Download Mathematics and Music: Composition, Perception, and by James S. Walker, Gary Don PDF

By James S. Walker, Gary Don

First and foremost look, arithmetic and song appear to be from separate worlds one from technology, one from artwork. yet in reality, the connections among the 2 return millions of years, similar to Pythagoras s principles approximately how one can quantify alterations of pitch for musical tones (musical intervals). Mathematics and track: Composition, conception, and Performance explores the numerous hyperlinks among arithmetic and various genres of track, deepening scholars realizing of track via mathematics.

In an obtainable means, the textual content teaches the fundamentals of interpreting track and explains how quite a few styles in song will be defined with arithmetic. The authors greatly use the robust time-frequency approach to spectrograms to investigate the sounds created in musical functionality. quite a few examples of song notation help scholars in figuring out uncomplicated musical rankings. The textual content additionally presents mathematical motives for musical scales, concord, and rhythm and features a concise advent to electronic audio synthesis.

Along with assisting scholars grasp a few primary arithmetic, this publication offers them a deeper appreciation of song through displaying how track is trained by way of either its mathematical and aesthetic structures.

Web Resource
On the e-book s CRC Press online page, scholars can entry movies of a number of the spectrograms mentioned within the textual content in addition to musical rankings playable with the loose track software program MuseScore. a web bibliography deals many hyperlinks to unfastened downloadable articles on math and song. the net web page additionally offers hyperlinks to different web content regarding math and tune, together with the entire websites pointed out within the e-book. "

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Extra resources for Mathematics and Music: Composition, Perception, and Performance

Example text

Altogether these 1 1 1 1 + 18 + 16 + 14 + 18 + 16 + 16 = 34 . durations produce the equation: 16 Dotted notes, ties, and slurs Some other aspects of scoring that we need to discuss are dotted notes, ties, and slurs. Dotted notes have a small dot on the right of the note symbol. 5 times the duration of the same 1 3 note without the dot. For example, a dotted eighth note has duration 18 + 16 = 16 . A tie indicates that two notes with the same pitch should be played as one, with a duration equal to the sum of the duration of the individual notes.

Based on this idea, we will say that multiplying 440 by r1/2 is raising the pitch of A4 by a quarter step (half of a half step). 892984123137. 892984123137 Hz is a quarter step above the pitch of A4 . 500000000000019. , about a quarter step above 440 Hz. 2 Cents The logarithm method of comparing two frequencies provides a very fine discrimination, one that accords well with human perception. 5 half steps above 440 Hz. Both of these results can be expressed in units of cents, a unit for measuring frequency difference that is widely employed in music.

This last example is interesting because the note F is also one half step above E. The notes E and F are enharmonic (have the same pitch). If a flat is applied to a note, then the note is lowered one half step. So D is one half step below D. There are enharmonic cases here as well. For instance, the notes C and B are enharmonic. Returning to our discussion of major scales, suppose we start on the fifth note D of the G-major scale. We will produce the scale known as D-major. 14, we get the following results: 2 half steps 2 half steps 1 half step 2 half steps 2 half steps 2 half steps 1 half step D −−−−−−→ E −−−−−−→ F −−−−−→ G −−−−−−→ A −−−−−−→ B −−−−−−→ C −−−−−→ D.

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