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! Sagittal high-tolerance temperament notation. George Secor. 2003-Aug-28, updated 2020-Jun-14 ! max_abs_slope 7.5 c_exp_range -6 10 nc_exp_range -1 5 fifth_size 703.5787 oct_size 2/1 ! !Lower bound Symbol Value Short -70.385 (!) 704/729 w -62.5 \!/ 32/33 v -55.0 (!) 704/729 w -43.3 \! 80/81 \ -35.0 !) 63/64 t -32.0 !/ 54/55 k -29.0 \! 80/81 \ -26.0 !) 63/64 t -15.0 15.0 |) 64/63 f 26.0 /| 81/80 / 29.0 |\ 55/54 y 32.0 |) 64/63 f 35.0 /| 81/80 / 43.3 (|) 729/704 m 55.0 /|\ 33/32 ^ 62.5 (|) 729/704 m 70.385
@Dave Keenan has suggested I plug it into Scala along with the scale it is meant to notate, which I believe I have correctly identified in the Scala scale archives and reproduced below:
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! secor29htt.scl ! George Secor's 29-tone 13-limit high-tolerance temperament (5/4 & 7/4 exact) 29 ! 58.08980 97.04984 140.19633 179.15637 207.15739 265.24719 296.73557 347.35372 5/4 414.31478 472.40458 496.42131 554.51111 593.47114 633.37025 679.56197 703.57869 761.66849 800.62853 843.77502 882.73506 910.73608 7/4 992.84261 1050.93241 1089.89245 1117.89347 1175.98327 2/1
The problem is that I don't feel super confident about the advanced harmonic theory that Dave and George grappled with to develop Sagittal. Maybe I'll get there one day! I just don't have enough of the mathematical and musical practice backgrounds to confidently notate this thing.
I was hoping that someone else might enjoy the puzzle of reverse-engineering this tuning in the form of its Sagittal notation, so that I could then confirm that Scala generates the correct notation for it using the configuration file we also maintain for that exact purpose. I know we have some puzzle lovers on this forum... come out, come out, wherever you are...
I have gone ahead and scooped up some useful resources for the endeavor:
https://yahootuninggroupsultimatebackup ... 53712.html
https://yahootuninggroupsultimatebackup ... .html#6889
https://yahootuninggroupsultimatebackup ... .html#7574
There's also this quote, from an unknown author, I found in a text file (not a post) from the same backup:
And this, which I lost track of where I found (sorry):a fabulous
near-just, non-equal well temperament included in
the Scala freeware archive under the filename
secor29htt.scl, best represented in Sagittal High
Tolerance Temperament notation (SAHTT). Among many
virtues, this temperament allows otonal ogdoads to
odd limit 15 in six key signatures. It has three
chains of tempered "fifth" (near 3/2) intervals
plus one inserted note.
I've attached the .mp3 file George mentions on one of these posts, which for whatever reason my code has failed to link up (vindicating Dave's insistence that not all possible files were processed properly). Quite a special little performance it is.a "near-just" temperament which, as a 29-note set, uses
multiple chains of the mildly tempered fifths to offer a great variety
of pure or near-pure ratios.