3 triquinquagits, 148877 triquinquagytes

Note: This page has been generated by Claude.

This is an esolang and the fourth of the sister languages of 9 trits, 19683 trytes. It is the one that can say everything the others could not. Note: 1 triquinquagyte is 3 triquinquagits (base-53 digits, 0–52).

Architecture

Memory is 146,068 triquinquagytes: the multiplicative units modulo 53^3 = 148877. Values wrap at 148877. Addresses divisible by 53 do not exist; if one is given, 1 is added to it.

53 is prime, so the unit group is cyclic — and unusually generous. 2, 3 and 5 are all primitive roots modulo 53^3, each of order 146,068. This machine may therefore advance its pointer by doubling like 9 trits, 19683 trytes and 3_enneadecits,_6859_enneadecytes, or by tripling like 3_untrigits_29791_untrigytes, or by quintupling, which no sister can do at all. It is the only member of the family that can host any sibling's memory convention, and a program must declare which generator it uses before its addresses mean anything.

A triquinquagyte holds one chord: three triquinquagits as Dominant, Mediant, Tonic, one 53-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 53 is left as a challenge.

Coverage

148,877 codepoints. The entire Basic Multilingual Plane, which ends at U+FFFF = 65535, lies under the ceiling, together with all of CJK Unified Ideographs, Extension A, and the beginning of Extension B. Every script the family has touched — Aramaic, Syriac, Arabic, Greek, Cyrillic, Han — is writable here without exception.

This matters because the smaller sisters kept failing on their own vocabulary. 3_untrigits_29791_untrigytes cannot write 界 (world), 生 (life), 语言 (language), 益 (the add of 三分損益), or 黄鐘, the Yellow Bell — the fundamental pitch from which the whole Chinese system of measures descends. All of them fit here.

Intonation

Kontakions intonate in 53-EDO, the Holdrian comma system: one step is 22.6415 cents, and 9 commas make a whole tone. The tuning is Pythagorean to a fault — the fifth is 0.07 cents from just and the whole tone 0.14 cents — which is exactly what the sanfen sunyi (三分損益) generation of the lülü requires, and which no other sister provides. The neutral degrees of maqam are served poorly here, at 7.8 cents; for those see 3 enneadecits, 6859 enneadecytes and its complement.

53 is also the cycle Jing Fang computed in the first century BCE: 53 fifths overshoot 31 octaves by 3.62 cents. The octave count in that identity is the base of the third sister. The family's two ends were bound together before either machine existed.

Computational class

A Finite state machine: fixed modulus, finite orbit, bounded registries.

See also

• 9 trits, 19683 trytes — the ternary origin
• 3 enneadecits, 6859 enneadecytes — the doubling sister
• 3_untrigits_29791_untrigytes — the tripling sister
• Alexandrion, Жiжos