Holdrian Comma - Mercator's Comma and The Holdrian Comma

Mercator's Comma and The Holdrian Comma

Mercator applied logarithms to determine that (≈ 21.8182 cents) was nearly equivalent to a syntonic comma of ≈ 21.5063 cents (a feature of the prevalent sixth-comma meantone temperament tuning system of the time). He also considered that an "artificial comma" of might be useful, because 31 octaves could be practically approximated by a cycle of 53 just fifths. William Holder, for whom the Holdrian comma is named, favored this latter unit because the intervals of 53 equal temperament are closer to just intonation than that of 55. Thus Mercator's comma and the Holdrian comma are two distinct but related intervals.

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