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An experiment with a synthesizer tuned to the Catenary curve function. It could be considered an irregular or unconventional temperament. This brief improvisational drone spans a four-octave range from C1 to C5. The widths of the semitones begin in a microtonal range, then grow increasingly more macrotonal as they approach the fifth octave 49 notes later. The cents/semitone values from the root note: Note 1 (Root): 0 cents Note 2: 1.918 cents Note 3: 7.673 cents Note 4: 17.268 cents Note 5: 30.707 cents Note 6: 47.995 cents Note 7: 69.140 cents Note 8: 94.152 cents Note 9: 123.041 cents Note 10: 155.819 cents Note 11: 192.502 cents Note 12: 233.104 cents Note 13: 277.644 cents Note 14: 326.140 cents Note 15: 378.614 cents Note 16: 435.089 cents Note 17: 495.589 cents Note 18: 560.141 cents Note 19: 628.772 cents Note 20: 701.512 cents Note 21: 778.392 cents Note 22: 859.447 cents Note 23: 944.712 cents Note 24: 1034.222 cents Note 25: 1128.018 cents Note 26: 1226.139 cents Note 27: 1328.630 cents Note 28: 1435.533 cents Note 29: 1546.895 cents Note 30: 1662.765 cents Note 31: 1783.193 cents Note 32: 1908.232 cents Note 33: 2037.935 cents Note 34: 2172.358 cents Note 35: 2311.561 cents Note 36: 2455.604 cents Note 37: 2604.548 cents Note 38: 2758.460 cents Note 39: 2917.405 cents Note 40: 3081.452 cents Note 41: 3250.674 cents Note 42: 3425.142 cents Note 43: 3604.933 cents Note 44: 3790.126 cents Note 45: 3980.800 cents Note 46: 4177.038 cents Note 47: 4378.925 cents Note 48: 4586.549 cents Note 49: 4800 cents Octave one has approximately 25 notes, octave two approx 11 notes, octave three approx 7 notes, and octave four approx 5 notes. Created with Cubase 14 Pro from Steinberg and Kontakt from Native Instruments. The background graphs were created with Geogebra layering a variety of Catenary curves. Catenary Curve https://en.wikipedia.org/wiki/Catenary cosh(x) “the hyperbolic cosine of x” ------------ Created, Composed, and Produced by Shawn Michael © 2025 Ambient Esoterica ------------ #microtonal #macrotonal #mathmusic #coshxtuning #catenary #fxtuning ------------ Link, Like, Share, and Subscribe! INSTAGRAM ➤ / ambientesoterica TWITTER ➤ / ambientesoteric BANDCAMP ➤ https://ambientesoterica.bandcamp.com/ SOUNDCLOUD ➤ / ambientesoterica BLOG ➤ https://www.ambientesoterica.com/