atomic

[Gene Ward Smith, Yahoo tuning group message 11565 (Fri Oct 22, 2004 9:49 pm)]

family name: atomic
period: 100 cents
generator: schisma (32805/32768) 0.00144 to 0.00145 cents flat in the 5-limit

5-limit

name: atomic
comma: Kirnberger atom |161 -84 -12>
mapping: [<12 19 28|, <0 1 -7|]
poptimal generator: 75/46032
TOP period: 99.9999960286 generator: 1.9551521919
MOS: 612, 624, 1236, 1848, 2460, 3072, 4296, 7980, 12276, 16572, 20868, 25164, 46032

7-limit

name: atomic
wedgie: <<12 -84 -192 -161 -338 -210||
mapping: [<12 19 28 34|, <0 1 -7 -16|]
copoptimal generator: 13/8004
TOP period: 99.9993850271 generator: 1.9490287082
TM basis: |-4 6 -6 3>, |-55 30 2 1>
MOS: 612, 624, 1236, 1848, 2460, 4308, 6156, 8004

11-limit

name: atomic
wedgie: <<12 -84 -192 -300 -161 -338 -517 -210 -406 -178||
mapping: [<12 19 28 34 42|, <0 1 -7 -16 -25|]
poptimal generator: 5/3084
TOP period: 99.9992719361 generator: 1.9478879037
TM basis: {9801/9800, 151263/151250, 184549376/184528125}
MOS: 612, 624, 1236, 1848, 3084

note: atomic is compatible with 12-et, and ultra-accurate in the 5-limit, making it useful for analyzing 12-note temperaments. The 46032 division divides the pythagorean comma into 900 parts and the Didymus comma (81/80) into 825 parts, giving therefore 75 parts to the schisma. It assigns the same number to the flatness of the 12-et fifth, and is the temperament which equates the schisma with the flattening of the 12-et fifth; whose near-identity was noted by Ellis and implicitly used by Kirnberger. In higher limits, atomic is not nearly so accurate but useful in connection with devising notation schemes compatible with 12-et.

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Encyclopedia of Microtonal Music Theory

atomic