Improvised 16th-century music and the language-like rules of human cognition

Improvised music and the language-like rules that shape how we process it

Music places enormous demands on the brain. New notes replace old ones in rapid succession, leaving the listener only a short window to process each sound. Human language imposes similar constraints, and researchers have long argued that these cognitive pressures push communication systems toward certain efficient forms. If that argument holds, the same statistical fingerprints found in language should also appear in music.

To test this idea, the study turned to a real historical practice rather than artificially generated musical stimuli. Researchers analyzed transcriptions of 16th-century improvisations — a living tradition passed down through detailed tutorials and treatises that spread across Europe during that era. These manuals laid out precise methods for improvising and included a predefined vocabulary of melodic fragments, not unlike the “licks” modern jazz musicians might use. A novel method for breaking melodies into meaningful fragments was developed especially for this corpus.

Results showed that these improvisations followed two central laws of quantitative linguistics: Zipf’s rank-frequency law and Zipf’s law of abbreviation. According to the study’s hypothesis, conforming to these laws allows optimal coding of musical information, which in turn aids cognitive processing for both the listener and the performer. The improviser may not consciously apply these rules, but the patterns appear crucial for making music manageable by the human brain.

Producing music, whether from memory, notation, or on the fly, demands astonishing coordination. A single note requires control of duration, pitch, timbre, articulation, and loudness. Beyond individual notes, the musician must manage gradual changes over whole sequences — speeding up or slowing down, sliding between pitches, shaping swells and fades.

Grouping sequences into larger syntactic units generates hierarchical structures. Levels of structure relate to other levels through an agreed-upon set of rules — the syntax of the style. In the monophonic stream examined here, three features stand out: it forms a hierarchy governed by rules; it is temporal, meaning auditory traces vanish as notes end; and the order in which notes appear matters critically to the meaning of the stream.

Human language shares these characteristics. Meaningless sounds — phonemes — combine into meaningful units like morphemes and words, and those units assemble into sentences and paragraphs. Every language has its own combination and composition rules that speakers and listeners must internalize to process speech efficiently. Christianen and Chater, coining the term “Now-or-Never bottleneck,” argued that linguistic information must be processed fast or it disappears forever. They proposed the brain meets this challenge with a “Chunk-and-Pass” strategy: incoming signals get broken into compressed groups — or chunks — that are then passed upward through comprehension levels. This compression can be “lossy,” meaning higher levels lack perfect detail, which can produce shallow or even mistaken interpretations.

That process is bidirectional. A performer or speaker starts at a conceptual level, divides it into words, and breaks those into articulated phonemes. A listener inverts the sequence, rebuilding the structure from received phonemes all the way up to whole concepts.

Working memory looms large when stimuli arrive in time. A note or a morpheme fades for good as soon as its duration ends. Earlier estimates placed short-term memory capacity at seven plus or minus two items; later proposals nudged it down to four plus or minus one. Yet people handle much longer sequences every day. An English conversation may run at 150 words per minute — about five or six syllables per second. That fluent pace reveals a structure at work. When the stimuli are random — a series of unrelated beeps, for example — performance tanks.

A parallel effect occurs in score reading. Eye-hand span — the distance ahead that a reader looks while playing — clusters around six or seven notes for skilled sight-readers and three or four notes for weaker ones. For both groups, that span shrinks when the note sequence is random.

This pattern of better performance when stimuli are organized can be explained by Shannon’s information theory. Compression ratios measure the efficiency with which a code packs uncompressed data. Random sequences produce smaller ratios and longer compressed outputs — in other words, they are harder to compress — which matches the drop observed in human performance under random conditions.

Two of Zipf’s laws illuminate the relationship between organization and compression cost. The law of abbreviation states that words occurring more often in a human language tend to be shorter, a pattern confirmed across nearly a thousand languages. Beyond human speech, the law shows up in animal communication systems, in dolphin surface behaviors, and even in the Unix command shell, suggesting a general property linked to processing economy rather than a quirk of any one language.

The second law — the rank-frequency law — holds that the most frequent word in a corpus will appear about twice as often as the second most frequent word, three times as often as the third most frequent word, and so on — a Zipfian distribution. This pattern has been found across written and spoken languages worldwide.

Mandelbrot mathematically proved that if a language’s word frequencies follow a near-Zipfian curve and if common words shorten, then the overall processing cost for transmitting average information content gets minimized. Other scholars since have suggested these laws make communication efficient, possibly because they respond directly to the pressures codified in the Now-or-Never bottleneck.

The argument builds like this: temporal-bound cognitive limits create a need for chunking; compression shreds wasted redundancy; Zipf’s abbreviations carve away length from high-frequency items; and the rank-frequency profile skews the word inventory so that a small set of common units saturates the message stream.

Zipfian distributions have turned up not just in language but across many scientific fields — economics, network science, physics — and a handful of earlier studies documented Zipfian patterns in melodic contours. However, those efforts typically measured only single melodic intervals and stopped before examining the law of abbreviation. Comparing single intervals to words falls short as an analogy because the inventory of distinct intervals is tiny — usually bound between a minor second and an octave, totaling at most eighteen types, against a lexicon of well over one hundred fifty thousand English words. A better parallel pairs intervals to phonemes and sequences of intervals to words. Manaris and colleagues took these steps and found Zipfian distributions after breaking melodies into binary and ternary sequence intervals rather than isolated notes.

Fixing the length of element groups runs into problems, too, since human groupings, whether note streams or sentences, respect syntax, not arithmetical segment boundaries. Dividing a sentence like “good morning everyone” into fixed-length slices yields meaningless pairs such as “go,” “od,” “mo,” “rn,” and so onward. Similarly, fixed segmentation of melodies ignores the punctuation provided by phrasing, cadence, and articulation.

The corpus analyzed comprised transcriptions of 16th-century improvisational practice. Because this style was taught through explicit conventions of smaller, repeatable fragments, researchers could segment each melody according to mutually reinforcing clues from two systems: concepts retrieved from 16th-century performance guides and insights drawn from modern cognitive models, specifically Lerdahl and Jackendoff’s generative theory of tonal music (GTTM) and the implication-realization model of melodic expectation. Inside those precisely carved melodic units — roughly analogous to morphemes — the study found both the Zipfian frequency distribution and the abbreviation effect holding consistently.

The results reinforced a broader hypothesis: the same communication-optimization pressures that shaped human language also help to structure improvised melody. The statistical fingerprints of language derived partly from the Now-or-Never bottleneck are not limitable to speech; they also arise in an art form operating under comparable cognitive demands.

No final rule here need to be wielded consciously by a musician. The shapes available to a 16th-century improviser and the way they are chosen and placed still seem to bend toward efficient coding, something that comes through once them viewed not as arbitrary gestures above time, but as signals needing exact constraints just as spoken words use.

Music scholars have long examined how to segment melodic sequences into meaningful units, analogous to words or morphemes in language (Cambouropoulos et al., 2001; Crawford, 1998; Lerdahl & Jackendoff, 1983; Lidov, 1979; Meredith et al., 2002; Narmour, 1990, 1992; Pearce et al., 2010; Rolland & Ganascia, 2000; Spevak et al., 2002). Several influential theories have directly addressed melodic segmentation by proposing distinct sets of rules. Notable examples include Lerdahl and Jackendoff's (1983) generative theory of tonal music (GTTM), which draws on Gestalt principles, and Narmour’s (1990, 1992) Implication-Realization (IR) model, grounded in similar Gestaltian ideas with a focus on music’s temporal dynamics and intervallic expectations. The segmentation rules tied to these approaches involve various musical fundamentals—melody, rhythm, and, in certain cases, harmony. Yet contradictions among these fundamentals can create segmentation ambiguities, a situation that frequently occurs in music, as illustrated in Figure 5.

Ambiguity in music can provide richness and added meaning, unlike functional utterances where it is a drawback. Nevertheless, segmentation ambiguity must still be resolved because a performance can present only one option. Figure 6 shows how the two grouping alternatives might be realized.

The resolution depends not solely on Gestalt, cognitive, or computational frameworks but also on cultural factors (Spevak et al., 2002; Thom et al., 2002). The aesthetic norms of a musical style and period, performance conventions, and the theoretical foundation supporting a composition’s creation all exert strong influence on the grouping process. The same melody might be grouped differently based simply on the period in which it was composed.

When examining regularities common to language and music, the method chosen to segment melody into meaningful units requires careful consideration. A minimal threshold for segmentation might be to avoid violating major cognitive theories such as GTTM and the IR model. If segmentation rules incorporate a given period’s cultural aesthetics, performance practices, and compositional theories, the resulting process can prove more reliable than relying solely on cognitive frameworks, because the extracted chunks probably reflect the actual construction process and can pinpoint the building blocks genuinely in use.

To minimize segmentation ambiguity, therefore, I selected a highly specific musical genre—16th-century improvisations—as a corpus. Within this genre, the segmentation algorithm is clearly defined and universally accepted across all 16th-century treatises. The corpus thus offers consensus on melodic building blocks, at least from the viewpoint of that era’s theoreticians.

Furthermore, a model designed specifically for improvisation rather than pure composition was preferable, given the core hypothesis that the Now-or-Never bottleneck drives Chunk-and-Pass processing theory and the formation of statistical regularities. An improvisational context ensures high pressure from the Now-or-Never bottleneck, affecting not only listeners hearing a piece for the first time but also the performer inventing improvisational fragments in real time.

The chosen style for the experiment was 16th-century division ornamentation practice (DOP). DOP flourished during the 16th century and the first two decades of the 17th century. Eleven division instruction manuals were issued by improvisers to help both professional and novice musicians master DOP skills. In DOP, the performer improvises ornamentations on the melodic line of a familiar composition—typically polyphonic works such as madrigals, chansons, and motets.

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The improvisational section was generally not created by inventing melodic sequences from nothing but instead by selecting pre-defined melodic sequences (referred to here as figurations) and combining them creatively. A considerable portion of the division instruction manuals functioned as suggestion lists for usable figurations.

Syntactic rules determine which figurations count as valid for embedding in different melodic contexts. Improvisers were meant to memorize the pre-defined figurations presented in the manuals and execute them during improvisation. In this regard, figurations resemble words retrieved from memory during sentence parsing.

The sources available to musicologists for studying DOP include (1) transcriptions of improvisations by famous practitioners like Bassano, Dalla Casa, and Ortiz—which I used to create the corpora; (2) division manuals intended to teach musicians DOP technique, representing a distinctive type of music treatise. These manuals offer a well-defined model of the algorithm needed to apply DOP, along with a “dictionary” (as noted above) of thousands of pre-defined melodic fragment sequences for use as improvisation material (analogous to jazz licks or riffs). I applied this model to reverse engineer the improvisational process, extracting the melodic fragments into groups (these represent musical building blocks, equivalent to morphemes in human language). Some manuals also include philosophical, cultural, and aesthetic context for DOP; (3) scholarly treatises offering quantitative advice, rules of thumb, and aesthetic-philosophical background—though I did not use any of these in this paper.

The corpora

Bassano’s corpus comprises all his transcribed improvisations. Motetti, Madrigali et Canzonie Francese (Bassano, 1591) contains 37 soprano divisions and 7 bass divisions, while 6 viola bastarda divisions were omitted. From his Ricercate publication (Bassano, 1585), two additional soprano divisions written on Rore’s madrigal Signor mio caro were included in the corpus.

Dalla Casa’s corpus includes all 91 of his transcribed divisions (bastarda divisions are omitted). These transcriptions are found in his two-part 1584 treatise Il vero modo di diminuir.

Ortiz’s (1553) corpus contains eight transcribed improvisations: four based on the madrigal O Felici Occhi Miei and four from the cancion Dolce Memoire.

The model for generating an improvisation, as defined in the 16th-century division manuals

The first instrumental division manual, titled Opera Intitulata Fontegara, was published by Sylvestro Ganassi, a musician of the Doge in Venice, in 1535. Fontegara is a recorder tutor that includes an extensive DOP section. It is unique, both historically and for this paper, because it provides a “bilingual” dictionary and an algorithm for employing that dictionary in improvisation.

The manual’s dictionary is structured as a collection of pairs. Each pair has a key and multiple values. I refer to each value as a figuration. In this paper, a figuration functions like a morpheme—an equivalence to be demonstrated later. A key is a sequence of two to five notes. Each figuration—a melodic fragment—is built from a longer melodic sequence of shorter note values than its related key; importantly, the figuration’s first and last notes share the same pitch class as the key’s first and last notes. Figure 7 presents an example of a melodic fragment from the original piece and its associated figurations.

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The algorithm for using the dictionary proceeds as follows:

1. Choose a melodic fragment from the original composition to be ornamented.
2. Identify the fragment using the keys in the dictionary.
3. Select one of the corresponding values for that key and insert it into the original composition in place of the chosen fragment.

Three operations can be applied to melodic fragments under this model:

1. Diatonic transposition (DT)—both the key and its value can be transposed diatonically to match the original composition’s melody.
2. Rhythmic transformation (RT)—any note in the key or value can be multiplied by a constant, as absolute note durations are relative; thus, a key made of quarter notes can become half-notes or eighth-notes.
3. Rhythmic alteration (RA)—minor variations to rhythmic patterns are allowed, such as altering a sequence of four eighth-notes to a dotted pattern (a dotted eighth followed by a sixteenth).

Figure 8 illustrates these operations applied to a simple figuration.

Another interesting case arises when figurations overlap—the last note of one figuration is the first note of the next. Sequences of such overlapping figurations are called chained figurations in this paper. Chained figurations let the improviser extend an improvisation across many melodic sequences.

Figure 9 gives examples of both chained and “simple” figurations. Brackets mark the figurations. Bracket 1 indicates a simple figuration whose last note does not start the following figuration. Figurations 2 and 3, by contrast, share note B (shown in red), forming a chained figuration represented by bracket 4.

Figure 7. An excerpt from Ganassi’s (1535) Fontegara manual. An example of figuration options for replacing a given melody fragment from the original composition. The improviser can choose any figuration according to taste. The figuration’s first and last notes match the original melody’s first and last notes.

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The model of melodic segmentation, based on the 16th-century model

Drawing on the 16th-century model, I created an algorithm that reverses the improvisational process of embedding figurations into the original melody, thereby extracting the generated figurations. This method segments the improvised versions by following 16th-century rules.

The algorithm appears in Figure 10.

Figure 11 shows an extraction example.

The algorithm adheres to the figuration definition established by the 16th-century model while following cognitive reasoning rules: all figurations in the corpora start and end on relatively strong beats; boundaries fall between harmonic intervals of identical pitch class (unison or octave), which serve as easily recognizable markers; and each figuration note is typically two or more times shorter than the notes in the original composition.

Figuration equality and figuration type definitions

Let figuration a = (a₁...aₙ) and figuration b = (b₁...bₙ) where aᵢ, bᵢ are notes.

Equality between figurations requires all notes constituting them to have identical pitches and durations, appearing in the same order. Mathematically:

a = b iff aᵢ = bᵢ for each i in 1…n (3)

Figurations share the same type if one can be converted into the other using DT, RT, or RA. For instance, each figuration in Figure 8 has the same type, since any can be transformed into another through these operations. Mathematically:

Type(a) = Type(b) iff there exists a sequence of operations op₁…opₘ such that opₘ(…op₁(a)…) = b (4)

The figuration operations are DT, RT, and RA (as defined earlier).

Algorithm: Extract Figurations

Input: original melody A, improvised melody B

Output: list L of figurations in B

Unisons = GetHarmonicUnisons(A, B)

For each unison[i], unison[i+1] in Unisons:

Figuration = ExtractNotesBetween(unison[i], unison[i+1])

If Len(Figuration) > 1:

L.append(Figuration)

Return L

Func GetHarmonicUnisons(melody A, melody B):

Return all unisons between A and B, where a unison is a note x and y and x.offsetTime = y.offsetTime (offsetTime is time from composition start to note onset)

Func ExtractNotesBetween(unison1, unison2):

Extract the improvised melody notes between unison1 and unison2

Figure 10. This algorithm extracted figurations from the improvised melody.

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Computational tools

I used the Music21 framework (Cuthbert & Ariza, 2010) for figuration extraction and Python 3 with the SciPy library (Jones et al., 2001) for all other statistical analyses.

Results

Corpora figuration extraction

Using the described algorithm, I extracted all figurations directly from the corpora, classified them by type, and calculated how often each figuration type occurred, as shown in Table 1. This step built a new dictionary for each improviser itemizing figurations and their occurrence frequencies. Each dictionary in this format surpasses the 16th-century division manuals’ dictionaries because it also provides frequency information for each figuration type, drawn directly and automatically from the actual improvisations rather than from performers’ subjective views about figuration use.

Ortiz, as noted, provided a relatively small sample of transcriptions, using fewer figuration types and instances. Bassano tends to reuse the same figuration types more frequently than the other composers.

Table 1. Extracted figurations from the corpora.

Figuration instances | Figuration types | Reuse ratio (instances/types) | No. of transcriptions

The rank-frequency law

Figure 12 shows the frequency distribution of the corpora figurations: the X-axis lists figuration types in order of rank-from most to least frequent, while the Y-axis gives each figuration type’s frequency. The distribution closely resembles that found in human language.

Furthermore, a recent study (Mehri & Jamaati, 2017) reported that α values (defined in equation [1]) for a corpus comprising Bible translations into 100 languages ranged from 0.765 to 1.442.

As Table 2 shows, each corpus’s α value fell within this range and exhibited high coefficients of determination (R²). The corpora therefore followed a near-Zipfian distribution, akin to natural languages.

The abbreviation law

To explore the connection between figuration type frequency and figuration length, in line with Zipf’s abbreviation law, I calculated the average frequencies of figuration types for each length value. A similar procedure has been applied to human language corpora (Kanwal et al., 2017).

Zipf’s word length can be interpreted musically in two plausible ways: length can refer to the figuration sequence length, i.e., the number of melodic intervals making up the figuration; formally, len_seq(a) = n for any figuration a = (a₁…aₙ). Or length can refer to the figuration duration length, i.e., the sum of the note durations in the figuration, formally, len_dur(a) = Σdur(aᵢ) for those notes.

Figures 13 and 14 show that the correlation between frequency and length is nonlinear and that figuration type distribution is non-normal. Therefore, instead of linear measures like Pearson's r, Kendall and Spearman nonparametric rank-correlation coefficients were applied.

The correlation results revealed moderate inverse relationships, as seen in Table 3, meaning the corpora followed the abbreviation rule just as human languages do.

Discussion

This paper demonstrated statistical similarities between improvisational 16th-century music and language, shown by adherence to Zipf’s (1949) two paramount linguistic laws: rank-frequency and abbreviation. The music corpora, comprising 151 transcribed improvisations from the 16th century (Bassano, 1591; Dalla Casa, 1584; Ortiz, 1553), support the hypothesis that 16th-century improvisational aesthetics were shaped not only by culture but also by principles of communicative optimization.

Furthermore, the discovered statistical regularities held across all improvisers, even though each used a unique figuration vocabulary. This cross-vocabulary validity strengthens the hypothesis’s universal nature, binding it not narrowly to specific vocabularies.

In language, communicative optimization has been proposed as necessary for overcoming—”

Previous studies that applied the rank-frequency law to melodic sequences (e.g., Hsü & Hsü, 1991; Manaris et al., 2003, 2005; Voss & Clarke, 1975, 1978) were unable to test the abbreviation law — the component required by the communicative optimization hypothesis (Bentz and Ferrer-i-Cancho, 2016) derived from Mandelbrot’s (1953) work. The reason is that those studies divided melodies into arbitrary single, binary, and ternary elements.

In the present study, melodies were segmented into their proper syntactic building blocks — figurations — following the rules defined by 16th-century theorists (e.g., Conforti, 1593; Ganassi, 1535; Ortiz, 1553). These rules also align with modern cognitive melodic segmentation frameworks (GTTM and IR). This syntactically informed approach produced melodic elements of varying lengths, labeled figurations. During the 16th century, all professional and amateur musicians were expected to learn and apply these figurations according to the period’s syntactic rules. These figurations, with their variable sequence lengths, follow the abbreviation law just as natural languages do. That adherence to Zipf’s laws supports the claim that communicative optimization is valid, not only for language but for the musical corpora examined here.

Furthermore, finding statistical parallels between language and music — expected given the Now-or-Never bottleneck hypothesis about information processing — points to two possibilities. Either a shared neural network processes both language and music (as domain-general theory suggests), or different brain areas process the two modalities using a common mechanism sensitive to these statistical properties. The corpora analyzed, however, consisted of a highly specific improvisation practice rather than any type of music. Further research across additional musical genres and other semiotic systems will be necessary to generalize these conclusions and to support the case that Zipf’s laws are not simply linguistic universals but semiotic system universals.