal was not only being split in two but also detuned against itself.

Um - I hope that's clear....and correct...


Roland HP 302 / Samson Graphite 49 / Akai EWI

Reaper / Native Instruments K9 ult / ESQL MOR2 Symph Orchestra & Choirs / Lucato & Parravicini , trumpets & saxes / Garritan CFX lite / Production Voices C7 & Steinway D compact

Focusrite Saffire 24 / W7, i7 4770, 16GB / MXL V67g / Yamaha HS7s / HD598
Re: The DPBSD Project! [Re: toddy] #1902278
05/24/12 09:02 AM
05/24/12 09:02 AM
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Originally Posted by toddy

However, 'phasers' as musical effects are almost always dynamic, in that the distance between the two (or more) signals is constantly changing (with a LFO (low frequency oscillator), usually).


Agreed - that's my understanding too.

Quote
That does not, as far as I can think, involve actual detuning.


I think it must involve a change of pitch (however slight), because the only way to alter the relative phase between the input and "phased" signal is to alter the speed at which the phased signal is sent to the output. If the speed(pitch) of the phased signal is kept constant, and at the same speed of the input, there will only be a constant delay, and thus a constant relative phase difference.

Greg.

Last edited by sullivang; 05/24/12 09:03 AM.
Re: The DPBSD Project! [Re: dewster] #1902285
05/24/12 09:20 AM
05/24/12 09:20 AM
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Yes, exactly - you can get a 'static' phase effect with no change of frequency. But it's not often used as a musical effect, although it does exist in real life (stamping your foot in an alley way or back entry, for example).

So of course you are right because the usual musical phase effect does involve detune or simulated detune (ie continuously changing phase shifts causing slight and changing shifts in pitch). It is, after all, a nice thickening effect imitating three piano strings or even string sections....hence the word 'Chorus Effect' for a similar device.

Question: do the best piano tuners actually set the strings out of tune with each other, or put them perfectly in tune? My guess is that they would put them as closely in tune as possible which would result in very slight phase shifts due to......what ever.

(amended reply)

Last edited by toddy; 05/24/12 09:50 AM.

Roland HP 302 / Samson Graphite 49 / Akai EWI

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Focusrite Saffire 24 / W7, i7 4770, 16GB / MXL V67g / Yamaha HS7s / HD598
Re: The DPBSD Project! [Re: dewster] #1902769
05/25/12 06:20 AM
05/25/12 06:20 AM
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Northern NJ
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LIMEX Vienna Grand Piano Expansion Board Review

[Linked Image]

This is a sample of a fairly obscure piano module, and the first submitted by PW forum member "galaksa".

PIX: http://www.mediafire.com/?wa7bb0zw6etfv4v
MP3: http://www.mediafire.com/?yuc2a1v8qewc36j

The concept behind this board is one that appeals to me: a module with most of the ROM dedicated to piano, and available as an expansion board or mounted in a box. The world could use more straight-up piano sound modules. This particular board employs ATMEL ATSAM9708 dual DSP / GPU to support 128 polyphony + effects - it was something of a shock for me to discover that something like this even exists outside of the proprietary realm. The wavefront AL3201B digital reverb engine on the board is also a very interesting part.

The distinguishing feature of this module is that it is unlooped. But the way this is accomplished is by making the note decay times really, really (really!) short. Notes sound like someone is quickly turning the volume down after several seconds. Don't quote me, but I think I'd prefer a bit of looping here to lengthen things. Or perhaps the removal of several layers, with the resulting freed up memory (LIMEX says 240 MB) used for longer decays. Heck, I'd take more stretching if it could add anything to these unnaturally fast decay times. The real solution here is of course more ROM containing a larger sample set, but good luck persuading DP manufacturers to go that route.

The other distinguishing feature is that it fails almost all the DPBSD tests. If manufacturers are going to give us such highly compressed fare, I at least expect some realistic pedal / key behavior to make up for it, but you won't find that here. It does have 7 velocity layers, but they are unblended and one of the transitions located somewhat above the center velocity is quite abrupt sounding. It's also fairly stretched. There is some kind of pedal sympathetic resonance going on, but it's on the threshold of audibility and therefore essentially moot.

Some analysis pix and text review:

[Linked Image]
Figure 1. Waveform view of the entire looping test, vertical zoom applied to see the noise floor. The decay rate is ultra fast, probably the fastest I've ever encountered and extremely fake sounding.

[Linked Image]
Figure 2. Spectral pan view of the stretch test, low end of the notes, normalized to -1dB to increase clarity. Stretch group transitions are audible over the low and mid notes, with inconsistent stereo L&R pan making some transitions even more audible.

[Linked Image]
Figure 3. Spectral frequency view of the layer test. There are 7 unblended velocity layers both visible and audible, with the transition at v=92 sounding quite abrupt.


--------------------------------------------
- LIMEX Vienna Grand Piano Expansion Board -
--------------------------------------------
FILE & SETUP:
- dpbsd_v2.0_limex_vienna_gp.mp3
- LIMEX Vienna Grand Piano expansion board.
- Preset "7-layers Grand Piano".
- M-Audio Revo 5.1, vanBasco's Midi Player, Steinberg WaveLab.
- Recorded by "galaksa".
PROS:
- Pedal sympathetic resonance of some sort but it is exceedingly subtle.
- Unlooped, but the samples are way too short.
- This is an unblended seven velocity layer sample set.
CONS:
- Fails the key sympathetic resonance test.
- Fails the silent replay test, note damps @ pedal up.
- Fails the quick damping test, note damps with quick pedal.
- Fails the late pedal partial damping test.
- Fails the half pedaling test.
- Ultra short note decay time, low notes ~10 sec, mid ~5 sec, hi 2 sec.
- Fairly stretched, and audibly so, particularly in the low and mid notes.
- Some stretch groups have inconsistent stereo L&R pan.
- Stretch distances: 6,3,2(x3),1,2,3(x3),1,3,2(x4),1,2,3,2,2,3,3,2,2,2,3,2,2,1,4,3,2,2,3,5 = 41 groups.
- Velocity switch @ vel=42,60,76,92,106,118.
- Velocity layer switches are visible and audible, the switch @v=92 is particularly jarring.
OTHER:
- Notes played @ vel=1 produce sound.
- Dampered | undampered transition: F6 | F#6
- Dynamic range 48dB (vel=1:127).
- MP3 levels: peak @ -1dB, noise floor @ -74dB.
- Date reviewed: 2012-05-23.

Re: The DPBSD Project! [Re: dewster] #1902776
05/25/12 07:24 AM
05/25/12 07:24 AM
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Hamamatsu, Japan
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Thanks for posting the review.

I'm curious, what exactly does this expansion board plug into? Is there some kind of controller/rack product capable of taking a selection of different boards?

Also, I note that there are several other piano voices available - do you suspect that they are the same core sample with filtering applied, or is separate wave data being used? Did you manage to calculate the approximate sample data size, based on the stretch groups, decays, and layers?

Cheers,
James
x


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Nord Electro 3 & occasional rare groove player.

"I agree that the User Manual is very good." - arc7urus, March 2019
Re: The DPBSD Project! [Re: toddy] #1902777
05/25/12 07:28 AM
05/25/12 07:28 AM
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Originally Posted by toddy

Question: do the best piano tuners actually set the strings out of tune with each other, or put them perfectly in tune? My guess is that they would put them as closely in tune as possible which would result in very slight phase shifts due to......what ever.


Good question. I have a book on piano tuning, and there doesn't seem to be any mention of deliberately detuning the unisons a bit to create a desired level of detuning/phasing. So, as you say, I suspect that they aim for perfect unisons, but never really achieve it, at least not for any appreciable length of time, due to the rigours of playing, temperature & humidity shifts etc. (note that the book covers rebuilding as well, so this aspect may be out of it's scope)

Greg.

Re: The DPBSD Project! [Re: Kawai James] #1902794
05/25/12 07:50 AM
05/25/12 07:50 AM
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dewster Offline OP
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Originally Posted by Kawai James
I'm curious, what exactly does this expansion board plug into? Is there some kind of controller/rack product capable of taking a selection of different boards?

If you go to the LIMEX products page and download the English flyer (you've probably already done this) you'll see both the module and the expansion board. galaksa was pretty sure they had the same piano sound. LIMEX offers a bunch of bare boards and a couple of enclosures presumably to stick them in - I'm not quite sure why (I'm all for it but it seems like strange marketing).

Originally Posted by Kawai James
Also, I note that there are several other piano voices available - do you suspect that they are the same core sample with filtering applied, or is separate wave data being used? Did you manage to calculate the approximate sample data size, based on the stretch groups, decays, and layers?

I don't have an MP3 sample of any of the other piano voices, but they are almost certainly the same sample set with possible filters / MIDI scaling applied.

Given 5 seconds on average of sampling time, 41 stretch groups, 7 layers:

5 * 41 * 7 = 1435 seconds

* 2 for stereo
* 2 for two bytes per sample
* 44100 samples per second

= 253 MB (LIMEX reports 240 MB)

Re: The DPBSD Project! [Re: dewster] #1902800
05/25/12 08:01 AM
05/25/12 08:01 AM
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Thanks again!


Employed by Kawai Japan, however the opinions I express are my own.
Nord Electro 3 & occasional rare groove player.

"I agree that the User Manual is very good." - arc7urus, March 2019
Re: The DPBSD Project! [Re: dewster] #1902819
05/25/12 08:59 AM
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My pleasure James!

Re: The DPBSD Project! [Re: dewster] #1902836
05/25/12 09:26 AM
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I know this has been explained before and I read it but just don't get it: Why the extreme limitation of ROM size (to 250MB) when it is common to list not only HDD and flash memory in Giga Bytes, but also even RAM memory - typically 4 - 6 Giga Bytes in a standard laptop computer.

If RAM - instantly available data storage, by definition - is so plentifully, why use such paltry amounts of ROM? After all, we spend so much time just squandering the memory in our laptops. It's like giving out kerosene driven jets to do shopping and pick up the kids from school, while making space expeditions run on paraffin driven lawnmower engines.

Last edited by toddy; 05/25/12 09:27 AM.

Roland HP 302 / Samson Graphite 49 / Akai EWI

Reaper / Native Instruments K9 ult / ESQL MOR2 Symph Orchestra & Choirs / Lucato & Parravicini , trumpets & saxes / Garritan CFX lite / Production Voices C7 & Steinway D compact

Focusrite Saffire 24 / W7, i7 4770, 16GB / MXL V67g / Yamaha HS7s / HD598
Re: The DPBSD Project! [Re: toddy] #1902887
05/25/12 10:54 AM
05/25/12 10:54 AM
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Originally Posted by toddy
I know this has been explained before and I read it but just don't get it: Why the extreme limitation of ROM size (to 250MB) when it is common to list not only HDD and flash memory in Giga Bytes, but also even RAM memory - typically 4 - 6 Giga Bytes in a standard laptop computer.

Yeah, I kind of get it and don't get it at the same time. This conundrum is pretty much why I started the DPBSD project in the first place.

Since price is generally the most important "option" this means manufacturers of most products have to cut corners, and I suppose DP manufacturers think ROM is a good place to do it - though I don't, and particularly not for flagships or the professional tier, where I expect a solo recording quality sample set / model / hybrid / etc.

You can't exactly compare PC hardware with embedded hardware - the PC performance/cost curve will always be ahead due to economies of scale.

Going with a larger sample set means, in order to persuade your potential customers to buy into the product concept, you have to talk about specs - I don't think many DP manufacturers are very comfortable doing this because it puts their lesser products in a bad light, and they'd rather be discussing how magical or whatever <insert inane intangible> their stuff is.

The larger ROM addressing space probably means a processor upgrade. More expensive (though not so much these days) and could strand inventory.

Consumers need DPs, they'll keep buying them regardless. All we can do is keep crabbing and hope they're listening.

Re: The DPBSD Project! [Re: dewster] #1909184
06/06/12 04:31 AM
06/06/12 04:31 AM
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Originally Posted by dewster
Originally Posted by toddy
I know this has been explained before and I read it but just don't get it: Why the extreme limitation of ROM size (to 250MB) when it is common to list not only HDD and flash memory in Giga Bytes, but also even RAM memory - typically 4 - 6 Giga Bytes in a standard laptop computer.

Yeah, I kind of get it and don't get it at the same time. This conundrum is pretty much why I started the DPBSD project in the first place.

Since price is generally the most important "option" this means manufacturers of most products have to cut corners, and I suppose DP manufacturers think ROM is a good place to do it - though I don't, and particularly not for flagships or the professional tier, where I expect a solo recording quality sample set / model / hybrid / etc.

You can't exactly compare PC hardware with embedded hardware - the PC performance/cost curve will always be ahead due to economies of scale.

Going with a larger sample set means, in order to persuade your potential customers to buy into the product concept, you have to talk about specs - I don't think many DP manufacturers are very comfortable doing this because it puts their lesser products in a bad light, and they'd rather be discussing how magical or whatever <insert inane intangible> their stuff is.

The larger ROM addressing space probably means a processor upgrade. More expensive (though not so much these days) and could strand inventory.

Consumers need DPs, they'll keep buying them regardless. All we can do is keep crabbing and hope they're listening.


It seems as if all of the piano companies got together a dozen years ago and agreed to stop posting specs at the same time and since then, the technology being used has not kept up with current advancements that are available and the prices have been on the rie as well. The V-Piano and Roland's SuperNatural piano sound are by far ahead techno-wise than Anything Yamaha offers however the hybrid AG series comes very close. As for the importance of this thread and what you do Dewster shall continue to be relevant and useful to all of us wanting to see the digital piano technology to finally match up to where it should be by now when we have smart-phones with more processing power, more memory, by the tenfold than what is found in any modern DP and costing far less. With the Ipad 3 becoming very popular, why so very few DP's without a voice editor that can be downloaded via an app? Granted we are at an age where technology is moving faster than we can upgrade. However in the DP world, with prices so high and product cycles lasting more than four years sometimes, it seems to be moving far too slowly and not keeping up with the best technology available that could improve the sound to even better standards.


Roland V-Piano, Yamaha CLP990, Yamaha S90
Re: The DPBSD Project! [Re: dewster] #1909332
06/06/12 11:24 AM
06/06/12 11:24 AM
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Roland FP-4 Review

[Linked Image]

voxpops was curious about Roland's SN vs non-SN so he sent me an MP3 of the Roland FP-4 for comparison purposes and I went ahead and did the review here. The DPBSD MP3 is of the default voice "GrandPiano1".

MP3: http://www.mediafire.com/download.php?d9nj7lkrtbii037
PIX: http://www.mediafire.com/download.php?4dhpkhqp7d5594e

The FP-4 fails most tests, though it does support half-pedaling and partial damping. It isn't stretched, which is nice. But the decays are short, and the attack and loop samples are really small, so the looping is pretty obvious on the low end and fairly static sounding on the high end. It has three velocity layers that are pretty much unblended, with the transition from the lowest to the middle sounding quite abrupt. Basically not a lot to write home about in the piano sound department and fairly dated spec-wise.

Going by the phase signatures of the stretch and layer tests, it appears to share the same root samples as the current overwhelmingly predominant SN piano voice - the "Concert Grand" voice in the RD-700NX & the lone SN piano voice in virtually all other SN DP offerings. I think every DP manufacturer should consider more frequent sample updates as the same old, same old can get really old after a while.

I think it's kind of a shame that Roland decided to seriously dumb down the internal architecture of the FP-4's successor, the FP-4F. Having all those in-line effects to choose from must add some spice to the FP-4 internal sounds, and they positioned this keyboard more in the pro category. I see a damper resonance effect in the FP-4 manual, but was unable to hear or see any difference between pedal up and pedal down in the pedal resonance test.

Some observations from voxpops:
Originally Posted by voxpops
Despite its dated technology, it's still a very usable gigging tool, mainly due to the lightweight but strong chassis, comprehensive effects, precise (if very light) action, and crisp-sounding main AP and EP samples. Other patches, such as organ and strings etc., are also quite usable. The built-in speakers are useful but somewhat underpowered for use as stage monitors, and prone to distortion with bass sounds. The interface is mainly self-explanatory, but there are plenty of menu functions for the setting up of EQ, "Sound Control" (much like the more recent "Sound Focus"), MIDI functions, registrations, effects, and so on. I would not trade this model for the FP-4F, due to the lack of user-accessible effects, less acceptable EPs, and (allegedly) more sluggish action.


[Linked Image]

[Linked Image]
Figures 1 & 2. Spectral pan view of the stretch test, normalized to -1 dB to bring out detail, mid notes, Roland FP-4 above, RD-700NX "Concert Grand" below. Essentially the same phase signatures in both models strongly suggests the employment of the same root sample set. No visible or audible stretching.

[Linked Image]

[Linked Image]
Figures 3 & 4. Spectral pan view of the layer test, highly compressed to bring out detail, Roland FP-4 above, RD-700NX "Concert Grand" below. It looks to me like they blended the layers in the FP-4 and are using this as stimulus for the SN decay process (whatever it is) in the NX. The FP-4 layer switches are quite audible, particularly the first.

[Linked Image]
Figure 5. Waveform view of the looping test, zoomed vertically in order to see the noise floor. Decay times are pretty short.


---------------
- Roland FP-4 -
---------------
FILE & SETUP:
- dpbsd_v2.0_roland_fp-4_gp1.mp3
- This is the default piano voice "GrandPiano1".
- MIDI sequenced with Anvil Studio, audio recorded with Tascam DP1, +7dB boost & MP3 via Reaper.
- Sequenced and recorded by "voxpops".
PROS:
- Passes the quick partial damping test.
- Passes the late pedal partial damping test, note decay is caught even after 0.5 seconds.
- Passes the half pedaling test.
- No visible or audible stretching, notes look random in the wave and phase views.
CONS:
- Fails the pedal sympathetic resonance.
- Fails the key sympathetic resonance.
- Fails the silent replay test @ pedal up (note damps).
- Fairly short note decay times (on the order of 1/2 Pianoteq).
- Attack sample lengths are (C1:C8): 2.7,2.1,2.0,1.9,1.2,0.8,0.4,? seconds.
- Loop sample lengths are (C1:C8): 0.9,0.8,0.7,0.8,0.5,?,?,? seconds.
- Lower note loops sound "loopy", higher note loops sound very static.
- This is a somewhat blended three layer sample set.
- Very audible (timbre, stereo) velocity layer switch @ vel=64,104.
OTHER:
- Notes played @ vel=1 produce no sound.
- Dynamic range 46.7dB (vel=1:127).
- Dampered | undampered transition: F#6 | G6
- MP3 levels: peak @ -0.7dB, noise floor @ -61dB.
- Date reviewed: 2012-06-05.

Re: The DPBSD Project! [Re: dewster] #1909562
06/06/12 05:07 PM
06/06/12 05:07 PM
Joined: Sep 2007
Posts: 15,111
Hamamatsu, Japan
Kawai James Offline
Yikes! 10000 Post Club Member
Kawai James  Offline
Yikes! 10000 Post Club Member

Joined: Sep 2007
Posts: 15,111
Hamamatsu, Japan
Interesting.

Anyone willing to submit an FP-4F recording?

James
x


Employed by Kawai Japan, however the opinions I express are my own.
Nord Electro 3 & occasional rare groove player.

"I agree that the User Manual is very good." - arc7urus, March 2019
Re: The DPBSD Project! [Re: dewster] #1909584
06/06/12 05:42 PM
06/06/12 05:42 PM
Joined: Dec 2009
Posts: 3,717
Suffolk, United Kingdom
E
EssBrace Offline
3000 Post Club Member
EssBrace  Offline
3000 Post Club Member
E

Joined: Dec 2009
Posts: 3,717
Suffolk, United Kingdom
Three quarters of a million views and counting.....


Roland RD-1000 | Yamaha CLP 645 | Broadwood Barless 7' 6"
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