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... Gouk, Penelope. Music, Science, and Natural Magic in Seventeenth-Century England. London: Yale University Press, 1999 Helmholtz, Herman von. On the Sensations of Tone; translated by A. J. Ellis, 4th edition 1885 Reprint, New York: Dover Publication, 1954 Lindley, Mark: ‘Temperaments, 9. Fretted Inst ...
... Gouk, Penelope. Music, Science, and Natural Magic in Seventeenth-Century England. London: Yale University Press, 1999 Helmholtz, Herman von. On the Sensations of Tone; translated by A. J. Ellis, 4th edition 1885 Reprint, New York: Dover Publication, 1954 Lindley, Mark: ‘Temperaments, 9. Fretted Inst ...
On Ben Johnston`s Notation and the Performance
... In the 16th century, the theorist Zarlino codified this ongoing praxis, stating that the natural intonation practiced by singers and instruments of flexible pitch was based on consonant intervals that could be expressed as ratios of the first six whole numbers (a set he called the senario). At the s ...
... In the 16th century, the theorist Zarlino codified this ongoing praxis, stating that the natural intonation practiced by singers and instruments of flexible pitch was based on consonant intervals that could be expressed as ratios of the first six whole numbers (a set he called the senario). At the s ...
The Establishment of Equal Temperament
... One of the greatest treasures that came from the Baroque era amidst the tuning and temperament controversies was The Well Tempered Clavier by Johann Sebastian Bach. It is comprised of two solo keyboard books written in 1722 and 1724 that include different pieces using all twenty-four major and minor ...
... One of the greatest treasures that came from the Baroque era amidst the tuning and temperament controversies was The Well Tempered Clavier by Johann Sebastian Bach. It is comprised of two solo keyboard books written in 1722 and 1724 that include different pieces using all twenty-four major and minor ...
Tunings and Temperaments Powerpoint
... "Just" Tuning (four different modes!) Mean-tone Tuning Well-tempered Tuning – J S Bach's Well-Tempered Clavier ...
... "Just" Tuning (four different modes!) Mean-tone Tuning Well-tempered Tuning – J S Bach's Well-Tempered Clavier ...
LucyTuning*LucyScaleDevelopments*LucyTuned Lullabies*Pi
... A. As accurate as you wish it to be. In practice this is determined by the pitch resolution of your equipment and instruments and/or the acuity of your ears. Q. How does LucyTuning reconcile the anomalies and contradictions of Just Intonation and other whole number ratio (WNR) tuning systems, which ...
... A. As accurate as you wish it to be. In practice this is determined by the pitch resolution of your equipment and instruments and/or the acuity of your ears. Q. How does LucyTuning reconcile the anomalies and contradictions of Just Intonation and other whole number ratio (WNR) tuning systems, which ...
Intonation, Tuning, and Blending
... 2. Tuning: (verb) to adjust to the correct or given standard of pitch. Agreement of pitch 3. Blending: (verb) (general)To mix in order to obtain a particular kind or quality; to have no perceptible separation. (music) The act of altering one’s tone color, vibrato, articulation, and style to match on ...
... 2. Tuning: (verb) to adjust to the correct or given standard of pitch. Agreement of pitch 3. Blending: (verb) (general)To mix in order to obtain a particular kind or quality; to have no perceptible separation. (music) The act of altering one’s tone color, vibrato, articulation, and style to match on ...
Page 1 of 8 NAHOO || Maths || The Relationship between
... Clearly this method of deriving scales, though mathematically sound, does not lend itself well to developed Western music, let alone any further melodic and harmonic intervals between chromatic notes. After a failed attempt by Gaffurius in 1496 to create a scientifically established temperament, Gio ...
... Clearly this method of deriving scales, though mathematically sound, does not lend itself well to developed Western music, let alone any further melodic and harmonic intervals between chromatic notes. After a failed attempt by Gaffurius in 1496 to create a scientifically established temperament, Gio ...
Slides
... evolution of tuning through the ages. Along the way, he challenges the widely held belief that equal temperament is a perfect, “naturally selected” musical system, and proposes a radical reevaluation of how we play and hear music. Ross W. Duffin, author of Shakespeare’s Songbook (winner of the Claud ...
... evolution of tuning through the ages. Along the way, he challenges the widely held belief that equal temperament is a perfect, “naturally selected” musical system, and proposes a radical reevaluation of how we play and hear music. Ross W. Duffin, author of Shakespeare’s Songbook (winner of the Claud ...
notes and equations
... An interval is a ratio between two frequencies. The interval between two musical tones is the ratio between their fundamental frequencies. A perfect interval is the ratio between two small integers (typically below 6). Commonly used perfect intervals are: name unison octave minor third major third f ...
... An interval is a ratio between two frequencies. The interval between two musical tones is the ratio between their fundamental frequencies. A perfect interval is the ratio between two small integers (typically below 6). Commonly used perfect intervals are: name unison octave minor third major third f ...
Prime Numbers in Music Tonality
... scale steps are played simultaneously as chords and as composers became more adventurous with dense chords and key changes in their work, this became unacceptable. Composers experimented with ways to adjust the system to minimize these problems, such as Well Temperament and Meantone Temperament, but ...
... scale steps are played simultaneously as chords and as composers became more adventurous with dense chords and key changes in their work, this became unacceptable. Composers experimented with ways to adjust the system to minimize these problems, such as Well Temperament and Meantone Temperament, but ...
Chapter 1: The Basics Microtonal Notation
... either the tone or the octave. For example, third-tone music may be described as 18-div and fifth-tone music as 30-div, and so on. While there is no categorical reason why the word ‘division’ should be associated with a division of the octave as opposed to a division of a tone (or any other interval ...
... either the tone or the octave. For example, third-tone music may be described as 18-div and fifth-tone music as 30-div, and so on. While there is no categorical reason why the word ‘division’ should be associated with a division of the octave as opposed to a division of a tone (or any other interval ...
lecture16
... Musical scale – a succession of notes in ascending or distending order • In Western music octave is divided in 12 semitones • Chromatic scale - all 12 semitones • Most music makes use of 7 selected notes (major or minor scales) • There are many ways to construct musical scales • Different scales are ...
... Musical scale – a succession of notes in ascending or distending order • In Western music octave is divided in 12 semitones • Chromatic scale - all 12 semitones • Most music makes use of 7 selected notes (major or minor scales) • There are many ways to construct musical scales • Different scales are ...
lecture16
... Musical scale – a succession of notes in ascending or distending order •In Western music octave is divided in 12 semitones •Chromatic scale - all 12 semitones •Most music makes use of 7 selected notes (major or minor scales) •There are many ways to construct musical scales •Different scales are diff ...
... Musical scale – a succession of notes in ascending or distending order •In Western music octave is divided in 12 semitones •Chromatic scale - all 12 semitones •Most music makes use of 7 selected notes (major or minor scales) •There are many ways to construct musical scales •Different scales are diff ...
About Diapason
... … from Greek (he) dia pason (chordon symphonia) … (the concord) through all (the notes) … “a burst of harmonious sound … a full deep outburst of sound” (Webster’s) … also an organ stop, and (earlier) the octave; (still earlier) the set of pitches which might “fill” an octave, i.e., a scale or mode. ...
... … from Greek (he) dia pason (chordon symphonia) … (the concord) through all (the notes) … “a burst of harmonious sound … a full deep outburst of sound” (Webster’s) … also an organ stop, and (earlier) the octave; (still earlier) the set of pitches which might “fill” an octave, i.e., a scale or mode. ...
11 – Music temperament and pitch
... music theory and practice, to variable success. All temperaments fall into three groups: Open temperaments, closed unequal temperaments and one equal temperament that dominates now. Historically earlier open temperaments use perfect intervals (fifth, forth, etc.) in basic music scales such as C. The ...
... music theory and practice, to variable success. All temperaments fall into three groups: Open temperaments, closed unequal temperaments and one equal temperament that dominates now. Historically earlier open temperaments use perfect intervals (fifth, forth, etc.) in basic music scales such as C. The ...
Modern Western Tuning System - Digital Commons @ Kent State
... most common and relevant of the Equal Temperament tuning systems is the 12TET which has 12 tones within the distance of an octave. Other Equal Temperaments exist such as 5, 7, 19, 22, and 31TET however for the purpose of understanding the math behind this system 12TET is the best representation as i ...
... most common and relevant of the Equal Temperament tuning systems is the 12TET which has 12 tones within the distance of an octave. Other Equal Temperaments exist such as 5, 7, 19, 22, and 31TET however for the purpose of understanding the math behind this system 12TET is the best representation as i ...
Maths and music - Project Jugaad
... between one note and another are what allow you to determine the interval, and what 'quality,' it has, i.e. major, minor, diminished, augmented. Learning intervals is simply counting and memorizing, not anywhere near a 'math function.‘ For acoustics, the physics of sound, a much greater degree of ma ...
... between one note and another are what allow you to determine the interval, and what 'quality,' it has, i.e. major, minor, diminished, augmented. Learning intervals is simply counting and memorizing, not anywhere near a 'math function.‘ For acoustics, the physics of sound, a much greater degree of ma ...
Lecture Set 07
... The lengths corresponding to intervals that sounded good were found to have ratios expressible as small integers. How perfect! God-like! MUST be true. The process can be continued to define additional intervals. ...
... The lengths corresponding to intervals that sounded good were found to have ratios expressible as small integers. How perfect! God-like! MUST be true. The process can be continued to define additional intervals. ...
Document
... Siegel, J. A., & Siegel, W. (1977). Absolute identification of notes and intervals by musicians. Perception & Psychophysics, 21 (2), 143-152. ...
... Siegel, J. A., & Siegel, W. (1977). Absolute identification of notes and intervals by musicians. Perception & Psychophysics, 21 (2), 143-152. ...
PHYSICAL THEORY OF MUSIC
... We confirmed that the length of a string or a pipe is inversely proportional to the frequency of the sound that is produced when subjected to oscillation. Two sounds are in harmony when they have many common harmonics. We achieve total synchronization when the frequency of one sound is the integral ...
... We confirmed that the length of a string or a pipe is inversely proportional to the frequency of the sound that is produced when subjected to oscillation. Two sounds are in harmony when they have many common harmonics. We achieve total synchronization when the frequency of one sound is the integral ...
CHAPTER 1 TONAL MODULATION WITH JUST
... (rounded off to the nearest tenth of a cent in the case of the Monophonic intervals) are used for both equal tempered intervals and Monophonic intervals as a unit of comparison.6 In the column for “Cents Deviation” the difference between the two versions is calculated. From this, one can see that th ...
... (rounded off to the nearest tenth of a cent in the case of the Monophonic intervals) are used for both equal tempered intervals and Monophonic intervals as a unit of comparison.6 In the column for “Cents Deviation” the difference between the two versions is calculated. From this, one can see that th ...
hw3
... b. Which interval is worst approximated (in cents) by an equally tempered interval? Other than the octave, which is best approximated? c. How many pure fifths are there in this scale? Draw lines on the template and identify them by letter names. (There is more than one.) d. How many pure major third ...
... b. Which interval is worst approximated (in cents) by an equally tempered interval? Other than the octave, which is best approximated? c. How many pure fifths are there in this scale? Draw lines on the template and identify them by letter names. (There is more than one.) d. How many pure major third ...
The Birth of - Early Music America
... the second century, Clement of Alexandria would gather music’s proportions into the Christian fold by proclaiming that Christ himself had decreed them. Yet another “divine” ratio gained prominence in the 13th century. This was the pure third, beloved particularly by the Renaissance-era English, and ...
... the second century, Clement of Alexandria would gather music’s proportions into the Christian fold by proclaiming that Christ himself had decreed them. Yet another “divine” ratio gained prominence in the 13th century. This was the pure third, beloved particularly by the Renaissance-era English, and ...
`frequency`. - Programma LLP
... It is actually very hard to define the feeling of consonance and dissonance, and Maths surely helps with it. Ever wonder why some note combinations sound pleasing to our ears, while others make us cringe? To understand the answer to this question, you’ll first need to understand the wave patterns cr ...
... It is actually very hard to define the feeling of consonance and dissonance, and Maths surely helps with it. Ever wonder why some note combinations sound pleasing to our ears, while others make us cringe? To understand the answer to this question, you’ll first need to understand the wave patterns cr ...
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent pitches is separated by the same interval. In other words, the pitches of an equal temperament can be produced by repeating a generating interval. Equal intervals also means equal ratios between the frequencies of any adjacent pair, and, since pitch is perceived roughly as the logarithm of frequency, equal perceived ""distance"" from every note to its nearest neighbor.In equal temperament tunings, the generating interval is often found by dividing some larger desired interval, often the octave (ratio 2/1), into a number of smaller equal steps (equal frequency ratios between successive notes). For classical music and Western music in general, the most common tuning system for the past few hundred years has been and remains twelve-tone equal temperament (also known as 12 equal temperament, 12-TET, or 12-ET), which divides the octave into 12 parts, all of which are equal on a logarithmic scale. That resulting smallest interval, 1/12 the width of an octave, is called a semitone or half step. In modern times, 12TET is usually tuned relative to a standard pitch of 440 Hz, called A440, meaning one pitch is tuned to A440, and all other pitches are some multiple of semitones away from that in either direction, although the standard pitch has not always been 440 and has fluctuated and generally risen over the past few hundred years.Other equal temperaments exist. They divide the octave differently. For example, some music has been written in 19-TET and 31-TET. Arabic music uses 24-TET. In Western countries, when people use the term equal temperament without qualification, they usually mean 12-TET. To avoid ambiguity between equal temperaments which divide the octave and ones which divide some other interval (or that use an arbitrary generator without first dividing a larger interval), the term equal division of the octave, or EDO is preferred for the former. According to this naming system, 12-TET is called 12-EDO, 31-TET is called 31-EDO, and so on.An example of an equal temperament that finds its smallest interval by dividing an interval other than the octave into equal parts is the equal-tempered version of the Bohlen–Pierce scale, which divides the just interval of an octave and a fifth (ratio 3/1), called a ""tritave"" or a ""pseudo-octave"" in that system, into 13 equal parts.String ensembles and vocal groups, who have no mechanical tuning limitations, often use a tuning much closer to just intonation, as it is naturally more consonant. Other instruments, such as some wind, keyboard, and fretted instruments, often only approximate equal temperament, where technical limitations prevent exact tunings. Some wind instruments that can easily and spontaneously bend their tone, most notably trombones, use tuning similar to string ensembles and vocal groups.