Consonance in Music and Mathematics: Application
... Since ancient Greece there is evidence of the relation between Music and Mathematics. This article aims to be one more contribution to the study of the links connecting both fields. Two main topics will be investigated and discussed along the following sections. Although, both of them will relate to ...
... Since ancient Greece there is evidence of the relation between Music and Mathematics. This article aims to be one more contribution to the study of the links connecting both fields. Two main topics will be investigated and discussed along the following sections. Although, both of them will relate to ...
Music, Cognition, and Computerized Sound: Chap14
... Beats are the chief means for tuning musical instruments precisely. Through a sense of pitch and a memory of intervals, those with musical ability can tune one note of a piano keyboard to approximately the right interval from another note. But it is by beats that the final tuning is made. In tuning ...
... Beats are the chief means for tuning musical instruments precisely. Through a sense of pitch and a memory of intervals, those with musical ability can tune one note of a piano keyboard to approximately the right interval from another note. But it is by beats that the final tuning is made. In tuning ...
Spectral analysis of different harmonies Implemented by Equal
... environment including instruments, musical scales, and tuning system also evolved. The tuning system and musical scales of Greek age also were significantly different from today’s equal temperament based tuning system and scales. For example, the Greek music what Aristoxenus suggests is entirely bas ...
... environment including instruments, musical scales, and tuning system also evolved. The tuning system and musical scales of Greek age also were significantly different from today’s equal temperament based tuning system and scales. For example, the Greek music what Aristoxenus suggests is entirely bas ...
The Octave - Bill Troxler
... The human mind interprets both notes in the octave as being essentially the same. That’s because the overtones of both notes are nearly identical. (More about overtones and harmonics later). Because tones that are an octave apart seem more or less identical, they bear the same name. The octave tone ...
... The human mind interprets both notes in the octave as being essentially the same. That’s because the overtones of both notes are nearly identical. (More about overtones and harmonics later). Because tones that are an octave apart seem more or less identical, they bear the same name. The octave tone ...
Pitch is directly related to frequency and my analysis of ragas is
... whereas a Western song seems 'jumpy' like a Piano. Because of this Indian classical music cannot be played effectively in a twelve key per octave instrument like a piano. Of course, several Western instruments have been 'adapted' with a little modification here and there, to play Indian classical mu ...
... whereas a Western song seems 'jumpy' like a Piano. Because of this Indian classical music cannot be played effectively in a twelve key per octave instrument like a piano. Of course, several Western instruments have been 'adapted' with a little modification here and there, to play Indian classical mu ...
Pythagorean tuning
... In the formulas, the ratios 3:2 or 2:3 represent an ascending or descending perfect fifth (i.e. an increase or decrease in frequency by a perfect fifth), while 2:1 or 1:2 represent an ascending or descending octave. The major scale based on C, obtained from this tuning is:[5] In equal temperament, pai ...
... In the formulas, the ratios 3:2 or 2:3 represent an ascending or descending perfect fifth (i.e. an increase or decrease in frequency by a perfect fifth), while 2:1 or 1:2 represent an ascending or descending octave. The major scale based on C, obtained from this tuning is:[5] In equal temperament, pai ...
Intervals and Pitch
... corresponds to human perception. Twelve units of pitch equals one octave. There are two ways to notate pitch: either using a note name (a letter from A-G) and a number to indicate the octave, or using MIDI notation, in which each key on the piano corresponds to a whole number from 21 to 108. Here is ...
... corresponds to human perception. Twelve units of pitch equals one octave. There are two ways to notate pitch: either using a note name (a letter from A-G) and a number to indicate the octave, or using MIDI notation, in which each key on the piano corresponds to a whole number from 21 to 108. Here is ...
Pitch- the relative “highness” or “lowness” of a sound
... Most pieces do not use all of the pitches available in the entire tuning system. The Mode or Key of a piece of music is the subset of pitches within a Tuning System that will be used. When those pitches are arranged in a sequential order from low to high, it creates a Scale. It is important to under ...
... Most pieces do not use all of the pitches available in the entire tuning system. The Mode or Key of a piece of music is the subset of pitches within a Tuning System that will be used. When those pitches are arranged in a sequential order from low to high, it creates a Scale. It is important to under ...
The demise of number ratios in music theory
... Medieval music theory was dominated by Pythagorean cosmic numerology. Today 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 accept ...
... Medieval music theory was dominated by Pythagorean cosmic numerology. Today 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 accept ...
Understanding Temperaments
... Temperaments in which the good fifths (11) are all the same size (except for the wolf), such as Aaron’s meantone we have just seen, are called regular. There is a whole range of such temperaments starting with fifths tempered yet more heavily (called negative meantones since the major thirds are sma ...
... Temperaments in which the good fifths (11) are all the same size (except for the wolf), such as Aaron’s meantone we have just seen, are called regular. There is a whole range of such temperaments starting with fifths tempered yet more heavily (called negative meantones since the major thirds are sma ...
A Non-Pythagorean Musical Scale Based on Logarithms
... positions corresponding to logarithmic pitches marked on the fingerboards. Specially-constructed flutes, xylophones and marimbas, specially-tuned harps, and other acoustic instruments might also be utilized in performances. Certainly the natural harmonics of each instrument will interfere to some de ...
... positions corresponding to logarithmic pitches marked on the fingerboards. Specially-constructed flutes, xylophones and marimbas, specially-tuned harps, and other acoustic instruments might also be utilized in performances. Certainly the natural harmonics of each instrument will interfere to some de ...
Stiff-string theory: Richard Feynman on piano tuning
... piano. One simply plays octaves and adjusts the tension in the untuned note until there are no beats. If the process is carried out carefully, the piano will sound good. In the end, tuning a piano is an art as well as a science. ...
... piano. One simply plays octaves and adjusts the tension in the untuned note until there are no beats. If the process is carried out carefully, the piano will sound good. In the end, tuning a piano is an art as well as a science. ...
Octave - Philip Tagg
... as ‘the same note’. For example, men are understood to be singing the same tune as women and children if both parties follow the same pitch contour at the same time in parallel octaves. The octave’s property of ‘unison at another pitch’ is also illustrated by the fact that: (i) a common chord consis ...
... as ‘the same note’. For example, men are understood to be singing the same tune as women and children if both parties follow the same pitch contour at the same time in parallel octaves. The octave’s property of ‘unison at another pitch’ is also illustrated by the fact that: (i) a common chord consis ...
Comparison of Interval Size in Equal Temperament and Just Tuning
... 2. A second player uses a tuner to adjust the upper note of the Equal Tempered interval (half step, whole step, etc.) up or down by the number of cents indicated in the “Difference” column. A pure beatless Just interval will result. For example: to play a Just tuned major third above C, look in the ...
... 2. A second player uses a tuner to adjust the upper note of the Equal Tempered interval (half step, whole step, etc.) up or down by the number of cents indicated in the “Difference” column. A pure beatless Just interval will result. For example: to play a Just tuned major third above C, look in the ...
History of Music Theory - Totally Ratted Limited
... late as the eighteenth century. When two tetrachords are placed within an octave and separated by a tone the resulting scale is known as a Diatonic scale. The two tetrachords in a diatonic scale are often called diatonic tetrachords. It is widely believed that Pythagoras constructed a tuning system ...
... late as the eighteenth century. When two tetrachords are placed within an octave and separated by a tone the resulting scale is known as a Diatonic scale. The two tetrachords in a diatonic scale are often called diatonic tetrachords. It is widely believed that Pythagoras constructed a tuning system ...
Simon Stevin - The Dozenal Society of America
... What was this new approach to music? Wu Zaiyu, a Chinese scholar-prince actually discovered it before Simon Stevin, who did a great job of spreading the idea in Europe. Both Wu Zaiyu and Stevin used mathematics to create equal distances in an octave. This equal distance between notes is called “Equa ...
... What was this new approach to music? Wu Zaiyu, a Chinese scholar-prince actually discovered it before Simon Stevin, who did a great job of spreading the idea in Europe. Both Wu Zaiyu and Stevin used mathematics to create equal distances in an octave. This equal distance between notes is called “Equa ...
The Emergence of the Idea of Irrationality In Renaissance
... Only in the late Middle Ages, the reality concerning perceptible proprieties of music once again developed: music became aimed at the empirical experiences and at practice. According to Dickreiter, this development was caused in the thirteenth century by the influence of the Arabic musical theory of ...
... Only in the late Middle Ages, the reality concerning perceptible proprieties of music once again developed: music became aimed at the empirical experiences and at practice. According to Dickreiter, this development was caused in the thirteenth century by the influence of the Arabic musical theory of ...
intervals and scales
... notes). Example 1 is a C Major scale; every letter in ascending order from C to high C. In choir practice we often sing major scales during our warmup. The order of semitones and whole tones in the scale defines the type of scale. The order of whole tones and semitones for a major scale is: W W S W ...
... notes). Example 1 is a C Major scale; every letter in ascending order from C to high C. In choir practice we often sing major scales during our warmup. The order of semitones and whole tones in the scale defines the type of scale. The order of whole tones and semitones for a major scale is: W W S W ...
RATIOS AND MUSICAL INTERVALS We like to think of an interval
... set of downward intervals = {x ∈ R | 0 < x < 1} = (0, 1) set of upward intervals = {x ∈ R | 1 < x} = (0, ∞) The interval created when f1 = f2 will here be called the unison interval. It is given by the ratio f : f (for any f ∈ R+ ), whcich corresponds via ϕ to the number 1. Each interval f1 : f2 has ...
... set of downward intervals = {x ∈ R | 0 < x < 1} = (0, 1) set of upward intervals = {x ∈ R | 1 < x} = (0, ∞) The interval created when f1 = f2 will here be called the unison interval. It is given by the ratio f : f (for any f ∈ R+ ), whcich corresponds via ϕ to the number 1. Each interval f1 : f2 has ...
Scales and Temperament - Department of Physics and Astronomy
... tuning system in which all the frequencies in an ‣ Aoctave are related by very simple integer ratios is said to use just intonation or just temperament ...
... tuning system in which all the frequencies in an ‣ Aoctave are related by very simple integer ratios is said to use just intonation or just temperament ...
The Great Highland Bagpipe Plays in WHAT Key?
... • If the interval between two notes is a ratio of small integers, such as 2/1, 3/2, or 4/3, they sound good together — they are consonant rather than dissonant • The twelve-tone equal-tempered scale is the smallest equal-tempered scale that contains all seven of the basic consonant intervals to a go ...
... • If the interval between two notes is a ratio of small integers, such as 2/1, 3/2, or 4/3, they sound good together — they are consonant rather than dissonant • The twelve-tone equal-tempered scale is the smallest equal-tempered scale that contains all seven of the basic consonant intervals to a go ...
doc
... (b) How many cents separate the A flat and G# that you calculated in your previous handout? [Hint: The frequency ratio Aflat:G# can be found by multiplying Aflat:C4 and C4:G#.] ...
... (b) How many cents separate the A flat and G# that you calculated in your previous handout? [Hint: The frequency ratio Aflat:G# can be found by multiplying Aflat:C4 and C4:G#.] ...
A Periodicity-Based Approach on Harmony Perception Including
... but also by the psychophysics of tone perception (Langner, 2007; Parncutt, 1989; Roederer, 2008). Thus, in order to better understand the process of musical creativity, the following questions should be addressed: 1. What are underlying (psychophysical) principles of music perception? 2. How can the ...
... but also by the psychophysics of tone perception (Langner, 2007; Parncutt, 1989; Roederer, 2008). Thus, in order to better understand the process of musical creativity, the following questions should be addressed: 1. What are underlying (psychophysical) principles of music perception? 2. How can the ...
Just Intonation Explained
... by 100. 9/8 (204 cents) is almost as close. Our modern system of tuning, called equal temperament, is a compromise. We divide the octave into 12 equal intervals not because it sound better that way - it doesn't at all, it's slightly buzzy with audible beating between sustained pitches - but so we ca ...
... by 100. 9/8 (204 cents) is almost as close. Our modern system of tuning, called equal temperament, is a compromise. We divide the octave into 12 equal intervals not because it sound better that way - it doesn't at all, it's slightly buzzy with audible beating between sustained pitches - but so we ca ...
The demise of number ratios in music theory
... • Quartertones simply lie between half-tone steps • Like half-tones, they are pitch categories - not ratios. Non-western music theories • Ratio theories exist in many music traditions • All are problematic for the same reasons ...
... • Quartertones simply lie between half-tone steps • Like half-tones, they are pitch categories - not ratios. Non-western music theories • Ratio theories exist in many music traditions • All are problematic for the same reasons ...
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.