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3 untrigits 29791 untrigytes
This is an esolang and a sister language of 9 trits, 19683 trytes. Unlike its sisters, its memory triples. Note: 1 untrigyte is 3 untrigits (base-31 digits, 0–30).
Architecture
Memory is 28,830 untrigytes: the multiplicative units modulo 31^3 = 29791. Values wrap at 29791. Addresses divisible by 31 do not exist; if one is given, 1 is added to it. Doubling fails here — the order of 2 modulo 31^3 is only 4805, so a doubling orbit shatters into small cycles. Instead 3 generates the full unit group (order 28,830), so the successor of cell a is address 3a: pointers advance by tripling, and memory is one tripling cycle whose address-order dump is a base-3 discrete logarithm table. The least ternary base moves in the most ternary way.
An untrigyte holds one chord: three untrigits as Dominant, Mediant, Tonic, one 31-EDO step per digit, one octave band per voice. The character notation and statement set are inherited from 9 trits, 19683 trytes; a digit-level encoding in base 31 is left as a challenge.
Intonation
Kontakions intonate in 31-EDO, the temperament championed by Huygens — quarter-comma meantone closed into a circle, with a near-just 5/4 major third and a good 7th harmonic. A playable 31-tone instrument exists: the Fokker organ in Amsterdam, on which an untrigyte Kontakion could be performed. The 29,791 codepoints reach into CJK.
Computational class
See also
- 9 trits, 19683 trytes — the ternary sister
- 3 enneadecits, 6859 enneadecytes — the doubling sister
- Жiжos