What did the melodies that accompanied rituals, theaters, or banquets in ancient Greece and Rome more than two thousand years ago actually sound like? A mathematical analysis of all the compositions that have survived from Antiquity has allowed researcher Dan C. Baciu, from the Münster University of Applied Sciences, to reconstruct their exact tuning and intonation.

According to this analysis, ancient musicians preferred pure intonation. However, they had a keen sense of their combinatorial limitations on instruments with fixed-length strings, such as lyres, and recognized the need for slight deviations from pure intonation during vocal performance to allow for greater tonal complexity. This spirit has its parallel in ancient atomic philosophy, which postulated that atoms sometimes deviated in order to allow for greater combinatorial complexity and unexpected effects.

The analysis is based on the 61 musical pieces that have come down to us from the Greco-Roman world, preserved in manuscripts and stone tablets. These pieces are written in two types of notation: so-called “instrumental,” probably intended for the lyre, and “vocal,” designed for singing or for wind instruments like the aulos (the characteristic double flute).

music ancient greece rome how it sounds
Interference patterns in pure and impure intervals. Credit: Dan C. Baciu

According to Baciu, all the pieces written in instrumental notation can be played with perfect tuning. That is, the musicians of the time managed to make note combinations harmonically pure, without dissonances or accumulated “out-of-tune” sounds—something that requires mathematical control of sound.

This perfect tuning is based on simple ratios: an octave is represented as 1/2, a fifth as 2/3, a fourth as 3/4, and so on. These fractions are not mere numerical curiosities but reflect physical relationships between the lengths of strings or sound frequencies. For example, if one string vibrates at a certain speed, another vibrating at twice that speed will sound an octave higher, and together they produce a “pure” sound, free of unwanted vibrations.

But this perfection has its limits. There are note sequences that, if tuned perfectly purely, end with a final note that is slightly “out of place” compared to the beginning. This is a phenomenon known as the syntonic comma, a tiny but audible difference between the starting point and the endpoint after a series of intervals.

Ancient composers were aware of this problem and meticulously avoided it in lyre music. In contrast, in vocal pieces, they accepted this imperfection and made it part of the performance. Instead of mathematically correcting the notes, singers made small adjustments with their voice: slides, inflections, and microtonal variations that enriched the melody and gave expressiveness to the singing.

music ancient greece rome how it sounds
The “Berlin Papyrus” contains a vocal and multiple instrumental compositions, which have been interpreted to belong together. Credit: Dan C. Baciu

This difference between instrumental music (mathematical, precise, restrained) and vocal music (free, expressive, changing) reflects an ancient symbolic duality: that of Apollo and Dionysus, two Greek gods who represented, respectively, reason and instinct. Apollo, god of the lyre, embodied order, foresight, and harmony. Dionysus, associated with the aulos and with wine, symbolized chaos, passion, and the unforeseen.

Lyre music, according to Baciu, is constructed like a kind of sonic oracle: precise, predictable, and sublime. Vocal music, on the other hand, adopts a more spontaneous attitude, with melodic curves that evoke the body, movement, and emotion. This idea is not just aesthetic but philosophical. According to the study, vocal modulations can be seen as a reflection of an ancient theory about the universe: atomism.

Greek philosophers Democritus, Epicurus, and later the Roman Lucretius imagined that everything in the universe was made of atoms—indivisible particles that moved through the void. But to explain change, complexity, and freedom, they introduced a crucial idea: atoms, from time to time, “swerve” slightly from their straight trajectory. This deviation, known as the “clinamen” or “swerve”, would allow for the emergence of chance and free will.

Baciu’s study proposes a bold parallel: just as atoms swerve to generate complexity, human voices also deviate from the pure tone to create richer and more expressive music. This small “inaccuracy” thus becomes a metaphor for freedom.

This play between linearity and curvature is also reflected in Greek architecture. The Parthenon, for example, appears to be made of straight lines, but in reality, its columns are inclined, its platforms are curved, and its proportions are carefully manipulated to create a more organic and vital visual effect.

In the same way, the melodic lines of ancient vocal music are not straight but curved, suggesting a connection between visual art and sound art. Everything seems to be governed by a sensibility that values the subtle, the deviated, the human.

SOURCES

Dan C. Baciu, Human touch? Acoustical analysis of ancient music reconstructs tuning and intonation, elucidating aspects of human behavior. Sci. Adv. 11, eadv3101(2025). DOI:10.1126/sciadv.adv3101

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