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. 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.