# Numerary nexus

Harry Partch, 11-limit tonality diamond.

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.

## Sources

1. ^ 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.