ASA 18 - Logarithmic And Linear Frequency Scales

Description

A musical scale is a succession of notes arranged in ascending or descending order. Most musical composition is based on scales, the most common ones being those with five notes (pentatonic), twelve notes (chromatic), or seven notes (major and minor diatonic, Dorian and Lydian modes, etc.). Western music divides the octave into 12 steps called semitones. All the semitones in an octave constitute a chromatic scale or 12-tone scale. However, most music makes use of a scale of seven selected notes, designated as either a major scale or a minor scale and carrying the note name of the lowest note. For example, the C-major scale is played on the piano by beginning with any C and playing white keys until another C is reached.

Other musical cultures use different scales. The pentatonic or five-tone scale, for example, is basic to Chinese music but also appears in Celtic and Native American music. A few cultures, such as the Nasca Indians of Peru, have based their music on linear scales (Haeberli, 1979), but these are rare. Most music is based on logarithmic (steps of equal frequency ratio Δf/f) rather than linear (steps of equal frequency Δf) scales .

In this demonstration we compare both 7-step diatonic and 12-step chromatic scales with linear and logarithmic steps.

References

A.H.Benade (1976), Fundamentals of Musical Acoustics (Oxford Univ., New York). Chap. 15.

E.M.Burns and W.D.Ward (1982), "Intervals, scales, and tuning," in The Psychology of Music, ed. D.Deutsch (Academic Press, New York). pp. 241-69.

J.Haeberli (1979), "Twelve Nasca panpipes: A study," Ethomusicology 23, 57-74.

D.E.Hall (1980), Musical Acoustics (Wadsworth, Belmont, CA) pp. 444-51.

T.D.Rossing (1982), The Science of Sound (Addison-Wesley, Reading, MA) Chap. 9

Frequency
Time Delay

Transcript

Eight-note diatonic scales of one octave are presented. Alternate scales have linear and logarithmic steps. The demonstration is repeated once.

Frequency
Time Delay

Transcript

Next, 13-note chromatic scales are presented, again alternating between scales with linear and logarithmic steps.