This is supplemental material for The experimental state of mind in elicitation: illustrations from tonal fieldwork that follows up on Section 2.4, which recast Hyman (2007)'s work on tonotactics in Thlantlang Lai in terms of experimental design. It introduces additional examples of using experimental design principles to generalize to elicitation methods beyond Pike's toneme discovery procedure.

These examples are divided into the following sections:

A references section follows.

## Coarsening and refining variable levels

One way to generalize beyond Pike's toneme discovery procedure is to generalize beyond the set of variables under consideration. In addition to considering other independent variables---explanatory as well as confounding variables--another way to generalize the set of variables is if we don’t add any new variables, but we change the definition of some of the variables. We could do this in such a way so that a re-defined variable is incomparable to the old one. For instance, we could change the levels for a factor SEGMENT from voiced and voiceless to singleton, geminate, and supergeminate. But there is no subset/superset relation between the original levels and the new ones, and this kind of re-defining a variable is effectively the same as adding a new variable.

There are also two ways we could redefine a variable so that is still comparable:

1. Coarsening the partition of the possible instantiations of the variable (increasing the number of levels of the variable)

2. Refining the partition of the possible instantiations of the variable (decreasing the number of levels of the variable)

When we coarsen the partition, we reduce the number of levels for a variable, merging levels with one another. When we refine the partition, we increase the number of levels for a variable, splitting levels. We might also both coarsen and refine in re-defining a variable.

One example of coarsening the partition is given in the table below. This is adapted from the study of contextual tonal variation in Mandarin in Xu (1997, p. 70). The explanatory variable of tonal class of the target syllable had 4 levels, following the 4-way tonal contrast in Mandarin (abstracting away from the neutral fifth tone). However, the explanatory variable of the pre-target tone, i.e., the tone class of the syllable preceding the target syllable, collapsed the 4-way distinction for Mandarin tonal classes into a 2-way distinction based on the tonal offset: both Tone 1, a high tone, and Tone 2, a rise, were classified as having a high offset, and both Tone 3 (low) and 4 (fall) were classified as having a low offset. In autosegmental-theoretic terms (Goldsmith 1990, Goldsmith 1976), one might say that the new variable assumes that contour tones are treated as tonal sequences (fall = HL, rise = LH) and pays attention only to the tone at the right edge of the syllable.

Tone Old level Mapping New level
Tone 1 High High $\mapsto$ H H
Tone 2 Rise Rise $\mapsto$ H H
Tone 3 Low Low $\mapsto$ L L
Tone 4 Fall Fall $\mapsto$ L L

Another example of coarsening the partition defined by a variable comes from Keating (2011), a cross-linguistic study of the acoustic parameters involved in distinguishing phonation types. Here, for the purposes of standardization for comparison with other languages, the 7-way tonal contrast in the White Hmong data from Esposito (2012) was coarsened into a 3-way contrast capturing the rough location of the tone within the pitch range—either high, mid, or low—for the same data, for the purposes of the cross-linguistic comparison in Keating (2011), see the table below:

Tone Old level Mapping New level
b-tone High-rising High-rising $\mapsto$ H H
null-tone Mid Mid $\mapsto$ M M
s-tone Low Low $\mapsto$ L L
j-tone High-falling High-falling $\mapsto$ H H
v-tone Mid-rising Mid-rising $\mapsto$ M M
m-tone Low-falling Low-falling $\mapsto$ L L
g-tone Mid-falling Mid-falling $\mapsto$ M M

An example of refinement of the partition induced by a variable would be the reverse of the mapping for Mandarin tones in Xu (1997): rather than collapsing a 4-way distinction into a 2-way distinction, one would refine a 2-way distinction into a 4-way distinction. Another instance of refinement would be the addition of a level for tonal class upon the discovery of evidence for a new tonal class in the course of fieldwork.

Those two examples of refinement both involve increasing the number of levels to some finite number, but refinements may also involve mapping from a set of a finite number of distinctions, e.g. 4 levels, to a set of potentially infinitely many distinctions, i.e.the set of real numbers.1 An example of this kind of refinement would be changing a length variable from counting syllables, e.g. 1 syllable, 2 syllables $\ldots$, to measuring absolute time, e.g. 343.25 milliseconds, 692.11 milliseconds. This kind of refinement might seem intuitively more drastic than refining a 2-way tonal distinction into a 4-way one, and it is: it’s a change in variable type (Stevens 1937), similar to a change in type in type-theoretical semantics (Gamut 1992, Ch.4; Carpenter 1997 Chs. 2, 3).

## Generalizing to different research questions

A more drastic way to generalize beyond Pike’s procedure is to apply principles of experimental design to other research questions. In this section, we give examples of research questions treating tone as a dependent variable rather than an independent variable (Tone as a DV), including examining phonetic tonal sandhi, i.e. tonal coarticulation, in White Hmong (Example 1); we also given an example of using a factorial design in uncovering evidence for a tonal case marker in Samoan (Example 2).

### Tone as a dependent variable

Thus far in this paper, we’ve considered tonal class as an independent variable manipulated by the fieldworker, but we’ve never considered tonal class as a dependent variable. This is not because tonal class cannot be treated as a dependent variable, but simply due to the nature of our research questions—we’ve focused on making hypotheses about possible tonal classes and their reflexes in the pitch contour and refining these hypotheses.

There are two main situations in which tone might appear in the dependent variable:

• in explorations of how tonal contrast is produced and perceived
• in explorations of phonological allophony and alternation

Some example research questions about exploring the dimensions of tonal contrast are:

• What effect does tonal class have on the pitch contour over a word?
• What parameters in the speech signal are available for discriminating different tonal classes?
• What cues in the speech signal do listeners use to identify tones?

Some examples of work along these lines appear in Connell (2000) (perception), Khouw (2007) (production and perception), and DiCanio (2009) (production).

In explorations of phonological allophony and alternation, tone makes an appearance in the dependent variable because the mapping between underlying tonemes and surface tones (or between surface tones) is of primary importance. Underlying form is manipulated as an explanatory variable, and the dependent variable is the surface form. Note that there must be a linking hypothesis about the mapping from observables (perhaps the pitch contour over a word) to surface tones in such an elicitation experiment. We presented an example of a factorial design in tonal fieldwork exploring allophony in the body of the paper in Section 2.4.

### Example 1: tonal realization in White Hmong

A similar factorial design for tonal bigrams, but for studying the phonetic realization of tones in White Hmong (Hmong-Mien, China) is given below. Since the focus is the acoustic variation induced by tonal classes, there is a large and detailed set of acoustic dependent variables.

• Research question: How are tones in White Hmong acoustically realized?

• Strategy: Control some known sources of variability in tonal realization and manipulate others to study a selected range of tonal variability.

• Research hypothesis:

• Linking hypothesis: Acoustic dimensions relevant for tonal discrimination in the production of White Hmong tones include f0-based parameters and various spectral parameters.

• Experimental unit: elicited sentences

• Explanatory variables

• $N_1$ tone: b, n, s, j, g, m, v
• $N_2$ tone: b, n, s, j, g, m, v

• Confounding variables
• prosodic position: isolation, sentence-medial
• carrier phrase: fixed with two phrases, with target words randomly assigned to one of the two phrases
• segmental features of words: fully [+sonorant] (fixed)
• CV skeleton: CVV (fixed)
• pragmatic context: out of the blue (fixed)

• Dependent variables
• mean fundamental frequency
• syllable onset fundamental frequency
• syllable offset fundamental frequency
• mean spectral tilt
• mean harmonic-to-noise ratio
Block IV Levels
Isolation $N_1$ tone b, n, s, j, g, m, v
$N_2$ tone b, n, s, j, g, m, v
Sentence-medial $N_1$ tone b, n, s, j, g, m, v
$N_2$ tone b, n, s, j, g, m, v

### Example 2: tonal case marking in Samoan

Moving back upwards towards the morphosyntax-prosody interface, this section gives an example of a 2$\times$2 factorial design examining the effect of the interaction of case-marking pattern (absolutive-oblique, ergative-absolutive) and word order (VSO, VOS) on the f0 contour in Samoan (Polynesian, Samoa), with the goal of examining the hypothesis that there is a high tone at the left edge of absolutive arguments. The experimental design involves minimal sets of sentences, keeping segmental material in test sentences constant except for the segmental case markers for ergative and oblique case. Some factors are controlled for optimizing our chances of observing prosodic realization realized in the f0 contour. First, words are fully sonorant so that the f0 contours is free from segmental perturbation. Secondly, arguments of long length, i.e. many words, are used to allow plenty of segmental material for intonational tonal events to be realized (Bruce 1977).

• Research question: Does Samoan have a high tone at the left edge of absolutive arguments?

• Strategy: Control any variables suspected to induce variation in surface realization of underlying tones and vary case-marking pattern and word order. To support our hypothesis, we must find an interaction effect on the intonational realization in the sentence, such that the presence of high pitch peak at the left edge of the second argument occurs when the levels of the two factors interact such that the second argument has absolutive case.

• Research hypothesis: Samoan has a high tone at the left edge of the absolutive argument.

• Linking hypothesis: A high tone in Samoan is realized as pitch peak realized at the edge of a prosodic word.

• Experimental unit: elicited sentence

• Explanatory variables

• case-marking pattern: absolutive-oblique, ergative-absolutive
• Word order: VSO, VOS

• Confounding variables
• constituent length: long (fixed)
• coordination: absent (fixed)
• segmental features of words: fully [+sonorant] (fixed)
• stress pattern: primary stress on penultimate mora (fixed)
• CV skeleton: CVCVCV (fixed)
• pragmatic context: out of the blue

• Dependent variable: presence of high pitch peak at the left edge of the second argument

The 2 $\times$ 2 factorial design is shown in the table below:

Word order erg-abs abs-obl
VSO V-erg-abs V-abs-obl
VSO V-abs-erg V-obl-abs

## References

1. Hyman, Larry M. 2007. Elicitation as experimental phonology: Thlantlang lai tonology. In Experimental approaches to phonology, ed. Maria-Josep Solé, Patrice Speeter Beddor, and Manjari Ohala, 7–24. Oxford; New York: Oxford University Press.
2. Xu, Yi. 1997. Contextual tonal variations in Mandarin. Journal of Phonetics 25. 61–83.
3. Goldsmith, John A. 1990. Autosegmental and metrical phonology. Basil Blackwell.
4. Goldsmith, John Anton. 1976. Autosegmental phonology. Doctoral Dissertation, Massachusetts Institute of Technology.
5. Keating, Patricia, Christina Esposito, Marc Garellek, Sameer Khan, and Jianjing Kuang. 2011. Phonation contrasts across languages. In Proceedings of the 17th International Congress of Phonetic Sciences, 1046–1049. Hong Kong, China.
6. Esposito, Christina M. 2012. An acoustic and electroglottographic study of White Hmong tone and phonation. Journal of Phonetics 40:466–476.
7. Stevens, S. S., J. Volkmann, and E. B. Newman. 1937. A scale for the measurement of the psychological magnitude pitch. The Journal of the Acoustical Society of America 8:185–190.
8. Gamut, L.T.F. 1992. Logic, language and meaning. Chicago: Chicago University Press.
9. Carpenter, Bob. 1997. Type-logical semantics. Cambridge, Massachusetts: MIT Press.
10. Connell, Bruce. 2000. The perception of lexical tone in Mambila. Language and Speech 43:163–182.
11. Khouw, Edward, and Valter Ciocca. 2007. Perceptual correlates of Cantonese tones. Journal of Phonetics 35:104–117.
12. DiCanio, Christian T. 2009. The phonetics of register in Takhian Thong Chong. Journal of the International Phonetic Association 39:162–188.
13. Bruce, Gösta. 1977. Swedish word accents in sentence perspective. Lund: CWK Gleerup.

1. The set of real numbers contains numbers like 3.0, 1.542, $\pi$, 2.9, 2.99, 2.999, 2.9999999999999999$\ldots$.