Major third

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.

Abstract: The purpose of the study was to examine intonation patterns concerning melodic and harmonic musical intervals compared to equal temperament. Forty-eight junior high school, high school, and college undergraduate musicians were assigned to one of four experimental conditions in a split-plot design. Subjects performed four diatonic intervals (major third, perfect fourth, perfect fifth, and major sixth) both melodically and harmonically. Results indicated no significant differences in overall intonation accuracy in relationship to performed ascending and descending directions or among the four test intervals. In relationship to sharpness versus flatness there were significant, if musically inconsequential, differences: when subjects descended, intervals were performed slightly sharper; when subjects ascended, intervals were performed slightly flatter. Junior high school subjects performed slightly sharper compared to college subjects. Differential verbal feedback and a headphone listening condition produced ...

Abstract: Bells have many modes of vibration whose modal shapes are characterized by the numbers of nodal meridians and nodal circles. In Western church bells and carillon bells, the bell is shaped so that the lowest mode frequencies are harmonically related. The subjective strike note is determined by three strong partial tones with frequencies nearly in the ratios 2: 3: 4. The pitch of a handbell, on the other hand, is determined by the frequency of the fundamental tone. In ancient Chinese bells, the vibrational modes occur in pairs, and two different tones result from striking at the sui and gu strike points. A new type of carillon bell has been developed in which the traditional minor third partial is replaced by a major third partial, thus changing the timbre of the bell.

Abstract: “Anyone who aspires to understand contrapunctus should write down the following matters.” So begins a short manual on counterpoint from the early fourteenth century that circulated widely under the authority of Jehan des Murs but is best identified (anonymously) by its incipit “Quilibet affectans.” The theorist’s remarks are straightforward indeed. Contrapunctus observes a strictly note-against-note texture. Only select intervals – some perfect in nature (unisons, fifths, octaves), others imperfect (minor third, major third, and major sixth) – are admitted between the voices, as are their octave compounds. The natural sequel to any authorized interval is that interval from the opposite category closest in size: minor third (imperfect) after unison (perfect); octave (perfect) after major sixth (imperfect). Although characterized as “natural,” these contiguous progressions are by no means mandatory. The motion of the cantus, the pre-existent melody to which another line is joined in counterpoint, may well prompt other intervallic successions. Within the latitude this affords, no perfect interval may be reiterated in direct succession, but any imperfect interval may be followed by another, or by several, of the same kind. Aside from such parallels, the two voices ought usually to proceed in contrary directions, so that when the cantus ascends, the new line descends, and vice versa. All contrapunctus must begin and end with perfect consonance. The compact array of precepts set forth in “Quilibet affectans” hardly seems to qualify as theory. It reads as a set of rudimentary guidelines for production of correct note-against-note polyphony in two parts. Yet the opening declaration that the path to understanding contrapunctus is to write these rules (rather than, say, to sing or to compose model progressions or phrases) does appear to claim some theoretical status for what follows (as does one stray reference to Boethius).