When plotting vowel space, why does using F2-F1 better resemble the idealized vowel chart than using F1?

When plotting the chart of the acoustic space of AmE vowels, we can represent F1 values on the y-axis and F2 values on the x-axis, like a chart on the page Formant Frequencies.

Alternatively, we can represent F1 values on the y-axis and F2-F1 values on the x-axis, like the chart on page 25.

It seems that the spatial distribution of vowels in the chart representing F2-F1 on the x-axis better resembles that in the IPA vowel chart, like the chart in an answer to the question How can I practice differentiating between the “æ” and “ɛ” sounds in English phonology?

I was wondering if this is true. And, if it is true, why?

• Possible duplicate of Why is the second formant plotted as F2-F1 in vowel space plots? Apr 4 '18 at 13:43
• This is IMO a distinct question: why is F2-F1 closer to an articulatory plot? The other question simply asks "why use F2-F1". Except the question has an error, since it's F2 that the difference replaces. Apr 4 '18 at 16:03
• @user6726: Oh, good point about the difference. Now I’m actually not sure about what this question is asking ... mooninnap, are you asking about the orientation of the chart? Apr 4 '18 at 17:05
• @user6726 Thanks pointing out that error. I just corrected it. Apr 4 '18 at 17:36
• I'd actually never noticed this convention. Do you think that using F2-F1 does better resemble the classic chart? Apr 4 '18 at 17:48

I don't entirely understand the why, but here is what I do know. The main reason for this convention is that F2-F1 gives a plot where the X axis better matches tongue position in back round vowels. The problem with bare F2 is that it makes vowels positions slope to the right as you go up (with [u o ɔ] not matching [ɯ ɤ ʌ]), but F2-F1 makes the back round vowels track actual tongue position, so that they slope to the left. The exact reason for this is somewhat mysterious to me.

Part of the mysterious nature of the relationship between formants, tongue position and vowel charts comes from the traditional habit of thinking of vowel articulations as being a governed by two independent factors. However, a lifetime of work by Fant and others has demonstrated that a better model is a tube with a constriction, so there is as a first approximation only one factor (the second approximation adds differences in tube length, as a function of lip protrusion).

Rounding lengthens the tube, which lowers all formants. The effect of rounding is greatest on F2, and it is greatest in back vowels. This bit of subtractive magic has the effect of "figuring out" what the lowering contribution of rounding is, and mostly removing it from the vowel plot. What is left, then, is an X value more based on tongue position, rather than the total length of the front tube.

• Thank you! This is helpful information. But isn't the effect of rounding greatest on F3, as languages like French and Dutch utilize F3 to distinguish rounded versus unrounded vowels? Apr 5 '18 at 16:54
• I was referring to just the standard vowel-plot formants, where rounding has more of an effect on F2. I don't actually know of any graphic standard for bringing F3 into the chart. Apr 5 '18 at 17:27