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Late 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.

Recordings

12

Total length

73:16

Limits used

17, 19

Rendered

June 29, 2026

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

   17-limit · 6:04 · 122 BPM · Density 3 · ±1¢

   Download MP3 ball9-t53c_lm17_r1.12_sf0.00_df3_sp07_t1_d06_04_t122.mp3

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

   17-limit · 8:53 · 114 BPM · Density 5 · ±3¢

   Download MP3 ball9-t54c_lm17_r1.12_sf0.00_df5_sp07_t3_d08_53_t114.mp3

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

   17-limit · 7:13 · 110 BPM · Density 2 · ±1¢

   Download MP3 ball9-t55c_lm17_r1.25_sf0.00_df2_sp07_t1_d07_13_t110.mp3

4. BWV 256 Ach lieben Christen, seid getrost

   19-limit · 6:10 · 122 BPM · Density 5 · ±3¢

   Download MP3 ball9-t56c_lm19_r1.12_sf0.00_df5_sp07_t3_d06_10_t122.mp3

5. BWV 257 Wär Gott nicht mit uns diese Zeit

   19-limit · 3:18 · 100 BPM · Density 1 · ±3¢

   Download MP3 ball9-t57c_lm19_r1.12_sf0.00_df1_sp07_t3_d03_18_t100.mp3

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

   17-limit · 3:51 · 84 BPM · Density 2 · ±3¢

   Download MP3 ball9-t58c_lm17_r1.75_sf0.00_df2_sp07_t3_d03_51_t084.mp3

7. BWV 259 Ach, was soll ich Sünder machen

   19-limit · 4:03 · 92 BPM · Density 1 · ±3¢

   Download MP3 ball9-t59c_lm19_r1.12_sf0.00_df1_sp07_t3_d04_03_t092.mp3

8. BWV 260 Allein Gott in der Höh sei Ehr

   19-limit · 8:47 · 114 BPM · Density 4 · ±3¢

   Download MP3 ball9-t60c_lm19_r1.75_sf0.00_df4_sp07_t3_d08_47_t114.mp3

9. BWV 261 Allein zu dir, Herr Jesu Christ

   19-limit · 4:38 · 104 BPM · Density 0 · ±3¢

   Download MP3 ball9-t61c_lm19_r1.25_sf0.00_df0_sp07_t3_d04_38_t104.mp3

10. BWV 262 Alle Menschen müssen sterben

    17-limit · 7:24 · 114 BPM · Density 3 · ±3¢

    Download MP3 ball9-t62c_lm17_r1.12_sf0.00_df3_sp07_t3_d07_24_t114.mp3

11. BWV 263 Alles ist an Gottes Segen

    19-limit · 5:47 · 84 BPM · Density 0 · ±3¢

    Download MP3 ball9-t63c_lm19_r1.25_sf0.00_df0_sp07_t3_d05_47_t084.mp3

12. BWV 264 Als der gütige Gott

    17-limit · 7:08 · 114 BPM · Density 4 · ±3¢

    Download MP3 ball9-t64c_lm17_r1.12_sf0.00_df4_sp07_t3_d07_08_t114.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.