Scales, Voice
... Just Diatonic Scale To get perfect triads, must sacrifice: There are two different size whole tones 9/8 (1.125) and 10/9 (1.111). ...
... Just Diatonic Scale To get perfect triads, must sacrifice: There are two different size whole tones 9/8 (1.125) and 10/9 (1.111). ...
Playing Melodically and Harmonically in Tune Michael Kimber One
... fifths apart. The third and fifth of a just triad are tuned in relation to the harmonic partials of its root. Note that the third of the just triad is a comma lower than if it had been derived by tuning only perfect fifths (Pythagorean). ...
... fifths apart. The third and fifth of a just triad are tuned in relation to the harmonic partials of its root. Note that the third of the just triad is a comma lower than if it had been derived by tuning only perfect fifths (Pythagorean). ...
Program Notes - Michael Harrison, composer and pianist
... In each age, composers have transformed the piano according to their needs; and his is the next great step in that development. The instrument you will be hearing is what he calls a "harmonically tuned" piano. A complete performance of Revelation consists of 12 intertwined sections, and lasts about ...
... In each age, composers have transformed the piano according to their needs; and his is the next great step in that development. The instrument you will be hearing is what he calls a "harmonically tuned" piano. A complete performance of Revelation consists of 12 intertwined sections, and lasts about ...
Slides - UMD Physics
... Temperament: an assignment of frequencies to all twelve notes from C to B It is impossible to find a temperament where all the octaves and fifths are perfect Pythagorean: all octaves and all but one fifth are perfect. One fifth is very off (pythagorean comma). ...
... Temperament: an assignment of frequencies to all twelve notes from C to B It is impossible to find a temperament where all the octaves and fifths are perfect Pythagorean: all octaves and all but one fifth are perfect. One fifth is very off (pythagorean comma). ...
Higher Music Literacy Unit 4 – Intervals
... distance of 8 notes between 2 notes of the same name. ...
... distance of 8 notes between 2 notes of the same name. ...
On Ben Johnston`s Notation and the Performance
... At the time, I did not know or need to know that this consonance was the result of a simple mathematical relationship, that the lower string was vibrating twice for every three vibrations of the upper one. However, when I began to learn about placing my fingers on the strings to tune other pitches, ...
... At the time, I did not know or need to know that this consonance was the result of a simple mathematical relationship, that the lower string was vibrating twice for every three vibrations of the upper one. However, when I began to learn about placing my fingers on the strings to tune other pitches, ...
Modern Western Tuning System - Digital Commons @ Kent State
... In my course of education the fields of Music and Math have fascinated me by their separation in description, math being considered a science and music a subject of art. However I now see them both as an art and a science. I am a cellist, pianist, and trumpeter and in my pursuit to master these in ...
... In my course of education the fields of Music and Math have fascinated me by their separation in description, math being considered a science and music a subject of art. However I now see them both as an art and a science. I am a cellist, pianist, and trumpeter and in my pursuit to master these in ...
The Pythagorean Comma The Spiral of Fifths and Equal Temperament
... comma equally over all twelve of the fifths, each one being flattened by 1/12 comma. This gives the equal tempered scale flexibility and simplicity at the expense of musical purity. Now twelve tempered fifths precisely equal seven octaves, which closes the circle of fifths. All intervals except the ...
... comma equally over all twelve of the fifths, each one being flattened by 1/12 comma. This gives the equal tempered scale flexibility and simplicity at the expense of musical purity. Now twelve tempered fifths precisely equal seven octaves, which closes the circle of fifths. All intervals except the ...
hw3
... b. Which interval is worst approximated (in cents) by an equally tempered interval? Other than the octave, which is best approximated? c. How many pure fifths are there in this scale? Draw lines on the template and identify them by letter names. (There is more than one.) d. How many pure major third ...
... b. Which interval is worst approximated (in cents) by an equally tempered interval? Other than the octave, which is best approximated? c. How many pure fifths are there in this scale? Draw lines on the template and identify them by letter names. (There is more than one.) d. How many pure major third ...
MSP_lecture3
... Construct as a geometric series - successive multiplication by 1.5 How many intervals to create – e.g., how to divide up the octave? Answer = 12 and still holds true today (for western music anyway) Interesting that we don’t use his system anymore but standardized on 12 ...
... Construct as a geometric series - successive multiplication by 1.5 How many intervals to create – e.g., how to divide up the octave? Answer = 12 and still holds true today (for western music anyway) Interesting that we don’t use his system anymore but standardized on 12 ...
Intonation, Tuning, and Blending
... intonation, you don’t have to worry about tuning. FALSE! tuning is a life-long journey that depends on which instruments you are playing with, what climate you are playing in, and what style the ensemble wishes to ...
... intonation, you don’t have to worry about tuning. FALSE! tuning is a life-long journey that depends on which instruments you are playing with, what climate you are playing in, and what style the ensemble wishes to ...
“Tuning and temperament” by Rudolph Rasch Know who and where
... We'll write this scale on the board with both ratios and large numbers. (Look at the small numbers on the woodcut: they appear to be the same as the ones on p. 199 but divided by 20!) The description tells where all the commas and dieses are, but more important is where the harmonic fifths and third ...
... We'll write this scale on the board with both ratios and large numbers. (Look at the small numbers on the woodcut: they appear to be the same as the ones on p. 199 but divided by 20!) The description tells where all the commas and dieses are, but more important is where the harmonic fifths and third ...
Lecture 14a: Additional Remarks on Tuning Systems In previous
... taking the 7th harmonic transposed down two octaves. The “major 7th chord”, which uses the root, plus a major third, fifth, and minor 7th above the root, is extremely common in classical harmony. In section 6.1 several examples of 7-limit system are given, together with an 11-limit system (dividing ...
... taking the 7th harmonic transposed down two octaves. The “major 7th chord”, which uses the root, plus a major third, fifth, and minor 7th above the root, is extremely common in classical harmony. In section 6.1 several examples of 7-limit system are given, together with an 11-limit system (dividing ...
Music 170 Homework problem set 6 (due Nov. 3) 1. Two pipes, both
... 1. Two pipes, both open at both ends, are tuned a perfect minor third apart. If the lower pitched one is 1/2 meter long, how long must the other (higher pitched) one be? 2. Three alpenhorns are tuned so that the second one is a perfect fifth above the first, and the third one is a perfect fifth abov ...
... 1. Two pipes, both open at both ends, are tuned a perfect minor third apart. If the lower pitched one is 1/2 meter long, how long must the other (higher pitched) one be? 2. Three alpenhorns are tuned so that the second one is a perfect fifth above the first, and the third one is a perfect fifth abov ...
MSP_lecture10
... Transitional attempt to create a transposable scale based on simple integer ratios ...
... Transitional attempt to create a transposable scale based on simple integer ratios ...
Music Theory 171 Questions on Chapters 3A, 3B and 3C 3A
... 2. What does this say about the relationship between the fifth, the fourth and the octave? 3. What is created between the fifth and the fourth, and what is its ratio? 4. The notes of the major, minor, Phrygian and Middle Eastern tetrachords and listed on this page. Transpose them to the key of D and ...
... 2. What does this say about the relationship between the fifth, the fourth and the octave? 3. What is created between the fifth and the fourth, and what is its ratio? 4. The notes of the major, minor, Phrygian and Middle Eastern tetrachords and listed on this page. Transpose them to the key of D and ...
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.