Microtonal systems and guitar composition

This thesis focuses on the use of microtones in guitar composition. In the course of this study the physical aspects of musical sound (pitch, loudness and quality/timbre), vibrational frequencies of strings, and the theory of musical scales and tuning systems are discussed. Whole-number ratios corresponding to musical intervals within the twelve-note/equal temperament scale are calculated in relation to the overtone series for the purpose of surveying consonance and dissonance within the tempered system. These are compared to the ratios for corresponding intervals within the overtone series. Whole-number ratios are also calculated for intervals involving the microtones referred to in this study.
The frequencies of the microtones are theoretically predicted and experimentally measured using a high-precision sound level meter and frequency analyser. A brief analysis of the consonant and dissonant quality of five different intervals involving tempered and microtonal notes played on both electric and acoustic guitars is carried out on a computer using a Fast Fourier Transform algorithm. Twenty-three graphs were produced as a result of this experiment. A brief analysis of the consonant and dissonant quality of a pitch interval involving two microtones was also taken. Whole-number ratios were calculated for each experiment and compared to recognized consonant whole-number ratios within the overtone series. Microtonal musical compositions, Guitar Opus 1 and Guitar Opus 2, show how the measured microtones can be utilized in musical composition.
The microtonal parts of the composition are discussed and illustrated in tabular format using the information gathered from the physical measurements. Whole-number ratios are calculated for part of the composition Guitar Opus 1 and the consonant and dissonant quality of the intervals used are discussed. Etude for Amplified Classical Guitar illustrates how microtonal notes can be utilized in composition along with tempered notes of similar loudness. In Etude for Electric Guitar with added frets, for modified electric guitar (11 extra frets added in between original frets), a melody is first played using tempered notes and then played as a microtonal melody by moving up or down a fret utilizing the added microtonal frets. The thesis concludes with a discussion of the use of different tuning systems in composition and their relationship to the microtonal system used in this project.

Tesis by Michael Nielsen



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