Mathematics of Music 1. INTRODUCTION 2. HISTORY OF FOURIER
... the harmonic series. The harmonic series is the series of tones created by multiplying a fundamental frequency by integers. This can be done based on any fundamental frequency, and each will result in a unique harmonic series. This is where pure intervals, intervals with frequencies related by small ...
... the harmonic series. The harmonic series is the series of tones created by multiplying a fundamental frequency by integers. This can be done based on any fundamental frequency, and each will result in a unique harmonic series. This is where pure intervals, intervals with frequencies related by small ...
View printable PDF of 6.4 AdditionalContemporaryScales
... For instance, the whole tone scale can only be transposed 1 half-step without repeating pitches. The composer Olivier Messiaen used them. See 6.11 Set Theory: Symmetric Sets. Microtonal scales = Scales that use intervals smaller than half steps. Common in non-Western music. Synthetic scale = A scale ...
... For instance, the whole tone scale can only be transposed 1 half-step without repeating pitches. The composer Olivier Messiaen used them. See 6.11 Set Theory: Symmetric Sets. Microtonal scales = Scales that use intervals smaller than half steps. Common in non-Western music. Synthetic scale = A scale ...
Musical Elements and Compositional Devices
... Two of these modes, the Ionian and Aeolian eventually became our major and minor scales. Aeolian Mode ...
... Two of these modes, the Ionian and Aeolian eventually became our major and minor scales. Aeolian Mode ...
Paige Studlack Malone Middle School Ms
... Music is a series of sound waves, pure and simple. Sound is measured in frequencies (cycles per second) labeled in Hertz. When you hear different, overlapping notes that sound good together, it is because their frequencies are consonant and the sound waves meet and cross at regular intervals. This p ...
... Music is a series of sound waves, pure and simple. Sound is measured in frequencies (cycles per second) labeled in Hertz. When you hear different, overlapping notes that sound good together, it is because their frequencies are consonant and the sound waves meet and cross at regular intervals. This p ...
A Crash Course in Renaissance Counterpoint
... In the period of the birth of basso continuo, it is certainly true that musicians and composers began to think more ‘vertically’ and less ‘horizontally,’ meaning that harmonic thinking in terms of block chords began to challenge the long-reigning contrapuntal procedures of Renaissance composition. T ...
... In the period of the birth of basso continuo, it is certainly true that musicians and composers began to think more ‘vertically’ and less ‘horizontally,’ meaning that harmonic thinking in terms of block chords began to challenge the long-reigning contrapuntal procedures of Renaissance composition. T ...
HERE - NWSS Music
... 79. Rubato: relates to tempo, when a strict tempo is temporarily abandoned for a more flexible, emotional response to time, melody and harmony 80. scale degree: a number assigned to each note of a major scale. For example, the first note would be 1, the second 2, the third 3... 81. staccato: short d ...
... 79. Rubato: relates to tempo, when a strict tempo is temporarily abandoned for a more flexible, emotional response to time, melody and harmony 80. scale degree: a number assigned to each note of a major scale. For example, the first note would be 1, the second 2, the third 3... 81. staccato: short d ...
COURSE TITLE - Metropolitan Community College
... Discuss the difference between major, minor, augmented, and diminished triads. A. Discuss the different intervals required to create each of four triads. B. Construct the four types of triads on the staff and at the keyboard. C. Build inversions of each type of triad. ...
... Discuss the difference between major, minor, augmented, and diminished triads. A. Discuss the different intervals required to create each of four triads. B. Construct the four types of triads on the staff and at the keyboard. C. Build inversions of each type of triad. ...
LABBS Harmony College 2003: Understanding the Barbershop Style
... harmonizing above the melody, the bass singing the lowest harmonizing notes, and the baritone completing the chord. The melody is not sung by the tenor except for an infrequent note or two to avoid awkward voice leading, in tags or codas, or when some appropriate embellishing effect can be created. ...
... harmonizing above the melody, the bass singing the lowest harmonizing notes, and the baritone completing the chord. The melody is not sung by the tenor except for an infrequent note or two to avoid awkward voice leading, in tags or codas, or when some appropriate embellishing effect can be created. ...
Milhaud Describes Polytonality
... twentieth century led composers and writers at this time to look for principles governing new harmonic resources. One such musician was Darius Milhaud, who in music of the 1920s experimented with the simultaneous use of multiple keys, each appearing in different strata of a piece. He called the phen ...
... twentieth century led composers and writers at this time to look for principles governing new harmonic resources. One such musician was Darius Milhaud, who in music of the 1920s experimented with the simultaneous use of multiple keys, each appearing in different strata of a piece. He called the phen ...
Tuning Continua and Keyboard Layouts - Computer
... tuning, but also across a range of tunings. For example, a 12-edo (equal divisions of the octave) major chord, a 19-edo major chord, and a Pythagorean major chord might all be fingered in the same way. This paper explores the scope of this idea by parameterising tunings using regular temperaments wh ...
... tuning, but also across a range of tunings. For example, a 12-edo (equal divisions of the octave) major chord, a 19-edo major chord, and a Pythagorean major chord might all be fingered in the same way. This paper explores the scope of this idea by parameterising tunings using regular temperaments wh ...
Generalizing Messiaen`s Modes of Limited Transposition to
... the only required input is the number of steps we want to consider, i.e. the minimum granularity to build aggregations. If we need an audio rendering too, two more inputs are necessary, namely the frequencies of the pitches that delimit the global interval to be divided. The algorithm can be decompo ...
... the only required input is the number of steps we want to consider, i.e. the minimum granularity to build aggregations. If we need an audio rendering too, two more inputs are necessary, namely the frequencies of the pitches that delimit the global interval to be divided. The algorithm can be decompo ...
Generalizing Messiaen`s Modes of Limited Transposition to a n
... From a historical point of view, only some temperaments have been considered, due to their application to specific context (e.g. in ethnomusicology) or to theoretical reasons (for instance, the adherence of a given interval in a temperament to its theoretical value in terms of frequency ratio). Our ...
... From a historical point of view, only some temperaments have been considered, due to their application to specific context (e.g. in ethnomusicology) or to theoretical reasons (for instance, the adherence of a given interval in a temperament to its theoretical value in terms of frequency ratio). Our ...
Western music history, pitch salience, key profiles, and the origins of
... tonal syntax from finite set of clear axioms? ...
... tonal syntax from finite set of clear axioms? ...
Music Theory Applied Music 2206/3206
... The pattern is ALWAYS as follows. Keep in mind sometimes you may need to add a sharp or flat. T-T-S-T-T-T-S (T=Tone and S=Semitone) To write a major scale, start on the first note of the scale, write up to an octave, and go back to the original note. For example, a C scale can be written wit ...
... The pattern is ALWAYS as follows. Keep in mind sometimes you may need to add a sharp or flat. T-T-S-T-T-T-S (T=Tone and S=Semitone) To write a major scale, start on the first note of the scale, write up to an octave, and go back to the original note. For example, a C scale can be written wit ...
AP THEORY_files/Notation
... Count the note you start on and the one you finish on Take the key you’re in into consideration ...
... Count the note you start on and the one you finish on Take the key you’re in into consideration ...
Choral Ensemble – Word
... Order or Time of Appearance:_______ Event #:______ Class:_____ Date:________ School:_______________________________________________________________ Name of Group:________________________________________________________ Selections:____________________________________________________________ _________ ...
... Order or Time of Appearance:_______ Event #:______ Class:_____ Date:________ School:_______________________________________________________________ Name of Group:________________________________________________________ Selections:____________________________________________________________ _________ ...
Math/Musical Instruments Unit
... If we play exactly the same pitch our sound waves will look the same Student A ...
... If we play exactly the same pitch our sound waves will look the same Student A ...
C - WordPress.com
... of movement or anticipation which this scale doesn’t provide when played as seen above. The sound of tension or anticipation can be created with this scale by playing from G to G, the Mixolydian mode. The appropriate chord would be G7 or an extension or substitute for theG7. ...
... of movement or anticipation which this scale doesn’t provide when played as seen above. The sound of tension or anticipation can be created with this scale by playing from G to G, the Mixolydian mode. The appropriate chord would be G7 or an extension or substitute for theG7. ...
Tonal Music
... Although they may not know the correct title, most people regardless of musical background have heard Beethoven’s Symphony #5 in C Minor. In addition to being very popular at symphonic concerts this compositions has been used as background music in everything from the dramatic plays to Warner Bros. ...
... Although they may not know the correct title, most people regardless of musical background have heard Beethoven’s Symphony #5 in C Minor. In addition to being very popular at symphonic concerts this compositions has been used as background music in everything from the dramatic plays to Warner Bros. ...
Intervals and Pitch
... hear the distance from 110 Hz to 220 Hz as being the same as the distance from 440 Hz to 880 Hz. Therefore, we use the system of pitch to measure frequency in a way that corresponds to human perception. Twelve units of pitch equals one octave. There are two ways to notate pitch: either using a note ...
... hear the distance from 110 Hz to 220 Hz as being the same as the distance from 440 Hz to 880 Hz. Therefore, we use the system of pitch to measure frequency in a way that corresponds to human perception. Twelve units of pitch equals one octave. There are two ways to notate pitch: either using a note ...
as a PDF
... Consequently, these notes are sensitive and have a specific way of resolving when the next functional category is achieved. Stabilizers (s) combine with foundation and active tones to produce complete triads. Most of the time they are inert, but sometimes they may also act like dissonances in terms ...
... Consequently, these notes are sensitive and have a specific way of resolving when the next functional category is achieved. Stabilizers (s) combine with foundation and active tones to produce complete triads. Most of the time they are inert, but sometimes they may also act like dissonances in terms ...
Adding New Pitches
... Acoustics obviously do play a partial role in our perception of intervals. For example, one cannot ignore the fact that two intervals commonly perceived as consonant, stable or simple are the octave and the fifth, and that these coincide with the first three partials, or the simplest frequency ratio ...
... Acoustics obviously do play a partial role in our perception of intervals. For example, one cannot ignore the fact that two intervals commonly perceived as consonant, stable or simple are the octave and the fifth, and that these coincide with the first three partials, or the simplest frequency ratio ...
Perception of musical consonance and dissonance: an outcome of
... pleasant, “stable” sound sensation produced by certain combinations of two tones played simultaneously. In contrast, dissonance is the unpleasant grating sound heard with other sound combinations. The common octave, for example, is judged as consonant, while playing two adjacent keys on the piano to ...
... pleasant, “stable” sound sensation produced by certain combinations of two tones played simultaneously. In contrast, dissonance is the unpleasant grating sound heard with other sound combinations. The common octave, for example, is judged as consonant, while playing two adjacent keys on the piano to ...
Just intonation
In music, just intonation (sometimes abbreviated as JI) or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a pure or just interval. The two notes in any just interval are members of the same harmonic series. Frequency ratios involving large integers such as 1024:927 are not generally said to be justly tuned. ""Just intonation is the tuning system of the later ancient Greek modes as codified by Ptolemy; it was the aesthetic ideal of the Renaissance theorists; and it is the tuning practice of a great many musical cultures worldwide, both ancient and modern.""Just intonation can be contrasted and compared with equal temperament, which dominates Western instruments of fixed pitch (e.g., piano or organ) and default MIDI tuning on electronic keyboards. In equal temperament, all intervals are defined as multiples of the same basic interval, or more precisely, the intervals are ratios which are integer powers of the smallest step ratio, so two notes separated by the same number of steps always have exactly the same frequency ratio. However, except for doubling of frequencies (one or more octaves), no other intervals are exact ratios of small integers. Each just interval differs a different amount from its analogous, equally tempered interval.Justly tuned intervals can be written as either ratios, with a colon (for example, 3:2), or as fractions, with a solidus (3 ⁄ 2). For example, two tones, one at 300 Hertz (cycles per second), and the other at 200 hertz are both multiples of 100 Hz and as such members of the harmonic series built on 100 Hz. Thus 3/2, known as a perfect fifth, may be defined as the musical interval (the ratio) between the second and third harmonics of any fundamental pitch.