Bridges workshop worksheet
... html&http://www.hpschd.nu/tech/tmp/mean.html. (This link goes to the quarter-comma meantone tuning page. You can find other temperaments in a drop-down menu at the bottom of that page.) ...
... html&http://www.hpschd.nu/tech/tmp/mean.html. (This link goes to the quarter-comma meantone tuning page. You can find other temperaments in a drop-down menu at the bottom of that page.) ...
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 ...
ASSESSING THE TUNING OF SUNG INDIAN CLASSICAL MUSIC
... denoted by Sa, Ri, Ga, Ma, Pa, Da and Ni 1 . Except for the tonic and the fifth, all the other swaras have two variations each, which account for 12 notes in an octave, called swarasthanas. It is a well accepted notion that a swarasthana is a region rather than a point [18]. Therefore, in Indian mus ...
... denoted by Sa, Ri, Ga, Ma, Pa, Da and Ni 1 . Except for the tonic and the fifth, all the other swaras have two variations each, which account for 12 notes in an octave, called swarasthanas. It is a well accepted notion that a swarasthana is a region rather than a point [18]. Therefore, in Indian mus ...
1 Basic Tuning for the Autoharp Introduction Setting The Foundation
... twelve half steps or chromatic semitones and seven diatonic steps in an octave interval. Chromatic - a scale having all twelve semitones in an octave, comparable to an octave of both white and black keys on piano. Diatonic - a scale having seven irregular steps in an octave, comparable to an octave ...
... twelve half steps or chromatic semitones and seven diatonic steps in an octave interval. Chromatic - a scale having all twelve semitones in an octave, comparable to an octave of both white and black keys on piano. Diatonic - a scale having seven irregular steps in an octave, comparable to an octave ...
Intervals 4
... study of music. In Western music, the concept of harmony is the result of the pitches interacting with one another. You should become fluent in identifying intervals at sight, and continue to develop your proficiency. In our musical system, the interval of an octave is divided into twelve equal 1/2 ...
... study of music. In Western music, the concept of harmony is the result of the pitches interacting with one another. You should become fluent in identifying intervals at sight, and continue to develop your proficiency. In our musical system, the interval of an octave is divided into twelve equal 1/2 ...
Aspects of mathematics and music in Ancient Greece
... produced from the ratios 2:1, 3:2 and 4:3 respectively. From a musical point of view, adding a fifth to a fourth, which requires multiplying their ratios, results in the octave, also true when expressed in mathematical terms (3/2 x 4/3 = 12/6 = 2/1). Considering the importance that the tetractys of ...
... produced from the ratios 2:1, 3:2 and 4:3 respectively. From a musical point of view, adding a fifth to a fourth, which requires multiplying their ratios, results in the octave, also true when expressed in mathematical terms (3/2 x 4/3 = 12/6 = 2/1). Considering the importance that the tetractys of ...
Introduction to Pitch Class Set Analysis
... Prime Form - A set is reduced to its prime form to allow comparison with other sets. If sets were compared in their original form, comparison would be problematic at best. This is the set's BNO represented by numbers. These numbers represent the distance in half-steps above the lowest note in the BN ...
... Prime Form - A set is reduced to its prime form to allow comparison with other sets. If sets were compared in their original form, comparison would be problematic at best. This is the set's BNO represented by numbers. These numbers represent the distance in half-steps above the lowest note in the BN ...
Program - Michael Harrison, composer and pianist
... being heard. This was necessary for keyboard and fretted instruments, however, it was not a problem with the voice or string instruments that were able to play subtly different versions of the same pitch so as to avoid the commas. In equal temperament all commas are completely obliterated by their e ...
... being heard. This was necessary for keyboard and fretted instruments, however, it was not a problem with the voice or string instruments that were able to play subtly different versions of the same pitch so as to avoid the commas. In equal temperament all commas are completely obliterated by their e ...
Musical Acoustics Interval, Scales, Tuning and Temperament
... • Ear: pitch discrimination of 0.03 semitones à 30 distinguishable pitches in one semitone. (much more than needed!). (one semitone = 1/12 of an octave) • Musicians select discrete frequencies in an array: SCALE • One of the frequencies = NOTE • Note is also a symbol in a musical staff, or refer ...
... • Ear: pitch discrimination of 0.03 semitones à 30 distinguishable pitches in one semitone. (much more than needed!). (one semitone = 1/12 of an octave) • Musicians select discrete frequencies in an array: SCALE • One of the frequencies = NOTE • Note is also a symbol in a musical staff, or refer ...
Physics of Music PHY103 Worksheet #4 Setup for fretted monochord
... Pitches are commonly measured with respect to the frequencies of the tempered scale with a concert A of 440Hz. These frequencies are listed in the table below. Tuners usually give the nearest note on the tempered scale and the difference between this not and the one you played. This difference is gi ...
... Pitches are commonly measured with respect to the frequencies of the tempered scale with a concert A of 440Hz. These frequencies are listed in the table below. Tuners usually give the nearest note on the tempered scale and the difference between this not and the one you played. This difference is gi ...
Frequency
... Here are the short answers. 1) Why did it take so long? There is such a thing as a natural pure tone scale which can only be truly enjoyed by someone playing solo on a monophonic instrument of limited range and which has no keyboard. This scale is seductively consonant and pleasant since it is based ...
... Here are the short answers. 1) Why did it take so long? There is such a thing as a natural pure tone scale which can only be truly enjoyed by someone playing solo on a monophonic instrument of limited range and which has no keyboard. This scale is seductively consonant and pleasant since it is based ...
Physics of Music
... separating the white notes indicates an interval of one tone between the white notes. The lack of a black note, such as between E and F, indicates an interval of a semitone. ...
... separating the white notes indicates an interval of one tone between the white notes. The lack of a black note, such as between E and F, indicates an interval of a semitone. ...
Investigate the mathematics behind the tuning systems of Wendy
... because the frequency ratios of their notes are closer to simple ratios than in 12tone equal temperament. However, our ears are not used to these tunings, so we might find them a bit strange when listening to The Beauty in the Beast for the ...
... because the frequency ratios of their notes are closer to simple ratios than in 12tone equal temperament. However, our ears are not used to these tunings, so we might find them a bit strange when listening to The Beauty in the Beast for the ...
The History of Musical Tuning and Temperament during the
... the idea that the sound of notes and scales have changed is a foreign concept. Over the past 2000 years, tuning and temperament has changed, from region to region, from musician to musician, and from year to year. The histories of tuning and temperament are important because to understand the music ...
... the idea that the sound of notes and scales have changed is a foreign concept. Over the past 2000 years, tuning and temperament has changed, from region to region, from musician to musician, and from year to year. The histories of tuning and temperament are important because to understand the music ...
Why are pianos out of tune?
... they're all pretty close, which is why each was successfully used for hundreds of years, but they do sound slightly different: in their usual versions, the Pythagorean system has sharp thirds, while just intonation has two bad major triads, and mean-tone has one bad fifth. See if you can hear the di ...
... they're all pretty close, which is why each was successfully used for hundreds of years, but they do sound slightly different: in their usual versions, the Pythagorean system has sharp thirds, while just intonation has two bad major triads, and mean-tone has one bad fifth. See if you can hear the di ...
Generalizing Messiaen`s Modes of Limited Transposition to a n
... The algorithm can be decomposed into 3 steps: 1. Calculating all the integer divisors of the global interval. The key requirement by Messiaen is covering such an interval through a number k > 1 of occurrences of the same pattern. This implies that each group is made of an equal (integer) number of s ...
... The algorithm can be decomposed into 3 steps: 1. Calculating all the integer divisors of the global interval. The key requirement by Messiaen is covering such an interval through a number k > 1 of occurrences of the same pattern. This implies that each group is made of an equal (integer) number of s ...
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 ...
Slightly Out of Tune: The Story of Musical Temperament
... years I have tried to lecture on topics that aren’t about the computer itself, but where the computer has played an important role. For example, last year I talked about the science of Chaos, where the computer is important in doing research. Although at first it might not seem that something as “co ...
... years I have tried to lecture on topics that aren’t about the computer itself, but where the computer has played an important role. For example, last year I talked about the science of Chaos, where the computer is important in doing research. Although at first it might not seem that something as “co ...
Scales - University of Rochester
... intervals like the major third closer to their ideal or perfect just ratios. Quarter-comma meantone is the most well known type of meantone temperament, and the term meantone temperament is often used to refer to it specifically. Uses exact 5:4s for major thirds, but flattens each of the fifths by a ...
... intervals like the major third closer to their ideal or perfect just ratios. Quarter-comma meantone is the most well known type of meantone temperament, and the term meantone temperament is often used to refer to it specifically. Uses exact 5:4s for major thirds, but flattens each of the fifths by a ...
Appendix 18 The Correlation Between Sound and Color
... centuries as a compromise between harmonic balance and ease of play. The true equal temperament scale was not available to musicians had to wait until the 1870's until the development of scientific tuning and measurement. The equal tempered scale was developed for keyboard instruments, so that they ...
... centuries as a compromise between harmonic balance and ease of play. The true equal temperament scale was not available to musicians had to wait until the 1870's until the development of scientific tuning and measurement. The equal tempered scale was developed for keyboard instruments, so that they ...
MSP_lecture3
... Usually synonymous with “Natural” or “Pythagorean” or other scales that use integer ratios to build their interval degrees ...
... Usually synonymous with “Natural” or “Pythagorean” or other scales that use integer ratios to build their interval degrees ...
Playing Melodically and Harmonically in Tune Michael Kimber One
... 4) a clear awareness of intervals 5) a comfortable and reliable technique 6) a thorough familiarity with the fingerboard 7) an artistic desire to create beautiful sounds 8) sensitivity to melodic and harmonic influences. The importance of the first seven points is commonly understood. The eighth poi ...
... 4) a clear awareness of intervals 5) a comfortable and reliable technique 6) a thorough familiarity with the fingerboard 7) an artistic desire to create beautiful sounds 8) sensitivity to melodic and harmonic influences. The importance of the first seven points is commonly understood. The eighth poi ...
Bringing some science to music
... Other combinations of tones that sound well have frequency ratios that are ratios of whole numbers (integers). It was believed olden times, that this last property makes music “perfect” and was therefore a gift from the gods, not to be screwed with. This allowed Pythagoras to create and unders ...
... Other combinations of tones that sound well have frequency ratios that are ratios of whole numbers (integers). It was believed olden times, that this last property makes music “perfect” and was therefore a gift from the gods, not to be screwed with. This allowed Pythagoras to create and unders ...
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.