2.4 Outputting the results  (Page 2/2)

Harmonic likelihood graph

The above graphical output method is the result of a secondary, less straight-forward analysis of our data. To show the merit of tailoring the inputs for the matched filter, we graphically represented the rating assigned to each harmonic in a given window. Note how there is one over-arching, dominant waveform for nearly every window (except those in which there exists only noise) but see also the lesser, but still non-trivial, strengths of its harmonics. Without filtering for octaves of a signal note, our algorithm would more likely be tricked into thinking the harmonics of a note were the note itself (or perhaps other notes being played).

The noise is less of an issue when the data is perceived in this manner; thus no threshold value is required to determine that which is silence and that which is not. This method is still not useful in analyzing a song in which multiple notes are played during a single moment in time. For that, we turn to the third and last graphical method of representation.

Musical score interpretation graph

The above graphical output method is the result of our attempts to present an intuitive representation of our data. The goal is to produce an output which is most useful for someone completely unfamiliar with graphical methods yet intimately familiar with music. Thus, we graph each window as an image with colors assigned to the various values of the data inside the window. The result is something that looks surprisingly like a musical score. The more "intense" or colorful a particular region seems, the more likely it is to be a note played within that window. The chromatic scale serves to display the merits of this startling technique with distinction.

The first graph below this paragraph is the graphical interpretation of Stravinsky's Three Pieces for Clarinet using this method for processing our data described in this section. It serves the same purpose as the preceding Stravinsky graphs.

The most useful application of this graphical method, however, is that one may readily view several notes playing at once. This form is best embodied in the final two graphs. To first gather some sense of how to interpret the graph when multiple instruments are playing, the second graph below this paragraph shows a stripped-down version of the output from our program when it is fed the first 90.703 seconds (4,000,000 samples) of Barber's Adagio for Strings as played by a clarinet choir. A choir in its most general sense is merely the gathering of multiple like-familied instruments. That is, all sorts of vocal instrumentation (soprano, alto, tenor, bass) form the most standard interpretation of choir. Thus, a clarinet choir is one in which several members of the clarinet family (Eb, Bb, A, Alto/Eb, Bass, Contrabass, etc.) play in one ensemble. The final graph on this page displays the output for Barber's Adagio For Strings in all its glory.

The two graphs sandwiching this paragraph show the three voices of clarinet that play. The top line is the lead clarinet (there is only one). If one listens to the song, one may quickly note the 'v' in the middle appearing in the sound byte ("byte" used here in a general sense). The second line is the supporting clarinets and the lowest line is the bass line (or harmonics thereof). Our algorithm was told to search for three notes to produce these two graphs.