Combination of tones (Road to discuss harmony) 1.Linear superposition If two driving forces are applied simultaneously, the response will be the sum of.

Slides:



Advertisements
Similar presentations
Musical Intervals & Scales Creator of instruments will need to define the tuning of that instrument Systems of tuning depend upon the intervals (or distances.
Advertisements

Why do a capella singers go flat…? The mathematics of tuning systems in music Colin
For those who have never played an instrument
MUSIC NOTES Noise Versus Music  What is the difference between noise and music?  Answer: The appearance of the waveform.  What is the difference between.
Music and Mathematics are they related?. What is Sound? Sound consists of vibrations of the air. In the air there are a large number of molecules moving.
Music Software projects New york university Adjunct Instructor Scott Burton.
Foundations of Physics
Scales & Intervals Theory I 9 th grade Ms. Wasko.
L 8-9 Musical Scales, Chords, and Intervals, The Pythagorean and Just Scales.
GROUP MEMBERS-  ZION- PROJECT LEADER  TYRESE-CHIEF RESEARCHER  MUSKAN-COMMUNICATIONS DIRECTOR  GHAZAL-DIGITAL ENGINEER.
Sound Chapter 13.
A.Diederich– International University Bremen – Sensation and Perception – Fall Frequency Analysis in the Cochlea and Auditory Nerve cont'd The Perception.
A.Diederich – International University Bremen – USC – MMM – Spring 2005 Scales Roederer, Chapter 5, pp. 171 – 181 Cook, Chapter 14, pp. 177 – 185 Cook,
A.Diederich– International University Bremen – USC – MMM – Spring 5 1 The Perception of Frequency cont'd.
Music Physics 202 Professor Lee Carkner Lecture 10.
A brief message from your TAs Tine Gulbrandsen Wahab Hanif.
Timbre (pronounced like: Tamber) pure tones are very rare a single note on a musical instrument is a superposition (i.e. several things one on top of.
The Science of Sound Chapter 8
Consonance & Scales Chris Darwin Perception of Musical Sounds: 2007.
PH 105 Dr. Cecilia Vogel Lecture 14. OUTLINE  units of pitch intervals  cents, semitones, whole tones, octaves  staves  scales  chromatic, diatonic,
A little music theory (mostly notation, names, …and temperament)
What are harmonics? Superposition of two (or more) frequencies yields a complex wave with a fundamental frequency.
The Science of Sound Chapter 8
Chapter 15 The Nature of Sound What is Sound??? Sound is a Longitudinal Wave traveling through matter.
Tuning Basics INART 50 Science of Music. Three Fundamental Facts Frequency ≠ Pitch (middle A is often 440 Hz, but not necessarily) Any pitch class can.
Review of Music Rudiments Music 1133 Pages The essence of music Music essentially has two basic components Sound - pitch, timbre, space Time - distribution.
Physics 371 March 7, 2002 Consonance /Dissonance Interval = frequency ratio Consonance and Dissonance Dissonance curve The Just Scale major triad construction.
Beats and Tuning Pitch recognition Physics of Music PHY103.
COMBINATION TONES The Science of Sound Chapter 8 MUSICAL ACOUSTICS.
Tuning and Temperament An overview. Review of Pythagorean tuning Based on string lengths Octave relationship is always 2:1 Fifth relationship is 3:2 “pure”
INTONATION: The control of overall pitch level and individual pitches in relation to other relevant pitches.
PHYS 103 lecture #11 Musical Scales. Properties of a useful scale An octave is divided into a set number of notes Agreed-upon intervals within an octave.
L 10 The Tempered Scale, Cents. The Tempered Scale.
Music Software Projects New York University Adjunct Instructor Scott Burton.
Physics 371 March 14, 2002 Scales (end) names of intervals transposition the natural scale the tempered scale meantone tuning.
AP Music Theory Mr. Jackson
Lecture Set 07 October 4, 2004 The physics of sounds from strings.
Music Software projects New york university Adjunct Instructor Scott Burton.
What’s that scale?? 1 Note Grades should be available on some computer somewhere. The numbers are based on the total number of correct answers, so 100%
Pitch, Rhythm, and Harmony Pg A musical sound has four properties: Pitch Duration Volume Timbre.
The 4 Parameters of Sound PITCH = the frequency of vibration (heard as “high” vs. “low”) DURATION = the length of time a sound lasts (heard as aspects.
Set 7 What’s that scale?? 1 Note Grades should be available on some computer somewhere. The numbers are based on the total number of correct answers,
Pitch Perception Or, what happens to the sound from the air outside your head to your brain….
The Ear As a Frequency Analyzer Reinier Plomp, 1976.
Pythagorean Scale (Pythagoras born about 580 B.C.)
A Brief Introduction to Musical Acoustics
Music Software projects New york university Adjunct Instructor Scott Burton.
Tuning and Temperament
MATHS IN MUSIC.
Harmonics & Music By Stephanie Tacit Grade 11 Physics.
COMBINATION TONES The Science of Sound Chapter 8 MUSICAL ACOUSTICS.
Musical Scales and Temperament
Pythagorean Scale (Pythagoras born about 580 B.C.)
(Road to discuss harmony)
(Road to discuss harmony)
INTRODUCTION TO MUSIC THEORY
Mean-tone temperament
Pythagorean Scale (Pythagoras born about 580 B.C.)
(Road to discuss harmony)
Physics 1200 Topic VII Tuning Theory
Pythagorean Scale (Pythagoras born about 580 B.C.)
Pythagorean Scale Most consonant intervals:
Tuning and Temperament
VI. Scales & Consonance Dr. Bill Pezzaglia
How is Music Related to Math?
Lab 7: Musical Scales The Just Scale The Tempered Scale Transposition
Why do a capella singers go flat…?
(Road to discuss harmony)
Musical Scales WHY NOT?.
Musical Intervals - Musical Scales
Presentation transcript:

Combination of tones (Road to discuss harmony) 1.Linear superposition If two driving forces are applied simultaneously, the response will be the sum of the responses to the driving forces individually. For instance: doubling the driving force doubles the response. In linear systems independent signals do not influence each other. Linear addition of two sound waves: Linear systems (examples): Loudspeakers, microphones and amplifiers should be linear to some extent. Is ear a linear system? Please review lecture 6 ( interference ) 1

2. Beats Slightly mismatched frequencies cause audible “beats” A.increase f 1 B.increase f 2 C.decrease f 1 D.decrease f 2 E.There is not enough information to choose Question: The beat frequency between tones with frequencies f 1 and f 2 is 2.0 Hz. In order to increase the beat frequency, one must __. Second-order beats are the beats between two tones whose frequencies are nearly but not quite in a simple ratio. They are also called beats between mistuned consonances. 2

f 1 = 16 Hz f 2 = 18 Hz Example 3

2a. Beats (calculations - optional) 4

3. Consonance and Dissonance Consonance - sounds that are pleasant Consonant intervals in descending order of consonance: λ 2 :λ 1 f 2 :f 1 examples # of half steps 1:1 1:1unison(C,C)0 1:22:1octave(C,C)12 2:33:2perfect fifth(C,G)or (F,C) 7 3:44:3perfect fourth(C,F)or (G,C) 5 3:55:3major six(C,A)or (Eb,C) 9 4:55:4major third(C,E)or (Ab,C) 4 5:66:5minor third(C,Eb)or (A,C) 3 5:88:5minor six(C,Ab)or (E,C) 8 5

Octave(C/C) 1 1:2 Perfect fifth (C:G) 2:3 1 Perfect fourth(C:F) 1 3:4 2:3 Octave(C’/C) 6

4. Helmholtz Theory (1877) Dissonance occurs when partials of the two tones produce beats per second The more partials of a tone coincide with the partials of another, the less chance that beats in the range will produce roughness This explains why simply frequency windows define most of the consonant intervals 7

4a. Consonance and Dissonance between two pure tones When two pure tones are sounded together, consonance or dissonance depends upon their frequency difference rather than on their frequency ratio If the frequency difference is greater than a critical band, they sound consonant If the frequency difference is less than a critical band, they sound dissonant According to Plomp and Levelt (1965) the maximum dissonance occurs at ¼ the critical bandwidth According to Kameoka and Kuriyagowa (1969) it also depends on the sound pressure level: Δf = 2.27(1 + (L p –57)/40)f ( f is the frequency of the primary tone, and L p is sound pressure level) The critical bandwidth changes depending on the octave of the two tones The higher the octave, the closer two notes could be and still be consonant 8

4b. Consonance & Dissonance between two complex tones In this case we have to consider the roughness between the fundamental notes as well as between the harmonics This is what explains why some intervals are more consonant than others In the case of the perfect fifth the two lower harmonics coincide and the two produce frequency differences within the critical bandwidth 9

5. Musical Scales and Temperament Musical scale – a succession of notes in ascending or distending order In Western music octave is divided in 12 semitones Chromatic scale - all 12 semitones Most music makes use of 7 selected notes (major or minor scales) There are many ways to construct musical scales Different scales are different ways of dividing octave (almost always) “Standard” scales: Pythagorean scale Mean-tone temperament Scale of just intonation Equal temperament Tuning – an adjustment of pitch in any instrument so that it corresponds to an accepted norm (scale) Temperament – a system of tuning in which the intervals deviate from acoustically pure (Pythagorean) intervals Intonation – the degree of accuracy with which pitches are produced 10

Scales and logarithms When we go from octave to octave up, each time we multiply frequency by 2 Examples: 1) If we go 3 octaves up, frequency is 2x2x2 = 2 3 = 8 times higher 2) If we go 7 octaves up, frequency is 2 7 = 128 times higher On keyboards and on musical staff distance between notes is changed linearly Examples: 1) If we go 3 octaves, it is 3 time as much as one octave 2) If we go 7 octaves, it is 7 time as much as one octave This means that keyboard and musical staff have logarithmic scale: distance between keys and notes is proportional to the logarithm of the frequency 11

Equal temperament (All semitones are the same) Semitone ratio: Whole tone: A440 B flat466 B494 C523 C sharp554 D587 D sharp622 E659 F698 F sharp740 G784 A flat831 A880 Octave is divided into 12 equal semitone intervals Advantage: 5 th and 4 th are reasonably good 3 d and 6 th are OK Modulation from key to key is easy (~6% up) 12