Numerary nexus
In the theory of Harry Partch, the numerary nexus is a number that serves as the shared numerical identity in a set of ratios that determines them as a tonality.[1] It is the common factor that appears in a set of ratios, appearing in either the numerator or denominator. In an otonality, the nexus appears in the denominator of all the ratios; in a utonality, it appears in the numerator.
The numerary nexus is central to the tonality diamond, where every row and column is organized by a shared nexus.
Examples
In the otonal set 7/7 (= 1/1), 7/6, 7/5, 7/4, the number 7 appears in the numerator of all intervals, so it is the nexus linking them.
The 11-limit tonality diamond contains six identities: (1, 3, 5, 7, 9, 11). The utonal set based on 5 as the numerary nexus is:
- 1/5, 3/5, 5/5, 7/5, 9/5, 11/5
Which, which octave-reduced and sorted by their size, gives:
See also
External links
References
- ↑ Harry Partch, Genesis of a Music, (1974)