Intonation of Harmonic Intervals: Adaptability of Expert Musicians to Equal Temperament and Just Intonation

Abstract

This study examines the deviation in the intonation of simultaneously sounding tones under the condition of an embedded melody task. Two professional musicians (trumpet players) were chosen as subjects to play the missing upper voice of a four-part audio example, while listening via headphones to the remaining three parts in adaptive five-limit just intonation and equal temperament. The experimental paradigm was that of a controlled varied condition with a 2 (tuning systems) ×× 5 (interval categories) ×× 5 (renditions) ×× 2 (players) factorial design. An analysis of variance showed a nonsignificant difference between the average deviation of harmonic intonation in the two systems used. Mean deviations of 4.9 cents (SD = 6.5 cents) in the equal-temperament condition and of 6.7 cents (SD = 8.1 cents) in the just-intonation condition were found. Thus, we assume that the musicians employed the same intonation for equaltemperament and just-intonation versions (an unconscious "always the same" strategy) and could not successfully adapt their performances to the just-intonation tuning system. Fewer deviations could be observed in the equal-temperament condition. This overall tendency can be interpreted as a "burn in" effect and is probably the consequence of longterm intonation practice with equal-temperament. Finally, a theoretical model of intonation is developed by use of factor analysis. Four factors that determine intonation patterns were revealed: the "major third factor," the "minor third and partials factor," the "instrumental tuning factor," and the "octave-minor seventh factor." To summarize, even in expert musicians, intonation is not determined by abstract tuning systems but is the result of an interaction among compositional features, the acoustics of the particular musical instrument, and deviation patterns in specific intervals.

Influences of Dynamic Level and Pitch Register on the Vibrato Rates and Widths of Violin and Viola Players

“…A sampling rate of 100 samples per second was used for the analysis of vibrato. Praat has been used in several recent investigations of pitch performance in music (Geringer & Allen, 2004;Geringer, Allen, & MacLeod, 2005;Kopiez, 2003).…”

Roughness Minimization Through Automatic Intonation Adjustments

“…It is generally represented as ratios to, or cents around, reference tones. Intonation is, in contrast, the adjusted frequency attained by an instrumentalist at performance time (Kopiez, 2003). A tuning system defines the gamut of tones available to construct scales and modes.…”

“…The maximum tuning deviation allowed by the adoption of this range is not likely to be perceived. In the selection of the default vicinity, we also considered the findings of Vos (1988), briefly discussed earlier, and Kopiez (2003), who observed that intonation deviations of trumpeters playing over 12-TET was of 4.9 cents and 6.7 cents in JT. With the imposition of a vicinity, pitch drift is not prevented but tethered. Therefore, special care must be taken in performance if pitch drift inhibition is desired.…”

“…Fine control of fundamental frequencies can be rather difficult: besides limitations imposed by some instruments, there is no consensus about instrumentalists' ability to adjust intonation to different tuning systems. Kopiez (2003) argues that even professional musicians use the same intonation strategy when playing in different tuning systems, and Eskelin (1994) and Howard (2005) have found that a cappella singers change their intonation to avoid dissonance when singing consonant chords. Neither is there consensus about an audience's ability to differentiate subtle pitch changes produced by different intonations.…”

Attention, communication and development of interpretation skills in chamber music pianists´education.

“…In this atmosphere, and by way of conscious listening, parameters such as tuning are checked. Tuning perception, as many studies support, differs between string and wind instruments and the voice (Geringer, 2012;Geringer, MacLeod & Sasanfar, 2015;Kopiez, 2003;Loosen, 1995). In the case of pianists, with a tempered instrument, tuning is not constantly adjusted, and Harlow (1969) maintains that pianists normally only tune their piano twice a year.…”