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 ...

Pythagoras to Secor - Joint Mathematics Meetings

... arises as a consequence of the unique factorization property of integers, applied to the pitches of musical notes. In this talk, we briefly review historically significant temperaments such as Pythagorean tuning and 12-tone equal temperament. We then introduce George Secor’s ”miracle temperament.” D ...

... arises as a consequence of the unique factorization property of integers, applied to the pitches of musical notes. In this talk, we briefly review historically significant temperaments such as Pythagorean tuning and 12-tone equal temperament. We then introduce George Secor’s ”miracle temperament.” D ...

INTONATION FOR WINDS

... The major 3rd has pitch in a ratio of 5:4. The major 3rd of A is C# and should have a pitch of 550Hz. But the tuner will indicate that 554.4Hz is “correct”, which is very far from what will sound good. You will need to play much lower to be in tune. The minor 3rd corresponds to a ratio of 6:5. T ...

... The major 3rd has pitch in a ratio of 5:4. The major 3rd of A is C# and should have a pitch of 550Hz. But the tuner will indicate that 554.4Hz is “correct”, which is very far from what will sound good. You will need to play much lower to be in tune. The minor 3rd corresponds to a ratio of 6:5. T ...

presentation source

... 1. Use just major third, divided into two equal intervals 2. This defines a wholetone interval - how many cents? (answer: 193.2 cents) ...

... 1. Use just major third, divided into two equal intervals 2. This defines a wholetone interval - how many cents? (answer: 193.2 cents) ...

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 ...

Slides - UMD Physics

... Nothing too good, nothing too bad … Fifths: r7 = 1.498 instead of 3/2=1.5 Fourths: r5 = 1.3348 instead of 4/3=1.3333 ...

... Nothing too good, nothing too bad … Fifths: r7 = 1.498 instead of 3/2=1.5 Fourths: r5 = 1.3348 instead of 4/3=1.3333 ...

Music 170 Homework problem set 6 (due Nov. 3) 1. Two pipes, both

... 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 above the second one. If the first one sounds at 100 Hz, at what frequency does the third, hig ...

... 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 above the second one. If the first one sounds at 100 Hz, at what frequency does the third, hig ...

Tuning and Temperament

... Tuning the Overall Pitch It is an obvious necessity that, when more than one instrument is to be played simultaneously, the players must adjust their instruments to the same basic pitch. This is the “tuning up” process that we all do very frequently. “Tuning up” is usually done with reference to a s ...

... Tuning the Overall Pitch It is an obvious necessity that, when more than one instrument is to be played simultaneously, the players must adjust their instruments to the same basic pitch. This is the “tuning up” process that we all do very frequently. “Tuning up” is usually done with reference to a s ...

Ask Hohner`s Harmonica Tech

... This applies to double reed models such as Tremolo and Octave tuned as well as to single reed models such as the Marine Band type. These harmonicas were originally designed to play melody notes along with chord accompaniment. This is called “Richter Tuning,” attributed to Mr. Richter who established ...

... This applies to double reed models such as Tremolo and Octave tuned as well as to single reed models such as the Marine Band type. These harmonicas were originally designed to play melody notes along with chord accompaniment. This is called “Richter Tuning,” attributed to Mr. Richter who established ...

Musical Interval and Ratio

... related to my works. Different types of Interval is used in Western countries. In Indian music each artiste has their different reference note (Sa) therefore it is very difficult to compare any two raga of different artistes with reference to frequency so I took ratio of each swar with reference not ...

... related to my works. Different types of Interval is used in Western countries. In Indian music each artiste has their different reference note (Sa) therefore it is very difficult to compare any two raga of different artistes with reference to frequency so I took ratio of each swar with reference not ...

Hearing Math and Seeing Music: a Workshop on Pitch Perception

... variety of tuning systems, or temperaments. Early temperaments tended to favor certain keys. For example, the quarter-comma meantone tuning system, popular in 16th and 17th century Europe, compromises by slightly flattening most fifths in order to make thirds more harmonious. The intervals used in t ...

... variety of tuning systems, or temperaments. Early temperaments tended to favor certain keys. For example, the quarter-comma meantone tuning system, popular in 16th and 17th century Europe, compromises by slightly flattening most fifths in order to make thirds more harmonious. The intervals used in t ...

The Pythagorean Comma The Spiral of Fifths and Equal Temperament

... Counting up by seven octaves (ratios of 2/1) from C 32.7 Hz winds up at C 4185.6 Hz but counting up by twelve fifths (ratios of 3/2) yields C 4242.7 Hz. This discrepancy is known as the Pythagorean Comma and has been a powerful challenge for instrument makers and tuners. Fixed note instruments like ...

... Counting up by seven octaves (ratios of 2/1) from C 32.7 Hz winds up at C 4185.6 Hz but counting up by twelve fifths (ratios of 3/2) yields C 4242.7 Hz. This discrepancy is known as the Pythagorean Comma and has been a powerful challenge for instrument makers and tuners. Fixed note instruments like ...

“Tuning and temperament” by Rudolph Rasch Know who and where

... What can be described by root extraction? Note: We use “tuning” to mean “setting the pitches of an instrument,” no matter what system we use to tune the instrument. In technical terminology, “tuning” can mean only one system (or set of systems) for setting pitches. “Temperament” is a different syste ...

... What can be described by root extraction? Note: We use “tuning” to mean “setting the pitches of an instrument,” no matter what system we use to tune the instrument. In technical terminology, “tuning” can mean only one system (or set of systems) for setting pitches. “Temperament” is a different syste ...

BG Vocab

... frets. 6. Octave: Range between one note and the same note repeated either lower or higher. (From the root “oct-” meaning “eight” because there are eight natural notes in an octave.) 7. Scale: an arrangement of notes in a system of ascending or descending pitch, usually within an octave 8. Chromatic ...

... frets. 6. Octave: Range between one note and the same note repeated either lower or higher. (From the root “oct-” meaning “eight” because there are eight natural notes in an octave.) 7. Scale: an arrangement of notes in a system of ascending or descending pitch, usually within an octave 8. Chromatic ...

cents

... A major diatonic scale has (the 8th would be an The intervals are not all semitones some are whole tone is about a factor of (1.06)2 = 1.12 ...

... A major diatonic scale has (the 8th would be an The intervals are not all semitones some are whole tone is about a factor of (1.06)2 = 1.12 ...

Chapter 15 - SFA Physics and Astronomy

... As the speed increases discrepancies in pitch are more difficult to detect. The sound level is greater at the player’s ear than the audience. He can make small adjustments. He is always better tuned than the audience demands. ...

... As the speed increases discrepancies in pitch are more difficult to detect. The sound level is greater at the player’s ear than the audience. He can make small adjustments. He is always better tuned than the audience demands. ...

`frequency`. - Programma LLP

... It is actually very hard to define the feeling of consonance and dissonance, and Maths surely helps with it. Ever wonder why some note combinations sound pleasing to our ears, while others make us cringe? To understand the answer to this question, you’ll first need to understand the wave patterns cr ...

... It is actually very hard to define the feeling of consonance and dissonance, and Maths surely helps with it. Ever wonder why some note combinations sound pleasing to our ears, while others make us cringe? To understand the answer to this question, you’ll first need to understand the wave patterns cr ...

The Birth of - Early Music America

... the second century, Clement of Alexandria would gather music’s proportions into the Christian fold by proclaiming that Christ himself had decreed them. Yet another “divine” ratio gained prominence in the 13th century. This was the pure third, beloved particularly by the Renaissance-era English, and ...

... the second century, Clement of Alexandria would gather music’s proportions into the Christian fold by proclaiming that Christ himself had decreed them. Yet another “divine” ratio gained prominence in the 13th century. This was the pure third, beloved particularly by the Renaissance-era English, and ...

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 ...

CHAPTER 1 TONAL MODULATION WITH JUST

... (rounded off to the nearest tenth of a cent in the case of the Monophonic intervals) are used for both equal tempered intervals and Monophonic intervals as a unit of comparison.6 In the column for “Cents Deviation” the difference between the two versions is calculated. From this, one can see that th ...

... (rounded off to the nearest tenth of a cent in the case of the Monophonic intervals) are used for both equal tempered intervals and Monophonic intervals as a unit of comparison.6 In the column for “Cents Deviation” the difference between the two versions is calculated. From this, one can see that th ...

PHYSICAL THEORY OF MUSIC

... We confirmed that the length of a string or a pipe is inversely proportional to the frequency of the sound that is produced when subjected to oscillation. Two sounds are in harmony when they have many common harmonics. We achieve total synchronization when the frequency of one sound is the integral ...

... We confirmed that the length of a string or a pipe is inversely proportional to the frequency of the sound that is produced when subjected to oscillation. Two sounds are in harmony when they have many common harmonics. We achieve total synchronization when the frequency of one sound is the integral ...

Document

... Siegel, J. A., & Siegel, W. (1977). Absolute identification of notes and intervals by musicians. Perception & Psychophysics, 21 (2), 143-152. ...

... Siegel, J. A., & Siegel, W. (1977). Absolute identification of notes and intervals by musicians. Perception & Psychophysics, 21 (2), 143-152. ...

Lecture Set 07

... The lengths corresponding to intervals that sounded good were found to have ratios expressible as small integers. How perfect! God-like! MUST be true. The process can be continued to define additional intervals. ...

... The lengths corresponding to intervals that sounded good were found to have ratios expressible as small integers. How perfect! God-like! MUST be true. The process can be continued to define additional intervals. ...

Maths and music - Project Jugaad

... between one note and another are what allow you to determine the interval, and what 'quality,' it has, i.e. major, minor, diminished, augmented. Learning intervals is simply counting and memorizing, not anywhere near a 'math function.‘ For acoustics, the physics of sound, a much greater degree of ma ...

... between one note and another are what allow you to determine the interval, and what 'quality,' it has, i.e. major, minor, diminished, augmented. Learning intervals is simply counting and memorizing, not anywhere near a 'math function.‘ For acoustics, the physics of sound, a much greater degree of ma ...

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.