Root (chord)

Abstract: The key or the scale information of a piece of music provides important clues on its high level musical content, like harmonic and melodic context, which can be useful for music classification, retrieval or further content analysis. Researchers have previously addressed the issue of finding the key for symbolically encoded music (MIDI); however, very little work has been done on key detection for acoustic music. In this paper, we present a method for estimating the root of diatonic scale and the key directly from acoustic signals (waveform) of popular and classical music. We propose a method to extract pitch profile features from the audio signal, which characterizes the tone distribution in the music. The diatonic scale root and key are estimated based on the extracted pitch profile by using a tone clustering algorithm and utilizing the tone structure of keys. Experiments on 72 music pieces have been conducted to evaluate the proposed techniques. The success rate of scale root detection for pop music pieces is above 90%.

Abstract: A compressor stator vane includes pressure and suction sides extending chordally between leading and trailing edges, and longitudinally between a root and a tip. The vane narrows in chord to a waist between the root and tip. The vane may also be bowed at its trailing edge in cooperation with the narrow waist.

Abstract: a maximum of twenty-five prototypes from the small musical patterns in Mozart's six works. In a few cases the prototypes derived by the two experiments were nearly the same. Of course, the computer doing these simulations does not think in terms of musical conceptseverything must be a number. So from the computer's point of view, the memory of a prototype is just an array of numbers, each number standing for the strength of the association between a particular musical feature and the prototype. Figure 9 presents the similar numerical arrays representing the prototypes stored in long-term memory #10 of both simulations, first in graphic form and then in a conjectured musical form. Both versions of this prototype have abstracted the voice-leading progression from a tonic chord in first inversion to a subdominant chord in root position. The main difference between the two seems to be the richer melodic memory of the ametric simulation. The ametric simulation, more sensitive to weak passing or neighboring tones, incorporated into this prototype hints of two secondary dominants (V^ of IV and vii of ii) while the metric simulation associated those patterns with other prototypes. On the sole basis of memory #10 one might assume that the ametric simulation did the better job by including more detail in its abstractions. But from a larger perspective the reverse is actually true. The metric version of memory #10 is the more focused of the two and thus less likely to be recalled at inappropriate moments. Judged by human standards, the ametric simulation consistently had This content downloaded from 157.55.39.144 on Mon, 25 Jul 2016 04:58:51 UTC All use subject to http://about.jstor.org/terms

Abstract: This paper proposes novel wing planforms that reduce induced drag by exploiting the slipstream in aircraft driven by propellers in tractor configuration. The novel planforms are determined by optimization through an extended lifting-line theory that accounts for slipstream effects and an optimizer that includes the option of using an appropriate number of Bezier polynomial weights as control parameters describing wing planform. The optimization package written for the purpose (PROWING) minimizes a user-selected cost function, subject to a wide class of geometric and mechanical constraints on such variables as root chord, tip chord, span, wing area, bounds on wing twist and chord, airfoil profiles, root bending moment, etc. A general feature of the optimal wing planforms so generated is that the chords are shorter within the slipstream and longer on either side of it. For a wing of aspect ratio 12 and prescribed wing area, PROWING predicts that an optimal planform can reduce induced drag by about 9.15%, wi...