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microtonal scale exploration in Central
microtonal scale exploration in Central

... Figure 1: On the right the pitch class histogram is displayed. The horizontal axis represents an octave, that is divided into 1200 cents. The annotations made by Tarsos are projected on it. The five numbers under the axis are the pitch classes that have been localized by peak detection. The pitch cl ...
Music Fundamentals Primer Lesson 4
Music Fundamentals Primer Lesson 4

... B, and D. There are three possible arrangements of these three notes within a single octave (shown in step 2). The one arrangement in which all of the adjacent intervals are thirds is the most compact form, which is called “root position” (marked with the asterisk). Once root position is found, we ...
Bringing some science to music
Bringing some science to music

...  12 tones per octave. Why 12? … soon. Played sequentially, ...
Investigate the mathematics behind the tuning systems of Wendy
Investigate the mathematics behind the tuning systems of Wendy

... frequency ratio of two consecutive notes is constant, so the degree (distance between consecutive pitches) should be chosen in order to get as close as possible to these ratios. Most existing equal-tempered tunings are based on an interval with frequency ratio 2:1, the octave, which is divided into ...
The demise of number ratios in music theory
The demise of number ratios in music theory

... there are still musicians, theorists, historians, composers, and psychologists out there who theorize with number ratios. But most intervals have two ratios (Pythagorean and just) that lie within a continuous range of acceptable tunings, so neither is “correct”. Ratios only make psychological sense ...
Just Intonation Explained
Just Intonation Explained

... The perfect fifth from D to A is now only 680 cents wide instead of an optimum 702, and it sounds awful. You may have noticed it has a wow-wow-wow growl to it, which you can hear in isolation here, that explains why such fifths have always been called "wolf" intervals. (Here you can hear it contrast ...
Intonation, Tuning, and Blending
Intonation, Tuning, and Blending

... understanding of your instrument’s intonation, you don’t have to worry about tuning.  FALSE! tuning is a life-long journey that depends on which instruments you are playing with, what climate you are playing in, and what style the ensemble wishes to ...
The Birth of - Early Music America
The Birth of - Early Music America

... earlier musicians might have labeled “reality” and “law” – were altered through a rational, repeatable procedure, governing how far pitches ought to stand from one another or how closely “they ought to cohere” – for purely subjective reasons. The first text that mentioned the process was by Leonardo ...
Theory Intro
Theory Intro

... How do minor and major differ? Ê How do minor scales differ from their “parallel” major? Ê Both scales begin on same note, differ at 3, 6, and 7 (these ...
Text S1.
Text S1.

... has significantly less ascending melodic intervals smaller than a major second (14.9% vs 31%, t= -9.20, P<0.001), and significantly more ascending melodic intervals equal to or larger than a major second (44.3% vs. 33%, t= 10.2, P<0.001). Figure S4B shows the distributions of prosodic interval size ...
MSP_lecture8 - New York University
MSP_lecture8 - New York University

... 2. play the "harmony 1" scale simultaneously with the base scale 3. play the "harmony 2" scale simultaneously with the base scale *This is known as parallel motion ...
Music Theory Essay. - Guitar Master Class
Music Theory Essay. - Guitar Master Class

... B C D E F G). The notes we usually use are made relative to a reference frequency of 440Hz. This reference frequency is given the name A. The difference between two pitches or notes is called an interval. If we play two notes of the same pitch then we say they are in unison. Doubling the frequency o ...
Musical Scales and Tonality - University of Toronto Scarborough
Musical Scales and Tonality - University of Toronto Scarborough

... Facts about musical systems • Musical cultures make use of variation in pitch • Use tones of low to high frequency, and combine them in various ways • Pitch and frequency are continuous ...
Intervals and Dissonance in Human Evolution
Intervals and Dissonance in Human Evolution

... Many other composers pursued similar directions, among them Dane Rudhyer. In his view the inclusion of dissonance is “identifying opposites; metaphysically it is the power of relating spirit to matter.” Like Anthroposophy, his system also related the complication of musical intervals to the developm ...
Frequency
Frequency

... Intervals can be added together in order to form other intervals. For example a Perfect 5th and a Perfect 4th placed back to back form an octave (C to F+F to C = C to C). Interestingly the same result is obtained by multiplying the ratios of the intervals being added.. In this example 4/3 x 3/2 = 12 ...
Review of Music Rudiments
Review of Music Rudiments

... SemiTone - Half Step ...
RATIOS AND MUSICAL INTERVALS We like to think of an interval
RATIOS AND MUSICAL INTERVALS We like to think of an interval

... Since A3 has frequency 220 Hz (being one octave below A4 ) we have f = 220 · 21/3 ≈ 277.18 . Therefore C4 should be tuned to 277.18 Hz. Microtuning and Cents. We will see later that mathematical tuning involves intervals which cannot be as an integer multiple of semitones. The term microtuning refe ...
History of Music Theory - Totally Ratted Limited
History of Music Theory - Totally Ratted Limited

... debate between music historians, but the belief most commonly held is that the intervals are calculated using the 3:2 ratio. As the note found at two thirds of the string length is consonant with the note found at the full length, then the note found by a further shortening of the string is consonan ...
Handout on Set Theory: Intervals and Atonality
Handout on Set Theory: Intervals and Atonality

... …which is the second melody! We sometimes say that first melody’s pitches transform into the se­ cond’s under the T5 operation, meaning transpose up 5 half-steps (and down an octave!). The second melody is related to the first by using the T7 operation (double check this for yourself). A big differe ...
MU 139 Power Point - Montgomery College
MU 139 Power Point - Montgomery College

...  A scale is a series of tones in a row, usually made up of whole steps & half steps. – The most common scales are:  Major scales  Minor scales ...
POTTER VOICE STUDIO INTERVALS , SCALES , KE Y
POTTER VOICE STUDIO INTERVALS , SCALES , KE Y

... An interval is the distance between two notes. Intervals are always counted from the lower note to the higher one, with the lower note being counted as one. Intervals come in different qualities and size. If the notes are sounded successively, it is a melodic interval. If sounded simultaneously, the ...
INTONATION FOR WINDS
INTONATION FOR WINDS

... So, to be in tune, the pitches are dependent on where in the scale they lie – and this will  change in the music as the key changes! To make it even more challenging, even the just  intonation described above should be modified to take into account the context of the  note e.g. leading notes sound b ...
Prime Numbers in Music Tonality
Prime Numbers in Music Tonality

... the cycle of fifths (because the ratio 3:2 has become the fifth step in the scale): ...
136 Cultural Foundations of Mathematics Rounding Again A notable
136 Cultural Foundations of Mathematics Rounding Again A notable

... In any case, it is clear that there was no mechanical rule in use for rounding, and that rounding as appropriate to ultimately greater precision was used. Thus, the numbers used in Indian mathematics, though very similar to floating point numbers, did not correspond exactly to any specific type of f ...
Slides
Slides

... an octave into twelve equally proportioned half-steps—has held a virtual monopoly on the way in which instruments are tuned and played. In his new book, Duffin explains how we came to rely exclusively on equal temperament by charting the fascinating evolution of tuning through the ages. Along the wa ...
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Quarter-comma meantone

Quarter-comma meantone, or 1/4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. This method is a variant of Pythagorean tuning. The difference is that in this system the perfect fifth is flattened by one quarter of a syntonic comma, with respect to its just intonation used in Pythagorean tuning (frequency ratio 3:2). The purpose is to obtain justly intoned major thirds (with a frequency ratio equal to 5:4). It was described by Pietro Aron (also spelled Aaron), in his Toscanello de la Musica of 1523, by saying the major thirds should be tuned to be ""sonorous and just, as united as possible."" Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude.
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