Chapter 5 Language-to-Music Mapping: Foot and Musical Beat
5.2 L I -to-L O Mapping: Foot Formation
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in the musical input serves to condition the musical beat assignment, but is removed in the musical output through the musical production grammar.
This study constructs a database of Mandarin children’s songs based on five lyric books that contain thirty-nine songs.4 These books are for children from zero to eight years old, and the lyrics are simple and close to children’s daily lives. The songs in the abovementioned books are new songs, but not traditional songs. The composing of the musical melodies is based on existing lyrics.
This chapter discusses three questions of the language-to-music mapping. First, how is a foot formed in the linguistic output? Second, how does the structure of the foot affect the assignment of musical beats? Finally, how does the musical structure emerge in the musical output?
5.2 L
I-to-L
OMapping: Foot Formation
Along the lines of Shih (1986) and Hsiao (1991), I consider the structure of the prosodic foot is formed in the linguistic output on four conditions. First, a pair of syllables that are ICs constitutes a binary foot. Second, adjacent syllables are paired into a disyllabic foot. Third, unparsed monosyllable joins its adjacent foot to form a bigger foot.
Finally, two adjacent syllables that syntactically branch in the opposite direction cannot form a foot.
A couple of trisyllabic examples are given in (104).
4 The five books are zao an wan an 早安晚安,xiao yu di 小雨滴, xiao hou zi 小猴子, and 1234 dong dong ti cao 1234 動動體操. One traditional song is included in one of the books, and is excluded from the database because it is not clear whether the lyrics or the music is composed first.
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(104) (a) ‘Hold a knife.’ (b) ‘Cut a pomelo.’
In (104), dao-zi and you-zi form two binary feet first. The leftover monosyllables, na and qie, then join the existing binary feet to form trisyllabic feet respectively.
Consider the first two syllables in (105).
(105) ‘(He) loves to somersault when (he) has nothing to do all day long.’
As in (105), after the three pairs of ICs, zheng-tian, mei-shi, and gen-tou, form binary feet, the adjacent unparsed syllables, ai and fan, are paired into a disyllabic foot.
Unlike ai and fan, the adjacent syllables, li and you, in (106) cannot form a foot, since they branch in the opposite direction.
拿 刀 子 切 柚 子
na dao - zi qie you - zi
Hold knife cut pemelo∣ ∣f ∣ ∣f
∣ ∣f ∣ ∣f
整 天 沒 事 愛 翻 跟 頭
zheng-tian mei-shi ai fan gen-tou
whole day nothing-to-do love turn somersault∣ ∣f∣ ∣f ∣ ∣f
∣ ∣f
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(106) ‘There is a big caterpillar in a big apple.’
In (106), ping-guo and mao-mao are ICs, and thus they are grouped into disyllabic feet respectively. At this point, li and you syntactically branch in the opposite direction so that they cannot form a foot; the unparsed you and da are then paired into a disyllabic foot.
The leftover monosyllables, da, li and chong, subsequently join the adjacent existing feet to trisyllabic and tetrasyllabic feet.
Foot constraints governing the foot formation are proposed in (107-110), based on the concepts developed in work by Shih (1986), Hsiao (1991), and Lin (2001).
(107) Align-E(IC, Ft):
Assign one violation mark for every pair of syllables that are ICs whose edges do not coincide with the edges of a foot.
(108) FtBin:
Assign one violation mark for every foot that contains more than two syllables.
(109)*MONO-FT:
Assign one violation mark for every monosyllabic foot in the output.
大 蘋果 裡 有 大 毛毛 蟲 da ping-guo li you da mao-mao chong
big apple inside have big caterpillar
∣ ∣f ∣ ∣f ∣ ∣f
∣ ∣f ∣ ∣f
∣ ∣f
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(110) Parse-σ:
Assign one violation mark for every syllable that is not parsed into any foot in the output.
The constraints Parse-σ and *MONO-FT must be undominated to ensure that every syllable is parsed into a foot but not a monosyllabic foot. Align-E(IC, Ft) is also ranked at the top to match IC edges with foot edges. FtBin is ranked at the bottom, such that a trisyllabic or larger foot can occur. A partial constraint ranking is posited in (111).
(111) LI-to-LO partial constraint ranking:
Parse-σ, Align-E(IC, Ft), *MONO-FT >> FtBin
Tableau (112) shows how this constraint ranking works.
(112) = (104)
Input: [na [dao-zi]NP]VP [qie [you-zi]NP]VP
拿 刀 子 切 柚 子 Hold knife cut pomelo ‘Hold a knife and cut a pomelo.’
Candidates:
a. (na (dao-zi)Ft)Ft (qie (you-zi)Ft)Ft
b.
na (dao-zi)
Ft)Ft (qie (you-zi)Ft)Ftc. (na dao)Ft (-zi qie)Ft (you-zi)Ft
d. (na)Ft (dao-zi)Ft (qie (you-zi)Ft)Ft
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LI-to-LO: Parse-σ, Align-E(IC, Ft), *MONO-FT >> FtBin Parse-σ Align-E(IC, Ft) *MONO-FT FtBin
a. **
b. *! *
c. *!
d. *! *
The footing pattern in (112b) is ruled out by Parse-σ, as na is left unfooted. The pair of the ICs, dao and zi, in (112c) is not aligned with any foot, incurring a fatal violation of Align-E(IC, Ft). The monosyllabic foot, na, in (112d) violates *MONO-FT, and thus is ruled out. As a consequence, (112a) is chosen as the optimal output.
The constraint ranking in (111) also correctly predicts that the fifth and sixth syllables in (113) form a disyllabic foot.
(113) = (105)
Input: [[zheng-tian]ADV[mei-shi]VP [ai [ fan [gen-tou]NP]VP]VP 整 天 沒 事 愛 翻 跟 頭
whole day nothing-to-do love turn somersault
‘(He) loves to somersault when (he) has nothing to do all day long.’
Candidates:
a. (zheng-tian)Ft (mei-shi)Ft (ai fan)Ft (gen-tou)Ft b. (zheng-tian)Ft (mei-shi)Ft ai (fan (gen-tou)Ft)Ft c. (zheng-tian)Ft (mei-shi)Ft (ai)Ft (fan (gen-tou)Ft)Ft d. (zheng-tian)Ft (mei-shi)Ft (ai)Ft (fan gen-tou)Ft
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LI-to-LO: Parse-σ, Align-E(IC, Ft), *MONO-FT >> FtBin Parse-σ Align-E(IC, Ft) *MONO-FT FtBin
a.
b. *! *
c. *! *
d. * (!) * (!) *
Again, (113b) violates Parse-σ, as ai is not parsed into any foot, whereas ai in (113c-d) constitutes a foot alone and violates *MONO-FT. The left edge of the pair of the ICs, gen and tou in (113d) is not aligned with the left edge of a foot, and thus is ruled out by Align-E(IC, Ft). Finally, (113a) emerges.
The same constraint ranking, however, renders an incorrect prediction in tableau (114).
(114) = (106)
Input: [[da [ping-guo]NP]NP
li]
PP [you [da [[mao-mao] chong]NP]NP]VP, 大 蘋 果 裡 有 大 毛 毛 蟲big apple inside have big caterpillar
‘There is a big caterpillar in a big apple.’
Candidates:
a. (((da (ping-guo)Ft)Ft
li)
Ft (you da)Ft ((mao-mao)Ft chong)Ftb. (da (ping-guo)Ft)Ft (li you)Ft (da (mao-mao)Ft chong)Ft
c. (da (ping-guo)Ft
li)
Ft you (da ((mao-mao)Ft chong)Ft)Ftd. (da ping-)Ft (guo li) Ft (you (da ((mao-mao)Ft chong)Ft)Ft
e. (da (ping-guo)Ft
li)
Ft (you (da ((mao-mao)Ft chong)Ft)Ft)Ftf. ((da (ping-guo)Ft)Ft li)Ft (you)Ft (da ((mao-mao)Ft chong)Ft)Ft
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LI-to-LO: Parse-σ, Align-E(IC, Ft), *MONO-FT >> FtBin
Parse-σ Align-E(IC, Ft) *MONO-FT FtBin
() a. ***!
b. **
c. *! ***
d. *! ***
e. ***!*
f. *! ***!*
The foot structure in (114b) erroneously wins over (114a) by one less violation of FtBin, as indicated by the black right-headed hand symbol . The real optimal output is (114a), as indicated by the parenthesized white right-headed hand symbol (). In order to obtain (114a), the constraint in (115) must be added to the partial constraint ranking provided in (111).
(115) NOSTRADDLE-Ft:
Assign a violation mark for every foot consisting of syllables that syntactically branch in the opposite direction.
NOSTRADDLE-Ft forbids syllables that syntactically branch in opposite direction to form a foot, which I refer to as a straddle foot. The enriched constraint ranking is provided in (116) and the top-ranking of NOSTRADDLE-Ft now successfully removes the straddling foot in (117b).
(116) LI-to-LO constraint ranking (enriched):
NOSTRADDLE-Ft, Parse-σ, Align-E(IC, Ft), *MONO-FT >> FtBin
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(117) = (114)
LI-to-LO: NOSTRADDLE-Ft, Parse-σ, Align-E(IC, Ft), *MONO-FT >> FtBin NOSTRADDLE-Ft Parse-σ Align-E(IC, Ft) *MONO-FT FtBin
(114a). ***
(114b). *! **
(114c). *! ***
(114d). *! ***
(114e). ***!*
(114f). *! ***!*
When the linguistic output is perceived into the musical input, the foot structure plays a role in assigning musical beats, as will be discussed next.