1. PH 105 Dr. Cecilia Vogel Lecture 13

2. OUTLINE  Timbre and graphs:  Time graph  Spectrum graph  Spectrogram  Envelope  scales  units  interval factors

3. Fourier Analysis  Fourier Synthesis meant from the spectrum, build the  Fourier Analysis means  from the waveform, find the  Let’s let the computer do it.  This yields a spectrum graph  or ____ graph  Amplitude vs

4. Pitch and Timbre —Graphs  Dominant influences on pitch and timbre: DEMOPitchTimbre time graph (p vs t) find period, f 1 =1/T waveform spectrum graph (A vs f) find f 1 * spectrum *f 1 might be lowest freq, but might not *Often overtones are nf 1.

5. Envelope  Envelope is the time variation of the sound  Often divided into:  attack = initial building up of sound  decay = decrease to sustained level  or to zero, if the sound is not sustained  sustain = sound held fairly steady  release = final decrease of sound to zero A D S R

6. ADSR  Attack, decay, and release  Are usually described by the time they last  Sustain  is usually described by the level (amplitude)  But all four may have their own  frequency, spectrum, amplitude, and duration

7. Spectrograms  time graphs  show time variation (x-axis is time)  spectrum graphs  show frequencies in spectrum (x-axis is frequency)  Spectrograms  show both  x-axis is time  y-axis is frequency  Amplitude is shown by heaviness of graphing

8. Bird Song Spectrograms  Top one (a)  three trills  many freq’s — noise- like  Bottom one (b)  first a low tone with many harmonics  rises and falls slightly  then higher, purer tone  falls slightly  finally lower, more noise-like tone

9. Octave  If two pitches  the frequency of one is  fundamental similarity in  often leads to  Octaves are further divided  into cents, semitones, whole tones

10. Logarithmic Frequency Measures UnitFactorEquivalent cents 1.000578 semitones 1.0595100 cents whole tones 1.12252 semitones 200 cents octaves 212 semitones 1200 cents

11. Cents  One cent interval has a ratio of 1.0006  1 cent above 440Hz is  Can you tell the difference between 440 Hz and 440.25 Hz?  a jnd is a ratio of 1.005  about 8-9 cents  10 cent above 440Hz is  Can you tell the difference between 440 Hz and 442.55 Hz? (10 cents)

12. Cents Calculation  Interval, I, in cents is related to the  Example, an octave has a ratio of

13. Semitone  An octave is often  each semitone is a factor of  multiply 440 Hz (an A) by  you’ll get about 880 Hz  Keys on a piano are separated by  12 semitones in order is a

14. Musical Staff  Musical notes are  the x-axis is  the y-axis is  Fig 8.9  Only the notes in spaces are written in.  Notes on lines are letters between.  Short lines indicate where sharp/flat would be, graphically.

15. Major Diatonic Scale  Western music uses a ____________ instead.  A major diatonic scale has  (the 8 th would be an  The intervals are not all semitones  some are  whole tone is about a factor of (1.06) 2 = 1.12  The intervals in major diatonic scale are   Start with any key on the keyboard.  You’ve played a major diatonic scale.

16. Example  Key of C (major diatonic scale)  play  CDEFGAB  C to D is a  C # /D b is between  similarly with  E to F is a 

17. Scale on Piano  one octave on keyboard  ignore the gray for now

18. Summary  Envelope — ADSR  equal pitch intervals are equal frequency factors  jnd, cents, semitone, whole tone, octaves  Scales  chromatic, 12 notes, 1 semitone apart  major diatonic, 7 notes, whole and semitone intervals  Staff