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Published by: University of California, Irvine | Language: English
Published by: University of California, Irvine | Language: English
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Overview and Introduction.
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Published by: University of California, Irvine | Language: English
Published by: University of California, Irvine | Language: English
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This presentation uses 3:2 ratios to create a 12-tone set very much like the twelve tone chromatic system in common use today. Despite its out-of-tune triads, this scale seems very functional but suffers from a gap in its frequencies, another comma, meaning it is not circular. Since the tonal pitch system relies on circularity (the ability
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Published by: University of California, Irvine | Language: English
Published by: University of California, Irvine | Language: English
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This presentation will expand the concept of octaves as a spectrum to incorporate the circle of fifths, a common diagram for study of music theory. Understanding the circle of fifths leads to a larger realization; tonal pitch systems are circular. The 5:4 major third will be added to the set of simple number ratio intervals we've studied, 2
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Published by: University of California, Irvine | Language: English
Published by: University of California, Irvine | Language: English
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This presentation will demonstrate how the 4:5:6 ratio known as a major triad works within the circular pitch system of tonal music. The concept of I, IV, and V (1, 4, and 5) harmonic functions will be explained using the basic mathematical structures already demonstrated.
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Published by: University of California, Irvine | Language: English
Published by: University of California, Irvine | Language: English
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This presentation explores how the major triads formed by the Pythagorean tuning system sound when compared with pure 4:5:6 major triads. The differences are subtle, but easy to hear and see using an oscilloscope, and begin to complicate the apparently simple system of using 3:2 and 4:5:6 ratios to form a tonal pitch system.
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Published by: University of California, Irvine | Language: English
Published by: University of California, Irvine | Language: English
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This presentation shows how 3:2 frequency ratios can be stacked to form a major scale (also known as a diatonic scale, diatonic collection, or diatonic set). Now we've progressed to the point of generating functional sets of frequencies--scales--using simple math and an understanding of how tonal pitch systems work. This kind of approach to
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Introduction to Pitch Systems in Tonal Music Part 7: The Minor Triad and a Circular System of Thirds
Published by: University of California, Irvine | Language: English
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This presentation introduces the 6:5 minor third and 10:12:15 minor triad. The tonal pitch system uses major and minor triads, and the pitch system in use has to accommodate this. These sounds and ratios lead to the construction of a diatonic circle of thirds and a further goal; tune a diatonic set so that all I IV V major and i iv v minor
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Published by: University of California, Irvine | Language: English
Published by: University of California, Irvine | Language: English
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This presentation uses 3:2 ratios to create a 12-tone set very much like the twelve tone chromatic system in common use today. Despite its out-of-tune triads, this scale seems very functional but suffers from a gap in its frequencies, another comma, meaning it is not circular. Since the tonal pitch system relies on circularity (the ability
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