Mesopotamia · Old Babylonian instructions from Ur
One altered string.
A different tuning.
A damaged clay text describes a practical procedure: test a pair of strings, change one, and test again. Work through the seven named tunings, and hear what that procedure can do.
You are hearing a modern fourths-and-fifths realization. See its assumptions.
Current tuning
išartum
Press a play button to listen. Start at a comfortable volume.
Tune this pair while it keeps sounding →
Inspect the last change’s overtones
Each mark is a sine partial in the selected synthetic sound. A vertical guide joins partials at exactly the same frequency. This explains the model’s ratios; it does not establish the ancient meaning of “clear.”
Nine strings, seven roles
String position runs front to back. The pitch trace is a numerical schematic, not the shape of an ancient instrument.
Dots share one logarithmic pitch axis. Lower pitch ← → higher pitch.
Change the reference pitch, sound, or starting tuning
Changing the initial tuning or companion model starts a new session. Reference pitch and sound preserve your moves. Both companion choices are models; their exact historical relationship is uncertain.
Inspect exact pitches and the retuning log
Every fraction is relative to the initial first string. No pitch is reset when a tuning name changes.
| String | Exact frequency ratio | Hertz | Shift from initial, cents |
|---|
| Move | Action | Changed strings | Resulting tuning |
|---|
Seven names form a cycle.
Do the pitches return too?
The reconstructed instructions pass through seven tunings. Loosening takes one direction; tightening reverses it. Any other named tuning is at most three moves away.
Compare both roads to this tuning
Fork these exact pitches; hear what the destination name leaves open.
Try the whole cycle
Make seven moves without resetting any pitch. Compare the first string with where it began.
The pitch shift is a consequence of this exact 4/3 and 3/2 realization. A returning name does not establish an ancient absolute pitch standard.
Our diagram of the reconstructed tuning sequence. The lines represent retuning steps, not an ancient drawing or a melody.
A surviving instruction is not the same
as a complete reconstruction.
Two Old Babylonian manuscripts from Ur preserve parts of a tuning text. Later witnesses supply named string pairs. Their combination lets scholars reconstruct a procedure; it does not supply an ancient recording, a measured instrument, or exact pitch ratios.
The first three loosening cases show how preservation varies. These are our summaries of the published translation. In an edition, ⟨ ⟩ marks a supplied omission; [ ] marks restoration across damage.
Show all seven tunings and their diagnostic pairs
| Tuning | Named pair, clear | Diagnostic pair, unclear | Loosen | Tighten |
|---|
Read a little Akkadian
Normalized romanization, not a cuneiform transcription or a claim about exact ancient pronunciation. š is conventionally “sh”; ḫ is a velar fricative; marks over vowels indicate length or contraction.
What this audible model assumes
String numbers describe positions. In this realization, strings 1–7 descend in pitch. A pair three string-steps apart is set to 4/3; one four steps apart is set to 3/2. The six clear pairs fix all seven pitches relative to the initial first string. The remaining pair is left unclear.
Retuning solves that unclear pair while holding its other string fixed. It changes only the selected string and its companion, when present. There is no hidden rescaling when the tuning name changes. Exact fractions remain exact; hertz and cents are modern display units.
The decaying sound combines six sine partials. The steady sound uses one. Neither reproduces an excavated instrument. Hearing roughness depends on spectrum, register, listening conditions and the listener; the source word zakû is not a universal pleasantness score.
Follow the sources
The original diagrams and synthesis here are our work. Modern article figures, tablet photographs and recordings are not bundled. Source links need an internet connection; the workshop and its source notes work offline.
Take the steps with you.
The study contains the initial and current pitches, every move, the model assumptions, source links, a diagram and your selected audio. It is a standalone HTML file; open it offline or print it to PDF.
Checking offline availability…