Real Audio

Hi Gang!
We just got a Real Audio server at the university and I am
putting microtonal streaming audio on my web page. Two things:

1. I don't know the law on putting other people's stuff on my page, but I
sure would like to put some Partch, Darreg, etc. there. Does anyone on
the list know the law on these matters?

2. I would like to put samples of the music of tuning forum members on my
page, so if any of you have some microtonal music you would like to post
there, please send it along and I will! First preference will go to
ra and .wav files since they are easiest, followed by CDs and audio
tapes. I do not have facilities for converting DATs. You can email me
with attached files, or send media to

John Starrett
3500 Clay St.
Denver, CO
80211

I will keep it up until the system administrator slaps me for hogging the
hard drive.

John Starrett
http://www-math.cudenver.edu/~jstarret

>Play ANY music fast enough and I suppose the errors become negligible.

I personally agree that the "clean" feeling of JI is best appreciated
with long, sustained chords. But even still, I personally have found that
you don't have to hear given harmonies in long sustained tones to notice
their tuning character. Even if you play them each for a short duration,
you can perceive a cummulative character to them provided that you play
enough of those short chords.

>For three notes, the average=0Aabsolute values for the devia=
>tions of the average partial frequencies from n=0Atimes the average =93gl=
>obal=94 frequency were: 0.44, 1.04, and 0.48 cents.

Thanks Dave, for the details on your results.

Do you have any way of characterizing your process' margin of error?
That is, could these sounds be absolutely exactly harmonic (short of noise
components and human/random fluctuations in the entire tone of course), and
your process could only detect their pitch within that accuracy (that of
course being quite impressive accuracy)? Or is it more likely, in your
view, that these pitch deviations from exact harmonic frequencies are very
definitely present in the overtone structures of the tones?

=09I recently joined the tuning forum and have followed the recent discus=
sion=0Aabout tuning resolution with interest. I have worked fairly exten=
sively with=0AFourier additive analysis and pitch extraction algorithms (=
which I received=0Afrom the University of Illinois=92 CERL music lab and =
further developed), and=0Ahave analyzed a number of digitally recorded vo=
ice and acoustic instrument=0Asounds (16 bit signed integer samples at a =
40 KHz sampling rate). In this=0Awork I was impressed by the closeness o=
f the frequencies of the partials of=0Amany, but not all instrument sound=
s to being exact integer multiples of the=0Abasis frequency as determined=
by pitch extraction (as a frequency vs time=0Atrajectory which I usually=
computed at points roughly a millisecond apart over=0Athe course of the =
sound). Frequently the deviations of time averaged partial=0Afrequencies=
from n times the time averaged basis frequencies (n an integer)=0Awere l=
ess than one cent.

=09Here are some results which I obtained: For three recorded soprano no=
tes of=0Aroughly one second duration with vowel sounds =93ah=94 and =93ee=
=94 at e4 and f4, I=0Aaveraged the =93global=94 frequency of the sound ov=
er the main portion of the note=0A(appreciable sound volume) and then ave=
raged the frequencies of the first 20=0Apartials over this same portion o=
f the note. For three notes, the average=0Aabsolute values for the devia=
tions of the average partial frequencies from n=0Atimes the average =93gl=
obal=94 frequency were: 0.44, 1.04, and 0.48 cents. For=0Athree recorded=
baritone =93ah=94 sounds at a2, g3, and c4, having durations of=0Aroughl=
y 2 seconds, these deviations in cents (average for first 20 partials)=0A=
were 0.57, 0.55, and 0.41. For a trombone f3 sound, the average absolute=
=0Avalue of the deviation of a partial=92s average frequency from n times=
the=0Asound=92s global frequency was .48 cents (first 20 partials).

=09The averages of the instantaneous deviations of the frequencies of par=
tials=0Afrom n times the global frequency over a set of time points space=
d a=0Amillisecond apart over the duration of the sounds appeared to be co=
nsiderably=0Agreater than this.

=09In the case of a flute d4 note a little under a second in duration, th=
e=0Adeviations in the average partial frequencies from n times the global=
=0Afrequency of the sound amounted to 4.55 cents, roughly ten times great=
er than=0Athese deviations were for the sung notes and the trombone note.

=09I analyzed a piano a2 sound of roughly 2 seconds=92 duration and here =
will give=0Athe cent deviations of the average partial frequencies from n=
times the=0Aaverage global frequency over the early portion of the sound=
just after the=0Apeak of the attack for the first 20 partials: Partial =
1: -11.4 cents; par. 2:=0A-6.7 cents; par. 3: -7.3; par. 4: -6.7; par. 5:=
-6.5; par. 6: -5.8; par. 7:=0A-4.8; par. 8: -3.5; par. 9: -1.1; par. 10:=
+1.0; par. 11: +5.1; par. 12: +5.0;=0Apar. 13: +7.9; par. 14: 10.4; par.=
15: +8.9; par. 16: +16.9; par. 17: +20.1;=0Apar. 18: +23.0; par. 19: +24=
6; par. 20: +29.1. The results for a c4 piano=0Anote I analyzed were si=
milar but not identical to those for the a2.

=09I've gone into some specific detail as I believe this is necessary in =
order=0Ato give a meaningful picture of the results of this work.

=09I have the impression that seemingly small shifts in the frequencies o=
f=0Amusical sounds can have surprisingly large effects on the cumulative=
=0Aimpression which the music creates.
=09
=09Note: I am doing non-real-time additive synthesis of musical notes on =
a=0AMacintosh 8500 computer for purposes of developing demonstrations and=
also=0Alistening tests for use in research in musical aesthetics. Recen=
tly I've had=0Aa piano retuned to quarter comma mean tone temperament and=
have been exploring=0Aits harmonies and have prepared a few demonstratio=
ns of pieces of music played=0Aside by side in equal temperament and in q=
uarter comma mean tone temperament.=0AMany have found the difference betw=
een the effects of these different tuning=0Asystems to be striking.

=09Dave Hill, La Mesa, CA=0A

At last, some hard data! Some problems, though ...

> advance. For the first 10 partials I obtained over that .7 sec. time
> stretch cent values for the RMS instantaneous deviation from harmonic o
> f: 3.20, 1.92, 1.08, 1.12, 1.72, 3.25, 4.08, 3.17, 2.58, and 1.95 respe
> ctively. I plotted the deviations from harmonic for some of the partia

Does this mean you're using FFT windows much smaller than 0.7s?
I think these values must be experimental artifacts. Try analysing
a sawtooth wave with equivalent vibrato and tremolo to calibrate
the uncertainty. Use an analog synth if you can.


I mentioned this business with conical tubes to show that there is
a quantifiable physical origin for inharmonicity. The periodicity
of the sounds presumably defaults to the player's ability to
blow a raspberry. Does this mean the resulting overtone series
is constructed from undertones of the original vibration? I think
a slide trombone must be pretty near cylindrical, so analysis of a
French horn or something would be more useful.

>Does this mean you're using FFT windows much smaller than 0.7s?

I don't think that Dave's system is/was even based upon FFTs, but I
probably ought to let him confirm that for sure.