sammûreturn to your tuning bench

Two roads,
one tuning.

Start with the same strings. Reach the same name. Do you arrive at the same pitches?

A modern fourths-and-fifths realization. Read the assumptions.

This room forks your bench at its actual pitches. Earlier retuning moves stay in both branches.

Try a fresh išartum start

Choose where the roads meet

Identical starting pitches

A · Loosen

    B · Tighten

      Same name. Different pitches.

      Hear A, then B

      Which B do you hear?

      Synthetic sound. Start at a comfortable volume.

      Filled circle: ADiamond: heard BDashed tick: starting pitch

      Equal distances mean equal frequency ratios. All nine strings use the same ruler. The sound control moves only the heard B marks.

      Check every string

      The exact A and B columns always retain the retuned pitches. Fractions are relative to the original session's initial string 1. “Heard B” follows the listening control.

      Same destination; pitches kept separately
      String A: exact ratio / Hz B: exact ratio / Hz B divided by A Heard B

      The HTML reading includes both routes, exact pitches, this listening comparison, fonts and their licenses. It opens offline.

      What returned?
      What did we add?

      The destination name identifies a pattern of clear and unclear string pairs in the reconstructed procedure. It supplies no absolute frequency to restore when the name returns.

      In this workshop's exact fourths-and-fifths model, the two endpoints differ by one common factor on every string. Transposing B by its reciprocal makes all nine frequencies equal to A. The raw result stays in the table.

      Text, reconstruction, calculation

      Sam Mirelman, Tuning Procedures in Ancient Iraq (2013), figure 5 on p. 52 and pp. 53–55, presents the tuning network and discusses the limits of a modern interpretation.

      Jay Rahn, Was Mesopotamian Tuning Diatonic? (2022), paragraphs 11–16, discusses both directions and repeated cycles. Paragraph 45 explains the editorial basis of the tightening terminology.

      nê’um means “loosen.” The contextual tightening reading is nasāḫum; its chapter is extensively restored. The words and their preservation are part of the evidence, while the exact fractions are our calculation.

      The 4/3 and 3/2 frequency ratios, hertz reference, exact arithmetic, synthetic timbre and comparison transposition are modern choices. Neither the numerical gap nor the transposition is a measurement or prescription preserved on a tablet.

      Read the preservation cases and Akkadian word notes