The relations between heavenly spheres are equal to those between musical intervals
Since the time of the ancient Greeks, we have known that two tones whose frequencies were related by a simple ratio like 2:1 (an octave) or 3:2 (a perfect fifth) produce the most pleasing, or consonant, musical intervals
Such theories formed a highly prestigious canon, providing a context to 17th-century attempts to establish 'mechanical' explanations for musical intervals
as well as the nature of sound itself.
Entertainment from around the region kept the stars busy while the occassional cheer from Centre Court, where Serena Williams was playing her first game, filled the musical intervals
Prosdocimo approves of Marchetto's views on practical issues, but objects strongly to his approach to the quantitative definition of musical intervals
More than 2000 years ago, Pythagoras reportedly discovered that pleasing musical intervals
could be described using simple ratios.
depict rising intensity in argumentation as he begins with a "soft and irresistible piano of voice which the nature of the argumentum ad hominem absolutely requires" (47) but rises to a contemptuous tone of voice with a third or fifth, much like Toby getting louder in whistling against something that strikes him as uncompassionate.
In the sixteenth century, the plays' topics were often religious, derived from biblical, hagiographic, and devotional sources; musical intervals
also became an integral part of the staging.
An order of consonance was assigned on the musical intervals
, which was shown mathematically sound and consistent with previous studies.
Yes, we just-tuning composers have attacked the deficiencies of 12-equal (one complaint about equal temperaments that echoes Werntz is that they are an arbitrary, "scientific"--thus "inhuman"--way of producing musical intervals
, themselves ipso facto "inhumanely" irrational), and there may be a natural impulse to counter-attack just tuning in response.
1990): "Intonation Variants of Musical Intervals
in Isolation and in Musical Contexts" en Psychology of Music no 18 Pags.
Pythagoras is said to have discovered the arithmetic basis for musical intervals
17) Moreover, whereas in the macrocosm writers who describe planetary distances as musical intervals
rather than as their generating ratios measure them in the Aristoxenean manner by tones and semitones,(18) in the microcosm the pulse could not be measured in such terms, but if expressed as a ratio might be assimilated by a Pythagorean to the corresponding interval.
This city of language assails him with humming and fragments, "a hodgepodge of dots and spirals," wavy lines and mutilated cuneiform, musical intervals
, whispering sibilants, chords and squeaks and silence.
Rings's writing separates itself from its contemporaries in two ways: first, by cogently summarizing and glossing the formalism of David Lewin's landmark publication, Generalized Musical Intervals
and Transformations (New Haven: Yale University Press, 1987; reprinted and revised, Oxford: Oxford University Press, 2007), hereafter GMIT; and second, by implementing Lewinian Generalized Interval Systems (GISes) and transformational models to create a fresh analytical perspective on tonal (i.