I've refined procedures in pitch tracker [snac~] (based on Philip McLeod's Specially Normalized Autocorrelation function (SNAC)), and renamed the object in the honour of the great 19th century explorer in the world of sound and frequencies, Hermann Helmholtz. The guy who listened through resonators to isolate frequencies in a sound.

[helmholtz~] is by default deaf for noise, but hears periodic sound no matter how faint. As a result, analysis frames containing transients, note jumps, or other signal segments with low autocorrelation are ignored. It's better to have no pitch report than an erroneous pitch report. Pitch estimation is precise up to +/- 0.1 Hz.

While regular methods need at least two periods in the analysis frame for detection, [helmholtz~] can do with a minimum of 1.2 periods. As a result, a female voice can be pitch-tracked with a frame of 512 samples at SR 44100, that is ~11 milliseconds. For a male voice and most instruments, 1024 samples are sufficient, that is ~23 milliseconds.

Remember that a time domain method can not distinguish multiple pitches in a stream, so [helmholtz~] must be used with monophonic channels only.

The object uses 0.6% CPU time per instance on my 2GHz CPU, with default settings, no analysis overlap. Since it only needs fundamental frequencies, it can be used in downsampled time as well, for example with resampling factor 0.25. Then you can do four overlapping analyses for the price of one, making things smoother as you get analysis results at a faster rate. Don't forget to resize the analysis framesize accordingly, otherwise you get long latency times.

I've extensively tested [helmholtz~] with my voice and all sorts of sweeping and jumping test tones. It does not seem to make mistakes with these sources. That may be different for other instruments, I'm eager to hear comments.

Attached file helmholtz~.zip contains source code, makefile, 32 bit binaries for OSX, Windows and Linux, help file and test patches.

Thanks to elden, who posted so many useful links on pitch shifting and tracking on this forum. [helmholtz~] would not have existed without all the info's. Find Philip McLeod's thesis introducing the SNAC function here:

http://miracle.otago.ac.nz/postgrads/tartini/papers/Philip_McLeod_PhD.pdf

Katja

P.s. [snac~], the experimental predecessor of [helmholtz~], is now discontinued.

Edit: find the latest [helmholtz~] now on:

http://www.katjaas.nl/helmholtz/helmholtz.html

http://www.pdpatchrepo.info/hurleur/helmholtz~.zip

Great work, Katja.

edit: I cannot believe how much better than [sigmund~] this is! Wow. I was going to use [sigmund~] in a research presentation next Tuesday. I am now using [helmholtz~]

It is also going in my performance system.

I have been sending some different oscillator banks to [helmholtz~] at specific frequencies (chromatic rise and fall from E0). I would like to convert the tracked frequency to MIDI note number with [ftom] but the resultant MIDI numbers are not stable, even after tweaking the parameters accordingly.

Anyone else having this problem?

edit: using [round] fixes this problem, but I thought I'd mention the result anyway.

Hey Ricky, thanks for your feedback. I almost forgot about [helmholtz~] since I do not use it (yet) in my own setups. In case you put it in a shared patch, note that [helmholtz~] is not part of Pd-extended and you have to supply [helmholtz~] binaries with the patch.

If [helmholtz~] is better than [sigmund~] for certain purposes, it probably should become part of Pd-extended (version 0.44 at earliest), but that is not a trivial thing.

Katja

@ricky said:

I have been sending some different oscillator banks to [helmholtz~] at specific frequencies (chromatic rise and fall from E0). I would like to convert the tracked frequency to MIDI note number with [ftom] but the resultant MIDI numbers are not stable, even after tweaking the parameters accordingly.

Can you post a patch with the problem (and workaround)?

@katjav said:

Can you post a patch with the problem (and workaround)?

Here we go. Sorry for the delayed response. [helmholtz~] is in the "gesture extraction" parent/subpatch.

I used it on Tuesday afternoon for a research presentation and it worked great at extracting note-event (attack) and rounding to desired MIDI pitch using [round] but I would like to use it like I would use [sigmund~] with the "pitch" argument. Using [round] is quite limiting, but it works within some scenarios, for sure.

The zipped file also includes audio samples and my pitch tracking abstraction using [sigmund~]. It also utilises Malham's "ambilib" library for ambisonics within Pd.

Ricky

http://www.pdpatchrepo.info/hurleur/pd_patch.zip

Hi Ricky,

Indeed [helmholtz~] has no note detection method built in. Attached patch illustrates a few solutions for different signal types. No universal method so far, but it may be possible to combine methods. Interesting challenge.

Katja

http://www.pdpatchrepo.info/hurleur/helmholtz~notedetection.pd.zip

This is great! Certainly a lot easier than using amplitude thresholds. Wow. Exciting stuff - some new abstractions to build this summer, I think. Please keep us posted on the development of this object.

Do you think it would be possible to detect the oscillation/beating interaction between two tones using an object like [helmholtz~]? - I would really like to develop a patch that did this so I could use the oscillation rate to control different processes.

e.g. An interval of a minor second would produce fast oscillations which could be used to control the rate of an oscillator.

@ricky said:

Do you think it would be possible to detect the oscillation/beating interaction between two tones using an object like [helmholtz~]? - I would really like to develop a patch that did this so I could use the oscillation rate to control different processes.

e.g. An interval of a minor second would produce fast oscillations which could be used to control the rate of an oscillator.

Nice idea! I think for measuring beating, you will need a pitch tracker that works below the threshold of human pitch perception.

Sure but something like [helmholtz~] or [sigmund~] could produce approx. oscillations, even in the time domain?

If you want to find beat frequencies, you need to convert the signal into a stream of instantaneous amplitudes and find the fundamental frequency in that stream.

Amplitudes can not be negative, so I was sceptical about the possibilities of interpreting such a stream as a signal and find it's pitch. Years ago I've spent a lot of time on this same question in vain. But to my surprise, [helmholtz~] translates a DC-filtered rectified sinusoid into a smooth sinusoid with measurable pitch. Couldn't believe my eyes, frankly.

So, up to a certain extent, it seems indeed possible to find beat frequencies. The notes must be played with similar amplitude (+/- 6 dB or so). Of course, beat frequencies can be low and therefore their detection needs a large analysis frame with long latency. See attached demo patch.

Katja

Edit: slightly revised patch uploaded. The [helmholtz~] binary is needed to use the patch, get it here:

http://www.katjaas.nl/helmholtz/helmholtz.html

http://www.pdpatchrepo.info/hurleur/helmholtz~-beattest.pd

Words cannot express how awesome this is - Is there a reference available anywhere so I can get my head around the math of the construction of the complex signal/computation of the amplitudes?

Further to this - doesn't this touch on A. Porres's work on dissonance curves from Pd Con?

Forgot to mention this: any harmonic recipe shows amplitude modulation, so you will also get a 'beat frequency' result for a single harmonic note. In this case, the modulation frequency equals the fundamental frequency or (less often) a higher harmonic.

It's funny that almost every tone, except a pure sinusoid, has amplitude modulation, but you just do not perceive it as such if the sound is harmonic.

The beat frequency matter relates to section 'Roughness' in Alexandre's Pdcon2011 paper. But I could not find a link to his [roughness] object or abstraction. Ricky, do you know where to find it?

About making complex signals I do not know of specific literature, but I did document my experiments on the topic:

http://www.katjaas.nl/hilbert/hilbert.html

Katja

It's funny that almost every tone, except a pure sinusoid, has amplitude modulation, but you just do not perceive it as such if the sound is harmonic.

A good book on auditory perception is "Auditory Scene Analysis" by Albert Bregman (McGill). Maybe you are familiar with it? Fluctuations which occur quickly are organised as a fused percept, relative to other musical cues (harmonic structure). Very interesting read.

I am not sure about [roughness] object, Katja. I know A. Porres is on the mailing list, maybe try him there? Also, his email is porres at gmail dot com. I may email him also.

Thanks for the resource. I will have a look momentarily. Having fun controlling LFOs for the moment

Not the most exciting purpose for a pitch tracker: a general-purpose tuner. Anyway, I needed one and thought, why not use [helmholtz~]. Shows note name, midi note number, frequency, and deviation. See attached.

Katja

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

Good evening,
I am just trying out your patch and it seems to be much more precise and quicker to react to changes than [sigmund~] as other users have noted. However, for some reason, when I run this audio sample of a trombone into [helmholz~], the second note is not detected at all and the numbers just stand still until the trombonist plays his third note; whereas [sigmund~] with the argument "notes" puts out the pitch of each note in the phrase without a problem.

Is there something I can do to remedy this, or am I better off using [sigmund~] for the trombone and mazbe [helmholtz~] for other instruments?

http://www.pdpatchrepo.info/hurleur/trombone1.wav

Good evening,
I am just trying out your patch and it seems to be much more precise and quicker to react to changes than [sigmund~] as other users have noted. However, for some reason, when I run this audio sample of a trombone into [helmholz~], the second note is not detected at all and the numbers just stand still until the trombonist plays his third note; whereas [sigmund~] with the argument "notes" puts out the pitch of each note in the phrase without a problem.

Is there something I can do to remedy this, or am I better off using [sigmund~] for the trombone and mazbe [helmholtz~] for other instruments?

http://www.pdpatchrepo.info/hurleur/trombone1.wav

Hello diemildefreude,

If you set [helmholtz~] to give output at lower fidelity level, for example [fidelity 0.5(, you will see that fidelity of the second note is much lower than [helmholtz~] default fidelity setting of 0.95. Also, you will notice that the pitch is actually detected with that lower fidelity setting. If you use patch [helmholtz~-soundfiletest] which comes with the helmholtz~ package, you can see the autocorrelation plot for the notes, and it becomes clear that the second note is particularly 'distorted', has lower harmonic content. This sound is typical for trombone, but you could experiment with fidelity settings to find the appropriate setting for trombone.

Katja

Hey guys, sorry to ask a question that I could just test myself, but my old MacBook recently died and my new laptop isn't compatible with my audio interface. But I'm curious if the beat frequency can be detected from a single note on a guitar string. Because the vertical restrictions of vibration at the bridge and nut of a guitar are different than the horizontal ones, the transverse waves along a string can travel at different speeds depending on their angle. This causes slow and subtle beating. I was trying to approximate this a while ago by using two detuned waveguides played together, but I was just sort of playing it by ear since I didn't know how to determine the beat frequency (and I have a feeling it may be amplitude-dependent and thus changing as the note decays; there is a frequency drop as the note decays as well)

Anyway, I'd love to hear if you all think [helmholtz~] can do this. Ricky, I know you've been working on analyzing features of guitars for your live performance setup. Maybe you could take a look? Like I said, I'd try it myself, but I need to save up for a new interface. If you can, thanks in advance.

I will be revisiting this at the end of June. I don't see why it wouldn't be possible? I will certainly look into it.