Neutral interval
In music theory, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major third is 400 cents, a minor third is 300 cents, and a neutral third is 350 cents. A neutral interval inverts to a neutral interval. For example, the inverse of a neutral third is a neutral sixth.
Roughly, neutral intervals are a quarter tone sharp from minor intervals and a quarter tone flat from major intervals. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together.
Second
A neutral second or medium second is an interval wider than a minor second and narrower than a major second. Three distinct intervals may be termed neutral seconds:
play , has a ratio between the higher-frequency tone to the lower-frequency tone of 12:11 and is about 150.64 cents wide, while the larger one,Interval
Interval may refer to:
Maths and physics
Music
Dramatic arts
- Entr'acte, a French term for the same, but used in English often to mean a musical performance played during the break
Sport
Other
Interval (graph theory)
In graph theory, an interval I(h) in a directed graph is a maximal, single entry subgraph in which h is the only entry to I(h) and all closed paths in I(h) contain h. Intervals were described in 1976 by F. E. Allen and J. Cooke. Interval graphs are integral to some algorithms used in compilers, specifically data flow analyses.
The following algorithm finds all the intervals in a graph consisting of vertices N and the entry vertex n0, and with the functions pred(n) and succ(n) which return the list of predecessors and successors of a given node n, respectively.
The algorithm effectively partitions the graph into its intervals.
Each interval can in turn be replaced with a single node, while all edges between nodes in different intervals in the original graph become edges between their corresponding nodes in the new graph. This new graph is called an interval derived graph. The process of creating derived graphs can be repeated until the resulting graph can't be reduced further. If the final graph consists of a single node, then the original graph is said to be reducible.
Partially ordered set
In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other. Such a relation is called a partial order to reflect the fact that not every pair of elements need be related: for some pairs, it may be that neither element precedes the other in the poset. Thus, partial orders generalize the more familiar total orders, in which every pair is related. A finite poset can be visualized through its Hasse diagram, which depicts the ordering relation.
A familiar real-life example of a partially ordered set is a collection of people ordered by genealogical descendancy. Some pairs of people bear the descendant-ancestor relationship, but other pairs bear no such relationship.
Formal definition
Podcasts:
