Math 5 Music and Sound Homework 3 due Fri Apr 20 but best if do relevant questions after each lecture Below you may take the speed of sound to be 340 m s 1 review tuning systems a The just minor third is 6 5 However going up by this interval a certain number of times how many is supposed to give an octave Compute the actual ratio difference from the octave and express it as a fraction of a semitone b Starting from a key note of C 262 Hz compute the frequency of the Pythagorean tuned F in the C major scale Also give the frequency of this note if it were equally tempered tuned relative to this C careful I did not say A was exactly 440 Hz rather work starting at the given C 2 The spectrum of a bell1 contains the following main partials in Hz 327 535 710 1169 1751 2348 Predict and explain with reasons what strike tone apparent frequency and corresponding musical pitch you would hear Would an additional partial at 2925 strengthen or weaken this impression and why 3 When I listen to the bell sound in AD DC s Hells Bells Audio Posting by JB Cholnoky I hear a strong impression of A3 220 Hz and I think you will too2 However there is no partial at 220 Hz or anywhere very near it Please explain this you will want to our sound analysis tools 4 Compute how the Helmholtz theory of dissonance would rate the consonance or dissonance of the following intervals counting only the partials up to 2000 Hz Assume the lower note is at 300 Hz in each case as in the worksheet Here s a scoring system that s a bit more realistic than the one in class count 1 for a fully dissonant pair of partials less than 10 different and 0 5 for a marginally dissonant pair between 10 and 15 different Let s say partials closer than 15 Hz the max beat frequency don t count as dissonant at all Please state how many fully and slightly dissonant partials there are in each case a the minor 6th use just tuning with 5 8 b the perfect 4th use just tuning c the minor 2nd i e one semitone use equal tempered tuning Discuss which interval is most dissonant and which the least according to the theory 5 Compute the wavelength of a pure sinusoid signal traveling through air at the following frequencies a the musical pitch C6 a very high soprano note b 15 000 Hz upper range of hearing c 20 Hz lower range of hearing 6 Assume the human ears are about 0 2 m apart and that the head poses no obstruction to the propagation of sound Let s imagine sound waves arrive from your right i e 90 degrees to the right of straight ahead 1 I took this example by tweaking one http www hibberts co uk ears htm 2 There s also a low E3 but I find it weaker of the partials 1 from the Mears 1850 bell you can hear at a Compute the time delay between a signal arriving at the left and right ears b If the signal arriving at the left is sin 880 t compute the phase at the right ear i e the value in in right ear signal sin 880 t 7 Here are two echoes I recorded on or near campus Analyse them with audacity in order to answer the questions Hint you will want to zoom in vertically by clicking on the y axis until you can measure accurately what you want a Mystery echo A I was standing in front of a wall which gave the strongest reflection ignore the other weaker ones How far away was I b Mystery echo B I stamped my foot a few times the last one was best What arrangement of walls might be causing the echo Please compute relevant distance s 8 Imagine a musician was playing an A4 440 Hz What frequency and musical pitch would you hear in the following admittedly unlikely situations a You re on the ground while the musician is in a silent jet plane moving at 170 m s 380 mph towards you b The same except moving away from you c The musician is on the ground and you re in the plane moving at 170 m s towards the musician Bonus If the musician played actual music would the speed tempo of the music change as well as the pitch 9 Analyse the sound Moving train whistle I recorded of a train blowing its whistle while coming towards me then away from me I was at rest relative to the ground Deduce how fast the train was moving in meters per second relative to the ground Hint I recommend you convert to WAV then use the praat spectrogram with 0 2 s window and 0 1000 Hz range then measure and compare carefully one or two partials of the first vs last blasts Bonus you may notice some of the partials of the last blast are present more quietly in the first what do you think might be causing this