Course:PHYS341/2018/Calendar/Lecture 21

Phys341 Lecture 21: Summary and web references

2018.03.02

Textbook 14.9-14.11; 15.5-15.7

Combination tones

Perception of pitch
- Frequently, but far from always, perceived pitch is determined:
  - By the lowest note of a chord
  - By the fundamental of a harmonic series
- There are significant exceptions.
  - Missing fundamental
  - Significantly inharmonic partials
  - Missing fundamental
Missing fundamental
- Can show this by opening two browser windows with
- http://www.szynalski.com/tone-generator/
- Play two tones a fifth apart, e.g. A4 and E5 (upper violin strings)
- (you may have to “correct” the equal temperament E5 from 659.255 Hz to 660 Hz)
- At same level: pitch usually perceived to be A3
- works even if tones fed into different ears
Implication for string instruments
- Many string instruments only weakly radiate the fundamental frequency of their lowest string.
- This doesn’t matter because we would hear it even if it was completely absent.
- In most cases the instrument will strongly radiate the second harmonic partial (an octave above).
- A note on Chromatic tuners
  - Electronic or chromatic tuners show how much a note deviates from 12-TET
  - The deviation is measured in cents ¢
  - 1 ¢ equals 1/100 of a semitone
  - 1200 ¢ equals one octave
  - Tuners will account for the missing fundamental:
  - e.g. play a violin A4 (440 Hz) and E5 (660 Hz) together (the upper two strings) and a tuner will show a pitch of A3 (220 Hz)
  - Because tuners work on 12-TET, they will mis-tune a violin E string to 659.255 Hz, whereas tuning by playing A and E together and listening to beats will give a “perfect” 660 Hz.
Interesting chords
- Dominant seventh https://en.wikipedia.org/wiki/Dominant_seventh_chord
  - “Corrected” to ratio 4:5:6:7
  - Top note flattened 31 cents
  - “Barber’s Shop Chord” (no beats)
- Tristan chord http://www.roh.org.uk/news/tristan-und-isolde-musical-highlight-the-tristan-chord
Auditory illusions
- Shepard tones https://en.wikipedia.org/wiki/Shepard_tone
- Tritone paradox https://en.wikipedia.org/wiki/Tritone_paradox