Numerary nexus: Difference between revisions
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See | 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.<ref>Harry Partch, ''Genesis of a Music'', (1974)</ref> | ||
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: | |||
: [[1/1]], [[11/10]], [[6/5]], [[7/5]], [[8/5]], [[9/5]] | |||
== See also == | |||
* [[Tonality diamond]] | |||
* [[Otonality and utonality]] | |||
== External links == | |||
* [http://www.tonalsoft.com/enc/n/nexus.aspx Numerary nexus] on [[Tonalsoft Encyclopedia]] | |||
== References == | |||
<references /> | |||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category: | [[Category:Otonality and utonality]] | ||
[[Category: | [[Category:Harry Partch]] | ||
Latest revision as of 22:04, 22 May 2026
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)