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The 29-limit consists of just intonation intervals whose ratios contain no prime factors higher than 29. It is the 10th prime limit and is thus a superset of the 23-limit and a subset of the 31-limit. The prime 29 is notable as being the prime that ends a record prime gap starting at 23. Thus, the 29-limit is in some sense analogous to the 11-limit as both include the prime ending a record prime gap.

Edo approximations

282edo is the smallest edo that is consistent to the 29-odd-limit. 1323edo is the smallest edo that is distinctly consistent to the 29-odd-limit. Intervals 29/16 and 32/29 are very accurately approximated by 7edo (1\7 for 32/29, 6\7 for 29/16).


Randy Wells

See also