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Singer

Piano

Piano

Piano

Time

Case 1: complete overlap

Case 2: partial overlap

Case 3: no overlap

(a)

(b)

(c)

(d)

t1 t2

t1' t2'

Figure6 Examplesof s(a) and s(b-d) respiration sig-nals illustrating different cases for the synchrony between inhala-tions: (b) complete overlap, (c) partial overlap and (d) no overlap.Circlesindicatethebeginningand theendof inhalations, correspond-ing to 10% and 90% of theamplitude of thepeak. Inhalations inter-vals are shown by the solid line segments (singer) and dashed linesegments (pianist). The inhalation interval of the singer is used asareference (a), and an overlap rate at inhalations is computed for the

s inhalations (seedetails in text).

condition). First, all signals corresponding to a given pieceand group are expressed in bars, in order to allow for tem-poral comparison between thedifferent conditions. Then, foreach s inhalation interval [t1 t2] in the collaborativecondition, the closest inhalation interval [t1 t2] in the testedsignal is selected (minimum to peak in the respiration signal)and an overlap rate s between the two inhalation intervals iscomputed as follows

s = min(t2, t2) max(t1, t1)min(t2 t1, t2 t1)

(1)

Threecasescanbeconsidered (completeoverlap, partial over-lap, no overlap) and are illustrated in Fig. 6. The showsan example of a s respiration signal centered on an in-halation (Fig. 6a) and three s respiration signals withvarying shifts (Fig. 6b-d). The inhalation interval for thesinger is indicated by thegrey area and the segments in solidline, while the inhalation interval for the pianist is indicatedby thesegments in dashed line.

In case of complete overlap (Fig. 6b), one of the twointervals is included in theother, and an overlap rate of100% isgiven.In caseof partial overlap (Fig. 6c), thetested respirationsignal starts after the ssignal, or endsbefore. In

0

1

2

Sing

er C

olla

b.

0

1

2

Pian

o Co

llab.

0

1

2

Pian

o So

lo

0

1

2

Sing

er S

olo

4 6 8 10 12 14 16 180

50

100

Time [bar]

Ove

rlap

rate

[%]

Figure7 Illustration of overlap ratesat s inhalation points forthe section of Piece A performed by Group 2. From the top:respiration signalsof singer collaborative, piano collaborative, pianosolo and singer solo conditions, and associated overlap rates. Verti-cal dashed lines indicate inhalation intervals in singer collaborativecondition, taken asareferenceof thecalculation of overlap rates. In-halation intervals in other respiration signals are indicated by starsand circles. The overlap rates are given at each s inhalationin black, grey and white for the singer solo, piano collaborative andpiano solo conditions, respectively.

this case, the overlap rate is the amount of overlap be-tween the two intervalsdivided by theshortest interval.If there is no overlap between the two intervals(Fig. 6d), Eq. 1 gives a negative value. For practicalreasons, the rate isset to zero in thesecases.

For each group, piece and condition (piano collaborative, pi-ano solo and singer solo), the overlap rate of each inhalationpoint is computed, then a global overlap score s is obtainedby taking the mean value of all rates. The overlap score ofthe s respiration in solo condition gives an indicationon theconsistency of thesi s respiration between the twoconditions. Comparing theoverlap scoresobtained for thepi-anist in thetwo conditionsshowshow the srespirationpatternsarealtered by thepresenceof thesinger in thecollab-orativecondition.The procedure is illustrated in Fig. 7, which shows the fourrespiration signals for the section of Piece A, performedbyGroup2, and theassociated overlap ratesat sinhala-tions. Dashed vertical lines indicate the inhalation intervalsofthe s respiration in the collaborative condition, taken

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