Editing 2657: Complex Vowels

This is another one of Randall's [[:Category:Tips|Tips]], this time a Linguistics Tip. The curly-haired linguist, [[Gretchen McCulloch]], manages to produce a cursed sound using complex vowels, which cannot be comprehended by normal humans like [[Cueball]] and [[Megan]], who both seem to get a headache from listening to the sound. The sound she makes was produced by extending the IPA vowel plane along an imaginary axis to form the complex vowels.

In phonetics based on the {{w|International Phonetic Alphabet}} (IPA), the space of {{w|vocal tract}} articulators determining {{w|vowel}}s <!-- (as opposed to unvoiced consonants) -- nasals and liquids don't care where the tongue is, in any language {acn} --> is represented as three dimensional, from the position of the tongue and lips. The vertical axis represents vowel height or ''closedness'' (i.e., how close or far the tongue is from the top of the mouth), and the horizontal axis represents front-to-back ''place'' (i.e., how close or far the top of the tongue is from the teeth.) The position of the tongue, along with the frequency of the {{w|vocal cords}} vibrating in the larynx from air being exhaled by the diaphragm, are the primary determinants of the fundamental and second {{w|formant}} frequencies of vowel sounds. A third dimension of vowel sounds is the "roundedness" of the lips, represented on the IPA vowel chart to the right by pairs of vowel phoneme {{w|glyph}}s. Other higher-dimensional vowel representations include {{w|diphthong}}s, which are simply two different sequential vowels slurred together; diphones, which represent the last half of one phoneme followed by the first half of the next; {{w|vowel shift}} mappings delineating different accents[https://core.ac.uk/download/pdf/47086396.pdf][https://www.sciencedirect.com/science/article/abs/pii/S0095447010000562] and long-term evolution of voiced phone sounds; and {{w|cepstrum|cepstral}} representations such as {{w|Mel-frequency cepstrum|mel-frequency cepstral coefficients}}.

[[Randall Munroe|Randall]] suggests increasing the range of vowel sounds available by using complex notation to indicate an additional dimension with an "imaginary" axis. In mathematics, {{w|complex number}}s are numbers including both real numbers and {{w|imaginary number}}s. A complex number can be expressed as, "''a'' + ''b''i," where ''a'' and ''b'' are real numbers, but the latter imaginary part is combined with 'i,' the square root of negative one, as depicted in the central expression in the comic by √<span style="border-top: 1px solid currentColor">-1</span> indicating a further dimension of coordinates. When expanding the one-dimensional number line with an imaginary axis, it becomes two-dimensional with the "''b''i" component {{w|orthogonal}} to the original "real" number line. Linguists never use the {{w|complex plane}} to represent vowel roundedness or any other higher-dimensional features of phonemes, although the properties of complex numbers could conceivably support representing physiological features of the vocal tract, such as prior position of the articulators.{{cn}}

This comic conflates complex numbers in mathematics with "complex vowels" in linguistics. Such complex vowels are implied to create sounds which cannot be properly processed by the human brain and represents one with a heavily modified "schwa" {{w|Ə}} phoneme, mirrored vertically and surrounded by multiple {{w|diacritics}} akin to the {{w|Zalgo text}} meme. The sound of this supposedly alien vowel has Cueball and Megan clutching their heads. Overall, Randall's complex vowels bear similarity to the cliché of "black speech" in {{w|Lovecraftian horror}}, a language created by alien beings with different vocal patterns than humans.

In linguistics, 'ə' is the {{w|schwa}} symbol, referred to in the title text and the depiction of complex phonemes, the most common vowel sound in English polysyllabic words (the 'a' in "comma" or the second 'e' in "letter.") Production of the schwa sound takes place with the tongue, jaw, and lips all in a relaxed, central position, and is often entirely optional in many if not most dialects of English. The pronunciation of "[ṡṡċċḣḣẇẇȧȧ]" in the title text is said to sound like the x in the word fire. In fact, there is no x in fire.{{Citation needed}} This is perhaps in line with the idea that complex sounds are incomprehensible to most humans, and likely also impossible to pronounce by anyone other than experts such as [[:Category:Comics featuring Gretchen McCulloch|Gretchen]]. Another example of weird diacritics is in [[2619: Crêpe]], and with Zalgo text in [[1647: Diacritics]]. The use of typography to create psychological stress is explored in [[859: (]].

:[A diagram shows the extrusion of the trapezoidal IPA vowel chart upwards into three dimensions. A point near the center is labeled with an equation that shows "ə + ½√-1 " as being equivalent to a made-up symbol that looks like two schwas mirroring each other with other markings above and below.]