Perturbation Theory, part 2
March 20, 2014 Lifes Persistent Questions
Lets step back and review what our standing wave patterns look like in an open tube And where they come from, exactly. Back to Perturbation Theory
Basic idea #1: vocal tract resonances (formants) are the result of standing waves in the vocal tract These standing waves have areas where velocity alternates between high and low (anti-nodes), and areas where velocity does not change (nodes) Perturbation Principles
Basic Idea #2: constriction at a velocity anti-node decreases a resonant frequency anti-node anti-node Perturbation Principles
Basic Idea #3: constriction at a velocity node increases a resonant frequency node node Labial Constrictions in the labial region are at anti-nodes for both F1 and F2. Labial constrictions decrease both F1 and F2 Palatal Labial Constrictions in the palatal region are at an F2 node and near an F1 anti-node F1 decreases; F2 increases Velar Palatal Labial Constrictions in the velar region are at an F2 anti-node and near an F1 anti-node F1 decreases; F2 decreases Pharynx Velar Palatal Labial Constrictions in the pharyngeal region are at an F2 anti-node and near an F1 node F1 increases; F2 decreases Larynx Pharynx Velar Palatal Labial Constrictions in the laryngeal region are at an F2 node and an F1 node F1 increases; F2 increases Different Sources For a particular articulatory configuration, the vocal tract will resonate at a certain set of frequencies no matter what the sound source is. Lets check out what Peter Frampton can do with a talk box and the Sonovox Now lets see what happens when we change our sound source to a duck call Duck Call Vowels Now lets filter the duck call with differently shaped plastic tubes. Care to make any predictions? duck call is placed here Another View [i] Duck Call Spectrograms
[i] Duck Call Spectra [i] How About These? duck call is placed on this side [i] vs. [e] [i][e] [u] vs. [o] [u][o] Philosophical Fragments
Consider the Cardinal Vowels, again. An age-old question: Why are the high, back vowels rounded And everything else unrounded? Rounding back vowels takes advantage of an acoustic synergy which lowers both F1 and F2. But is there anything wrong with rounding the other vowels? Five Vowel Spaces Many languages have only three or five vowels, separated evenly in the vowel space in a triangle Heres a popular vowel space option: iu eo a Five-Vowel Spaces Gujarati Vowel Space A Bad Vowel Space Five vowels in a vowel system are rarely, if ever, distributed thusly: [i] [e] [] Why? Adaptive Dispersion Theory
Developed by Bjorn Lindblom and Johan Liljencrants (Swedish speakers) Adaptive Dispersion theory says: Vowels should be as acoustically distinct from each other as possible (This helps listeners identify them correctly) Solanguages tend to maximize the distance between vowels in acoustic space Note: lack of ~distinction in Canadian English. Swedish Unrounded Vowel Stats Number of languages with the following unrounded vowels (out of 316, from the UPSID database): i: : : 4 : 54 e: : 4 (e: 113): 77( : 6) : : : 4 : 38 a: 14(a: 274): 22 Rounded Vowel Stats Number of languages with the following rounded vowels (out of 316, from the UPSID database): y: : 6u: 254 : : 48 : o: 88 : 5(o : 133) : : 100 : : 5 Rounded/Unrounded Ratio of number of languages with rounded vowels divided by number of languages with unrounded vowels, for particular parts of the vowel space: .056 .065(22.2) The Good, the Bad and the
High, front region of the vowel space: Unrounded vowels are preferred (good) (271) Rounded vowels are dispreferred (bad) (21) High, back region: Unrounded vowels are bad (4) Rounded vowels are good (254) Low, back region: Unrounded vowels are better (22) Rounded vowels are worse (5) Low, front region: Rounded vowels are really bad. (0) Bad Vowel #1: [y] [y] has both labial and palatal constrictions
Why is this bad? Bad Vowel #2: [ ] [] has only a velar constriction Why is this bad? Bad Vowel #3: [ ] [ ] has a pharyngeal and a labial constriction
Why is this bad? Really Bad Vowel #4: [] [ ] has both laryngeal and labial constrictions Why is this bad? Advanced Tongue Root Some languages have an added articulatory feature for vowels, called advanced tongue root found in a lot of West African languages What are the acoustic consequences of advancing the tongue root? Ultrasound This is a speaker of Kinande. Kinande is spoken in Congo.
(from Gick, 2002) Ultrasound: +ATR vs. -ATR
advanced (+ATR)retracted (-ATR) ATR vowels in Akan Akan is spoken in Ghana +ATR vs. -ATR ATR Vowel Spaces DhoLuo is spoken in Kenya and Tanzania F3 and, revisited English has pharyngeal, palatal and labial constrictions These constrictions conspire to drastically lower F3 F3 and, revisited Retroflex Vowels Retroflexion is a feature which may be superimposed on other vowel articulations. Retroflexion is contrastive in vowels in Badaga, a language spoken in southern India. Retroflex Vowel Spectrograms
[be] F3 and [y] [y] has both labial and palatal constrictions
What effect would these constrictions have on F3? [i] vs. [y] [li][ly] Overrounded Vowels Note: there is typically more rounding on [u] than [o] and on [o] than all the way down the line... It is possible to have [u]-like rounding on lower vowels over-rounding in Assamese Assamese is spoken in Bangladesh. Overrounded Vowel Spectrograms Overrounded Vowel Spectrograms