[sdiy] Consider this DAC

[cheater cheater]

On Sat, Mar 13, 2010 at 14:47, Simon Brouwer <simon.oo.o at xs4all.nl> wrote:
> Antti Huovilainen schreef:
>>
>> On Sat, 13 Mar 2010, Paul Perry wrote:
>>
>>> The thing about a DC cou[[led DAC that gives 16 bit accuracy...
>>> that's going to be at least 4 bits better than the drift and noise floor
>>> of the rest of your system.
>>> Unless you are a very good analog engineer (certainly, far better than
>>> I.)
>>
>> Surely achieving < 1mV (for max 5V signal) noise floor and drift can't be
>> quite that hard?
>
> 1mV out of 5V only corresponds to about 12 bits accuracy... at 5V full scale
> 1 LSB of a 16-bit DAC is 0.076 mV.
>>
>> Plus of course there's the thing where you want higher resolution than
>> accuracy to avoid stepping even if you don't particularly care if your
>> filter cutoff is off by a 2 cents.
>
> Then it is far cheaper to get a 16 bit DAC with only the 1-LSB DNL and much
> worse INL.
> For example TI DAC8411IDCKT which costs 6.62 EUR in single quantity
> (Farnell) and has max. +- 12 LSB max INL.
>
> IMO that should even be accurate enough for any control voltage including
> VCO pitch. According to http://en.wikipedia.org/wiki/Cent_%28music%29 humans
> are only able to distinguish 5 to 6 cents in pitch difference at best.

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.