John Carlos Baez (npub1nf4…nqe4) re https://johncarlosbaez.wordpress.com/2026/01/28/tiny-musical-intervals/
The only problem I spot with the Python code is that the check for "non-trivial" triples is redundant. Except for <0,0,0> there should be no non-trivial triples, and that is already excluded. Instead, this means no triples closer than 10 micro-cents would be printed.
Removing this check and extending the search range gives some more values on the frontier:<code>0.000884 cents | 1+5.103919569e-07 | [-573, 237, 85] | Tenney: 1146.0<br>0.000187 cents | 1+1.077468461e-07 | [2033, 90, -937] | Tenney: 4351.3<br>0.000159 cents | 1+9.185490346e-08 | [399, -1412, 792] | Tenney: 4475.9<br>0.000028 cents | 1+1.589178367e-08 | [1634, 1502, -1729] | Tenney: 8029.2<br>0.000006 cents | 1+3.442373941e-09 | [-7470, 2791, 1312] | Tenney: 14940.0<br>0.000002 cents | 1+1.373041014e-09 | [-22109, 20086, -4189] | Tenney: 63671.1<br></code>
none have as big a jump in cent accuracy as the quark of Baez.
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2026-01-30 02:13:10 UTC
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"content": "nostr:npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4 re https://johncarlosbaez.wordpress.com/2026/01/28/tiny-musical-intervals/\n\nThe only problem I spot with the Python code is that the check for \"non-trivial\" triples is redundant. Except for \u003c0,0,0\u003e there should be no non-trivial triples, and that is already excluded. Instead, this means no triples closer than 10 micro-cents would be printed.\n\nRemoving this check and extending the search range gives some more values on the frontier:\u003ccode\u003e0.000884 cents | 1+5.103919569e-07 | [-573, 237, 85] | Tenney: 1146.0\u003cbr\u003e0.000187 cents | 1+1.077468461e-07 | [2033, 90, -937] | Tenney: 4351.3\u003cbr\u003e0.000159 cents | 1+9.185490346e-08 | [399, -1412, 792] | Tenney: 4475.9\u003cbr\u003e0.000028 cents | 1+1.589178367e-08 | [1634, 1502, -1729] | Tenney: 8029.2\u003cbr\u003e0.000006 cents | 1+3.442373941e-09 | [-7470, 2791, 1312] | Tenney: 14940.0\u003cbr\u003e0.000002 cents | 1+1.373041014e-09 | [-22109, 20086, -4189] | Tenney: 63671.1\u003cbr\u003e\u003c/code\u003e\n\nnone have as big a jump in cent accuracy as the quark of Baez.\nnostr:note1fz27l2hk40v5y63msuqzqvru5028q70gzpdfk37pqldlhuzjs07q528j0h\n",
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