Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Digest Number 1400

Hi Andy,

> Robert. An excellent post and absolutely not out of context. This is exactly
> the sort of thing we are discussing.

> Thats a wonderful analogy between drawing a squigly line to represent
> something and actually showing an accurate model of something. I couldn't
> agree more.

> What would be your thoughts then on taking longer pieces and doing an
> analysis of them. Does it need to be multiple performances of the same work,
> or would it be significant to do longer songs measuring all the way through.

> Or perhaps several songs measuring the average accuracy compared to
> the notated score? I dont think it will be possible to get hundreds of
> recordings of the same work if nothng else for practical reasons, but it
> might be possible to get many recordings and scores of different songs that
> fit certain criteria dont ya think? How many works, or minutes, or notes, or
> what have you, do you think would be necessary to analyze in order to come
> out with evidence that is statistically significant?

> This post was great because it discussed really making models of this sort of
> thing. I would love to discuss this more.

Easiest thing would be if one has a piece with notes that are notated
to differ by a single cent. Then one could use them as Bernouilli trials
using a simple true / false test - either the one that is supposed to
be higher in pitch is, or is not. Then, if one can find, say, 36 such examples,
and at least 27 have the one that is notated higher played higher, one
can conclude that it is highly statistically significant. If 24 do, then
it is still pretty significant at the 95 % level.

The more accurately the notes are actually played, the smaller the sample
one will need.

I'm sure one could also do a more refined analysis using less notes,
but stats isn't my maths subject area - could ask a statistician for help.

Bernouilli trials however are simple and an easy technique to apply.

What I could do sometime is to do a zip of some midi clips for anyone who
wants to to test their own pitch resolution for listening to music.
That way round is particularly easy to do.

I'd just do a clip of 0 cents followed by n cents, or vice versa, for
all values of n from 1 to n, say.

Then do 100 random copies of each one, put it in a zip, and leave out
the key that tells you which clip is a copy of which original (but leave
in the original of each clip, so that one can try those first, and try to
train oneself to hear the distinction - that is okay to do, and won't invalidate
the results). I have a program that does any desired number of random copies
of any clip and at the same time makes a key to them that one can look up later
to find out which is which. (Could also include the program in the zip for
anyone who wants to make more random copies).

Then another zip with the "solutions".

Then to test oneself, try one better than the best resolution one is sure
one can hear, and test as many of the clips as one has time
for, and then find out how many one got right, and then do the easy
calculation to find out the significance of the result:

if n = number of clips tested, find
s=sqrt(n/4)

then anything further than 3*s from the mean is highly significant,
and more than 2*s is also very significant at 95 % level.

Maybe one could do a poll too, and then we could possibly find out
what is the minimum pitch resolution of the Tuning List population
- without actually finding any individual's pitch resolution.

I'm curious to know what can be achieved in the way of pitch resolution for
hearing!

> > Nicely put. But, as you see, after reflection and more
> > experiments, I still think it is within reach of amateurs
> > to learn play beyond what they can actually hear!

> > Then by doing so, or attempting to do so, maybe their hearing can
> > get refined to finer pitch discrimination too, over a period of time.

> Great stuff Robert! My point with wind instruments wasn't that you couldn't
> play small intervals. Surely this would vary from instrument to instrument
> and player to player. On a side note, Ben Johnston told me a few days ago
> that he stopped giving microtonal fingerings to performers, for wind inst,
> because if his performers used the ones he gave they would always be slightly
> different pitches than his intention, and so he therefore stopped giving
> alternate fingerings and made players find the fingerings on their own. I
> dont know how long hes been doing this.

Actually that was in reply to Jon Szanto's post. Yes, that makes sense.

Perhaps giving a fingering intended for a range of notes may be more
appropriate than a single fingering for each note? E.g. the idea of
giving one fingering intended for about five distinct microtonal notes.

Kind of turns things a bit on their head. On recorder we are used to having
alternate fingerings of notes. Now, one also has alternate microtonal
notes for fingerings as well!

> cent on some instruments. Certainly it might be possible on others. I would
> also guess it would be much more difficul to play small microtones on a
> violin than a double bass obviously because the string length is much shorter
> and then requires smaller finger moves. Is it still possible however???, well
> maybe it sure might be....
...

I'm also interested to know if 1200-tet is possible on the violin. Some
time since I did much in the way of practicing string instrument, but
I have a feeling it might be, by micro adjusting position of finger,
maybe rolling it very slightly or something.

Cheers,

Robert

Re: [tuning] Digest Number 1400

🔗Robert Walker <robertwalker@ntlworld.com>

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com