Spectral slices of overtone singing, animated

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As part of my on-going exploration of the many ways in which F0 is not pitch and pitch is not F0, I did a little demo/experiment with a sample of Anna-Maria Hefele's "Polyphonic Overtone Singing" video:

Here's an 8.85-second audio clip from that video, starting at 43.45 seconds:

Here's a spectrogram of that segment:

(The blue line at the top is Praat's attempt at pitch tracking, which follows the fundamental (at about 275 Hz) rather than the variable-strength harmonics which we hear as a time-varying melody.)

And here's the fun part, an animation of sequential spectral slices from the same clip. I've slowed the performance by about a factor of three — the spectral slices were calculated 100 times per second, in overlapping 15-millisecond windows (code available on request), whereas the animation runs at 30 frames per second. I extended the audio to match the duration of the video, without changing the pitch, using sox's tempo feature (i.e. "sox Hefele1X1a.wav Hefele1X1b.wav tempo 0.3051724 50"):

More later on what this means (for those who don't get it already), and applications of the same kind of visualization to "creak", "throat singing", "voice quality", etc. etc.


  1. Peter B. Golden said,

    October 25, 2022 @ 3:14 pm

    Very similar to Turkic "throat singing" well known in Siberia and among some of the Central Asian Turkic peoples and among the Mongols.

  2. jhh said,

    October 25, 2022 @ 3:50 pm

    Forgive me, but what does "FO" mean?

  3. Ross Presser said,

    October 25, 2022 @ 3:59 pm

    F0 (eff zero) means the fundamental frequency of the voice, as opposed to F1, F2 which are formants. More than that I don't know.

  4. Philip Taylor said,

    October 25, 2022 @ 4:02 pm

    It's F0 ("eff zero"), not FO ("eff oh"), JHH, hence "the frequency at which vocal chords vibrate in voiced sounds. This frequency can be identified in the sound produced, which presents quasi-periodicity, the pitch period being the fundamental period of the signal (the inverse of the fundamental frequency)". [Fundamental Frequency, Pitch, F0 | SpringerLink]

  5. Stephen Goranson said,

    October 25, 2022 @ 4:15 pm

    I have long appreciated the Music of Tibet: The Tantric Rituals, recorded by Huston Smith of MIT in 1968 (Anthology AST-4005), with overtone chanting.
    Even so, Anna-Maria Helefe was awesome.

  6. Victor Mair said,

    October 25, 2022 @ 5:27 pm

    "Overtone singing" (10/10/14)


    "Polyphonic overtone singing" (4/18/18)


  7. Jerry Packard said,

    October 25, 2022 @ 5:49 pm

    Wow, good work.

  8. David Deden said,

    October 25, 2022 @ 8:35 pm

    Yeah, wow. Like just yada yada then whoa!

  9. Doug Marmion said,

    October 25, 2022 @ 9:24 pm

    And here's the wonderful Tuvan group Huun-Huur-Tu, performing in the khoomei style, ie overtone singing: https://www.youtube.com/watch?v=i0djHJBAP3U

  10. Bob Ladd said,

    October 27, 2022 @ 1:08 am

    I'm surprised that Philip Taylor didn't point out that in UK English F0 is often (or even usually) "eff nought" rather than "eff zero".

  11. Philip Taylor said,

    October 27, 2022 @ 1:50 am

    But is it, Bob ? While some (perhaps many ? most ?) Britons do indeed pronounce the digit zero as /nɔːt/ (or /noːt/), I would suspect that most if not all Britons who are aware of the concept of "F0" would pronounce it as /ef ˈzɪə rəʊ/, just as almost all Britons who know what a computer program is refer to it as a computer program and not a computer programme.

  12. Breffni said,

    October 27, 2022 @ 3:36 am

    That’s fascinating. I’d be interested to know how you deal with the nuances of F0 vs pitch in introductory teaching – e.g., do you teach that F0=pitch to a useful first approximation and leave the complexities to advanced classes?

    [(myl) A student (or anyone else) who does any "pitch tracking" will soon encounter period-doubling and period-halving phenomena, as well as problematic voicing decisions and other such things. So pretending that "pitch is F0" (either in production or in perception) is as obviously wrong as pretending that planets are point masses, and as such would be a form of scientific malpractice, even in introductory classes.]

  13. Bob Ladd said,

    October 27, 2022 @ 10:50 am

    @Philip Taylor – My comment was based purely on empirical observation. In my normal professional life I have plenty of occasion to encounter people – British and otherwise – who know what F0 is, and some of the British ones definitely say eff-nought. I haven't done a systematic survey, though, and Laver's gigantic phonetics textbook (CUP, 1994), possibly with an international audience in mind, actually suggests pronouncing the abbreviation eff-zero. I vaguely recall that the man himself used to say eff-nought, but I'm no longer sure.

  14. Philip Taylor said,

    October 28, 2022 @ 5:09 am

    Well, clearly there may be people who say "eff nought" — that is an undeniable fact. The reason that I suggested that those familiar with the concept of "F0" are unlikely to do so was that, in my experience, once one starts higher education, what one called "nought" when doing sums at primary school soon becomes "zero" in higher education. I do not know for certain when I first encountered "zero" in such a context, but certainly when I was learning differentiation from first principles at the age of around 17, I was taught "In the limit, as x tends to zero, …", then I encounted "suppressed zero graph" and eventually "poles and zeros" — to the very best of my belief, I never encounted "nought" in a higher-education context. And I have to admit, the first time I read of "the noughties", I had no idea to what the author was referring, although of course it later became clear.

  15. Philip Taylor said,

    October 28, 2022 @ 10:32 am

    Odd, I could swear that I typed a Greek delta before the "x" in "as x tends to zero" … Here's another, to see if it appears this time — "".

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