Nicola Vicentino and the Enharmonic Diesis

... sources. I will then discuss Vicentino‟s adaptation of the Greek genera, his theory of interval affect, and the features of his 31-tone tuning system. The discussion will focus on Vicentino‟s advocacy for the use of microtonal step of the minor enharmonic diesis as a means of affective expression. C ...

... sources. I will then discuss Vicentino‟s adaptation of the Greek genera, his theory of interval affect, and the features of his 31-tone tuning system. The discussion will focus on Vicentino‟s advocacy for the use of microtonal step of the minor enharmonic diesis as a means of affective expression. C ...

Tripod Notation article

... If you find the major and subminor triads on the full lattice, you should see that the subminor triad is formed by lowering the third of a minor triad by the same amount that a minor third is smaller than a major third. The difference is the interval I called a semitoe before. So we can say that a m ...

... If you find the major and subminor triads on the full lattice, you should see that the subminor triad is formed by lowering the third of a minor triad by the same amount that a minor third is smaller than a major third. The difference is the interval I called a semitoe before. So we can say that a m ...

The History of Tuning

... string instrument was used to back the voice. The above example is a religious poem (in Classical Greek) the smaller symbols above the text poem are the notes that are intended to be sounded when the poem is sung. Pythagoras (600BC) was the first, in the West, to write about forming scales for strin ...

... string instrument was used to back the voice. The above example is a religious poem (in Classical Greek) the smaller symbols above the text poem are the notes that are intended to be sounded when the poem is sung. Pythagoras (600BC) was the first, in the West, to write about forming scales for strin ...

Mathemusical Thought - LUC Sakai

... 2. Our pitches are divided into white notes and black notes, depending on which piano key they correspond to. 3. A single step along our sequence, from one pitch to the very next pitch (to the left or right, whether black or white) is called a half step. A distance of two steps along our sequence i ...

... 2. Our pitches are divided into white notes and black notes, depending on which piano key they correspond to. 3. A single step along our sequence, from one pitch to the very next pitch (to the left or right, whether black or white) is called a half step. A distance of two steps along our sequence i ...

The Classical Indian Just Intonation Tuning System

... being an inverted fifth (panchama) from the immediately higher sa, still it was found useful to work out the series of fourths as well. The knowledge of the 22 srutis was obtained by working out these two cycles. The scale of equal temperament, which became a necessity in Europe on account of the ex ...

... being an inverted fifth (panchama) from the immediately higher sa, still it was found useful to work out the series of fourths as well. The knowledge of the 22 srutis was obtained by working out these two cycles. The scale of equal temperament, which became a necessity in Europe on account of the ex ...

Semantic manual - Semantic Daniélou

... Disjunctions are commas, larger by about one-third of a comma, in the number of twelve, found at the boundaries between the different chromatic notes of the Semantic-53 scale. In 5-limit, their rather complex ratio is either 20 000 / 19 683, or 3 125 / 3 072. In 7-limit, it comes down to the equival ...

... Disjunctions are commas, larger by about one-third of a comma, in the number of twelve, found at the boundaries between the different chromatic notes of the Semantic-53 scale. In 5-limit, their rather complex ratio is either 20 000 / 19 683, or 3 125 / 3 072. In 7-limit, it comes down to the equival ...

Appendix I: Microtonality in 20 Century Western Art Music: A

... when composers pushed the boundaries of their pitch systems ever closer to an (at least theoretical) equality of all common intervals, it was a logical conclusion to consider applying intervals smaller than a semitone to the newly discovered chromatic pitch systems in which notes increasingly relate ...

... when composers pushed the boundaries of their pitch systems ever closer to an (at least theoretical) equality of all common intervals, it was a logical conclusion to consider applying intervals smaller than a semitone to the newly discovered chromatic pitch systems in which notes increasingly relate ...

Intonation Variables in the Performance of Twelve

... directed his study specifically to measurement of the sizes of harmonic intervals in ensemble performance, and he found that here, too, Pythagorean values appear to be most representative of actual practice, thirds and tenths beginning to approach their just or natural values only when long-held.10 ...

... directed his study specifically to measurement of the sizes of harmonic intervals in ensemble performance, and he found that here, too, Pythagorean values appear to be most representative of actual practice, thirds and tenths beginning to approach their just or natural values only when long-held.10 ...

A Style of Music Characterized by Fibonacci [Numbers]

... “that standard proportion which underlies the arrangement of the human form, the construction of the more beautiful animals, the construction of plants, namely in the form of their leafarrangement, the forms of various crystals, the arrangement of the planets, the proportions of architectural and sc ...

... “that standard proportion which underlies the arrangement of the human form, the construction of the more beautiful animals, the construction of plants, namely in the form of their leafarrangement, the forms of various crystals, the arrangement of the planets, the proportions of architectural and sc ...

Beyond Temperament: Non-Keyboard Intonation in the 17th and

... what they describe. Georg Muffat (1698) even warned sharps, although the exact difference is not specified. violinists to resist the temptation to play leading notes Recorder charts are the most informative, since the instrument's inflexible blowing technique requires altertoo low (sic). Tosi said t ...

... what they describe. Georg Muffat (1698) even warned sharps, although the exact difference is not specified. violinists to resist the temptation to play leading notes Recorder charts are the most informative, since the instrument's inflexible blowing technique requires altertoo low (sic). Tosi said t ...

Tuning Systems

... once popular in Europe. All tuning systems are based on the physics of sound4 . But they all are also aected by the history of their music traditions, as well as by the tuning peculiarities of the instruments used in those traditions. Pythagorean (Section 2.1: Pythagorean Intonation), mean-tone (Se ...

... once popular in Europe. All tuning systems are based on the physics of sound4 . But they all are also aected by the history of their music traditions, as well as by the tuning peculiarities of the instruments used in those traditions. Pythagorean (Section 2.1: Pythagorean Intonation), mean-tone (Se ...

The Rosegarden Codicil: Rehearsing Music in Nineteen

... We are using the term ‘microtonal tuning’ here to mean simply any tuning with more than twelve notes per octave, though we realise that the term is sometimes defined more broadly. For example, the definition could be so broad as to include all tunings other than the one based on the ubiquitous Weste ...

... We are using the term ‘microtonal tuning’ here to mean simply any tuning with more than twelve notes per octave, though we realise that the term is sometimes defined more broadly. For example, the definition could be so broad as to include all tunings other than the one based on the ubiquitous Weste ...

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

... which is much larger than even an entire standard whole tone. Clearly two pitches in such a large interval would not be mistaken for the same note, so connecting Plato’s pyknomata with Kennedy’s division is misleading.19 It is possible that Kennedy here is potentially relating his scale to the moder ...

... which is much larger than even an entire standard whole tone. Clearly two pitches in such a large interval would not be mistaken for the same note, so connecting Plato’s pyknomata with Kennedy’s division is misleading.19 It is possible that Kennedy here is potentially relating his scale to the moder ...

... which is much larger than even an entire standard whole tone. Clearly two pitches in such a large interval would not be mistaken for the same note, so connecting Plato’s pyknomata with Kennedy’s division is misleading.19 It is possible that Kennedy here is potentially relating his scale to the moder ...

Musical Scales - Rick Bradford Home Page

... The Table covers all values of r from 0 through 24 (just once each), although the entries have been ordered by increasing frequency. This covers two whole octaves and the start of a third. The frequencies in the second octave have been divided by 2 for ease of comparison with the first. A nice thing ...

... The Table covers all values of r from 0 through 24 (just once each), although the entries have been ordered by increasing frequency. This covers two whole octaves and the start of a third. The frequencies in the second octave have been divided by 2 for ease of comparison with the first. A nice thing ...

Musical Harmony, Mathematics, and Esotericism

... note between B and C, or between E and F. Western music offers a basic seven-note, diatonic, scale, which, through the use of sharps and flats, can be expanded to a twelve-note, chromatic, scale. The relation between two notes is referred to as an interval. Within an octave, intervals range from the ...

... note between B and C, or between E and F. Western music offers a basic seven-note, diatonic, scale, which, through the use of sharps and flats, can be expanded to a twelve-note, chromatic, scale. The relation between two notes is referred to as an interval. Within an octave, intervals range from the ...

Pitch vs Frequency There is a relationship between pitch and

... Frequencies come in all values. between any two frequencies, no matter how close together they are, there is always some other frequency. However, for the purpose of music, this infinitude of possibilities it too great. Over the centuries, the set of all possible frequencies has been categorized int ...

... Frequencies come in all values. between any two frequencies, no matter how close together they are, there is always some other frequency. However, for the purpose of music, this infinitude of possibilities it too great. Over the centuries, the set of all possible frequencies has been categorized int ...

file here.

... or bring down, that “A” by one octave. This we can do by dividing the ratio 27:8 by the ratio of the octave, which you remember is 2:1. Work out the arithmetic and you get 27:16. This is the ratio of the Major Sixth.4 (3:2)4 give us the next ascending perfect fifth (in our example, from “A” up to “E ...

... or bring down, that “A” by one octave. This we can do by dividing the ratio 27:8 by the ratio of the octave, which you remember is 2:1. Work out the arithmetic and you get 27:16. This is the ratio of the Major Sixth.4 (3:2)4 give us the next ascending perfect fifth (in our example, from “A” up to “E ...

Estimation of harpsichord inharmonicity

... intonation to form perfectly consonant intervals if required, but fixed-pitch instruments such as keyboard, some fretted, and some percussion instruments, need to commit to a tuning scheme for the duration of a piece, if not an entire concert. In the Western musical tradition at least, this gives ri ...

... intonation to form perfectly consonant intervals if required, but fixed-pitch instruments such as keyboard, some fretted, and some percussion instruments, need to commit to a tuning scheme for the duration of a piece, if not an entire concert. In the Western musical tradition at least, this gives ri ...

Hybrid Thinking in Meloharmony

... Renaissance (Pietro Aron is a prominent name in this context) the major third became a just 5/4 within meantone keyboard tunings, while the fifth was heavily tempered (down by 5.4 cents against just 3/2). The unequal size of the intervallic steps (from 76 to 117 cents, with the famous "wolf" between ...

... Renaissance (Pietro Aron is a prominent name in this context) the major third became a just 5/4 within meantone keyboard tunings, while the fifth was heavily tempered (down by 5.4 cents against just 3/2). The unequal size of the intervallic steps (from 76 to 117 cents, with the famous "wolf" between ...

Scales in Music

... kind of interval scale. For example, if we take base-2 logarithms of the various ratios above, we get the following scale, which looks more familiar. ...

... kind of interval scale. For example, if we take base-2 logarithms of the various ratios above, we get the following scale, which looks more familiar. ...

From Pythagoras to Johann Sebastian Bach: An

... intellectual activity which can be found, and yet related, supporting each other, as if to show forth the secret connection which ties together all the activities of our mind.”1 Dissonance and irrationality, fractals and subdivisions, intervallic leaps and modular arithmetic: math is embedded in mus ...

... intellectual activity which can be found, and yet related, supporting each other, as if to show forth the secret connection which ties together all the activities of our mind.”1 Dissonance and irrationality, fractals and subdivisions, intervallic leaps and modular arithmetic: math is embedded in mus ...

Dynamic Tonality - William A. Sethares

... Transpositional invariance is exposed by isomorphic notelayouts [10], and so is tuning invariance [12]. A button-field is a two-dimensional geometric arrangement of note-controlling buttons. A note-layout is a mapping of notes to a button-field. The word isomorphic comes from the Greek roots “iso” ( ...

... Transpositional invariance is exposed by isomorphic notelayouts [10], and so is tuning invariance [12]. A button-field is a two-dimensional geometric arrangement of note-controlling buttons. A note-layout is a mapping of notes to a button-field. The word isomorphic comes from the Greek roots “iso” ( ...

# 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.