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June 2026

Just intonation — Chords tuned to whole-number frequency ratios drawn from a tonality diamond, found by simulated annealing and then threaded together with Viterbi optimisation. These are successive passes at the same idea, newest first — each refines the tuning search and the orchestration over the one before it.

The first full pass in just intonation.

Recordings
12
Total length
73:28
Limits used
17, 19
Rendered
June 1, 2026

  1. BWV 253 Ach bleib bei uns, Herr Jesu Christ

    17-limit · 3:01 · 96 BPM · Density 0 · ±1¢

    Download MP3 ball9-t53a_lm17_r1.12_sf0.00_df0_sp07_t1_d03_01_t096.mp3

  2. BWV 254 Ach Gott, erhör mein Seufzen und Wehklagen

    17-limit · 3:23 · 80 BPM · Density 2 · ±3¢

    Download MP3 ball9-t54a_lm17_r1.62_sf0.00_df2_sp07_t3_d03_23_t080.mp3

  3. BWV 255 Ach Gott und Herr, wie groß und schwer

    19-limit · 2:23 · 68 BPM · Density 1 · ±2¢

    Download MP3 ball9-t55a_lm19_r1.38_sf0.00_df1_sp07_t2_d02_23_t068.mp3

  4. BWV 256 Ach lieben Christen, seid getrost

    19-limit · 3:19 · 56 BPM · Density 0 · ±3¢

    Download MP3 ball9-t56a_lm19_r1.50_sf0.00_df0_sp07_t3_d03_19_t056.mp3

  5. BWV 257 Wär Gott nicht mit uns diese Zeit

    19-limit · 3:06 · 60 BPM · Density 0 · ±3¢

    Download MP3 ball9-t57a_lm19_r1.38_sf0.00_df0_sp07_t3_d03_06_t060.mp3

  6. BWV 258 Wo Gott der Herr nicht bei uns hält

    19-limit · 4:36 · 106 BPM · Density 5 · ±3¢

    Download MP3 ball9-t58a_lm19_r1.12_sf0.00_df5_sp07_t3_d04_36_t106.mp3

  7. BWV 259 Ach, was soll ich Sünder machen

    19-limit · 17:20 · 110 BPM · Density 3 · ±2¢

    Download MP3 ball9-t59a_lm19_r1.25_sf0.00_df3_sp07_t2_d17_20_t110.mp3

  8. BWV 260 Allein Gott in der Höh sei Ehr

    17-limit · 3:00 · 80 BPM · Density 1 · ±2¢

    Download MP3 ball9-t60a_lm17_r1.50_sf0.00_df1_sp07_t2_d03_00_t080.mp3

  9. BWV 261 Allein zu dir, Herr Jesu Christ

    17-limit · 17:33 · 106 BPM · Density 4 · ±1¢

    Download MP3 ball9-t61a_lm17_r1.12_sf0.00_df4_sp07_t1_d17_33_t106.mp3

  10. BWV 262 Alle Menschen müssen sterben

    19-limit · 4:59 · 110 BPM · Density 2 · ±1¢

    Download MP3 ball9-t62a_lm19_r1.75_sf0.00_df2_sp07_t1_d04_59_t110.mp3

  11. BWV 263 Alles ist an Gottes Segen

    19-limit · 3:49 · 100 BPM · Density 3 · ±3¢

    Download MP3 ball9-t63a_lm19_r1.12_sf0.00_df3_sp07_t3_d03_49_t100.mp3

  12. BWV 264 Als der gütige Gott

    17-limit · 6:59 · 110 BPM · Density 4 · ±3¢

    Download MP3 ball9-t64a_lm17_r1.50_sf0.00_df4_sp07_t3_d06_59_t110.mp3

Filenames encode the settings each render used: lm17 is a 17-limit tonality diamond, r1.12 the ratio factor, df2 the orchestration density, t1 a tolerance of one cent, and the trailing t106 the tempo.