Musical Analysis - Examples

Mathematics

Our main mathematical tool is Spectrograms. These provide pictures of the time-frequency content of musical passages, a dynamic spectral analysis. Spectrograms (also known as sonograms, or short-time Fourier transforms, or Gabor transforms) have been employed in linguistics, in the study of animal calls, and in musical theory for many years. More details about their definition can be found by clicking on the link above, or here.

Some Basic Musical Theory

Music has multiple dimensions. There are at least 10 dimensions that are basic to human perception of music. We list them below (click on them for further discussion, including some musical illustrations).

Tone Pitch Timbre Rhythm Tempo Contour Loudness Spatial location Reverberation Vibrato

Notice how, for the most part, these features of music are culturally universal. These dimensions are also displayed, for the most part, as clearly identifiable patterns in the spectrograms (although some aspects, such as rhythm and tempo, often require further processing of the spectrogram).

Music displays a dialectical development in the relations between its various dimensions (for further discussion, click here). Music also displays hierarchical structures within its dimensions (for further discussion, click here).

Musical Examples

Click on the links below for analyses of several musical examples using the basic musical theory described above.

Finale of Stravinsky's Firebird Suite

Some Chinese Folk Songs

Rhythmic Analyses

Musical passages for a Bach piece and a Tchaikovsky piece

A Beatles song

Avant-garde music

An "Indian Hip-Hop" song (Chaiyya Chaiyya)

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