How Miraculous Things Happen
|
|
- Piers Morton
- 6 years ago
- Views:
Transcription
1 for keyboard sampler and soundfile by Kyle Gann 997
2 Kyle Gann More than a year before I wrote this piece my then elevenyearold son Bernard began to insist repeatedly that I write a piece called. I don't know where he got the idea. I began my fourth Tuning Study without a title and finally realized that Bernard's title had an intriguing relationship to what I was writing; enough so to try out the title and see where it led the piece. I was dealing after all with the transformation of disappointment into triumph or on a more literal level the gradual transformation of minor into major along a series of microtonal steps. The piece is dedicated naturally to Bernard. The scale employed contains 24 pitches per octave in an elevenlimit justintonation system two of those pitches appearing only in the final measures. Although there are 24 pitches this is not at all a quartertone scale; some pitches are crammed close together others approximate the regular chromatic scale. The scale given in Ben Johnston's notation) is as follows Pitch A A^ A B B BL C7 C C^ C CL D7 Ratio Cents D DL E E F7 E F FL G G GL A In Johnston's notation raises a pitch by 0 lowers it by 0 raises it by lowers it by 6 L raises it by 6 ^ raises it by 2 and FAC CEG and GBD are all perfectly tuned 46 major triads. The basic line was a series of ratios leading from B 09) to D 4). The tuning results from the pitches from B up to C and from D down to C accompanied by the chords most relevant to the key of A needed to support them and make their harmonic function clear the root of each chord is given in boldface)
3 Cents Melody B B BL C7 C C^ C CL D7 D Hamonies G G A A A B A BL B A D E FL F7 E G F FL G F D7 DL D D E For instance the C C7) that is the seventh of the subdominant chord is different from the C that is the third of the tonic minor and the B that is the fifth of the dominant chord is different from the B BL) that is the tonic of the chord in which A is the seventh; these differences purely theoretical in most contexts here become quite audible. The effect I find is that the pitches are so well supported by pure harmonies that people often fail to be disturbed by the slight pitch shifts. Some musicians don't even register that I'm using more than 2 pitches to the octave because the harmonies sound so pure simple and familiar. opens in A minor and keeps trying to move from B through C up to C to become A major; but every time it reaches C the bass shifts to create F minor. At the end of the work A moves up through A^ to A for a close in F major. The piece succeeds in moving to a major key but not the key it was originally aiming for. That's how it seemed to me miraculous things happen. Kyle Gann
4 To Bernard Kyle Gann 997 Flute q = 00!! & ')) ) ' '))!! & ' ' )) )) ' ) ' ' )) )) Organ)!! & ')) ') '))!! & &. ) ) 0 0 ). Piano!! & & & 0) & Bass Guitar!! ) ) ) 0) 0 ) 0 ) Copyright Monroe Street Music ) 0 ) 0
5 2 2. ' ' ')) 0) ) ) ') ') ' ' ' )) )) ' ) ') ' ')) ') 0 0 ). ) 0 ). ) ) ) ) Pno. ' 0) & ). 2 ) Bass Guit. ) 0 ) ) ) 0 ) 0 ) 0 )
6 ' ) ) ') ' )) ) ' 9 ' ' )) 0 )) ' ' )) )) ' ) ' ') 0) ')) ') 0). 0) ) 2) ) ) 0 2 Pno. 0 ) ) ). 0) & & Bass Guit. ) ) ) 0 0) 0 ) 0 ) 0 )
7 4 ' ') ) )!! 4 ) )!! ' ' ' ) 0 )) 4 0 ) ' ') 0)!! 4 0) )!! ' 0) 2. Pno.!! 2 & ') ) Bass Guit. ) ) )!! 0 0) ) ) ) 0)
8 6 ')) ') 0) ) ') 0 ' ' )) )) ' ) ' ' ) 0 )) ')) ') ' ') 0) 0 0) 2. ) ) ) Pno. 0) 0 & & 0) ' 0 & Bass Guit. 0 ) 0 ) 0 ) ) ) ) 0 0)
9 6 20!! ') 0) ) ) )!! ') 0) )!! 4 0!! ) ) ) 4 0 )!! 4 0)!! ) ) 4 0)!!!! ) ) ') ) 2 Pno.!! ' ) ) &!! 0 ) ) ). 2 Bass Guit.!!!! ) ) ) 0) ) ) ) ) ) 0)
10 ')) ) ' ' ') ) ) 2 7 ' ' )) )) ' ) ' ' ' ) 0 )) ')) ') ' ') 0) 0). ) ) ) 0 ) ) ) Pno. & & & & Bass Guit. 0 ) 0 ) 0 ) ) ) ) 0 0)
11 27!! 4 0 ) ) )!! 4 ) )!! 4 0!! ) ) ) 4 0 )!! 4 0)!! ) ) 4 0)!!. ) ) ) )!! 0) ) Pno.!! & &!! 0 ) ) ) ) Bass Guit.!! )!! ) ) 0) ) ) ) ) ) 0)
12 0 ) ) ') ' )! ) 0) ) 9! ) ) 4 ) ' )! ) 4) '!. 0 ) ' 2. ) ) Pno. &! 0) ) ) & & Bass Guit.! ) ) ) 0) 0) ) ) ) )
13 0! ') ' ) ) 0) ) 0 )! 4 ) ' '! 4) ' '!. ) & 2. ) ) ) 0 Pno.! ) ) 2 ' & & Bass Guit.! ) 0) 0) ) ) ) ) ) )
14 6! ') ' 2. ) 0) ) 0 ) ) )! 4 ) ' ' ) ) ) )! 4) ' ' ) )!. ) & & 2 ) ). Pno.! ) ' & & & Bass Guit.! ) 0) 0) ) ) ) ) ) ) ) )
15 2 40! ') ' ) ) 0) ) 0 )! 4 ) ' '! 4) ' '!. & 2 ) ) 0 Pno.! ) & 0 & & Bass Guit.! ) 0) 0) ) ) ) ) ) )
16 7 ) ) )7 ) ' 4 ')) ) ) ) ) ) ) ' ' '' )) ) ) ) ) ) ) ' ')) )). ). ) ) Pno. & & & 2 Bass Guit. ) ) ) ) ) ) ) 0) ) )
17 4 47!! 4 2. ) ' )) 7 ) ) 7 ) )!! ' )) ' '' )) )7 ) )7 )!! ' )) )) ' ' )) 7 ) ) 7 ) )!! & & Pno.!! & 2 0) ) ) Bass Guit.!! ) ) ) 0) ) ) ) ) 0) ) )
18 0! ' ')) & q = 70 Pno.! & 2)! &! 4 )! 4) & &!. ) & &! ). ) 0) &! Bass Guit.! ) ) ) ) ) 0) ) ) ' 2! 60) )! 0)) 60) )!!
19 6 0 )! 60) ) ) ) )! 2 ) 2). 0)! ) ) ) )! 2 ) 2).)! ) ) ) ) ) ) ) ) 0 )! 6 0 ) ) ) ) )! 0) 0) ) ) ) )!
20 7 6! 0) ) ) )!!9 0 ) 6 0 ) ) ) ) ) 0) 0)! 0) ) ) ) ) )!!9 )!9 ) 0) ) )!9 ) ) ) )! 6 ) 2)! 0) ) ) ) ) ) ) ) 6 )! 0) 60) ) ) ) ) 0)! 0) ) ) ) ) )! ) ) ) ) )
21 69!9 0)!9! 0) ) ) ) 0) 60) )!9 ) ) ) ) )!9 ) )! ) 0) ) ) ) 0) ) ) )! 0) )!! 7 ) )!9 ) 0) )!9! ) ) 0) ) ) ) 0) ) ) )!9! ) ) ) ) ) )!9! ) )! ) 0) )!9 & & &! 0) )
22 9! 77! 0) ) ) ) 0)! 6 0 ) ) ) ) ) 0 0)! 0) ) ) ) )!! 0 0) ) 0)!9 0) ) ) ) ) ) ) 0)!9! 0) ) ) ) 0) ) 0 0!9! ) ) ) ) )!9!!9 ) )! ) 0) )! 0) ) ) 0) ) 0 )
23 20! 0 ) ) ) ' 0 0 ) ) ' 0 0 ) ) ' 0 0 ) ) ' 0) 9 ) ) ) ' 0 ) ) ) ) ' ' 0 ) ) ) ) ' 0 ) ) ) ' 0) )
24 2! 9 ' 0 ) ) ' 0 ) ) ) 0) 0 ) ) 96 ' 0) )!; 9 ) 0)) 0 ) )!; 9 ' ) ) '!;!; 9 9 ) )!; ' 0 9 )
25 ) 9 ) ) 0) 9 0) ) ) 0) 0) 9 ) ) 0) 9! ' ) ' ) ) ) ) 9 ) )!! < ) ) ) ) ) 9 ) )! ) ) ) ) 9!! ) ) 0) ) 9!! 9!! ) ) ) 0) )! 0 ) ) ) )
26 2 ) ) ) ) ) = ) ) 0) ) ) ) 0 ) ) ) ) 0) ) ) 0 ) ) 6 0)) 6 ) ) 0 ) )
27 24!! ) ) 0 ) 7 ) ) )7 )!! ' ) 7 0 ) ) 7 ) ) )!! ' ) 0) 7 ) ) 7 ) )!!. &!! &!! ' ) 0) ) )
28 2 )!! ) ) ) ) = < 7 ) ) )7 ) 0 = )!! ' ) ) ) 0 =)!! ' ) ) )!! & &!! 0!! ) ) ' ) ) )
29 26 22 < < ) )7 ) )7 ) < ) ) < ' 7 ) ) 7 ) ) ' 7 ' ) 7 ) ) ) ' 2 <.). 2 = 2 =. ' ' ) )
30 2. < )7 ) )7 )!9 < ) ) ) ) ) 27 < < 7 ) ) 7 ) ) 6 7 ) ) 7 ) ) 6 <!9 0) ) ) ) ) )!9 0) ) )!9 6!9 ) )!9 < 0) ) )
31 2 0 ) ) ) ' ) ) ) ) ) ) ' ) ) ) ) ) ' ) ) & ) ) ) ' ) )
32 29 4!! < 0!! ) ) <!! < '!! ) ) <!! '!! ) )!!!!!! 2 2 ) 2!!!!!! < ' ) ) <
33 0 7!! < < < )!! ' ) ) ) ) ) ) )!! ' ) ) ) ) )!! 2 ) 2 & 2 ) ) ) )!! = 2) 6!! ' ) ) ) ) )
34 40 ) ) ) ) ) ) ) ) ) ). 2 ) ) ) ) 2 ) ) ) )
35 ) ) ) ) ) )) ) ) ) ) 6 ) ) ) )
36 4 ) ) ) ) ) ) ) ) ) ) 2. ) ) ) ). 2. ) ) ) )
37 4 4 Accelerate to tempo at measure 4 ) ) ) ) ) ) ) ) ) ) ) ) ) ). ) 2 ) ) ) )
38 0 ) ). ) ) ) ) ' ) ) ) ) ) ) ' ) ) ) ) & & ' ) ) ) )
39 6 2 9 ) 0 = 2 )) )) )) )) 9 ' ) < )) )) )) )) )) )) 9 ') )) )) )) )) )) 9 9 & & 9 ') < )) )) )) ))
40 4 q = 00 Tempo )!! 0 ) ) ) ) ) 0) 7!! !! Through m. 6 this line isn't a steady pulse but decelerates smoothly at a rate of.44 each note.0044 as long as its predecessor) &!! 4 0 )!! 4 0 ) )!! ) ) 0) Bass Guit.!! ) ) 0)
41 ) 2 & ' ' ) ) Bass Guit. ) )
42 9 6 ' & ' ) 0 ) ' ) 0 ) ) 0 0) Bass Guit. ) 0 0)
43 40 7 & 22 ' ' ' ' Bass Guit. ) ) ) ) ) ) ) )
44 4 9 0) 2 ) ) 6 6 & 4 ' ) 0 ) ' ) 0 ) ) 0 0) Bass Guit. ) 0 0)
45 ) ) 6 2 & ' ) ' ') ' ) 0 ) ) ) Bass Guit. ) 0 ) ) )
46 4 62 ) ' ' ) 0 ) ' ' ) ) 0 ) ) Bass Guit. ) ) ) 0 0) ) ) ) 0 0)
47 44 64 ) ) 0 '. 0 ) 6 & & 4 2 ')) ') ' ' )) ') ' 0 ) 0 ) 0 ) ) ) Bass Guit. 0 ) 0 ) 0 ) ) )
48 4 67!! 0 4 0) &!! 6!! & & 9!! ' 4 0 ) 7 ) ) 7 ) ) '!! 4 0) )7 )) )7 )) Bass Guit.!! ) ) ) ) ) ) 0) ) )!! ) ) ) ) ) ) 0) ) )
49 46 70! ' ' 2!! ) )! ') '!! ) )) )! 4!! 2 & &!!! 4 4 ) 0 )! 4 )!! 4 0) Bass Guit.!!!! ) 0) 0) ) ) ) ) ) ) 0)!! ) 0) 0) ) ) ) ) ) ) 0)
50 47 72! 0 0) &! 4 4 ) ) &! 4) &! 7 ) ) 7 ) ) 4 ) 7 ) ) 7 ) ) )7 )) )7 ))! 4 ) )7 )) )7 )) Bass Guit. 7 ) ) 7 ) )! ) 0) 0) ) ) 7 ) ) 7 ) ) 7 ) ) 7 ) )! ) 0) 0) ) ) 7 ) ) 7 ) )
51 4 7! ) 0) ) 0 0 ) 6 ) ) ' )) ))! 4) 4 ) & & &! 4) & & & Pno.! 4) & & &! 4 ) & & &! & & &. )! & & & ). ). ) Bass Guit.!! ) ) 0) 0) ) ) ' 0) 0) ) ) ' 2 & & 2 & &
52 0) 6 ) ) 79 ' )) )) & 49 Pno. & & & ) 0 2 & ). ) 2 0 ' May 997 Lewisburg PA
Know your major scales
page 8 Know your major scales Major and minor scales use every note name (A B C D E F G), but start on different notes. The notes of a scale move stepwise by intervals of a tone or semitone. The pattern
More informationOn crystal growth in harmonic space James Tenney ( )
On crystal growth in harmonic space James Tenney (1993-98) It seems clear, intuitively, that a concern for harmonic coherence would lead to the use of relatively compact, connected sets of points in harmonic
More informationMusical Modulation by Symmetries. By Rob Burnham
Musical Modulation by Symmetries By Rob Burnham Intro Traditionally intervals have been conceived as ratios of frequencies. This comes from Pythagoras and his question about why consonance intervals like
More informationTHE RATIONAL NUMBERS AS INTERVALS
CHAPTER IX THE RATIONAL NUMBERS AS INTERVALS The rational numbersq are a subset of R containing Z, andwealsohave the containments Z + Q + R +.Wehavenotedthat elements of R + are in 1-1 correspondence with
More informationScott Wendholt on You and the Night and the Music
Scott Wendholt on You and the Night and the Music Transcription and Analysis by eff McGregor www.smallslive.com www.jeffmcgregormusic.com 2 Dmin w. Emin ( b 5) A Scott Wendholt on "You and the Night and
More informationNeptunian Night for three retuned, computer-driven pianos
for three retuned, comuter-driven ianos y Kyle Gann 20 Technical Secifications The 33-itch tuning of the three ianos (the same in every octave) is as follos, given first in the numer of cents aove E-flat,
More informationOn the Euler Scale and the µeuclidean Integer Relation Algorithm
1 On the Euler Scale and the µeuclidean Integer Relation Algorithm Hermann Heßling Berlin University of Applied Sciences (HTW), D 12459 Berlin, Germany The equal tempered 10 tone scale e n/10 (n = 0, ±1,
More informationIt only took one drop of strong base to dramatically raise the ph of solution A. The ph of the other solution hasn't
MITOCW buffers Here are two solutions, A and B, to which I've added universal indicator. Here's the color key. As you can see, both of these solutions are around ph 6, very slightly acidic. Now I'm going
More informationThe Role of Continued Fractions in Rediscovering a Xenharmonic Tuning
The Role of Continued Fractions in Rediscovering a Xenharmonic Tuning Jordan Schettler University of California, Santa Barbara 10/11/2012 Outline 1 Motivation 2 Physics 3 Circle of Fifths 4 Continued Fractions
More informationALGEBRA PROBLEMS FOR MAA MINI-COURSE ON GEOMETRY AND ALGEBRA IN MUSIC THEORY JOINT MATHEMATICS MEETING IN NEW ORLEANS, JANUARY 9, 2011
ALGEBRA PROBLEMS FOR MAA MINI-COURSE ON GEOMETRY AND ALGEBRA IN MUSIC THEORY JOINT MATHEMATICS MEETING IN NEW ORLEANS, JANUARY 9, 2011 THOMAS M. FIORE 1. Pitches and Pitch Classes (1.1) (Pitch Classes
More informationMITOCW big_picture_derivatives_512kb-mp4
MITOCW big_picture_derivatives_512kb-mp4 PROFESSOR: OK, hi. This is the second in my videos about the main ideas, the big picture of calculus. And this is an important one, because I want to introduce
More informationMITOCW ocw f99-lec23_300k
MITOCW ocw-18.06-f99-lec23_300k -- and lift-off on differential equations. So, this section is about how to solve a system of first order, first derivative, constant coefficient linear equations. And if
More informationMITOCW MITRES18_005S10_DiffEqnsMotion_300k_512kb-mp4
MITOCW MITRES18_005S10_DiffEqnsMotion_300k_512kb-mp4 PROFESSOR: OK, this lecture, this day, is differential equations day. I just feel even though these are not on the BC exams, that we've got everything
More informationPhysics 111. Lecture 31 (Walker: ) Wave Superposition Wave Interference Standing Waves Physics of Musical Instruments Temperature
Physics 111 Lecture 31 (Walker: 14.7-8) Wave Superposition Wave Interference Physics of Musical Instruments Temperature Superposition and Interference Waves of small amplitude traveling through the same
More informationdue to striking, rubbing, Any vibration of matter spinning, plucking, etc. Find frequency first, then calculate period.
Equilibrium Position Disturbance Period (T in sec) # sec T = # cycles Frequency (f in Hz) f = # cycles # sec Amplitude (A in cm, m or degrees [θ]) Other Harmonic Motion Basics Basic Definitions Pendulums
More informationConsonance of Complex Tones with Harmonics of Different Intensity
Open Journal of Acoustics, 04, 4, 78-89 Published Online June 04 in SciRes. http://www.scirp.org/journal/oja http://dx.doi.org/0.436/oja.04.4008 Consonance of Complex Tones with Harmonics of Different
More informationWeber Fechner s law, uncertainty, and Pythagorean system
Proc. 11th Sci. Conf., Žilina, November 17 19, 2003, section: Mathematics in Interdisciplinar context, pp. 47 50. ISBN 80-8070-122-9, EDIS, Žilina 2003 Weber Fechner s law, uncertainty, and Pythagorean
More informationChapter 17. Superposition & Standing Waves
Chapter 17 Superposition & Standing Waves Superposition & Standing Waves Superposition of Waves Standing Waves MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 2 Wave Interference MFMcGraw-PHY
More informationMITOCW watch?v=rwzg8ieoc8s
MITOCW watch?v=rwzg8ieoc8s PROFESSOR: ih bar d psi dt equal E psi where E hat is equal to p squared over 2m, the operator. That is the Schrodinger equation. The free particle Schrodinger equation-- you
More informationMath/Music: Structure and Form Fall 2011 Worksheet on Continued Fractions
Math/Music: Structure and Form Fall 20 Worksheet on Continued Fractions Playing around with π The famous mathematical constant π is irrational, with a non-repeating, non-terminating decimal expansion.
More informationMITOCW ocw f07-lec39_300k
MITOCW ocw-18-01-f07-lec39_300k The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free.
More informationFOURIER ANALYSIS. (a) Fourier Series
(a) Fourier Series FOURIER ANAYSIS (b) Fourier Transforms Useful books: 1. Advanced Mathematics for Engineers and Scientists, Schaum s Outline Series, M. R. Spiegel - The course text. We follow their notation
More informationy = log b Exponential and Logarithmic Functions LESSON THREE - Logarithmic Functions Lesson Notes Example 1 Graphing Logarithms
y = log b Eponential and Logarithmic Functions LESSON THREE - Logarithmic Functions Eample 1 Logarithmic Functions Graphing Logarithms a) Draw the graph of f() = 2 b) Draw the inverse of f(). c) Show algebraically
More informationarxiv: v1 [cs.sd] 14 Nov 2017
Optimal Tuning of Two-Dimensional Keyboards Aricca Bannerman, James Emington, Anil Venkatesh arxiv:1711.05260v1 [cs.sd] 14 Nov 2017 Abstract We give a new analysis of a tuning problem in music theory,
More information0z z. z { z { z z { { { z z s ^ ^ E E ^ E ^ { { E { { E z z ^ E. 4. A Funny Pair. 5. Skate Board Sam. 6. Half Notes Happen. 7. Catch that Note 1{ {
NOTES ON THE FIRST STRIN E F 1 1. Our First Note E z z z Open z z z Play the open E strin. z z z z s 2. Our Second Note F { { { { { { { { Play first finer on E strin. { { { x 1 3. Playin E and F 0z z z
More informationT Y H G E D I. Music Informatics. Alan Smaill. Jan Alan Smaill Music Informatics Jan /1
O Music nformatics Alan maill Jan 23 2017 Alan maill Music nformatics Jan 23 2017 1/1 oday More on Midi vs wav representation. hythmic and metrical analysis. Alan maill Music nformatics Jan 23 2017 2/1
More information6: STANDING WAVES IN STRINGS
6: STANDING WAVES IN STRINGS 1. THE STANDING WAVE APPARATUS It is difficult to get accurate results for standing waves with the spring and stopwatch (first part of the lab). In contrast, very accurate
More informationDiscrete Fourier transform (DFT)
Discrete Fourier transform (DFT) Alejandro Ribeiro January 19, 2018 Let x : [0, N 1] C be a discrete signal of duration N and having elements x(n) for n [0, N 1]. The discrete Fourier transform (DFT) of
More information25. REVISITING EXPONENTS
25. REVISITING EXPONENTS exploring expressions like ( x) 2, ( x) 3, x 2, and x 3 rewriting ( x) n for even powers n This section explores expressions like ( x) 2, ( x) 3, x 2, and x 3. The ideas have been
More informationMITOCW R11. Double Pendulum System
MITOCW R11. Double Pendulum System The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for
More informationMAT120 Supplementary Lecture Notes
MAT0 Supplementary Lecture Notes Overview of Numbers Integers: {..., 3,,, 0,,, 3,...} Rational Numbers:, 3, etc., quotients of integers a b, b 0; finite or repeating decimal expansions. Irrational Numbers:,,
More informationMITOCW watch?v=ufu6b7ohb8m
MITOCW watch?v=ufu6b7ohb8m The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To
More informationMITOCW 5. Traveling Waves without Damping
MITOCW 5. Traveling Waves without Damping The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources
More informationSolving Multi-Step Linear Equations (page 3 and 4)
Solving Multi-Step Linear Equations (page 3 and 4) Sections: Multi-step equations, "No solution" and "all x" equations Most linear equations require more than one step for their solution. For instance:
More informationChapters 11 and 12. Sound and Standing Waves
Chapters 11 and 12 Sound and Standing Waves The Nature of Sound Waves LONGITUDINAL SOUND WAVES Speaker making sound waves in a tube The Nature of Sound Waves The distance between adjacent condensations
More informationMITOCW 6. Standing Waves Part I
MITOCW 6. Standing Waves Part I The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free.
More informationPHY 103: Standing Waves and Harmonics. Segev BenZvi Department of Physics and Astronomy University of Rochester
PHY 103: Standing Waves and Harmonics Segev BenZvi Department of Physics and Astronomy University of Rochester Sounds of the Universe NASA/JPL, September 2016 2 Properties of Waves Wavelength: λ, length
More informationTHE HEXATONIC SYSTEMS UNDER NEO-RIEMANNIAN THEORY: AN EXPLORATION OF THE MATHEMATICAL ANALYSIS OF MUSIC
THE HEXATONIC SYSTEMS UNDER NEO-RIEMANNIAN THEORY: AN EXPLORATION OF THE MATHEMATICAL ANALYSIS OF MUSIC KENNETH OSHITA Abstract. Neo-Riemannian theory developed as the mathematical analysis of musical
More informationBayesian harmonic models for musical signal analysis. Simon Godsill and Manuel Davy
Bayesian harmonic models for musical signal analysis Simon Godsill and Manuel Davy June 2, 2002 Cambridge University Engineering Department and IRCCyN UMR CNRS 6597 The work of both authors was partially
More information9.1 Harmonic Motion. Motion in cycles. linear motion - motion that goes from one place to another without repeating.
9.1 Harmonic Motion A bicyclist pedaling past you on the street moves in linear motion. Linear motion gets us from one place to another (Figure 9.1A). This chapter is about another kind of motion called
More informationWaves Part 3A: Standing Waves
Waves Part 3A: Standing Waves Last modified: 24/01/2018 Contents Links Contents Superposition Standing Waves Definition Nodes Anti-Nodes Standing Waves Summary Standing Waves on a String Standing Waves
More informationSound 2: frequency analysis
COMP 546 Lecture 19 Sound 2: frequency analysis Tues. March 27, 2018 1 Speed of Sound Sound travels at about 340 m/s, or 34 cm/ ms. (This depends on temperature and other factors) 2 Wave equation Pressure
More informationUnified Music Theories for General Equal-Temperament Systems
Unified Music Theories for General Equal-Temperament Systems Brandon Tingyeh Wu Research Assistant, Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan ABSTRACT Why are
More informationUniversity of Colorado at Boulder ECEN 4/5532. Lab 2 Lab report due on February 16, 2015
University of Colorado at Boulder ECEN 4/5532 Lab 2 Lab report due on February 16, 2015 This is a MATLAB only lab, and therefore each student needs to turn in her/his own lab report and own programs. 1
More information-Electromagnetic. Waves - disturbance that propagates through space & time - usually with transfer of energy -Mechanical.
Waves Waves - disturbance that propagates through space & time - usually with transfer of energy -Mechanical requires a medium -Electromagnetic no medium required Mechanical waves: sound, water, seismic.
More informationAsCent. Composed for the Key Stage Two or Key Stage Three Classroom by. Keir C. Crawley
AsCent Composed or the Key Stage To or Key Stage Three Classroom by Keir C Craley AsCent Notes rom the Composer AsCent is the culmination o a number o ideas and experiences, irst o hich as the need to
More informationA Quantitative Study of Relationships Between Interval-width Preference and Temperament Conditions in Classically-trained Musicians Byron Pillow
A Quantitative Study of Relationships Between Interval-width Preference and Temperament Conditions in Classically-trained Musicians Byron Pillow Spring 2016 University of South Dakota National Music Museum
More informationThermodynamics Problem Set. The amount of heat necessary to raise a body one degree of temperature (K or o C) is called:
Thermodynamics Problem Set 1. 100 o C converted to both the Fahrenheit scale and the kelvin scale is which of the following? a. 238 o F, 373.15 K b. 88 o F, 273.15 K c. 238 o F, 273.15 K d. 212 o F, 373.15
More informationExercises The Origin of Sound (page 515) 26.2 Sound in Air (pages ) 26.3 Media That Transmit Sound (page 517)
Exercises 26.1 The Origin of (page 515) Match each sound source with the part that vibrates. Source Vibrating Part 1. violin a. strings 2. your voice b. reed 3. saxophone c. column of air at the mouthpiece
More informationŒ Œ Œ Œ. t bv. Œ bv. ŒŒŒŒ t. & 4 t ŒŒŒŒ bv "B FLAT" 1. Our First Note. 2. Our Second Note. 3. Three's a Crowd. 4. Four In a Row
Welcome to the wonderful world of flute playing. Your teacher has shown you how to hold your instrument and make a sound on the mouthpiece. Let's play our first song! 1. Our First Note t Œ Œ Œ "G" Œ t
More information7-6. nth Roots. Vocabulary. Geometric Sequences in Music. Lesson. Mental Math
Lesson 7-6 nth Roots Vocabular cube root n th root BIG IDEA If is the nth power of, then is an nth root of. Real numbers ma have 0, 1, or 2 real nth roots. Geometric Sequences in Music A piano tuner adjusts
More informationEuler and music. A forgotten arithmetic function by Euler
OCTOGON MATHEMATICAL MAGAZINE Vol. 17, No.1, April 009, pp 65-71 ISSN 1-5657, ISBN 978-973-8855-5-0, www.hetfalu.ro/octogon 65 Euler and music. A forgotten arithmetic function by Euler József Sándor 6
More informationClifton Callender* Clifton Callender* Continuous Transformations Continuous Transformations
Music Theory Online The Online Journal of the Society for Music Theory Table of Contents MTO Home SMT Home Join SMT Volume 10, Number 3, September 2004 Volume 10, Number 3, September 2004 Copyright 2004
More informationPHY 103 Impedance. Segev BenZvi Department of Physics and Astronomy University of Rochester
PHY 103 Impedance Segev BenZvi Department of Physics and Astronomy University of Rochester Midterm Exam Proposed date: in class, Thursday October 20 Will be largely conceptual with some basic arithmetic
More informationTHE CALCULUS OF A NEW MUSICAL SCALE FREQUENCIES
Proceedings of the International Conference on Theory and Applications of Mathematics and Informatics - ICTAMI 004, Thessaloniki, Greece THE CALCULUS OF A NEW MUSICAL SCALE FREQUENCIES by Emil Olteanu
More information1 Hz = 1 1. f = 2L. WENDY S XENHARMONIC KEYBOARD
WENDY S XENHARMONIC KEYBOARD JORDAN SCHETTLER. MOTIVATION Wendy Carlos is an American composer and one of my favorite musical pioneers. She helped to popularize and improve the Moog synthesizer with the
More informationarxiv: v3 [physics.pop-ph] 14 Nov 2015
Revising the Musical Equal Temperament Haye Hinrichsen arxiv:508.02292v3 [physics.pop-ph] 4 Nov 205 Universität Würzburg, Fakultät für Physik und Astronomie Campus Süd, Am Hubland, 97074 Würzburg, Germany
More information-Electromagnetic. Waves - disturbance that propagates through space & time - usually with transfer of energy -Mechanical.
Waves Waves - disturbance that propagates through space & time - usually with transfer of energy -Mechanical requires a medium -Electromagnetic no medium required Mechanical waves: sound, water, seismic.
More informationIntroduction Basic Audio Feature Extraction
Introduction Basic Audio Feature Extraction Vincent Koops (with slides by Meinhard Müller) Sound and Music Technology, December 6th, 2016 1 28 November 2017 Today g Main modules A. Sound and music for
More informationLecture 21: Decay of Resonances
Lecture 21: Decay of Resonances Recall that a resonance involves energy bouncing back and forth between two means of storage. In air resonances in cavities, energy is going back and forth between being
More informationThe Trumpet: Demystified Using Mathematics
Jeff Ward The Trumpet: Demystified Using Mathematics Abstract Presented, is a model of how a trumpet works, starting from the simplest tube and increasing the complexity until faced with a realistic model.
More informationEQ: How do I identify exponential growth? Bellwork:
EQ: How do I identify exponential growth? Bellwork: 1. Bethany's grandmother has been sending her money for her birthday every year since she turned 1. When she was one, her grandmother sent her $5. Every
More informationA Generalized Dual of the Tonnetz for Seventh Chords: Mathematical, Computational and Compositional Aspects
ridges 2018 onference Proceedings eneralized ual of the Tonnetz for Seventh hords: Mathematical, omputational and ompositional spects Sonia annas 1 and Moreno ndreatta 2 1 University of Pavia and University
More informationLecture 18. Waves and Sound
Lecture 18 Waves and Sound Today s Topics: Nature o Waves Periodic Waves Wave Speed The Nature o Sound Speed o Sound Sound ntensity The Doppler Eect Disturbance Wave Motion DEMO: Rope A wave is a traveling
More informationPHY-2464 Physical Basis of Music
Physical Basis of Music Presentation 21 Percussion Instruments II Adapted from Sam Matteson s Unit 3 Session 34 Sam Trickey Mar. 27, 2005 Percussion = striking Percussion instruments divide nicely into
More informationMITOCW MIT8_01F16_w02s05v06_360p
MITOCW MIT8_01F16_w02s05v06_360p One of our classic problems to analyze using Newton's second law is the motion of two blocks with a rope that's wrapped around a pulley. So imagine we have a pulley, P,
More informationbase 2 4 The EXPONENT tells you how many times to write the base as a factor. Evaluate the following expressions in standard notation.
EXPONENTIALS Exponential is a number written with an exponent. The rules for exponents make computing with very large or very small numbers easier. Students will come across exponentials in geometric sequences
More informationA MusicXML Test Suite and a Discussion of Issues in MusicXML 2.0
A MusicXML Test Suite and a Discussion of Issues in MusicXML 2.0 Reinhold Kainhofer, reinhold@kainhofer.com Vienna University of Technology, http://www.fam.tuwien.ac.at/ GNU LilyPond, http://www.lilypond.org/
More informationBut, there is always a certain amount of mystery that hangs around it. People scratch their heads and can't figure
MITOCW 18-03_L19 Today, and for the next two weeks, we are going to be studying what, for many engineers and a few scientists is the most popular method of solving any differential equation of the kind
More information6: Polynomials and Polynomial Functions
6: Polynomials and Polynomial Functions 6-1: Polynomial Functions Okay you know what a variable is A term is a product of constants and powers of variables (for example: x ; 5xy ) For now, let's restrict
More informationSolve Quadratic Equations by Using the Quadratic Formula. Return to Table of Contents
Solve Quadratic Equations by Using the Quadratic Formula Return to Table of Contents 128 Solving Quadratics At this point you have learned how to solve quadratic equations by: graphing factoring using
More informationCONTINUED FRACTIONS Lecture notes, R. M. Dudley, Math Lecture Series, January 15, 2014
CONTINUED FRACTIONS Lecture notes, R. M. Dudley, Math Lecture Series, January 5, 204. Basic definitions and facts A continued fraction is given by two sequences of numbers {b n } n 0 and {a n } n. One
More informationAnswer: 101 db. db = 10 * log( 1.16 x 10-2 W/m 2 / 1 x W/m 2 ) = 101 db
54. A machine produces a sound with an intensity of 2.9 x 10-3 W/m 2. What would be the decibel rating if four of these machines occupy the same room? Answer: 101 db Four of these machines would be four
More informationG r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice exam
G r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice exam G r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice Exam Instructions The final exam will be weighted as follows: Modules 1 6 15 20% Modules
More informationTo prepare for this lab, you should read the following sections of the text: Sections 3.4, 11.3, and 12.1 OVERVIEW
Section: Monday / Tuesday (circle one) Name: Partners: Total: /35 PHYSICS 107 LAB #4: WIND INSTRUMENTS: WAVES IN AIR Equipment: Thermometer, function generator, two banana plug wires, resonance tube with
More information1 f. result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by
result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by amplitude (how far do the bits move from their equilibrium positions? Amplitude of MEDIUM)
More informationHome About Edge Features Edge Editions Press Edge Search Subscribe
Home About Edge Features Edge Editions Press Edge Search Subscribe The Third Culture Edge 87 Printer version "Something else has happened with computers. What's happened with society is that we have created
More informationSound. Speed of Sound
Sound TUNING FORK CREATING SOUND WAVES GUITAR STRING CREATING SOUND WAVES Speed of Sound Sound travels at a speed that depends on the medium through which it propagates. The speed of sound depends: - directly
More informationVoicing Transformations and a Linear Representation of Uniform Triadic Transformations
Voicing Transformations and a Linear Representation of Uniform Triadic Transformations Thomas M. Fiore and Thomas Noll http://www-personal.umd.umich.edu/~tmfiore/ Preprint on arxiv Preview Math Results:
More informationMITOCW watch?v=rf5sefhttwo
MITOCW watch?v=rf5sefhttwo The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To
More informationLecture 14 1/38 Phys 220. Final Exam. Wednesday, August 6 th 10:30 am 12:30 pm Phys multiple choice problems (15 points each 300 total)
Lecture 14 1/38 Phys 220 Final Exam Wednesday, August 6 th 10:30 am 12:30 pm Phys 114 20 multiple choice problems (15 points each 300 total) 75% will be from Chapters 10-16 25% from Chapters 1-9 Students
More informationUNIFORM TRIADIC TRANSFORMATIONS AS VIEWED FROM GROUP THEORY
UNIFORM TRIADIC TRANSFORMATIONS AS IEWED FROM GROUP THEORY DANIEL C. MAYER Abstract. We show that finite non-abelian groups, more precisely, semidirect products and wreath products, with interesting algebraic
More informationKEY TERMS. compression rarefaction pitch Doppler effect KEY TERMS. intensity decibel resonance KEY TERMS
CHAPTER 12 SECTION 1 Sound Waves Summary The frequency of a sound wave determines its pitch. The speed of sound depends on the medium. The relative motion between the source of waves and an observer creates
More informationSuperposition and Standing Waves
Physics 1051 Lecture 9 Superposition and Standing Waves Lecture 09 - Contents 14.5 Standing Waves in Air Columns 14.6 Beats: Interference in Time 14.7 Non-sinusoidal Waves Trivia Questions 1 How many wavelengths
More informationCan You Hear Group Theory in Music?
Can You Hear Group Theory in Music? Sean O Reilly June 11th, 2015 1 Introduction 1.1 Goal The goal of this project is to use topics found in group theory, set theory, and combinatorics to systematically
More informationTwo Musical Orderings
Two Musical Orderings Marcus Pendergrass mpendergrass@hsc.edu August 9, 2012 The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.
More informationTopics in Mathematics: Mathematics and Music Section 1.1: Musical Notation and a Geometric Property January 25, 2018
Topics in Mathematics: Mathematics and Music Section.: Musical Notation and a Geometric Property January 5, 08 Duration: Geometric Sequences note head stem flag = Figure : Some basic symbols and terminology
More information3: Linear Systems. Examples. [1.] Solve. The first equation is in blue; the second is in red. Here's the graph: The solution is ( 0.8,3.4 ).
3: Linear Systems 3-1: Graphing Systems of Equations So far, you've dealt with a single equation at a time or, in the case of absolute value, one after the other. Now it's time to move to multiple equations
More informationPolynomials; Add/Subtract
Chapter 7 Polynomials Polynomials; Add/Subtract Polynomials sounds tough enough. But, if you look at it close enough you ll notice that students have worked with polynomial expressions such as 6x 2 + 5x
More informationMITOCW ocw f99-lec16_300k
MITOCW ocw-18.06-f99-lec16_300k OK. Here's lecture sixteen and if you remember I ended up the last lecture with this formula for what I called a projection matrix. And maybe I could just recap for a minute
More informationHi, I'm Jocelyn, and we're going to go over Fall 2009, Exam 1, problem number 2.
MIT OpenCourseWare http://ocw.mit.edu 3.091SC Introduction to Solid State Chemistry, Fall 2010 Transcript Exam 1 Problem 2 The following content is provided under a Creative Commons license. Your support
More informationDemo Version Requires Adobe Reader or PDF Expert to play audio. Guitar Lovers. Theory, Tunings, Exercises. edited by.
Demo Version Requires Adobe Reader or PDF Expert to play audio Guitar Lovers S t u d i e s Theory, Tunings, Exercises edited by Thomas Schilling Table Of Contents Theory Note Location 4 Modes + Scales
More informationMITOCW MITRES18_005S10_DerivOfSinXCosX_300k_512kb-mp4
MITOCW MITRES18_005S10_DerivOfSinXCosX_300k_512kb-mp4 PROFESSOR: OK, this lecture is about the slopes, the derivatives, of two of the great functions of mathematics: sine x and cosine x. Why do I say great
More informationTheory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati
Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 7 Instability in Rotor Systems Lecture - 2 Fluid-Film Bearings
More informationarxiv: v1 [physics.pop-ph] 10 Aug 2015
Revising the Musical Equal Temperament Haye Hinrichsen arxiv:508.02292v [physics.pop-ph] 0 Aug 205 Universität Würzburg, Fakultät für Physik und Astronomie Campus Süd, Am Hubland, 97074 Würzburg, Germany
More informationWhy the Kirnberger Kernel Is So Small
Why the Kirnberger Kernel Is So Small arxiv:0907.5249v1 [physics.pop-ph] 30 Jul 2009 Don N. Page Theoretical Physics Institute Department of Physics, University of Alberta Room 238 CEB, 11322 89 Avenue
More informationOscillations and Waves
Oscillations and Waves Periodic Motion Simple Harmonic Motion Connections between Uniform Circular Motion and Simple Harmonic Motion The Period of a Mass on a Spring Energy Conservation in Oscillatory
More informationChapter 15 Mechanical Waves
Chapter 15 Mechanical Waves 1 Types of Mechanical Waves This chapter and the next are about mechanical waves waves that travel within some material called a medium. Waves play an important role in how
More informationG. P. Telemann Flute and Violin Fantasias Arranged for Viola. Arranged and edited by Benjamin Whitcomb
G. P. Telemann Flute and Violin Fantasias Arranged for Viola Arranged and edited by Benjamin Whitcomb There is a fair amount that has already been written about the Telemann fantasias, and I refer you
More informationAn experimental study of acoustical properties of tubular tower bells
Proceedings of 2th International Congress on Acoustics, ICA 21 23-27 August 21, Sydney, Australia An experimental study of acoustical properties of tubular tower bells Jie Pan and Sören Bergmann School
More information