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Early July 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.

Recordings
12
Total length
64:57
Limits used
17, 19
Rendered
July 2, 2026

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

    17-limit · 8:08 · 114 BPM · Density 3 · ±1¢

    Download MP3 ball9-t53c_lm17_r1.12_sf0.00_df3_sp07_t1_d08_08_t114.mp3

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

    17-limit · 4:04 · 104 BPM · Density 2 · ±3¢

    Download MP3 ball9-t54c_lm17_r1.12_sf0.00_df2_sp07_t3_d04_04_t104.mp3

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

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

    Download MP3 ball9-t55c_lm17_r1.25_sf0.00_df1_sp07_t1_d03_17_t096.mp3

  4. BWV 256 Ach lieben Christen, seid getrost

    19-limit · 5:25 · 118 BPM · Density 1 · ±3¢

    Download MP3 ball9-t56c_lm19_r1.12_sf0.00_df1_sp07_t3_d05_25_t118.mp3

  5. BWV 257 Wär Gott nicht mit uns diese Zeit

    19-limit · 5:52 · 92 BPM · Density 4 · ±3¢

    Download MP3 ball9-t57c_lm19_r1.12_sf0.00_df4_sp07_t3_d05_52_t092.mp3

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

    17-limit · 5:59 · 118 BPM · Density 4 · ±3¢

    Download MP3 ball9-t58c_lm17_r1.75_sf0.00_df4_sp07_t3_d05_59_t118.mp3

  7. BWV 259 Ach, was soll ich Sünder machen

    19-limit · 6:21 · 118 BPM · Density 5 · ±3¢

    Download MP3 ball9-t59c_lm19_r1.12_sf0.00_df5_sp07_t3_d06_21_t118.mp3

  8. BWV 260 Allein Gott in der Höh sei Ehr

    19-limit · 4:43 · 96 BPM · Density 5 · ±3¢

    Download MP3 ball9-t60c_lm19_r1.75_sf0.00_df5_sp07_t3_d04_43_t096.mp3

  9. BWV 261 Allein zu dir, Herr Jesu Christ

    19-limit · 5:04 · 60 BPM · Density 0 · ±3¢

    Download MP3 ball9-t61c_lm19_r1.25_sf0.00_df0_sp07_t3_d05_04_t060.mp3

  10. BWV 262 Alle Menschen müssen sterben

    17-limit · 6:20 · 110 BPM · Density 3 · ±3¢

    Download MP3 ball9-t62c_lm17_r1.12_sf0.00_df3_sp07_t3_d06_20_t110.mp3

  11. BWV 263 Alles ist an Gottes Segen

    19-limit · 3:48 · 34 BPM · Density 0 · ±3¢

    Download MP3 ball9-t63c_lm19_r1.25_sf0.00_df0_sp07_t3_d03_48_t034.mp3

  12. BWV 264 Als der gütige Gott

    17-limit · 5:56 · 106 BPM · Density 2 · ±3¢

    Download MP3 ball9-t64c_lm17_r1.12_sf0.00_df2_sp07_t3_d05_56_t106.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.