(A) Two examples of syllables, represented in terms of their sonogram (top member of each pair of panels) and the extracted pitch versus time (bottom member of pairs).
(B) Plot of pitch at one time point versus the next time point (Δt = 1.02 ms). All such pitch pairs in all syllables from a single trial with 750 syllables are shown, representing a total of 31,303 pitch changes. Particular pitch jumps are placed within the context of their individual syllables at right (top syllable, 98 ms in duration; bottom syllable, 33 ms in duration).
(C) Pitch pairs analyzed for single 210-s trials from 45 different mice, containing in aggregate 15,543 syllables and over 600,000 pitch pairs. The distribution of pitch pairs is represented as a two-dimensional histogram; the correspondence between grayscale and number of observations is indicated in the color bar at right. Polygons define the clusters corresponding to the three jump types “u,” “h,” and “d.”
(D) Numbers of each type of pitch jump per trial (45 mice, one trial each).

(A) Pairs of pitch waveforms are temporally aligned using dynamic time warping, and pairwise distances (root mean squared difference) are computed. Using multidimensional scaling (MDS)/isomap, projections are found that approximately preserve the distances between pairs.
(B) Isomap analysis of all pitch waveforms in the trial analyzed in Figure 2B. Points are colored according to the presence or absence of low jumps as in Figure 3B.
(C) A different isomap projection, focusing only on syllables containing low jumps. Sonograms of representative syllables in both clusters are shown in the insets. Pitch waveforms are from the same trial analyzed in Figure 2B.

(A) Sequences of syllables in a phrase. Here, “hdu” syllables have been classified as “A” or “B” depending on whether the lower frequency band fell or rose, respectively. SS and “h” (with a brief grace note) are labeled “C”.
(B) Example of a phrase repeated three times without interruption in the original song. The three repeats are shown one above the other, aligned on the start time for the phrase. See Audio S4 for entire sound recording.
(C) Long time scale changes in syllable type. Syllable type is categorized by whether low jumps are present (LJ⁺) or absent (LJ⁻). Shown is the number of syllables without low jumps, out of the most recent 20 syllables. Insets contain sonograms from the indicated portions of the sequence.
(A) and (C) are from the same trial analyzed in Figure 2B; (B) is from a different mouse.

All seven mice with four or more qualifying trials (see text) are analyzed.
(A) Syllable usage for three of the more common syllable types for three different mice. Error bars represent the standard error of the mean across trials.
(B) Patterns of syllable usage on individual trials across mice. Each point corresponds to a single trial, where the trials from a particular mouse are marked with a consistent color and marker. For mice 1–3, colors are consistent between (A) and (B). Placement of points in the plane reflects the pairwise “distance” between trials, where that distance measures the overall differences in percentage of each syllable type (see Materials and Methods). Projection into two dimensions was performed by isomap.
(C) Temporal regularities in song structure. Transition probabilities for all qualifying trials grouped by mouse.

A cotton swab containing female mouse urine (top) was introduced at approximately 30 s into a 210-s trial. Arrow indicates the time of first contact with the cotton swab. Recorded acoustical power is represented as a function of time and frequency, with shading increasing with power. Power below 25 kHz was truncated. Bottom, an expansion of a 2-s period showing vocalizations in greater detail. Individual syllables, as identified by an automated algorithm, are spanned by magenta lines below.

(A) Syllable with both a fundamental and first harmonic.
(B) Abundance of frequency (vertical axis is frequency, continued from [A]) in syllables with (LJ⁺) and without (LJ⁻) low jumps.
(C) Average pitch (top) and mean ± standard deviation log₁₀(power) (bottom) as a function of time, surrounding a downward low jump (for syllables with low jumps) or surrounding the upward crossing of 75 kHz (for syllables without low jumps). Power units are arbitrary but consistent between syllable types. Color scheme is as in (B).
(D) Syllable showing extensive temporal overlap and independent frequency modulation among the different notes in the syllable. Syllables are from the same trial analyzed in Figure 2B.

(A) Sonograms of representative syllables, showing a range of oscillatory behavior.
(B) Overlay of pitch waveforms for all 361 syllables lacking pitch jumps from the trial analyzed in Figure 2B. Time and frequency axes have been shifted and globally stretched independently for each syllable to bring waveforms into maximal overlap with a sine wave. The root mean squared error in fit to the sine wave is indicated by dashed lines.
(C and D) Histogram of starting (C) and ending (D) phases.
(E) Relationship between the oscillation rate (measured in periods/millisecond) and amplitude of the best-fit sine wave. Only syllables with at least 0.3 periods (160/361) are shown; syllables spanning a smaller fraction of a period do not permit an accurate measurement of oscillation rate or amplitude.

(A) A three-state Markov model, where the states correspond to syllables with (“1”) or without (“0”) low jumps, and to a gap of greater than 0.5 s in the sequence. Arrows indicate possible choices for the next state; transition probabilities are calculated from the observed sequence of syllables and gaps.
(B) Observed numbers of the eight distinct three-syllable combinations, and the number expected from two models: “syllable prevalence” picks the next syllable randomly based on the proportion of each type, whereas “transition probability” employs the Markov model diagrammed in (A).
(C) Comparison of transition probabilities to type 1 syllables with the prevalence of type 1 syllables. “Prevalence of 1” is n₁/(n₀ + n₁), where n_i is the number of syllables of type i; prevalence of transition g→1 is calculated as n_g→1/(n_g→0 + n_g→1), where n_i→j is the number of observed transitions from state i to state j (g = gap); and prevalence of 1→1 is n_1→1/(n_0→1 + n_1→1). Each point represents the results from a single trial, of 81 qualifying trials (see text).