Playing about with the Recital Pro

Is my newly acquired Alesis Recital Pro digital piano keyboard out of tune or is my musical acumen failing with age?

First some facts. The Recital Pro is an 88 key keyboard so spans from lower A0 to upper C8 with an overall pitch range of just over 7 octaves. It boasts 12 basic voices with various additional functions. Some of the voices (namely "Clavi", "Acoustic bass" and "Fingered bass") sound an octave lower than normal giving effectively an overall range of just over 8 octaves, although this shift is tacitly cancelled when layering with a normal voice. Moreover the whole range can be "transposed" by up to 12 semitones up or down extending the effective range to about 10 octave but q.v.. 

In what follows the term "normal" will refer to the standard piano pitches with A4 (above middle C) having the frequency 440Hz (this being Concert Pitch by definition).

The keyboard extends downwards 4 octaves and upwards 3 and a bit octaves from A4 so we have:

C8    ~4186Hz      (highest normal note, all C frequencies per equal temperament)

A7     3520Hz

A6     1760Hz

A5      880Hz

A4      440Hz   (standard pitch)
C3     ~261.6Hz (middle C, 2ft open pipe e.g. flute)

A3      220Hz

A2      110Hz

A1       55Hz

C1      ~32.7Hz (16ft open pipe)

A0       27.5Hz (lowest normal note)

With voice "Fingered bass" selected the lowest note becomes C0 at 16.35Hz and the A below at 13.75Hz, and with decent headphones on (because the internal speakers have poor low frequency response) the sound is impressive and reminiscent of a real (acoustic) organ at 32ft register. The sound is a combination of deep bass and tangible throbbing (at 13.75 times per second). Of course, the listener is probably hearing the harmonics (or "partials") rather more than the fundamental, witness with the purer voice "Acoustic bass" for which the deep bass is hardly audible, but this fact hardly detracts from the experience because non-linearities themselves can create undertones giving the illusion of bass deeper than the equipment should be able to produce.

But one can go even lower in pitch with "Transpose" set to its minimum of "-12" i.e. 12 semitones lower. With this setting the lowest note to sound is C#0 which calculates as 8.66Hz and sounds little more than a throbbing, and this simulates the 64ft organ open pipe register.

Similarly with "Transpose" set to positive amounts one can explore the Recital Pro's upper register. In principle, by playing the top note, with the settings up to the maximum of "+12" one should get up to B8 at 7902.13Hz. In fact with the standard "Piano" voice there is already hardly any output at top C even without any transposing (as indeed with an acoustic piano).  Apart from obviously the voices that sound an octave below normal, the voice "Synth" perhaps does the best at top C. Then, as the "Transpose" setting is increased up to "+12" sampling alias artefacts become very evident and at "+12" the apparent pitch seems actually lower than with setting "00". Which suggests that, internally, the digital pitch engine is sampling maybe lower than the industry standard 44.1kHz or at least there is insufficient anti-aliasing filtering. All this is a bit academic because I have no call to be making noises at this high a frequency. But maybe younger players with better hearing might want to. 

Both effortless low frequency response and high frequency response plagued with aliasing are of course typical of any digital audio system.

But back to my opening gambit. I play mostly by ear so hit notes that my "ear" thinks are correct, rather than reading them from a music score. I have found with my Recital Pro that I not infrequently find myself playing notes in the lower register that are entirely incorrect and yet taking a while to notice it. Which I cannot remember doing on an acoustic piano. Or I find, even when the score confirms I am playing the correct note, it just doesn't sound right.

Now, as I've said this may be due to my ailing musical acumen or else it could be a real effect and I'd be interested to hear if my readers have any similar experiences or observations. If it is a real effect then I suspect it is related to the Railsback effect observed in acoustic pianos and thus possibly simulated in their digital counterparts.

The deal here is that real (acoustic) piano strings have thickness as well as length. Based on length alone (and thus assuming no effect of bending at either end), a string can vibrate with fundamental and harmonics. By definition the frequencies of the harmonics are integer multiples of that of the fundamental. But if the resistance to bending near the fulcrums is taken into account what were harmonics become mere overtones i.e. no longer having exact integer relationship with the fundamental indeed becoming "inharmonic". In a piano the lower pitch strings have to be made heavier than mere scale would demand in order that their length and thus the overall dimensions of the instrument should remain feasible for the average owner. Not only that but the lower the pitch, then more the "ear" is aware of the overtones over and above the fundamental because of the tail-off of low frequency response of the ear and of the piano's sounding board. To compensate the piano tuner favours the first few overtones over and above the fundamental and thus has to effectively detune the lower strings.

A similar effect applies to the higher strings where it becomes necessary for mechanical robustness to make the strings thicker than mere scale would demand, thus increasing inharmonicity.

The overall effect is the Railsback curve which sort of averages, I suppose, what piano tuners have been trained to do as part of their art. Which of course applies to acoustic pianos and contributes to their overall sound quality.

Enter the digital piano. Of course, when tuned, there is now no reason to copy the Railsback curve as far as mechanics are concerned as there are none. But what does persist is the piano players' expectations, and the article linked above suggests that digital pianos do regard Railsback and perhaps that is why the lower register of my Recital Pro sometimes seems over of tune to my ears.

Comments please!

Tempermental

I used to think I was reasonably musical. I reckoned I could tune a guitar, understand music theory, improvise on the piano, and generally appreciate music better than the average person. Not having yet met the average person I cannot be sure that I was wrong but I have met several non-average people and have come to the conclusion that there are many who are a good deal more musical than I am. Which peeves me because I thought I had a corner. Hence my Song of Albion posts. Which I might yet continue anyway.

As an example - I love the piano - both playing it and listening to it being played. Of course I can tell if a piano is wildly out of tune but I am unaware of the nuances of out-of-tune-ness that some of my friends claim they can detect. But at least I am interested in out-of-tune-ness.

I invented my musical slide rule whilst at school and was intrigued by the idea of enharmonic notes which it manages to discriminate between. Which led to discovering just intonation and the Pythagorean comma.

Pythagorean Comma

Which goes like this:  The seven notes of the major scale are kind of "God-given" in that they result naturally from the vibrations in pipes or strings. The third harmonic of a string or open pipe is a "just" perfect fifth above the second harmonic, the ratio of the frequencies being exactly 3:2. The just perfect fifth is the purest sounding interval after the octave (ratio 2:1) because the ratio is so simple. So two notes are consonant if the ratio of their frequencies is simple. If you start at the bottom A of the piano keyboard and ascend by fifths 12 times you will get to the top A, seven octaves up. If these had been just fifths you arrive at slightly higher than A, this discrepancy being the "comma".

just perfect fifth = frequency ratio 3:2 = 1.5
1.5 raised to power of 12 = 129.746337890625 = 1.0136 x 128 (2 raised to the power 7, thus the top A)
equal temperament semitone = 2 raised to power of 1/12 = 1.0595

thus the Pythagorean comma is about 1/5th of an equal temperament semitone.

The purpose of equal temperament tuning is to divide the octave in 12 exactly equal semitones and thus to avoid the comma.  At the expense of intervals no longer being "just" and therefore not being truly consonant. But it means that music can modulate into remote keys - whereas with just intonation remote keys are out of tune. So equal temperament has heralded the complex harmonies that are commonplace in today's music.

Thus all keys should sound the same thus dispelling the myth that flat keys sound soft and sharp keys sound crisper. Or is it a myth? In fact the piano is not tuned to equal temperament. Because of the stiffness of the piano "strings" the higher harmonics are out of tune - this is called "inharmonicity". To compensate so that higher and lower notes played together don't sound discordant the piano is actually "stretched" or deliberately tuned away from equal temperament.

Railsback curve

Which begs the question - which is the more correct? Just intonation seems to be closer to what I describes as "God given". But then, frankly, who cares? The keyboard (which almost implies equal temperament) is here to stay. And who wants to go back to Gregorian chant? And most of us don't understand the distinction and of those that do, most cannot tell the difference.

And then most of the keys on a piano strike three strings or "unisons" because they are in theory tuned in exact unison see here. Except that this site says "a piano tuner's "secret" is that not all three strings have to be perfectly in tune, a slight difference (which you'll get anyway in a couple of months with regular playing) actually beefs up the tonal quality of the note (chorus effect)". This site claims the reason is to increase the loudness to compensate for the larger bass strings, but I think this is weak reasoning. The force imparted by a given amount of thump on a piano key will be divided three ways when striking three strings thus defeating this argument. Wikipedia and other sites explain that, because the three strings are coupled by the bridge, having three strings lengthens the decay rate although giving an initial sharp decay provided they are tuned in unison - this sounds more believable to me. A side effect of coupling is that it will affect the frequency of vibration thus giving another potential departure from true equal temperament.

This site claims that the three "unisons" may intentionally be de-tuned by an amount that is culture dependent - "The effect is to change what stage of a played note the tuning resolves for maximum appeal. In the American style, the attack, or initial sound is emphasized for optimum 'in-tuneness' tonality. In the Japanese style, the sustain, or the sound of the note after the initial strike fades is where the highest degree of 'in-tuneness' resolves. In the European style, influencing the overall color of the note is the goal."

Which views are rather confusing and not always consistent.

I have access to several pianos including a grand. I cannot comment on their relative degrees of in-tune-ness - at the moment they all sound OK to me - but the one I hands-down prefer is an upright: for its crispness of tone, its responsiveness to and lightness of touch, and its great dynamic range.