[sdiy] Consider this DAC

[Tom Wiltshire]

Cheater,

I notice you're *not* offering an alternative definition of  "good  
enough".
Simon had a crack, and you and Antti have both provided a reasonable  
case for why 2.5 cents isn't close enough. I concur, it isn't.

So what are you offering? What's *your* best guess? Better still,  
what have you practically demonstrated to be sufficient for your needs?

I'm always looking for other people who've made their own judgements  
about this kind of stuff, because it seems to me that there is a lot  
of compromise in synth building (indeed, engineering in general) and  
that making the right compromises in the right places is one of the  
things that separates the great instruments from the good ones. I  
find that failure to compromise effectively on a design leads to  
failure to actually get the thing done, since you finish up wasting  
time chasing some unrealistic goal or other. Better to choose 2.5  
cents and get it running and be proved wrong than decide 0.1 cents is  
what it must achieve and never hear it to know.

For what it's worth, the Roland Juno 106 gets by with a worst-case  
pitch error of 1.4 cents. That's not the pitch resolution,  
necessarily, just the amount it deviates from the notes of the  
equally-tempered scale. Most of the range is much better than that  
(<0.5cent). The DCO is only a 16-bit counter, so no-one remarks on  
it's amazing DCO smoothness (unsurprisingly), but at the same time,  
lots of people still find it a useful synth. It constantly amazes me  
what you can get away with!

The whole question became a moot point for me as soon as I started  
basing everything on a 32-bit NCO. Instant frequency accuracy up the  
wazoo!

Thanks,
Tom


On 13 Mar 2010, at 14:58, cheater cheater wrote:

>
> Simon, I am impressed with your technical knowledge of digital
> electronics. However you still need to study some psychology to talk
> about pitch perception like that. Throwing around statements like the
> above, after ripping them out of context, makes for a lot of
> disinformation and establishes very destructive myths.
>
> What you have brought up is the experimentally established 'just
> noticable difference' threshold. Just noticable difference, even
> though it sounds like regular english, is a specific term in
> psychology; it is bemoanable, but outside of the scope of this
> discussion, that names for such concepts are constructed in a way that
> allows people to use them without knowing that they are, in fact,
> "sharp" - or, simpler said, exact - scientific definitions.
>
> Without knowing what sort of experiment and situation the sample data
> actually reflects, it is in no way intelligible.
>
> You can skip the next paragraphs until the -------- line, unless
> you're interested in what a JND actually is.
>
> The definition of the JND can be put into words as such: first we
> expose someone to a stimulus, for example showing a light of a certain
> length. Then after the stimulus is over another one, slightly
> different, is created in the same way. The two stimuli are quantified
> with a single dimension, and assigned a single number. So for example
> a person is exposed to a light source of color 227.1 and then,
> *later*, of color 227.132. For such pairs of stimuli, a test subject
> is asked whether they were different or not. For statistical reasons,
> for each pair which is included in the testing suite, the test is
> repeated hundreds or thousands of times.
>
> Each pair (I1, I2) in the test suite is assigned a difference, this is
> our Delta I. If across all measurements there is a specific Delta I
> below which a significant amount of subjects do not notice a
> differende, but above which they do, then that's the just noticable
> difference value.
>
> (notably, if the JND seems to depend on the base value of I1, then a
> different scale can sometimes be used; the logarithmic scale of pitch
> has a more or less constant JND, whereas the linear scale of frequency
> in Hz has one that rises as I1 rises, that's why the JND for
> successive perception of tone height is expressed in cents, i.e. the
> distance on the logarithmic scale)
> -------------
>
> The key word above is *later*. The test subjects are played back a
> tone at some pitch, and then *later*, after that note is *finished*,
> they are played a second tone. It is a huge difference from the way we
> are defining the required accuracy of a musical instrument; to see
> why, consider this:
>
> at 5000 Hz, the difference of 1 cent is almost 3 Hz:
>
> 5 000 * 0.000577789 ~= 2.888945
>
> Even consider something as small as 0.3 cents:
>
>  	
> 5 000 * (1.000577789^0.3) = 5 000.86651
>
> This gives us a difference of ~0.8 Hz. This means that if I play two
> notes *at the same time* and they have this difference in pitch, I
> will be able to hear them pulsate in
>
> 1 / (0.86651 Hz) ~= 1.15405477s
>
> so about 1.2-second intervals. I don't know about you, but I can hear
> this sort of thing very clearly. I would say that the JND here is much
> lower, and should be expressed in Hz; furthermore, it will decrease
> with the amount of coexisting notes and the note length and increase
> with the richness of tone, to mention some easy to notice variables in
> the equation. The test here would look like this: first we play two
> notes at one pitch difference, then two notes at another pitch
> difference, and we ask if the subject notices a difference.
>
> The speed of vibration between notes is very important in chromatic
> and generally harmonic compositions.
>
> 2.5 cents of inaccuracy can mean a difference between one note slowly
> and pleasantly pulsating with another note's 3rd harmonic, and it
> grating at a displeasurable 7 Hz.
>
> Your so-called just noticable difference of 2.5 cents can be a
> catastrophe in musical terms.
>
> D.
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at dropmix.xs4all.nl
> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy