2.4 Outputting the results

This module comprises three different graphical interpretations of the output data mentioned in the previous module. I will offer this brief introduction on the general layout of the subsections to follow so that you, the reader, may be better prepared to interpret the information:

At the beginning of each sub-section you will find the representative graph of the most simple "song" we could imagine: a chromatic scale. For those not well-versed in music, a chromatic scale is one in which the instrument 'outputs' a series of notes, each note directly above or below its predecessor in frequency. Note: "scale," in this sense, implies either a constant increase or decrease of tone; therefore if one note is directly above its predecessor, the following note must be directly above this one note. Likewise for the alternate direction.

Following this graph will be a description. At the end of the description will be placed another graph or three. The distinction between the original chromatic scale and these secondary graphs is an important one: the individual (Michael Lawrence) who played the original samples also played the chromatic scale; the secondary graphs are interpretations of recordings done by professionals. Thus, not only do we find we have an unbiased test-set, we see how the samples sampled at 22050 Hz compare with a recording sampled at 44100 Hz. Our upsampling algorithm created to deal with just such a discrepancy is covered in the following module.

Most likely note graph

The above graphical output method is the result of the most straight-forward analysis of our data. Each window is assigned a single number which represents the note most likely to have been played within that window. This graph-type is the only one in which noise plays a considerable role; setting the threshold to zero results in "most likely notes" being chosen for each window in which there is only noise. Thus we have to tell the algorithm that only noise exists for those windows (i.e. it is silent). Our value for silence is -1. "1" corresponds to the lowest note on a Bb clarinet (an E in the chalameau register; in concert pitch, a D below middle C). Each incremental advance above that is one half-step (a half-step is the term used to describe two notes considered 'next' to one another in frequency).

The following graph is the output of our program when fed a professionally-recorded solo clarinet (playing the first 22.676 seconds (1,000,000 samples) of Stravinsky's Three Pieces for Clarinet ). The chromatic waveform was created by the same individual who recorded the samples; thus the Stravinsky waveform represents an unbiased application of our algorithm against one instrument. This graph is meaningless for a song in which multiple notes occur; thus there is no output corresponding to a song in which multiple instruments play.