I was reading the second chapter of Three Areas of Experimental Phonetics by Peter Ladefoged (1967), in which he summarizes the studies he conducted in the 1950s and 1960s which demonstrated practical limitations of Daniel Jones's Cardinal Vowel system.

In it, I was struck by the fact that Ladefoged couldn't ascertain the frequency values of the first and second formants of high and back vowels because for high vowels "the first formant has a very low frequency" and for back vowels "the first and second formants are too close together" (p. 101). He then goes on to say this difficulty may have bearing on our perception of vowel quality, one effect of which being that the distance between the cardinal [i] and [e] is smaller than those of some other combinations (p. 103).

Figures 40 and 41 from pages 101-2

The chapter concludes, albeit tentatively, that (pp. 132-3):

(1) The acoustic quality of most vowel sounds can be conveniently specified by stating the frequencies of their first two or three formants.

(2) This is not true of vowels which are called in traditional terms close vowels, nor of so-called back vowels. It is not at all easy to analyse these vowels in terms of their formants.

(3) The perceptual quality of a vowel usually depends on the relationship between the pitches of the formants of that vowel and the pitches of the formants of other vowels pronounced by the same speaker.

(4) The listener to speech uses his past experience to form an adaptation level, the immediate past experience of a particular voice being the most important factor in this process.

(5) Neither of points 3 and 4 above has been shown to be true for the vowels mentioned in 2 above.

But as far as I know, linguists of today have no problem getting the F1 and F2 of high and back vowels. Is point 2 above still true? If not, why was it so difficult? And what made it easy (e.g. some kind of technological advancement)?

And what about point 5? It is still true that the acoustic distances between the cardinal [i] and [e] and between [u] and [o] are greater than those between [e] and [ɛ] and between [o] and [ɔ]. Is this just a random coincidence on the part of Daniel Jones or perhaps the phonology of French or German, or are these values indeed perceptually (more or less) equidistant? AFAIK the latter is true, but if so, was Ladefoged's assumption (in 1967) that the incongruity between acoustics and perception stems from certain formant frequencies being too close to one another correct? (EDIT: I'll ask this point separately here.)

1 Answer 1


Is point 2 above still true?

Not any more, thankfully!

If not, why was it so difficult?

Back when this paper was written, spectrograms of sound were right on the cutting edge of technology. They generally involved hooking a microphone up to a huge bank of band-pass filters, each of which was receptive to a certain frequency range, and making ink marks proportional to the amount of energy in each range.

As you might imagine, this wasn't a trivial process. If you wanted ten frequency bands on your spectrogram, you'd need ten different tuned filters; if you wanted a hundred frequency bands (which would be considered ridiculously low nowadays!), you'd need a hundred of them. It didn't scale particularly well. And linguists, who generally didn't (and still don't) get enormous equipment budgets, had to make do with whatever they could afford.

This is why back vowels were so hard to measure. The difference between F₁ and F₂ is small, so on a low-resolution spectrogram, they tend to get smeared together into a big, imprecise blob.

Similarly, the lower-frequency parts of the spectrogram tend to be louder and noisier. Even with modern spectrograms, there tends to be a lot of unhelpful noise down there, making formants harder to pick out. Back then, when the resolution was lower, F₁ for close/high vowels would tend to get drowned out by all the noise.

And what made it easy (e.g. some kind of technological advancement)?

Digital signal processing (DSP)!

The Fourier transform has been known since the early 1800s, but it was always a mathematical process, not something that could be applied to experimental data. But with the advent of DSP, and the "Fast Fourier Transform" (FFT) algorithm in particular, it turned into something that computers can do near-effortlessly. Now the frequency-domain resolution only depends on how much processing power you can devote to it, and even a low-end smartphone can make something orders of magnitude more precise than a tuned filter bank.

(Also, linear predictive coding (LPC)—this is the modern way to find formants, rather than examining spectrograms by hand. Now the entire process can be automated: put a recording in, get precise formant values out, in a way that would have been utterly inconceivable back in the 60s!)

  • Thank you for such a nice answer. If you don't mind a couple of followup questions: (1) When exactly did getting those formants become available? Around 1980, I assume? (2) Do you know about point 5, i.e. the reason behind the skewed correlation of acoustics and perception? (3) I actually can't really imagine, what did those filters look like? (I'm an uninformed millennial after all...)
    – Nardog
    Sep 4, 2019 at 23:49
  • @Nardog (1) Not sure, unfortunately, but sometime between the 60s and the 90s. (2) I haven't heard that before, so my guess would be: they just can't say for sure because of the measurement difficulties. (3) Electrically, they're basically an inductor hooked up to a capacitor, with the ratio of the two determining the frequency. I've never actually seen or used one myself, but I'd hazard a guess they looked like not particularly exciting circuit boards…I'll check with an EE friend and get back to you.
    – Draconis
    Sep 5, 2019 at 1:57
  • 1
    Cooley and Tukey's FFT paper came out in 1965. Publications applying FFT to speech signals started in 1970s, at which time mini-computers (PDP-11) were already common and relatively affordable. Schafer and Rabiner's classic book "Digital Processing of Speech Signals" came out in 1978.
    – Gene Ruso
    Sep 5, 2019 at 3:46

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