The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the different groups of voices are heard out through the different channels of headphones. Is created demonstration program for the pan of the chords of midi synthesizer.

LetK be a 2-knot. The conormal Lift ΛK ofK is a Legendrian submanifold in the unit cotangent bundle U∗R4. One can use Legendrian homology on ΛK to define an invariant of K which is a differential graded algebra partly generated by the Reeb chords of ΛK . We try to count and specify these Reeb chords by describing the conormal lifts, of 2-knots given as closed 2dimensional braids, as 1-jet graph...

R. E. Jamison proved that every cycle of length greater than three in a graph has a chord—in other words, the graph is chordal—if and only if every k-cycle is the sum of k − 2 triangles. This result generalizes to having or not having crossing chords and to having strong chords, with similar characterizations of a variety of graph classes that includes chordal bipartite, distance-hereditary, an...

This entry provides a geometric proof of the intersecting chords theorem. The theorem states that when two chords intersect each other inside a circle, the products of their segments are equal. After a short review of existing proofs in the literature [1, 3–5], I decided to use a proof approach that employs reasoning about lengths of line segments, the orthogonality of two lines and Pythagoras ...

Among the three primary tonal functions described in modern theory textbooks, pre-dominant has highest number of representative chords. We posit that one unifying feature function is its attraction to V, and experiment reported here investigates factors may contribute this perception. Participants were junior/senior music majors, freshman people from general population recruited on Prolific.co....

It has been argued that convexity in the Euler lattice can be interpreted in terms of consonance (Honingh and Bod 2005). In this paper, a second hypothesis is presented that states that compactness in the Euler-lattice is an indication of consonance. It will be investigated if, and to which degree convexity and compactness are in agreement with the consonance of chords according to Euler’s meas...

We define a diamonded odd cycle to be an odd cycle C with exactly two chords and either a) C has length five and the two chords are non-crossing; or b) C has length greater than five and has chords (x,y) and (x,z) with (y,z) an edge of C and there exists a node w not on C adjacent to y and C, but not x. In this paper, we show that given a diamonded odd cycle-free graph G, G is perfect if and on...

Reward has been shown to change behavior as a result of incentive learning (by motivating the individual to increase their effort) and instrumental learning (by increasing the frequency of a particular behavior). However, Palminteri et al. (2011) demonstrated that reward can also improve the incidental learning of a motor skill even when participants are unaware of the relationship between the ...