Nicola Vicentino and the Enharmonic Diesis

... on Vicentino‟s advocacy for the use of microtonal step of the minor enharmonic diesis as a means of affective expression. Chapter Two explores the harmonic and voice-leading possibilities of Vicentino‟s system of 31-tone equal temperament (31-TET). I develop a system of categorizing harmonic relatio ...

... on Vicentino‟s advocacy for the use of microtonal step of the minor enharmonic diesis as a means of affective expression. Chapter Two explores the harmonic and voice-leading possibilities of Vicentino‟s system of 31-tone equal temperament (31-TET). I develop a system of categorizing harmonic relatio ...

Generalized Interval System and Its Applications

... an octave of the C Major scale in treble clef. These steps and scales play an integral role in naming intervals. In Table 1 all possible interval names are shown. However, augmented and diminished intervals are not used as often as major and minor intervals are used. Moreover, augmented fourth and d ...

... an octave of the C Major scale in treble clef. These steps and scales play an integral role in naming intervals. In Table 1 all possible interval names are shown. However, augmented and diminished intervals are not used as often as major and minor intervals are used. Moreover, augmented fourth and d ...

Outlining the prime

... overall effect is levity in balance and with ease. However, we can equally extend the fifth downward and observe how the fifth affects us then. Intellectually we are tempted to postulate that the inverse is true and that the fifth down from a given note will expand downward in easy gravitational man ...

... overall effect is levity in balance and with ease. However, we can equally extend the fifth downward and observe how the fifth affects us then. Intellectually we are tempted to postulate that the inverse is true and that the fifth down from a given note will expand downward in easy gravitational man ...

Chapter 1: Introduction to Pairwise Well-Formed Scales

... The notion of a pairwise well-formed scale is my own extension of the theory to a class that includes (but is not limited to) some scales that incorporate the step interval of the augmented second. These scales are prominent in world musics, and have been appropriated by composers of Western art mus ...

... The notion of a pairwise well-formed scale is my own extension of the theory to a class that includes (but is not limited to) some scales that incorporate the step interval of the augmented second. These scales are prominent in world musics, and have been appropriated by composers of Western art mus ...

Scales and temperaments: the fivefold way

... major triad in some form. In western music it is regarded as the fundamental building block on which chords and scales are built. Scales in which the frequency ratio 5:4 are included were rst developed by Didymus in the rst century b.c. and Ptolemy in the second century a.d. The dierence between ...

... major triad in some form. In western music it is regarded as the fundamental building block on which chords and scales are built. Scales in which the frequency ratio 5:4 are included were rst developed by Didymus in the rst century b.c. and Ptolemy in the second century a.d. The dierence between ...

(pdf)

... on a torus is based on the fact that each vertex has degree 6, which means that the graph is 6 − regular. On the other hand the graph of the diatonic scale generalized Tonnetz embeds on a Möbius strip because each vertex is of degree 4, or the graph is 4 − regular. That is why the graph based on th ...

... on a torus is based on the fact that each vertex has degree 6, which means that the graph is 6 − regular. On the other hand the graph of the diatonic scale generalized Tonnetz embeds on a Möbius strip because each vertex is of degree 4, or the graph is 4 − regular. That is why the graph based on th ...

rudiments of music

... (b) Name the order in which the Tones and Semitones occur in Major Scales. (c) Between which degrees of Maier Scales do. Semitones o.ccur? (d) Why is a Majo.r Scale so. called? (e) What is a Tetrachord, and how many are there in a Majo.r Scale? (J) In starting Scales from any other note than C what ...

... (b) Name the order in which the Tones and Semitones occur in Major Scales. (c) Between which degrees of Maier Scales do. Semitones o.ccur? (d) Why is a Majo.r Scale so. called? (e) What is a Tetrachord, and how many are there in a Majo.r Scale? (J) In starting Scales from any other note than C what ...

Semantic manual - Semantic Daniélou

... observed between intervals composed of one same total number of commas + disjunctions, but differing according to their position in the scale, by their number of disjunctions. Because of a perfectly balanced distribution of commas and disjunctions within the octave, for the same sum of commas + disj ...

... observed between intervals composed of one same total number of commas + disjunctions, but differing according to their position in the scale, by their number of disjunctions. Because of a perfectly balanced distribution of commas and disjunctions within the octave, for the same sum of commas + disj ...

pdf - Santa Fe Institute

... A comparison of these ½-matrices shows that in a WT system like W3 the degree of error varies considerably over intervals and keys (shown here as diagonals and rows). Smaller errors in W3 tend to be found in central keys (beginning on the first, 5th, and 7th degrees) and in important intervals like ...

... A comparison of these ½-matrices shows that in a WT system like W3 the degree of error varies considerably over intervals and keys (shown here as diagonals and rows). Smaller errors in W3 tend to be found in central keys (beginning on the first, 5th, and 7th degrees) and in important intervals like ...

Tuning, Tonality, and 22

... fact that 12-equal is not the historical basis for the diatonic scale; in fact the converse is true, and 12equal was chosen over other meantone tunings only for convenience. Balzano focuses on certain grouptheoretical properties of 12-equal and of the diatonic scales within it. For example, his view ...

... fact that 12-equal is not the historical basis for the diatonic scale; in fact the converse is true, and 12equal was chosen over other meantone tunings only for convenience. Balzano focuses on certain grouptheoretical properties of 12-equal and of the diatonic scales within it. For example, his view ...

RESEARCH ARTICLE Metrics for Scales and Tunings

... major12) without undue strain, yet may not be particularly easy to perform when the pitches are translated to a subset of 10edo. Thus it is desirable to have a metric that allows a statement such as syntonicJI is closer to 12edo than to 10edo. It is intuitively plausible that tunings may be “close t ...

... major12) without undue strain, yet may not be particularly easy to perform when the pitches are translated to a subset of 10edo. Thus it is desirable to have a metric that allows a statement such as syntonicJI is closer to 12edo than to 10edo. It is intuitively plausible that tunings may be “close t ...

The Structure of Plato`s Dialogues and Greek Music Theory: A

... western music, where scales count as a well-founded concept: scales tend to be restricted to a small number of possible intervals between adjacent elements (e.g. semitones and tones, or tones and minor thirds), which often endows them with particular properties. Moreover, they are typically confined ...

... western music, where scales count as a well-founded concept: scales tend to be restricted to a small number of possible intervals between adjacent elements (e.g. semitones and tones, or tones and minor thirds), which often endows them with particular properties. Moreover, they are typically confined ...

... western music, where scales count as a well-founded concept: scales tend to be restricted to a small number of possible intervals between adjacent elements (e.g. semitones and tones, or tones and minor thirds), which often endows them with particular properties. Moreover, they are typically confined ...

BASIC MATHEMATICAL AND MUSICAL CONCEPTS Sets and

... One sees that the sequence of intervals 1, 1, 12 , 1, 1, 1, 12 for the standard scale is not equal to any of its non-trivial cyclic permutations, and hence no non-trivial permutation of the standard scale is a standard scale. This underlies the fact that the the seven scales obtained by permuting th ...

... One sees that the sequence of intervals 1, 1, 12 , 1, 1, 1, 12 for the standard scale is not equal to any of its non-trivial cyclic permutations, and hence no non-trivial permutation of the standard scale is a standard scale. This underlies the fact that the the seven scales obtained by permuting th ...

Fundamentals of Music G9-12

... There are fifteen different major scales-seven that use flatted notes, seven that use sharped notes, and one natural scale. Another way to think of major scales is as two tetra chords; that is, as two fournote patterns. As long as you reproduce the whole/half step pattern, you create a major scale f ...

... There are fifteen different major scales-seven that use flatted notes, seven that use sharped notes, and one natural scale. Another way to think of major scales is as two tetra chords; that is, as two fournote patterns. As long as you reproduce the whole/half step pattern, you create a major scale f ...

Interval Scale as Group Generators - Base des articles scientifiques

... an interval scale {2, 3, 4}. These intervals are closely related to tonal music. The intervals 3 and 4 are constituent of major and minor triads, and 2 is one of the most important melodic intervals in tonal music. In spite of his use of twelve-tone technique, Berg is famous for pieces that hold som ...

... an interval scale {2, 3, 4}. These intervals are closely related to tonal music. The intervals 3 and 4 are constituent of major and minor triads, and 2 is one of the most important melodic intervals in tonal music. In spite of his use of twelve-tone technique, Berg is famous for pieces that hold som ...

Just Intonation Explained

... Scientists have devised a standard unit for measuring the size of perceived intervals resulting from two frequencies vibrating at a given ratio. This unit is called a cent because it equals 1/100th of a half-step. A half-step is the smallest interval between two notes on the piano. There are 12 half ...

... Scientists have devised a standard unit for measuring the size of perceived intervals resulting from two frequencies vibrating at a given ratio. This unit is called a cent because it equals 1/100th of a half-step. A half-step is the smallest interval between two notes on the piano. There are 12 half ...

doc

... The standard scale used on piano keyboards is the chromatic scale—the pattern of black and white keys with 12 semi-tones comprising an octave. This choice of 12 semi-tones is a convention, and one could imagine using other scales. The 12-semitone scale happens to be a reasonably good one because the ...

... The standard scale used on piano keyboards is the chromatic scale—the pattern of black and white keys with 12 semi-tones comprising an octave. This choice of 12 semi-tones is a convention, and one could imagine using other scales. The 12-semitone scale happens to be a reasonably good one because the ...

The Tetrachord (Ancient)

... the basic harmonic vocabulary of fourths and fifths; however, there were still no semitones, tritones or major sevenths to make singing difficult. 5) Strong tonality was developed in melodic compositions because the scales were made permanently uneven. 6) One major triad along with its lower relativ ...

... the basic harmonic vocabulary of fourths and fifths; however, there were still no semitones, tritones or major sevenths to make singing difficult. 5) Strong tonality was developed in melodic compositions because the scales were made permanently uneven. 6) One major triad along with its lower relativ ...

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 ...

Frequency

... the technique described above 3/2 x 3/4 = 9/8 which is the ratio of a major 2nd. This technique is used to discern the effect of tuning intervals downwards. Individual notes. Ratios can be used to represent individual notes within the context of a key. For example the note G could be represented by ...

... the technique described above 3/2 x 3/4 = 9/8 which is the ratio of a major 2nd. This technique is used to discern the effect of tuning intervals downwards. Individual notes. Ratios can be used to represent individual notes within the context of a key. For example the note G could be represented by ...

john beaulieu

... posture resonate with and entrain to it. Intervals have been used this way for thousands of years. The ancient Chinese philosopher Lao Tzu referred to “the perfect fifth,” (the interval created by the tones C and G) as the sound of Universal harmony, balancing the forces of Yin and Yang. In India, t ...

... posture resonate with and entrain to it. Intervals have been used this way for thousands of years. The ancient Chinese philosopher Lao Tzu referred to “the perfect fifth,” (the interval created by the tones C and G) as the sound of Universal harmony, balancing the forces of Yin and Yang. In India, t ...

ASSESSING THE TUNING OF SUNG INDIAN CLASSICAL MUSIC

... they report a slightly better fit for 12 interval scales compared to 22 shruti scales in [2]. However, no substantial differences were found between the considered scales (including the 12-interval equal-tempered one). In subsequent papers [3, 4], the same authors provided evidence for the existence ...

... they report a slightly better fit for 12 interval scales compared to 22 shruti scales in [2]. However, no substantial differences were found between the considered scales (including the 12-interval equal-tempered one). In subsequent papers [3, 4], the same authors provided evidence for the existence ...

# Interval (music)

In music theory, an interval is the difference between two pitches. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio.In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). Examples include the minor third or perfect fifth. These names describe not only the difference in semitones between the upper and lower notes, but also how the interval is spelled. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G♯ and G–A♭.