# Numerary nexus

In musical tuning, a **numerary nexus** is an identity shared by two or more interval ratios in their numerator or denominator, with different identities in the other.^{[1]} For example, in the Otonality the denominator is always 1, thus 1 is the numerary nexus:

1 2 3 4 5 - - - - - etc. 1 1 1 1 1 3 5 (-) (-) 2 4

In the Utonality the numerator is always 1 and the numerary nexus is thus also 1:

1 1 1 1 1 - - - - - etc. 1 2 3 4 5 4 8 (-) (-) 3 5

For example, in a tonality diamond, such as Harry Partch's 11-limit diamond to the right, each ratio of a right slanting row shares a numerator and each ratio of a left slanting row shares an denominator. Each ratio of the upper left row has 7 as a denominator, while each ratio of the upper right row has 7 (or 14) as a numerator.

## See also

## Sources

- ↑ Rasch, Rudolph (2000). "A Word or Two on the Tunings of Harry Partch",
*Harry Partch: An Anthology of Critical Perspectives*, p.28. Dunn, David, ed. ISBN 90-5755-065-2.

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