Mathematics of Music 1. INTRODUCTION 2. HISTORY OF FOURIER
... 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 integer ratios, as found by Pythagoras when he cut strings in half, come from and where we get the ratios for the ...
... 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 integer ratios, as found by Pythagoras when he cut strings in half, come from and where we get the ratios for the ...
Neo-Riemannian Theory and the Analysis of Pop
... Progressions like that of Example 2(a) appear throughout the pop-rock repertory. In the remainder of this article, I discuss the general features of such progressions, then present a series of analyses. The analyses fall into three categories: sequences, progressions involving chromatic motions with ...
... Progressions like that of Example 2(a) appear throughout the pop-rock repertory. In the remainder of this article, I discuss the general features of such progressions, then present a series of analyses. The analyses fall into three categories: sequences, progressions involving chromatic motions with ...
Yet Another 72-Noter - Masters Program in Digital Musics
... in Fig. 15, invoke, by means of the 11:4 of the SYMBOL E: Bb, a fundamental of Bb, then present an accumulation of progressively more complex harmonic ratios. These would have been but a succession of two simple appoggiatura resolutions without the addition of the second pedal on SYMBOL Eb. They res ...
... in Fig. 15, invoke, by means of the 11:4 of the SYMBOL E: Bb, a fundamental of Bb, then present an accumulation of progressively more complex harmonic ratios. These would have been but a succession of two simple appoggiatura resolutions without the addition of the second pedal on SYMBOL Eb. They res ...
Standards-Based Learning Power Standards Music 4 th Grade
... Analyzes, understands, and applies the elements pitch and melody while creating, performing, and responding to music. a. Improvises and performs a melody. b. Matches pitches within a musical composition while singing in appropriate vocal ranges. c. Incorporates basic melodic patterns and simple melo ...
... Analyzes, understands, and applies the elements pitch and melody while creating, performing, and responding to music. a. Improvises and performs a melody. b. Matches pitches within a musical composition while singing in appropriate vocal ranges. c. Incorporates basic melodic patterns and simple melo ...
Basic Music Theory - 547 Canuck Squadron
... There are _____ quarter-rests in a whole-rest. There are _____ half-rests in a whole-rest. There are _____ sixteenth-rests in a quarter-rest. There are _____ eighth-rests in a quarter-rest. There are _____ quarter-rests in a half-rest. There are _____ sixteenth-rests in a half-rest. There are _____ ...
... There are _____ quarter-rests in a whole-rest. There are _____ half-rests in a whole-rest. There are _____ sixteenth-rests in a quarter-rest. There are _____ eighth-rests in a quarter-rest. There are _____ quarter-rests in a half-rest. There are _____ sixteenth-rests in a half-rest. There are _____ ...
Percussion
... Rhythmic pulse has minor Pulse changes are more frequent. Frequent disruptions to pulse Little or no rhythmic pulse to throughout. Pulse does not interruptions in feel, or pulse Interruptions to the pulse are and rhythmic flow. Technical the music. Tempo is rarely felt deviate from the original temp ...
... Rhythmic pulse has minor Pulse changes are more frequent. Frequent disruptions to pulse Little or no rhythmic pulse to throughout. Pulse does not interruptions in feel, or pulse Interruptions to the pulse are and rhythmic flow. Technical the music. Tempo is rarely felt deviate from the original temp ...
Inner Octaves and Eastern Music
... guidance can be offered. There are three areas of significant differences. The first is the intentional use of microtones embedded in monophonic melodies. The second difference is the principle that guides the composition of the melodies which serve as the framework for the playing of microtones. In ...
... guidance can be offered. There are three areas of significant differences. The first is the intentional use of microtones embedded in monophonic melodies. The second difference is the principle that guides the composition of the melodies which serve as the framework for the playing of microtones. In ...
Harmony Graph, a Social-Network
... 3.2.2 Average Path Length In Section 3.1 we mentioned that there exist "long bridges" in the Harmony Graphs of 12-tone serial works. This can be best described in terms of the average path length (APL). Actually, in our experiments, we find that APL is the most significant characteristic to distingu ...
... 3.2.2 Average Path Length In Section 3.1 we mentioned that there exist "long bridges" in the Harmony Graphs of 12-tone serial works. This can be best described in terms of the average path length (APL). Actually, in our experiments, we find that APL is the most significant characteristic to distingu ...
From Pythagoras to Johann Sebastian Bach: An
... Whereas music is the language of the soul, math is the language of the universe. Yet, the parallels of these two drastically contrasting subjects are multitudinous. H. Von Helmholtz marvels, “Mathematics and music, the most sharply contrasted fields of intellectual activity which can be found, and y ...
... Whereas music is the language of the soul, math is the language of the universe. Yet, the parallels of these two drastically contrasting subjects are multitudinous. H. Von Helmholtz marvels, “Mathematics and music, the most sharply contrasted fields of intellectual activity which can be found, and y ...
Playing Musical Tiles - SJU
... as possible. In order to achieve this, voice-crossing—occurring when two voices change positions in the ordering of voices from low to high—is avoided. If we restrict ourselves to twelve-tone equal temperament, the closest distinct chords are those that differ by a semitone in one voice only (note ...
... as possible. In order to achieve this, voice-crossing—occurring when two voices change positions in the ordering of voices from low to high—is avoided. If we restrict ourselves to twelve-tone equal temperament, the closest distinct chords are those that differ by a semitone in one voice only (note ...
Tonal Harmony Chapter 23 Enharmonic Spellings and Enharmonic
... modulation is taking place. REMEMBER to always look for the common chord by backing up one chord from the chord that signals the modulation Any V7 chord or secondary V7 in the first key can be reinterpreted as a Ger+6 chord in the new key The reverse is also possible In the majority of cases, the co ...
... modulation is taking place. REMEMBER to always look for the common chord by backing up one chord from the chord that signals the modulation Any V7 chord or secondary V7 in the first key can be reinterpreted as a Ger+6 chord in the new key The reverse is also possible In the majority of cases, the co ...
Non-Chord Tones
... by step in the same direction. • Neighboring tone (n)- Approached by step and left by step in the opposite direction. • Suspension (s)- Approached by same tone and left by a step down. • Retardation (r)- Approached by the same tone and left by a step up. ...
... by step in the same direction. • Neighboring tone (n)- Approached by step and left by step in the opposite direction. • Suspension (s)- Approached by same tone and left by a step down. • Retardation (r)- Approached by the same tone and left by a step up. ...
Aspects of Raga in North Indian Classical Music
... “Raga Kedar was believed to cure diseases and melt stones if correctly performed. For example, jailers allegedly used to teach inmates, for an appropriate fee, how to sing raga Kedar. If the stones of the of the inmate’s cell did not melt, the jailer would claim that the raga had not been performed ...
... “Raga Kedar was believed to cure diseases and melt stones if correctly performed. For example, jailers allegedly used to teach inmates, for an appropriate fee, how to sing raga Kedar. If the stones of the of the inmate’s cell did not melt, the jailer would claim that the raga had not been performed ...
Grade: K - Kenosha Unified School District
... symphonic band and orchestra, ostinato mezzo piano, mezzo forte, D.C. al Fine, unison, fortissimo, pianissimo, dotted notes and dotted rests) Standard: 5. Describes, analyzes and evaluates music Benchmarks: • Recognizes the musical forms of AB, ABA, theme and variations and rondo • Recognizes instru ...
... symphonic band and orchestra, ostinato mezzo piano, mezzo forte, D.C. al Fine, unison, fortissimo, pianissimo, dotted notes and dotted rests) Standard: 5. Describes, analyzes and evaluates music Benchmarks: • Recognizes the musical forms of AB, ABA, theme and variations and rondo • Recognizes instru ...
Disciplining Knowledge in Music Theory
... The tradition of strict counterpoint continued this process of abstraction in two subsequent directions: one traced the emergence of “voice-leading principles” from Renaissance polyphony through strict counterpoint to Schenker’s landmark definitions; the other followed the abstraction of melody and ...
... The tradition of strict counterpoint continued this process of abstraction in two subsequent directions: one traced the emergence of “voice-leading principles” from Renaissance polyphony through strict counterpoint to Schenker’s landmark definitions; the other followed the abstraction of melody and ...
Document
... The Theory MAP lessons over six levels (Primer to Five) give students an aid to the reading of pitch and rhythmic values, elements of musical expression, and exploring how music is put together. These MAP Theory Levels correlate and support progress with the MAP piano, brass, voice and percussion fo ...
... The Theory MAP lessons over six levels (Primer to Five) give students an aid to the reading of pitch and rhythmic values, elements of musical expression, and exploring how music is put together. These MAP Theory Levels correlate and support progress with the MAP piano, brass, voice and percussion fo ...
2 steady beats of sound - Elm Grove Middle School Band
... Time Signature • The Time Signature appears at the beginning of the music after the clef sign. • The Time Signature has two numbers, one above the other. • The top number tells you how many steady beats are in each measure. • The bottom number tells you what value note illustrates the steady beat. ...
... Time Signature • The Time Signature appears at the beginning of the music after the clef sign. • The Time Signature has two numbers, one above the other. • The top number tells you how many steady beats are in each measure. • The bottom number tells you what value note illustrates the steady beat. ...
Year 10 Specialist Music Program 2017
... covered earlier in the lesson. Then using the loop pedals loop a basic 12 bar blues rhythm and write a melody over the top that includes a 8 bar improvisation using the blues scale. The use of bended pitch should be encouraged and can be notated by a small “scoop” line either extending upward toward ...
... covered earlier in the lesson. Then using the loop pedals loop a basic 12 bar blues rhythm and write a melody over the top that includes a 8 bar improvisation using the blues scale. The use of bended pitch should be encouraged and can be notated by a small “scoop” line either extending upward toward ...
Daniel Liles
... Rameau’s argument was that the origins of music can be found in nature in mathematical harmonic structures (chords). From these chords Rameau was able to determine that each chord is generated from a single fundamental tone (commonly known as a tonic).1 The relationships found between two or more f ...
... Rameau’s argument was that the origins of music can be found in nature in mathematical harmonic structures (chords). From these chords Rameau was able to determine that each chord is generated from a single fundamental tone (commonly known as a tonic).1 The relationships found between two or more f ...
Unit 3 – Scales, Keys & Modes
... Key Signatures are written at the beginning of every staff. They show which pitches are to be sharp or flat consistently throughout the piece, and helps determine the key or tonal center. Major Scales help determine which accidentals make-up its key signature. For example: the G Major Scale has an F ...
... Key Signatures are written at the beginning of every staff. They show which pitches are to be sharp or flat consistently throughout the piece, and helps determine the key or tonal center. Major Scales help determine which accidentals make-up its key signature. For example: the G Major Scale has an F ...
Chapter 5 - Wilson Central High School Band
... Parallel-key pentachords are the same except for the 3rd scale degrees. The minor key pentachord has a lowered 3rd (b3) scale degree (flat in this case means lowered…not necessarily a flat note) ...
... Parallel-key pentachords are the same except for the 3rd scale degrees. The minor key pentachord has a lowered 3rd (b3) scale degree (flat in this case means lowered…not necessarily a flat note) ...
List of musical symbols - paulandersonguitar.com
... Clefs define the pitch range of the staff on which it is placed. A clef is usually the leftmost symbol on a staff. Additional clefs may appear in the middle of a staff to indicate a change in register for instruments with a wide range. In early music, clefs could be placed on any of several lines on ...
... Clefs define the pitch range of the staff on which it is placed. A clef is usually the leftmost symbol on a staff. Additional clefs may appear in the middle of a staff to indicate a change in register for instruments with a wide range. In early music, clefs could be placed on any of several lines on ...
Gyo¨ rgy Ligeti and the Aka Pygmies Project
... employ marketing techniques whose novelty hinges on cultural border-crossing. From John Hassel’s experiments with the Zimbabwean mbira on Vernal Equinox to Glen Velez’s excursion in percussion techniques from around the globe on Rhythmicolor Exotica, crossover music and ethnic polystylism has practi ...
... employ marketing techniques whose novelty hinges on cultural border-crossing. From John Hassel’s experiments with the Zimbabwean mbira on Vernal Equinox to Glen Velez’s excursion in percussion techniques from around the globe on Rhythmicolor Exotica, crossover music and ethnic polystylism has practi ...
Traditional sub-Saharan African harmony
Sub-Saharan harmony is based on the principles of homophonic parallelism (similar chords changing simultaneously), homophonic polyphony (independent parts moving together), counter melody (secondary melody) and ostinato-variation (variations based on a repeated theme). Polyphony (contrapuntal and ostinato variation) is common in African music and heterophony (the voices move at different times) is a common technique as well. Although these principles of traditional (precolonial and pre-Arab) African music are of pan-African validity, the degree to which they are used in one area over another (or in the same community) varies. Specific techniques that used to generate harmony in Africa are the ""span process"", ""pedal notes"" (a held note, typically in the bass, around which other parts move), ""Rhythmic harmony"", ""harmony by imitation"", and ""scalar clusters"" (see below for explanation of these terms).