Octaves on digital piano

[Theo Verelst]

Working on some sounds (in a rather experimental way) I was taken back in thoughts to my early days of learning chords on my self designed and built square wave organ/synthesizer. The way octaves were on there was fixed through the use of pure digital divide by two hardware.

 

On the high school piano at the time (early 80's) of course I learned after practice time that the octaves could be tuned to either be much louder like "stacked" or somewhat timed apart like maybe a classical pianist would play.

 

My feeling is the mix logic in digitals, combined with a lacking sense of accurate timing makes octaves rather boringly the same and certainly not as loud as on a normal piano.

 

Agreed, the amplification of the keyboard might not like the, what is it +12 dB increase in audio levels that could come from good octaving.

 

What's your experience ?

 

TV

 

[stoken6]

The problem with digital pianos is not the "mix logic" or the lack of "sense of accurate timing".

 

The problem with the amplification is not that it dislikes +12db increase in level.

 

IMHO there is a subtle difficult-to-model effect that links the mechanical action of a keypress, to the strike of a string, sympathetic resonance of the soundboard (and the whole instrument) and multiple room reflections - all of which isn't captured by sampling from a coincident pair of mics.

 

Cheers, Mike.

[Gretel]

Where exactly would +12dB here come from? Or 10dB?

[Al Coda]

Where exactly would +12dB here come from? Or 10dB?

 

Don´t mind ...

That´s just only THEOretical values !

 

 

A.C.

[PianoMan51]

Theo, youve got some splaining to do!

 

Take one note. Add a second at the same amplitude. (Any note, octave or not.)

 

= +3dB or possibly +6dB if perfectly phase synced.

 

Now, our engineering degreed colleague, from whence comes 12dB?

 

Bonus points if youre coherent.

[Tom Williams]

Now, our engineering degreed colleague, from whence comes 12dB?

If you're going to take jabs at Theo, please use decent grammar ("whence" means "from where" -- "from whence" is redundant).

Otherwise you might open yourself up to others (like me) taking jabs at you.

 

Or better yet, challenge Theo without unnecessary jabbing.

[Tom Williams]

On to the actual question: I also question the 12dB number -- that's quite a lot. I think that due to several factors, like timing, phase relationships, and (for weaklings like me) the fact that some of us have to hit harder to play an octave, there may be a slightly greater loudness. For example, I might play E4, F4, G4 on succeeding fingers mezzo-forte, but if I play E4+E5 on thumb plus 4th finger, then move my wrist/arm and play F4+F5 on thumb + 4th finger, etc., I am likely to use more muscle in the attack, playing the pair louder than I would have played either note. Could that account for it?

[PianoMan51]

Now, our engineering degreed colleague, from whence comes 12dB?

If you're going to take jabs at Theo, please use decent grammar ("whence" means "from where" -- "from whence" is redundant).

Otherwise you might open yourself up to others (like me) taking jabs at you.

 

Or better yet, challenge Theo without unnecessary jabbing.

Free grammar and etiquette lessons!

[Kurt W]

Where exactly would +12dB here come from? Or 10dB?

One octave is 12 halfnotes, my theory (Kurts theorem) is that each step adds 1 dB. Why make it more difficult than necessary?

 

[Tom Williams]

Where exactly would +12dB here come from? Or 10dB?

One octave is 12 halfnotes, my theory (Kurts theorem) is that each step adds 1 dB. Why make it more difficult than necessary?

Semi-random thoughts on the subject:

• There is no such relationship. If that were true then each octave would be about 16 times louder than the one below it. High C on the piano would be 8.7 bels, or about one half billion times, louder than low A.
  
• The fact that both sets of numbers are 12 is pretty arbitrary. If we used Wendy Carlos's 19 tones per octave microtonality as our scale instead, that would not make the increase 19 dB.
  
• The only hard and fast rule (and even it is an oversimplification) is that each octave gives you a doubling of frequency.
  

[J. Dan]

Ignoring the 12dB comment for a minute and addressing the initial comparison.... in a device doing square waves with divide-down technology, everything is in phase and you're adding some volume from each of the same harmonics - i.e. the note 1 octave down will have the same harmonics plus the new fundamental but with slightly higher amplitudes. So my guess is the PERCEPTION is not much of an increase in loudness. In fact, if they WEREN'T perfectly in phase, the result could only be REDUCED volume due to some phase cancellation.

 

Now look at a real Acoustic Piano. First of all, they are tuned using stretch tuning so that an Octave is not precisely an octave. The harmonic content is already much more complex, and the harmonics from the strings of the different octaves are going to be different to begin with, plus not being perfect octaves at the fundamental, plus the different paths the sound takes to reach your ears. My thought is that the result is many more harmonics, not just adding some amplitude to the same ones, so that the PERCEPTION is a much louder result.

 

Just some thoughts.

[Theo Verelst]

The way I made things, and the way my own projects add notes together potentially is just linear addition, which makes it so that every doubling of the number of notes where the peaks are in phase will lead to double the max amplitude. For square waves which are in phase that's easy to imagine, and so 2 notes is twice the peak amplitude, and so for 2 * 2 notes, four times the maximum amplitude of the mixed wave compared to the max amplitude of a single wave, where the square waves in the example are of exactly the same amplitude.

 

Of course the power of the combined tones isn't the square of the amplitude maximum, but a function of the integral of the combined waves, through their composition (in simple example: per addition).

 

But the max amplitude (as opposed to the average) will require 2*6dB = 12dB extra headroom, not matter how you look at it for my example.

 

T

 

[J. Dan]

Shouldn't it be 4 times the amplitude before taking the Log to get to dB's? Or am I confusing myself?

[Gretel]

No Dan, Theo is right here. A factor of 4 in the amplitude means 12dB:

 

20*log10(4) = 12 (or, alternatively, if you want to consider to equation for converting instantaneous powers into dBs it would be 10*log(4^2) = 12)

 

That being said, now talking about headroom and maximum signal amplitudes when stacking four notes is a bit different compared to what the OP was about, or what I thought the OP was about.

[PianoMan51]

Bonus points awarded! Two hand of octaves with in-phase waveforms. +12dB.

 

Theo, you so rarely answer questions, let me suggest that this is an excellent turn of events.