Hello,

This post is related to and inspired by elden's topic on pitch and formant shifting

http://puredata.hurleur.com/sujet-6614-upsampling-audio-signals-using-automatable-sampling-frequency

but I do not want to clutter that thread too much with my experiment results so therefore started this new thread on pitch tracking, a subtopic of time domain pitch shifting.

ACF (autocorrelation function) and SDF (squared difference function) are used a lot in time domain pitch tracking or fundamental period identification. In Pd, I was trying how autocorrelation looks like. I also constructed another function, of which I don't even know if it has a name. For the moment, I'll call it IPPASS: 'instantaneous power of phase aligned signal segment'. It can be considered a modification or extension of autocorrelation. It seems to me that IPPASS might be useful in pitch detection, as it can much better indicate periodicity in case of missing fundamental. However, I'm not yet sure how to make it work in practical implementation, if it is possible at all.

In attached patch IPPASS02.pd, ACF and IPPASS functions are plotted for a synthesized test signal with variable harmonic recipe. The concept of period detection with ACF is, to make harmonics line up so together they peak at the fundamental interval. In addition to that, IPPASS employs periodic amplitude modulations in the signal.

By no means these functions are rock solid true/false indicators. The 'art of peak picking' is another aspect of pitch tracking. Read Philip McLeod and Geoff Wyvill on ACF, SDF and the art of peak picking:

http://miracle.otago.ac.nz/tartini/papers/A_Smarter_Way_to_Find_Pitch.pdf

Katja

http://www.pdpatchrepo.info/hurleur/IPPASS02.pd

Thanks for pointing to the article, Nau. It's interesting, the YIN technique is used in STK class LentPitshift. (http://www.music.mcgill.ca/~francois/MUMT_618/Report/Report.pdf)

Today I started to try and port LentPitshift to Pd, just for evaluation purpose. Not too much progress though. First I wanted to write a flext wrapper, but did not even manage to compile the flext / STK / Pd example project 'clarinet' after a few hours of puzzling. Then tried stk2pd, very nice initiative but only for stk instruments, not stk effects, as it turned out. Anyway, if it succeeds, it gives the opportunity to check YIN and Lent's method in PD.

Katja

Edit: [lent~] was built in the end. It is here:

http://puredata.hurleur.com/sujet-6734-lent-pitch-shift-mickey-mouse

Hi Katjav,

Congratulations !
I saw the post about your [lent~] object, but couldn't test it as I am an Ubuntu 10.4 user.
And thank you for your homepage (http://www.katjaas.nl/home/home.html), very stimulating.

This pitch tracking and other pitch shifting topics do interest me for two reasons : first I'm studying Freq domain processing at the time, and these topics are very inspiring. Two, I sometimes transform my violin into a "midi controller", 'midifying' it using [sigmund~]. Of course the results are modest,and a new pitch tracking algorithm in Pd would be highly stimulating.

It would be so nice to keep only the 'YIN' part of the code and make a Pd object that could compete with [sigmund~] for mono sources. I'm no C programmer, just experienced it ten years ago, rather hovering than digging deep.
So if you think this is possible and if you wish to, it would be so nice if you could consider making it for me, and the community. I really think many Pders use [sigmund~] and [fiddle~] and would appreciate an alternative object, so your contribution would be appreciated by a lot of people ! I don't know if this is very complicated or rather straightforward, so please excuse me if I dare asking you such a work.
Of course if you think this is possible but don't want to do it, I'll try it the next months, learning something I'm not sure I want to

Thank you,

Nau

Nau, can you explain what problem you have with [sigmund~]? In my experience it is fairly accurate and it has a lot of options.

The YIN pitch tracker as implemented in LentPitShift is less accurate, and moreover it is very CPU-intensive.

From my experiments so far, it seems that Philip McLeod's SNAC method is the best time domain solution. It is fairly efficient, probably accurate and stable. Moreover, it needs no Hann windowing, therefore it can work with smaller analysis frame. Although it is not immune for octave errors, improvement may be possible with more refined peak picking algorithms as described by Paul Boersma:

http://www.fon.hum.uva.nl/paul/papers/Proceedings_1993.pdf

I'm planning to write the SNAC method in a Pd class and test it thoroughly, in preparation for a time domain pitch shifter.

So what is the advantage of an autocorrelation-based pitch tracking method, over a frequency domain method like [sigmund~]? For me, the difference would be that it's simpler. I've done frequency domain pitch tracking some time ago, and found that it is hard to find the fundamental there, if it is relatively weak. In time domain it is easier: the fundamental gives the largest peak, even if it is weaker than the second harmonic. And in case of doubt, I could compute the IPPASS, which is unambiguous in such cases.

Autocorrelation is most efficiently calculated via frequency domain. This means, it can not be more efficient than a frequency domain pitch tracking method. If SNAC turns out to work well enough, I would probably use it in downsampled time, because the signal stream has to be filtered anyway. Say your analysis frame needs to be 1024 samples at samplerate 44100, 4 times downsampling would enable an analysis of only 256 samples. Latency is still 1024 samples of course, but you could do 4 analyses 'at the price of 1', and have a new pitch indication every 256 samples.

Katja

Thank you Katjav.

you're right, [sigmund~] works fairly well. But octave shifts are not rare, and are my major concern. Violin is rather noisy, especially in transients, but I imagine I shouldn't dare dreaming of sensible improvements in transients, as I know this is a common problem in pitch tracking.

Thank you for your comments and explanation about pitch tracking, you have the eagle eye's view while I have the bug's eye view Now I understand that YIN is less interesting topic to be explored than others.
I'll keep on studying !

Thank you,

Nau

@nau said:

[sigmund~] works fairly well. But octave shifts are not rare, and are my major concern.

I'm still working on the pitch tracking topic, and curious to know about your experience, Nau. If you have octave jumps with [sigmund~], are they downward jumps or upward jumps in general? Or both?

Transients are a special case indeed. They tend to have fairly high frequency content, and a noisy character as compared to sustained notes. [sigmund~] has 'maxfreq' and 'stabletime' parameters which can help excluding transients and noise. Steep filtering at (for example) ~1 KHz also helps to get more stable pitch detection. But the best solution would be to combine transient detection and pitch detection in one comprehensive analysis process. Most transients can be detected within one or two milliseconds, as their magnitude rise is very sudden.

Nau, I have another, off topic question for you. I've seen it stated more than once that violin tones played together slightly out of tune do not produce the 'beat' or 'roughness' phenomenon, or at least less so than other instruments. Can you confirm this from experience? My father and I had once set up a Pd experiment to test the statement and quantify amplitude modulation. But the point is, we're no violin players. I wonder, could you record two slightly out of tune violin tones, a few seconds each, for this test? That would be cool.

Katja

@nau said:

Thank you Katjav.
you have the eagle eye's view while I have the bug's eye view

perfect analogy. love it

Hi Katjav,

I remember mainly higher-octave jumps, but maybe is this just of matter of perception. I'd need to play with it again and check it properly. I'll try steep filtering along. I forgot to mention another common problem encountered with my basic [sigmund~] implementation : as note-off are sent using a fixed low threshold value, sometimes a unique note is played with two or more separated notes. A classic case is the strong pizzicato on the lower string (G), as sound amplidtude exhibits an envelope that decreases below the threshold and goes back up again, producing a new note on, and then decreases again to produce the last note off. But I learned things in the meanwhile that could lead to improvements of my old patch. Amplitude calibration has taken me some time, and this make me think now that I should 'pre-process' the incoming sound to maximize stability and performance (compression ?, steep lo-pass,...)

About perception of beats with violins, I never heard that violins play 'unison' in a less ugly fashion than other instruments, and when I play with a friend of mine 'unison' are always tricky. But I'm just an amateur player, as you will hear with the three samples I recorded for you.
I had to power off the heating fan for recording and my playing is quite shivery I used the fine tuners to detune, but I'm not sure the amount of detune was well chosen in regard to the test. Tell me, I can re-record something better if you give me guidelines.

http://www.sendspace.com/file/4l9sag

Nau

Thanks for recording the violin notes for me Nau. I hope you did not catch a cold after turning the heating off.

The "beatless violin hypothesis" can be found in Arthur Benade's 'Fundamentals of Musical Acoustics' amongst others. See a possibly unofficial copy of the relevant chapter here (at about 3/4 down in the text):

http://www.zainea.com/violinfamily.htm

some citations:

"While I was still an undergraduate I noticed that one does not hear clear-cut beats between mistuned violin tones of the sort that painfully advertise slight errors between two wind instrument sounds. 1t was not difficult for me to recognize at that time that the weakness of the beats implied unsteadinesses in the sticking and slipping of the rosined bow on the string." ...
" On the one hand it allows larger tuning errors to be made in ensemble playing before the discrepancies become unacceptable, and on the other it permits the composer to write a wide variety of chords having many degrees of consonance and dissonance."

Recently I've seen that statement repeated more often, but don't remember where exactly. Anyway, I did a quick patch to check the amplitude modulations in the sum signal of your two original recordings. Of course, there's already a lot of amplitude modulations in the originals. Still it is very well possible to observe and quantify the beat phenomenon. See attached patch (to be used with your recordings).

'Thank you for watching this episode of MusicalMythBusters'.

Katja

http://www.pdpatchrepo.info/hurleur/violinbeats.pd

I had to surrender. IPPASS is a nice idea, but Philip McLeod's SNAC is unbeatable in terms of speed and accuracy. Find a new pitch tracker [helmholtz~] based on SNAC here:

http://puredata.hurleur.com/sujet-6776-helmholtz-guess

Katja