What are harmonics? Superposition of two (or more) frequencies yields a complex wave with a...
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![Page 1: What are harmonics? Superposition of two (or more) frequencies yields a complex wave with a fundamental frequency.](https://reader038.fdocuments.us/reader038/viewer/2022103005/56649d7e5503460f94a618b4/html5/thumbnails/1.jpg)
What are harmonics?
Superposition of two (or more) frequencies yields a complex wave with a fundamental frequency
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The Missing Fundamental
• Your brain so likes to track the fundamental of a set of harmonics that it will perceptually fill it in even when it is absent
missing fundamental
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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 other) of many related frequencies called harmonics
Pronounciation of “timbre”
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Timbre
• the characteristic of a particular set of harmonics is called timbre– e.g. the set of harmonics generated when a particular key is pressed
on a piano
• timbre is why we can tell the difference between the same notes played on difference instruments
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Timbre
• Although any musical “note” is a superposition of harmonics, you still hear it as a single pitch (you hear its tone height)
• The pitch that you hear is (usually) the fundamental frequency (except in the artificial case of the “missing fundamental”)
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Musical Intervals
• in music, notes are played together or in quick succession
• pairs of notes share a relationship called an interval
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Musical Intervals
• Within each pair, the higher pitch (f2) is some multiple of the lower pitch (f1):– e.g. 200 hz and 400 hz -- f2 is two times f1
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Musical Intervals
• f1= 400 f2 = 800
– (f2 = 2 x f1)…octave
• f1= 400 f2 = 600
– (f2 = 3/2 x f1)…perfect 5th
• f1= 500 f2 = 800
– (f2 = 8/5 x f1)…minor 6th
• f1= 400 f2 = 550
– (f2 = 11/8 x f1)
octave
perfect 5th
minor 6th
not quite a perfect fourth?!
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Consonance and Dissonance
• Consonance is the degree to which two tones played together sound “good”
• Dissonance is the opposite
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Consonance and Disonance
• Consonance seems to decrease with increasing complexity of the ratio of the tones
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Music is combinations of intervals played in series (with some rhythm)
• Combination of three different intervals is a chord (major or minor)
• Additional intervals modify the sound of the chord
major minor
3 notes/3 intervals
4 notes/6 intervals (dominant 7)
4 notes/6 intervals (major 7)
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Auditory Scene Analysis
• Sounds don’t happen in isolation, they happen in streams of changing frequencies
• How does the system group related auditory events into streams and keep different streams separate?
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Auditory Scene Analysis
• Solving this problem is called Auditory Scene Analysis
• One important principle is proximity –in pitch, time, or spatial location
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Auditory Scene Analysis
• Effect of proximity:
Pitc
h Do you hear this?
Pitc
h
Or this?
Slow Fast
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Auditory Scene Analysis
• Effect of proximity:
Pitc
h
Do you hear this?
Pitc
h
Or this?
closefar
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Auditory Scene Analysis
• Effect of proximity:– auditory system groups together events
that happen close together in time and frequency