Published on January 16, 2008
Harmonic Analysis with CoolEdit2000: Harmonic Analysis with CoolEdit2000 Phys 332W Lab 3 Sept 14, 2006 Slide2: Goals: To familiarize yourself with the tools of harmonic analysis in CoolEdit2000. To analyse the harmonic structure of several tones and noise from real sound sources. Equipment Musical instrument: Voice, Recorder, Guitar, Keyboard, CD recording, Computer with CoolEdit Initialization Launch CoolEdit From the Options menu, select Monitor Record Level From the Options menu, select Windows Mixer From the View menu, select Show CD Player Slide3: CoolEdit Initialization, cont’d In Windows Mixer, select source for recording In Volume Control, select Options, Properties, Recording Select your sound source: Microphone Line-in (keyboard, etc) CD Recorder Cool Edit: Cool Edit The next few pages show some concepts of cool edit, and how to interpret the frequency spectrum. Use these for reference, we will skip to the procedures slide. Recording: Recording Record several seconds of music. Use sample rate=44100 Mono or Stereo, 16 bit Select a single note, and highlight it with the cursor. In the Analyze menu, select Frequency Analysis. Select FFT size 32768, Blackman-Harris, and hit Scan Use the cursor in Frequency window to get exact frequencies and amplitudes (dB) of major intensity maxima Find the peak frequencies by matching the db reading in the cursor window with the value on the vertical axis. Slide6: Here are sample frequency data from the downbeat of the second movement of the J.S. Bach 1st Violin Concerto If you open the exel file, on Sheet-1 you can see the excel formula for computing the trendline (straight-line fit). The magenta points are 10 times the difference between the data and trendline (simple integer multiples of fundamental. Slide7: J.S. Bach 1st Violin Concerto, 1st Movement Slide8: Here are sample frequency data from the downbeat of the first movement of the J.S. Bach 1st Violin Concerto This is the same exel file. On Sheet-2 you can see the excel formula for computing the trendline (straight-line fit). Notice that is is a chord, the first few harmonics are not multiples 1,2,3 of the funadamental but 5/4, 3/2, 4/2, 5/2 multiples. The magenta points are 10 times the difference between the data and trendline Procedures: Procedures Open two different pre-recorded sound files (Recorder, Pan Pipes, Selmer Clarinet, Piano+Organ) from the directory Phys332/Lab14Sept2006. Time Domain: Expand the horizontal scale of a fragment of the wave until you see about 10 full oscillations of the wave. Make a sketch of 1-2 oscillations. Measure the period T of oscillation (time for the wave pattern to repeat itself). Make sure you include units (seconds). Record this value on paper or in a spreadsheet. Calculate the fundamental frequency f=1/T. Frequency Domain: Frequency Domain Select approximately 1 sec of the wave (if you use a recording of actual music, you may need to use a shorter interval to include only a single pitch. Select Spectrum under Analysis. Each time you make a change, click “scan” in Analysis window. Comment on any changes you observe in the spectra if you change the filter type (Gauss, Welsh, Blackman-Harris), or FFT size (2048-32768). Are the frequency peaks narrower or broader? Is there more or less noise? Use the cursor to find the frequencies fn of the first 5 strong harmonics. Is there a 60 Hz signal in your recording? Do not include this in your list of 5, but record the strength of 60Hz relative to your first strong harmonic. Are your harmonics (approximately) in simple integer multiples of the first harmonic? Frequency Domain Description: Frequency Domain Description Comment on any difference you observe in comparing your two different sound sources Harmonics more/less well defined. Pitch/frequency peak sharper or broader. Even,or odd Harmonics prominent. For the first two strong harmonics from each source record the intensity difference between the peak level of the harmonic, and the noise level in between the peak and the next harmonic. How do these differences compare between your two sources? Is one source more “noisy” than the other? Musical Noise & Background Noise: Musical Noise & Background Noise Use a sample of “silence” in your data file to display the frequency spectrum of the background noise. Record the intensity of the noise at the same frequencies you noted the noise levels on the previous step. Is the “musical noise” larger than the background noise? Make a sketch of the “musical noise” (the background to the harmonics, and superpose a sketch of the background noise. Record a couple seconds of noise in 224. How does it compare to the background noise of the samples? Intensity & deciBel scale (dB): Intensity & deciBel scale (dB) Intensity is measured in the dB scale. Intensity I is measured as a ratio to some reference intensity I0. A difference of 10 dB is therefore a factor of 10 change in intensity. A difference of 20 dB is a factor of 100 change in intensity Write-up: Due Tue 9/26/06: Write-up: Due Tue 9/26/06 Make a plot of your frequency values versus harmonic number. Either with ruler or excel, (or other program) draw a best straight line fit. Compute and tabulate the difference between each of your overtone frequencies, and some simple integer (or rational 5/4, 3/2,…) multiples of the fundamental. fn = (fn-nf1) Comment on how closely in tune these overtones are. How small is fn/fn ? One musical half step is a 6% change in frequency Two pitches f1 and f2 (including a phantom overtone) will beat (oscillate in amplitude) with frequency f1-f2. If (f1-f2)/(f1+f2) < 0.02 this produces tremulo If (f1-f2)/(f1+f2) > 0.02 this produces a clashing dissonant sound. A more sophisticated way of doing this is calculating residuals in excel. Answer the other questions/instructions in text.