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Music of the Deep: An acoustic blueprint of sperm whale codas

Mudit Sinha, Sanika Chavan

arXiv:2610.33974v1cs.SD

TL;DR

Click count and timing do not capture all the acoustic organization in sperm-whale codas, raising the question of how that organization compares with music. The study compares codas with musical recordings across within-unit and sequence structure, timing, caller information, acoustic variation, and synthetic clips. Codas share some sequence properties with music but show a different within- and across-unit relationship, while WhAM clips remain distinguishable from natural codas in five of six acoustic comparisons after strict matching.

  • Problem

    Earlier work found acoustic organization within clicks and across coda sequences, but how those levels relate to music remained an open question.

    Source: §I · p. 1

  • Method

    The study compares codas with performed music across unit composition, sequence relations, timing, caller-related information, emotion-reference acoustic variation, and synthetic recordings.

    Source: A. Dataset · p. 3, B. Extracting acoustic features and… · p. 3

  • Results

    Codas have normalized sequence uncertainty of 0.566 versus 0.503–0.550 for three musical references, yet repeat the same form at neighboring positions in 71.3% of sampled sequence versus 21.7–44.6% for the references.

    Source: A. Coda sequences share some patterns… · p. 5

  • Takeaways & Limitations

    The acoustic blueprint treats waveform, unit composition, between-coda relations, local timing, and reproducible variation as distinct measurable properties of natural codas.

    Source: B. Why this leads to an acoustic… · p. 8

    The observed two-level combination has not been established as unique beyond the tested musical references, and recorded order does not identify continuous behavioral bouts.

    Source: §VI · p. 8

Abstract

from arXiv · show

Sperm-whale codas are usually described by the number and timing of their clicks. Earlier acoustic studies showed that individual clicks and longer coda sequences contain additional organization. We ask how that organization compares with music, whose smaller sounds also form larger units and ordered sequences. We compare codas with performed violin music, drum grooves, and sung melodies. Their sequences resemble music in some measures of predictability, yet codas show a different relationship between the smaller sounds within a unit and the order of units across a sequence. This combination was not observed in the musical references tested. Coda timing also varies coherently and carries information about individual callers. The recordings show another striking property: broad, reproducible variation along acoustic dimensions associated with human ratings of emotion, with a range comparable to human audio in most eligible tests. These findings motivate an acoustic blueprint that describes natural codas beyond their click timing. Its importance is apparent in synthetic audio: WhAM produces recognizable coda-like recordings, yet the tested clips remain distinguishable from natural codas in five of six acoustic comparisons after strict matching. The blueprint provides a fuller way to study natural codas and to evaluate how faithfully synthetic recordings represent them.

I. INTRODUCTION

Earlier work established acoustic organization within clicks and across coda sequences, but left open how those levels compare with music. This study compares codas and musical recordings at both levels and broadens the description to include timing, caller information, and reproducible acoustic variation.

I. INTRODUCTION

  • Earlier studies found that click sounds and whole-coda sequences contain acoustic organization beyond click count and inter-click timing, but their relationship to music remained open.The study asks whether the sounds within a unit and the order of units resemble music in the same way.Source: §I · p. 1
  • The study compares codas with performed Bach violin music, drum grooves, and sung melodies by examining repetition, prediction, within-unit composition and order, and between-unit sequence relations.Pretrained audio encoders provide numerical descriptions, allowing common analyses without treating whale clicks as equivalent to musical notes.Source: §I · p. 1
  • The study also tests whether coda clicks show coordinated timing changes and caller-related timing differences, and whether codas span acoustic dimensions associated with human emotion ratings.These dimensions describe recorded sound, not emotions experienced by whales.Source: §I · pp. 1–2
  • Codas share some sequence properties with music, but the tested musical systems do not show the same combination of relationships within and across units.The proposed acoustic blueprint brings together waveform, sequence organization, temporal delivery, and other reproducible variation without treating them as one property.Source: §I · p. 2
  • WhAM generates recognizable coda-like clips, yet they remain distinguishable from natural recordings under strict matching; this comparison does not identify why the generator falls short.It illustrates what timing-only or resemblance-based evaluation can miss.Source: §I · p. 2

II. RELATED WORK

Prior work described coda timing and acoustic organization, while music research established organization at multiple scales; direct comparisons between codas and music remained absent. The study makes that comparison using held-out recording sources and a dataset of whale codas and structured musical references.

II. RELATED WORK

  • Earlier studies established acoustic organization within clicks and across whole-coda sequences, but did not determine whether it resembles musical organization.Music offers a reference with sounds organized into units and units related to preceding events; the study compares organization at both scales.Source: §II · p. 2
  • Pretrained audio encoders provide numerical acoustic features for matched statistical comparisons without making whale clicks equivalent to musical notes.Whale recordings also vary with source orientation, propagation, and equipment, so acoustic groups are defined separately and evaluated on unseen recordings, with direct checks of whale groups.Source: §II · p. 3
  • The study examines caller-related timing and coda variation along valence and arousal directions validated on human recordings, without assigning emotions to whales.It also compares isolated WhAM clips with natural recordings under fixed acoustic descriptions, leaving the cause of any mismatch open.Source: §II · p. 3

A. Dataset

  • The sequence analysis uses 1,501 isolated sperm-whale codas from Dominica recordings collected between 2005 and 2018, with order indexed within date-by-social-unit groups.The index establishes order but does not identify continuous encounters or behavioral bouts.Source: A. Dataset · p. 3
  • The main comparison uses performed Bach violin music, Groove drum performances, and Meertens sung melodies, evaluating on held-out source groups.The constituent tests include 1,479 eligible codas; the acoustic-state analysis uses 1,497 coda waveforms, and reference corpora are sampled for matched opportunities despite different native units and durations.Source: A. Dataset · p. 3
  • A separate panel of Groove MIDI, Essen folk melodies, and Bach chorales tests variety of possible next events under additional musical descriptions.Its event definitions are reported separately from the main comparison.Source: A. Dataset · p. 3

B. Extracting acoustic features and grouping similar sounds

The analysis groups recordings by acoustic features and tests sequence predictability alongside the relationship between sounds within units and units across sequences. It distinguishes constituent identity from constituent order while evaluating predictions on held-out sources.

B. Extracting acoustic features and grouping similar sounds

  • Six fixed pretrained audio-encoder families are combined through standardized features, principal component analysis, k-means, and encoder agreement to form acoustic states, analysis labels rather than known biological or musical categories.The main comparison uses 32 states, tests 16 and 64, evaluates with source recordings held out, and checks coda groups using ordinary spectral measurements adjusted for recording variables.Source: B. Extracting acoustic features and… · p. 3

C. Measuring repetition, continuation, and sequence prediction

  • Sequence analyses measure repetition, successor variety, and normalized conditional entropy, which represents uncertainty about the next state after the current state is known.Transition opportunities are matched against randomized sequences preserving state frequencies; held-out predictions compare one, two, or three prior states, with checks collapsing repetitions and explicitly modeling them.Source: C. Measuring repetition, continuation,… · p. 4

D. Testing constituent composition and ordering

  • Constituent tests ask whether sound identities improve prediction of a unit’s acoustic form beyond timing, duration, and sound count.The ordering test holds onset positions and the exact constituent set and counts fixed while rearranging which sound occupies each position, distinguishing order from composition.Source: D. Testing constituent composition and… · p. 4
  • The second level compares predictions across complete coda or musical-bar sequences to test whether references share the codas’ relationship between within-unit and across-unit organization.The additional music panel uses its own event definitions rather than merging them with the main comparison.Source: D. Testing constituent composition and… · p. 4, C. Measuring repetition, continuation,… · p. 4

E. Measuring click timing and identifying callers

The methods examine coordinated click timing, caller-related timing, emotion-reference acoustic variation, sensitivity to targeted edits, and whether synthetic clips match natural recordings. The WhAM comparison matches recording duration and, in a stricter test, overlaps on measured recording and acoustic variables.

E. Measuring click timing and identifying callers

  • Local timing analyses subtract each coda type’s typical interval pattern, test whether neighboring intervals vary together against randomized patterns, and also examine pulse, nested meter, and coda-edge changes.Caller identity is predicted from rhythm and fine timing on excluded recording dates, with metadata and within-social-unit randomized-label baselines and balanced accuracy.Source: E. Measuring click timing and… · p. 5

F. Mapping emotion-relevant acoustic variation

  • Valence and arousal reference directions are learned from human-rated music and environmental audio, validated on held-out human recordings, and applied to codas without emotion labels.Coda ranking stability is tested across fits and held-out dates; the middle 80% spread is compared with human recordings, with ratios from 0.5 to 2.0 prespecified as comparable and controls for duration, level, click count, and typical interval.Source: F. Mapping emotion-relevant acoustic… · p. 5

G. Testing altered and synthetic codas

  • Targeted tests shuffle whole-coda order, rearrange within-coda intervals, or replace caller-specific timing, with controls for whether differences reflect editing severity.These tests measure sensitivity to changes, not the biological reason for the original patterns.Source: G. Testing altered and synthetic codas · p. 5
  • WhAM clips are compared with natural clips using six fixed acoustic measurements and squared MMD2, with independent natural samples as a reference for sampling variation.The stricter comparison duration-matches first, then balances two natural reference groups against generated clips among clips overlapping on measured recording and acoustic variables; it cannot identify the cause of a difference or assess between-coda sequences.Source: G. Testing altered and synthetic codas · p. 5

IV. RESULTS

Codas resemble the tested music in some whole-sequence measures, but differ in how constituent sounds relate to units and in how earlier codas contribute to prediction. Their click timing also varies together and carries caller-related information.

A. Coda sequences share some patterns with music but repeat more

  • Normalized next-unit uncertainty is similar across codas (0.566) and the musical references (0.503–0.550), but the same form appears at neighboring positions more often in codas (71.3%) than in music (21.7–44.6%).New transitions continue to appear on held-out dates, while successor variety remains about 89–94% of the frequency-matched random expectation.Source: A. Coda sequences share some patterns… · p. 5, Figure 2 · p. 6

B. Codas show a different two-level pattern from the tested music

  • Codas show a combination not found in the tested music: constituent composition helps identify coda form, original ordering adds no detectable advantage, and earlier coda context improves prediction.At the primary 32-state resolution, the coda two positions back adds 0.188 bits per target (95% interval [0.101, 0.275]); the gain is not a fixed second-order rule.Source: B. Codas show a different two-level… · p. 6, Figure 2 · p. 6

C. Click timing varies together and identifies callers

  • Coda timing varies coherently: when one click interval is longer or shorter than usual, the next tends to change in the same direction.This resembles one measurable aspect of flexible musical timing, but does not establish stable nested meter or musical intention.Source: C. Click timing varies together and… · p. 6
  • On unseen recording dates, timing-based caller predictions outperform shuffled caller labels and the available recording-metadata baseline.Fine timing adds information associated with the recorded individual.Source: C. Click timing varies together and… · p. 6

D. Codas show broad emotion-relevant acoustic variation

Codas show broad, reproducible variation along emotion-reference acoustic dimensions, and targeted edits and WhAM comparisons reveal measurable differences in the broader acoustic descriptions. The findings support a blueprint spanning multiple acoustic properties, while the music comparison remains bounded to the tested references and measurements.

D. Codas show broad emotion-relevant acoustic variation

  • Coda positions are reproducible in all 23 encoder–reference combinations that pass human-audio validation; in 19, whale recordings’ central range is comparable in size to human audio, and 16 retain this after adjustment.The result concerns acoustic dimensions associated with human emotion ratings, not emotions experienced by whales.Source: D. Codas show broad emotion-relevant… · p. 6, Table II · p. 7

E. Altered and synthetic codas reveal measurable acoustic differences

  • Targeted edits change measured acoustic relationships: shuffling whole-coda order affects all six descriptions, rearranging intervals affects all six waveform descriptions, and replacing caller-related timing affects four.The effects depend on the type and severity of each edit; they do not explain why whales produced the original patterns.Source: E. Altered and synthetic codas reveal… · p. 7

A. What the comparison with music reveals

  • Codas and the three tested musical references share some patterns in how forms follow one another, but the tested references do not reproduce the coda combination across within-unit and across-unit organization.The comparison does not establish a universal difference between whale sounds and music; the original-order test also differs from Rhythm’s test of timing at fixed click composition.Source: A. What the comparison with music… · pp. 7–8

E. Altered and synthetic codas reveal measurable acoustic differences

  • WhAM recordings remain distinguishable from natural codas in five of six acoustic descriptions, including after strict matching on measured recording properties.The matched comparison uses 17 generated clips and two independent natural reference groups, and tests isolated sounds rather than longer-sequence organization.Source: Figure 3 · p. 7, E. Altered and synthetic codas reveal… · p. 7

B. Why this leads to an acoustic blueprint

Coda acoustics comprise distinct properties that cannot be captured by one rhythm or sequence measure. The proposed blueprint brings those properties together in a testable description of natural codas.

C. Why the blueprint matters for synthetic codas

WhAM generates clips recognizable as coda-like, but the tested clips remain acoustically distinguishable from sampled natural recordings. This comparison identifies a gap that recognition- or timing-based checks could miss, without diagnosing its cause.

  • Five of six acoustic descriptions distinguish tested WhAM clips from sampled natural codas under strict measured-variable matching.Recognizable coda-like click trains therefore do not ensure a match to the fuller observed acoustic distribution.Source: C. Why the blueprint matters for… · p. 8
  • The experiment cannot determine which property causes the discrepancy or show that a missing blueprint caused it.Source: C. Why the blueprint matters for… · p. 8
  • The comparison does not test whether WhAM generates realistic sequences of codas.It reveals a gap that timing-only or recognition-based checks could miss.Source: C. Why the blueprint matters for… · p. 8

VI. LIMITATIONS

The reported comparisons have limits in sampling, unit interpretation, sequence coverage, and acoustic attribution. The results should be read within those boundaries.

  • The comparison covers sampled Dominica EC-1 codas and the musical sources analyzed, and the two kinds of units are not equivalent.Learned acoustic states are analysis labels, not demonstrated biological categories; the two-level combination is not established as unique beyond the tested references.Source: §VI · p. 8
  • Coda order is known within date-by-unit groups, but continuous behavioral bouts are not identified.Predictive gains vary with state resolution and repetition-aware modeling, and a nondetected ordering advantage in one test does not show that order is always unimportant.Source: §VI · p. 8
  • Recorded spectra can reflect source orientation, sound propagation, and equipment as well as emitted sound.Source: §VI · p. 8
  • Emotion-reference results measure acoustic variation, not whale emotional states; the WhAM comparison uses a limited sample of isolated clips and does not identify the cause of the difference.Source: §VI · p. 8

VII. CONCLUSION

Across three structured musical references, codas show a distinctive measured combination of acoustic organization, timing, and emotion-relevant variation. The authors propose a testable acoustic blueprint for studying natural codas and evaluating synthetic recordings.

VII. CONCLUSION

  • Codas share some sequence patterns with music, but the tested references differ in how constituent sounds relate to whole units across two levels.Coda timing and caller-related information, alongside broad reproducible variation along emotion-relevant acoustic directions, add to this organization.Source: §VII · p. 8
  • The blueprint brings coda properties together as a testable description, rather than classifying codas as music or language.Source: §VII · p. 8

VII. CONCLUSION; SUPPLEMENTARY MATERIAL

  • Recognizable coda-like clips do not necessarily match natural recordings acoustically, so the blueprint offers a basis for evaluating generated sounds.Detailed methods, control and sensitivity analyses, tables, and figures are provided in the supplementary material.Source: §VII · p. 8, SUPPLEMENTARY MATERIAL · p. 8

AUTHOR DECLARATIONS

The authors report no related conflicts, describe the study as a secondary analysis without new animal interventions, and disclose editorial use of AI tools. The source package includes aggregated outputs but not executable comparison pipelines or raw per-source ledgers.

Conflict of Interest

Ethics Approval

  • The study reanalyzes released recordings and annotations without new animal handling, tagging, playback, or field intervention.Approvals and permits for original collection are those reported by the source projects.Source: Ethics Approval · p. 9

Use of AI-Assisted Tools

  • AI-assisted tools supported editorial restructuring, journal-format conversion, and language refinement; the authors reviewed the scientific content and take responsibility for the manuscript.Their review covered numerical results, citations, interpretations, and final wording.Source: Use of AI-Assisted Tools · p. 9

DATA AVAILABILITY

  • The source package includes aggregated comparative outputs, provenance hashes, and editorial files, but not executable pipelines or raw per-source ledgers.Complete analysis scripts and auditable per-source outputs should accompany the final public reproducibility release.Source: DATA AVAILABILITY · p. 9
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