Math 5: Aural postings

Please post real-world examples of mathematical, musical, or sonic phenomena we discuss in class, either in the form of discussion, articles, links, spectrograms, pictures, or best of all sound files (either from recordings, found, or produced by yourself). If you post a sound file, please describe what it is, why we should care, what phenomena it relates to. You do not have to post every single week, but should aim for 5-7 interesting posts in total. The more you do (and more thoughtful and interesting!), the more credit. We will discuss them at the start of each Monday lecture. Happy aural hunting!

Enter your post in the window below. You must provide your name (note: "Your name" doesn't mean a description of the posting, rather your actual name). If you don't provide your name and submit the comment, the comment will disappear from the text field and you will have to type it again. To avoid frustration I suggest you compose your comment on a text editor then paste in when you're ready. Scroll down to read previous posts.

For uploading sound files there is a 2MB limit, ie about 2 minutes of MP3 or OGG format, but only 12 seconds of WAV. Therefore I recommend you use MP3 or OGG (convert using audacity). In all cases keep them short! Your uploaded files will remain on the Math Dept server. Unfortunately you cannot remove a comment or file yourself; email me if you must have something removed. We all take it for granted you won't post dumb/offensive material.

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<B>...</B>, etc for formatting purposes. I encourage you to include links like this: <a href="">check it out!</a>
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Name: Maggie Flanagan
Date: December 01, 2011 (13:26)
File uploaded: Lassie Noir.wav
Comment: Lassie Noir - Math Mystery Sound Drama Follow our canine hero in her journey to solve the mystery of the gaping hole. You can draw her surroundings using the audio clues provided. - How fast was the police car going? - How deep was the hole? - How long was the dark passage? - What was the surface area of the room full of glass? What do you think the room was made of? - What was the velocity of the elevator? - How long was the dead end passage? Enjoy!

Name: Yoo Jung Kim
Date: November 27, 2011 (13:50)
File uploaded: 135047WaterSubmerge440Hz.wav
Comment: According to Robert J. Urick in "Principles of Underwater Sound," "When the surface is smooth, water forms an almost perfect reflector of sound," but water can also "manipulate its frequency content." As a practice experiment for my final project, I downloaded a 30 second clip of 440 Hz pure frequency generated on audacity on my cell phone and encased it in a Ziploc bag before dropping into a placid bathtub with an estimated water volume of 0.1m x 1.20 m x 55 m. The sound was recorded via mac mic outside of the water. In the sound file, the phone is fully submerged at 7 seconds. After the phone is fully submerged, the slightest sound still remains, meaning that the surface of the water did not form an almost perfect reflector of sound. This could have been caused by the relative shallowness of the water, and I intend on repeating the experiment with a larger depth. An unexpected result of the experiment was that when I took the spectrum of the muffled frequency on Audacity, there were two new peaks at 123 Hz and 150 Hz, along with the expected 440 Hz. Perhaps the new tones were the result of scattering or reflective loss, both of which are concepts that will be presented in my project presentation.

Name: Chuanqi Sun
Date: November 22, 2011 (19:47)
File uploaded: flutter echo.wav
Comment: East Wheelock Flutter Echo: A Flutter Echo Zone newly discovered in front of the arc wall at the back door of East Wheelock. (My first and last aural postings are both in East Wheelock!)

Name: Yoo Jung Kim
Date: November 21, 2011 (13:04)
File uploaded: Maskingeffect.wav
Comment: Second attempt at masking Hello! I got it to work! From the previous attempt, I changed the frequencies to 500 Hz and 1000 Hz like your sample and tried to go back and forth between single and double tone. I also took Professor Barnett's advice of generating even quieter tones. In the first 15 seconds, I compared to a 500 Hz at amp 1 to bursts of 1000 Hz pure tone with amps declining by a factor of half, so: 1, 0.5, 0.125, 0.0625, 0.03175, and 0.015875. Playing the 1000 Hz tone itself, all of the amplitudes of the tone can be heard. When playing the 500 Hz and the 1000 Hz tone together, the 1000 Hz becomes barely perceptible around 0.03175, (which occurs on t=10 sec), and the 1000 Hz tone becomes imperceptible around 0.015875, which occurs on t=12sec. This validates the masking effect. For the last 15 seconds, I compared to a 1000 Hz at amp 1 to bursts of 500 Hz pure tone with amps declining by a factor of half, so, again: 1, 0.5, 0.125, 0.0625, 0.03175, and 0.015875. The two tones can be heard straight through, which again validates masking, that intense sound at low frequency "masks" a quiet sound at high frequencies.

Name: Yoo Jung Kim
Date: November 21, 2011 (09:03)
File uploaded: DisappearingTones.wav
Comment: Lacking Masking? I tried to emulate Professor Barnett's example of disappearing tones as demonstrated last frieda. Masking is when an intense sound at low frequency "masks" a quiet sound at high frequencies. In a single audio file, I try to give two such cases, with a 0.8 amplitude pure 220 Hz against a 880 Hz tone with a gradually decreasing amplitude and and then a 0.8 amplitude 880 Hz tone with against a 220 Hz tone with a gradually decreasing amplitude. All things given, the First exampled should have allowed for the 880 Hz tones to be masked, but I could still hear it through my headphones. Are there other qualities needed for masking to occur?

Name: Evan Griffith
Date: November 21, 2011 (01:02)
File uploaded:
Comment: Here is an audio file (and Praat image) of one of the choral warm-ups we sing in the Handel Society Choir which focuses on enunciating vowels. Listen to the clip, and then look at the Praat image where you can see the resulting formants!

Name: Yoo Jung Kim
Date: November 14, 2011 (21:59)
File uploaded: koreanalphabet.wav
Comment: An interesting component of the Korean alphabet is that one syllable is written as a single character that is a combination of a consonant and a vowel (and usually an "underlying" second consonant). In this .wav file, I spoke out all the simple consonants in the korean alphabet with the vowel "ah" (essentially the first simple combinatory line of the Korean alphabet), which produced varying formants. As expected, the frequency remained relatively the same, but the shape of the formant changed on the basis of the consonant.

Name: Zoë Furlong
Date: November 14, 2011 (19:52)
File uploaded: Inuit throat singing.wav
Comment: (Sorry, meant to post this last week) Since we have been learning about Tuvan throat singing, I wondered how it compared to Inuit throat singing. The two types of singing are clearly different but the fact that they are both referred to as "throat singing" made me wonder about the similarities and differences. By viewing the spectogram of Inuit throat singing, we can see that the singers don't tune their formants as precisely as the Tuvan throat singers do. In this audio sample, the first formant seems to be around the 8th harmonic.

Name: Chuanqi Sun
Date: November 14, 2011 (00:37)
File uploaded: formant.ogg
Comment: I record some aphorism and use praat and audacity to change 1)formant 2)pitch 3)both each time. To my disappointment, none of these succeed in changing the gender of the voice.

Name: David Jiang
Date: November 12, 2011 (21:57)
File uploaded: Pure tone in room.WMA
Comment: I played a pure tone at 440Hz and then walked around the room. The room is the production room at the campus radio station, so there are a lot of physical objects that could effect the sound. The room is rectangular in shape with a large L-shaped table in the middle. As I walked around the room, the volume of the tone changed. In one corner, it was particularly loud, in another particularly soft. The changes become very clear if you look at the wave form as the file plays. The frequency is clearly the same, but the amplitude varies.

Name: Katelyn Onufrey
Date: November 09, 2011 (13:37)
File uploaded: 12345.wav
Comment: In this recording, I sang "1,2,3,4,5,4,3,2,1" in notes that ascended and then descended. When you look at the formants in the spectrogram, it can be seen that they are all over the place and change because the vowel sound is changing. Then, I sang the vowel sound "aa" in the same sequence of notes and the formants were clear and steady.

Name: Michael Blum
Date: November 09, 2011 (00:28)
File uploaded: Whistling While Humming.ogg
Comment: In this posting, I recorded myself singing a note, whistling that note, and then attempting to do both at the same time. Something very strange happens when the whistling and singing are done simultaneously: many partials that were not present in either the singing or whistling appear.

Name: Yichuan Wang
Date: November 07, 2011 (21:56)
File uploaded: Oil of Clove NMR_Finished
Comment: This signal (not necessarily although still could be mechanical sound waves) is recorded by a Nuclear Magnetic Resonance machine measuring the spin of hydrogens contained in a type of organic molecule found in the oil of cloves (often used as cooking spices). The NMR machine excites the molecule at a range of frequencies and measures which frequencies cause the hydrogen nucleus to flip their spins. ppm = (observed shift downfield of Tetramethylsilane [zero reference pt] (Hz)) / (spectrometer freq (MHz)) Partials at the following frequencies (in Hz): 123, 192, 257, 287, 338, 353, 482 (the tallest), 558, 672. It sounds like hitting a hollow metal container, so I suspect that the partials would be similar to that of a bell. Tao = −8.69 / −66.26 = 0.131 s

Name: Chuanqi Sun
Date: November 04, 2011 (17:16)
File uploaded:
Comment: 2. Tibetan singing bowl I have two bowls like this at home. It is said that the bowl sounds the best when you achieve true inner piece. The bowl contains modes that have very close frequencies. You can here the beats.

Name: Chuanqi Sun
Date: November 04, 2011 (17:01)
File uploaded:
Comment: Aural + Visual Posting! 1. Non-Newtonian Fluid on a Speaker Cone I found this really interesting. It seems that the shape of the fluid is not only an art expression, but can also be modeled with mathematics.

Name: Austin Greenfield
Date: November 02, 2011 (08:09)
File uploaded: Tubehit.ogg
Comment: In this audio file, I took a tube that was used to send a poster in the mail and compared the hitting sounds when open and closed. I found that the closed-open pipe sounded about an octave lower (slightly less) than the open-open pipe. I also used the equations given in class to find that the supposed length of the open tube is .667m whereas that of the closed-open tube is .6343m. These values are only about 5% off from each other.

Name: Katelyn Onufrey
Date: November 02, 2011 (01:38)
File uploaded: with_water_-_higher_f.wav
Comment: This is the second part of my post. This part contains the sound of me blowing into the same poland spring bottle, now filled about 1/4 of the way up with water. When analyzed with Praat, I found that now the strongest partial moved to 307.9 Hz, with a fundamental frequency at about 187 Hz. The fundamental frequency before the water was the same as the strongest partial. This shows that the frequency increased when water was added. This is because the volume decreases and because volume is on the bottom half of the fraction in the formula, the frequency will increase.

Name: Katelyn Onufrey
Date: November 02, 2011 (01:34)
File uploaded: no_water_-_lower_f.wav
Comment: This posting will have two parts and I will upload the second sounds in another post. This first part contains the sound of me blowing into an empty poland spring water bottle. When analyzed with Praat, I found that the strongest partial was at 176.1 Hz.

Name: Michael Blum
Date: November 02, 2011 (00:40)
File uploaded: Clapping in front of mouth.ogg
Comment: In the uploaded file, I recorded myself clapping in front of my mouth. As I opened and closed my mouth, I changed the volume of my mouth (the 'pipe'), and the resonant frequency subsequently changed as well.

Name: Yichuan Wang
Date: October 31, 2011 (14:16)
File uploaded: My Water Bottle filled with about a quarter full of water, struck by my mechanical pencil_Finished
Comment: I filled my metal water bottle with some water, to about a quarter of the bottle’s volume. Then with a mechanical pencil, I struck the part of the bottle’s wall that’s not directly touching the water. Seeing in Praat the partials that aren’t all harmonically related, I deduce that that there are at least 11 different modes of vibration. Partials at the following frequencies (Hz): 2280, 3394 (GCF of 1132 with 2280; & 1132 would be the lowest perceived pitch by the human ear), 4786, 4902, 5552, 5877, 5993, 6248, 6504, 6597, 6736 (may be the 2f of 3394), …. Tao = 8.69 / [(87.85-47.28)/(2.05-0.88)] = 0.25 s The decay time is within reasonable expectation for a metal water bottle.

Name: Evan Griffith
Date: October 30, 2011 (20:35)
File uploaded:
Comment: Here I am playing the same note on the pipe organ with two different sounds. The first sound comes from a flue pipe. That means it is produced via vibrating air molecules (similar to the tin whistle we were shown in class). The next sound in the audio is produced by a reed pipe. Reed pipes have a metal strip which only vibrates at a certain frequency when air is blown in. In the attached audio, you can hear that the reed pipe produces a harsher sound than the flue pipe. When you look at the images attached from Praat, you can see that there are many more higher partials present in the reed sound.

Name: Zoë Furlong
Date: October 26, 2011 (18:05)
File uploaded: glass percussion.wav
Comment: I tapped a glass of wine with a pencil. The strongest partials are at 1687, 4429, and 4545 Hz. The other partials are far weaker and seem to vary with each different hit. Through Praat (and its "show intensity" option), I calculated tau to be around 0.12 seconds.

Name: Alex Barnett
Date: October 26, 2011 (12:06)
File uploaded:
Comment: In Y.-J.'s post below she notices the amplitude of the longest-decay-time mode of a wineglass drops but then *increases* again, drops again, increases, etc. This contrasts our "decaying pure tone model". What do you think could be causing this? Hint: What if there were *two* modes near this freq, with very close natural frequencies? Here's a fun (if geeky) video showing two wineglass modes far apart in freq, but without discussing the possibility that nearby mode frequencies exist too.

Name: Michael Blum
Date: October 26, 2011 (01:49)
File uploaded: Peanut Can.ogg
Comment: I recorded myself hitting a tin can with a plastic object. The first hit contained many partials, some unrelated; the second hit had strong partials at 588 Hz; the third hit contained strong partials around 919 Hz; and the fourth hit was very similar to the second. Using Praat and the formula τ=(-8.69)/(slope), I derived τ to be ~0.036 seconds.

Name: Yoo Jung Kim
Date: October 26, 2011 (01:33)
File uploaded: wineglass1.wav
Comment: I hit a wineglass with a metal spoon. The strongest partial was found at 1270 Hz and other partials were distributed at around 300, 270, 250. Through Audacity, I estimated Tau to be around 0.1 seconds. An odd thing I noted about this graph is that after the initial sound dies off, there is a slight increase at around 0.65 seconds that seem to decrease more slowly.

Name: Katelyn Onufrey
Date: October 26, 2011 (01:19)
File uploaded: hairspraycan.wav
Comment: In this recording I hit a can of hairspray with a pencil. The strongest tone was partial is at 761.5 Hz, and there are some others 683.9 Hz, 532.8 Hz, and 362.2 Hz. These are unrelated. Using Audacity to measure the slope, I found out that tao is 0.0457 seconds.

Name: Evan Griffith
Date: October 25, 2011 (22:08)
File uploaded: bowl.mp3
Comment: In this recording I am striking a metal mixing bowl with my fist. Estimating with Audacity, I found Tao = 0.24. I used Praat to look at the harmonics being produced. There is a very prominent tone produced at 650Hz, however the overall sound is still that of a bell. You can see other harmonics faintly, many of which are in no pattern.

Name: Xander Arnold
Date: October 25, 2011 (21:41)
File uploaded: HW5.wav
Comment: I hit the prongs of a typical household fork with the handle of a spoon of the exact same metal and make. The frequencies from the prongs rang at around 3900Hz, 6200Hz, 7400Hz, 8500Hz, 9400Hz, and some less distinct higher ones. The decay time of the partial at 7400Hz was well beyond 3secs and that of the partial at 3900Hz was just slightly less than that. The rest of the partials had a decay time roughly around 1 sec.

Name: Chuanqi Sun
Date: October 25, 2011 (19:34)
File uploaded: bar.wav
Comment: I hit the towel bar in my bathroom with a toothbrush It is a complex vibration because the partials are not harmonically related (257/371/544/963/1510) It has a decay time of approximately 0.34 sec

Name: David Jiang
Date: October 25, 2011 (17:11)
File uploaded: HW5-7.ogg
Comment: Hitting my metal bowl on my wooden desk. According to praat, we see partial frequencies at 853, 1444 and 2335. Using the part of the Intensity graph closest to a line to get slope, tau is approximately .16s

Name: Michael Blum
Date: October 24, 2011 (20:40)
File uploaded: Guitar Harmonics.ogg
Comment: I recorded myself playing what are usually called “harmonics” on the guitar. These are certain places on the fretboard where a player can isolate certain partials of an open string (I assume that they are nodes/in some way related to nodes). First, I played an open E string, then I played the harmonic that lies over the fifth fret (five semitones from E), then the harmonic over the seventh, the ninth, the 15th, and the 17th. When viewed in Praat, the harmonics show some of the individual partials of the first open E string.

Name: Chuanqi Sun
Date: October 24, 2011 (02:16)
File uploaded: Marry_Has_a_Little_lamb.aiff
Comment: Water Bottle + H2O = Wonderful Music! (demonstrating how change in mass affects the pitch of an oscillator)

Name: Zoë Furlong
Date: October 21, 2011 (15:28)
File uploaded: Quetzal_Clap.mp3
Comment: An attempted investigation into the “Mayan Acoustical Engineering” at the site of Chichen Itza, a pyramid in Mexico... The echoes of clapping in front of a pyramid face produce a very unique sound, one that is supposedly quite similar to the call of the Quetzal bird (very important in Mayan cosmology). Here I have attached the sound of a tourist clapping in front of the pyramid steps. There is a twangy pitch produced by the periodic echos from the steps (similar to a flutter echo). It almost seems that the pitch slides down in the duration of each echo. However, when I zoomed into the echo on Praat and played tiny parts of the echo sequentially, I found that the clapping sound throughout the echo became higher and softer. This would make sense if the width of the steps became shallower as the pyramid rose (as we discussed briefly in class); however, the only information I could find regarding the steps was that the staircases rose at an angle of 45 degrees. I hope to investigate further…

Name: Yoo Jung Kim
Date: October 20, 2011 (10:26)
File uploaded: 102632Psycho Violin Screech.mp3
Comment: Second Posting In a spectrum of the first three screeches of the sound clip taken through praat, I saw approximately three prominent partials at around 2500 Hz, 5000 Hz, and 7500 Hz, which is approximately harmonic in intervals of 2500 Hz. In the following notes, one hears additional frequency playing on top of the original frequencies, again, using praat, I saw that the most prominent partials were around 1360 Hz, 2500 Hz, 2700 Hz, 4000 Hz, 5000 Hz, 5300 Hz, 6600 Hz, and 7500 Hz. The new frequencies (1360 Hz, 2700 Hz, 4000 Hz, and 5300 Hz) increase at a steady interval of ~1300 Hz. According to Helmholt'z theory of Dissonance, dissonance occurs if two frequencies are more than 15 hz and less than 10 percent apart. This occurs prominently between 2500 Hz and 2700 Hz (~7.4%) and 5000 Hz and 5300 Hz (~5.7%), which demonstrates physical evidence to the dissonance that we perceive in our ears.

Name: Yoo Jung Kim
Date: October 17, 2011 (09:33)
File uploaded: Psycho Violin Screech.mp3
Comment: After learning about dissonance and hearing the Brentano Quartet perform last week, I immediately thought about the violin screech in Alfred HItchcock's Psycho, arguably one of the most iconic and dissonant sound in cinema--or, at least, that's what I thought. I downloaded the .mp3 file off the internet and plotted it in the pratt spectrogram. While I had expected to find numerous unrelated pitches in dissonant relationships, I found that there was a dominant and steady interval in the frequency. Most notably, in the fourth violin screech, the spectrogram shows a distinct bands at around ~450 Hz, ~900 Hz, ~1350 Hz, and ~1800 Hz, with the thickest band occurring at around 1350 Hz. This is about 41 cents above E6. This demonstrates that Psycho's Violin Screech may not be as dissonant as I had originally thought.

Name: Chuanqi Sun
Date: October 17, 2011 (02:23)
File uploaded: Doppler.aiff
Comment: Doppler's Effect on Tempo I held my roommate‘s Electrical metronome when running towards my computer in the corridor. To magnify the effect, instead of recording the metronome in still, I ran away from my computer the second time. I mix the two tracks with their beginning aligned to each other. To further magnify the effect, I copy and paste the track while maintaining the tempo of each. You can hear how their tempos go off from each other. So, Doppler's effect does change the tempo! Special Thanks to Philip for his metronome!!

Name: Yichuan Wang
Date: October 16, 2011 (22:55)
File uploaded: 225513Finished
Comment: This is the clarinet opening of the famous Rhapsody in Blues by George Gershwin. We have seen how the spectrogram curves upward in a certain pattern for string instruments in class. I wanted to see whether there is any difference for a wind instrument playing a similar passage. It is interesting to note that right when the melodic line starts to rise in pitch, the “non-sliding” portion, the spectrogram looks like a paint brush. Then, when the pitch sliding action happens, the rising harmonics look thicker/rougher than those of string instruments, indicating differences in timbres.

Name: Yichuan Wang
Date: October 16, 2011 (22:28)
File uploaded: Finished
Comment: I recorded the sound of my suite-mate’s bike brakes when they are wet (on a rainy day). He has a bike that has disc brakes. The disc brakes are made of the same material and are of the same structure and size. The pitch of the rear brake noise is higher than that of the front. A possible explanation for this is that the front brake pads are more worn out than those of the rear. Either the thickness of the brake pads themselves causes the pitch difference, or the kinetic friction coefficient of the brake pads may change when worn and causes the pitch difference. Included are the spectrum and spectrogram of the sound recordings along with the sound files themselves. Front Brake: Partials at 766 Hz, 825 Hz (12 cents flatter than Ab5. Seems to be the greatest common factor frequency, the higher partials seem to be the harmonics of this one), 1639 Hz, 2457 Hz (tallest of all), 3280 Hz, 4150 Hz, 4909 Hz, 5750 Hz, 6555 Hz, 7380 Hz, 8216 Hz, 9095 Hz, …. Interesting pattern seen on the spectrum of the front brake: for each regional maximum partial seen, there is a slightly smaller partial right before it. It almost look like a set of twin towers. Front Brake Spectrogram: The brake noise consist of a high pitched squeal. Nonetheless, it’s pretty amazing to see, on the spectrogram, that the harmonics of this pitch go well up to ~17,960 Hz, very close to 20,000 Hz, the highest frequency within the range of human hearing. There may be even higher harmonics present, but the frequency range of my MacBook Pro microphone is limited. A clean pitch/tonality was first heard. (Clean, as that the harmonic lines are not smeared.) Later on, maybe when the disc brake got hot and/or dry, it sounded more like noise than a pitch. The harmonics are smeared, as seen on the spectrogram. Rear Brake: Partials at 768 Hz, 875 Hz, 907 Hz (52 cents sharper than A5. Seems to be the greatest common factor frequency, the higher partials seem to be the harmonics of this one.), 1545 Hz, 1767 Hz, 1816 Hz, 2403 Hz, 2663 Hz, 2741 Hz, 3538 Hz, 3668 Hz, 4603 Hz, 5474 Hz, …. Highest harmonic (on spectrogram, covered up by the red dotted line) ~18,380 Hz. The rear brake’s pitch/tonality isn’t as clear as the that of the front. There may be more dissonance in this one.

Name: Evan Griffith
Date: October 15, 2011 (22:23)
File uploaded: falseoct.mp3
Comment: Here I am play an F2 on a pipe organ followed by a C2 (simultaneously). When I play the C2, the sound that is heard is an F1. This is called a "resultant tone" and is the result of a common subharmonic of the two notes I am playing. So even though I play an F2 and then C2, F1 is a common subharmonic so that is what we "hear". F1 is at an extremely low frequency (around 44 Hz). See if you can hear it. See the link below for more. You'll notice some familiar ratios involved and concepts we've studied in class.

Name: Michael Blum
Date: October 12, 2011 (23:14)
File uploaded: Week
Comment: In the attached .ogg file, two waves—sin(880πt) and sin(880πt – π)—are played individually, then they are played together (see "Audacity Screenshot.png"). Although the output sound would normally be amplified 2x when two waves are played together, in this case, the combined sound is extremely low, almost inaudible. This is due to the way in which the respective phases of both waves interact with each other. When one wave reaches its crest, the other reaches its trough (see "Close-Up on Waves.png"). When the two are added, they cancel each other out as a result.

The attached audio file is a simulation of what happens when two receivers of sound are at exactly the distance that it takes for a wave to complete ˝ of a full cycle.

Name: Maggie Flanagan
Date: October 12, 2011 (00:18)
File uploaded: Echos Across 500m.wav
Comment: This is a simulated gunshot echo off a cliff face 500m away. Complementary bird sounds.

Name: David Jiang
Date: October 09, 2011 (23:25)
File uploaded: Maria tritone.ogg
Comment: Here is an example when a tritone, which we showed in class to be one of the more dissonant intervals, can be used as part of a beautiful melody. The first two notes of "Maria" from Leonard Bernstein's musical "West Side Story" are an E flat and an A, which are 6 semitones (or a tritone apart). However, the A then goes to a B flat, which is a perfect fifth above the beginning E flat. Therefore, we go from dissonance to resolution. First, I play the first two notes (e flat and a) separately and then together as a tritone to show its dissonance. I then play all three notes, and then the perfect fifth together. Finally, there is the actual sound recording.

Name: Chuanqi Sun
Date: October 09, 2011 (09:01)
File uploaded: Missing Fundamental.ogg
Comment: Missing Fundamental I used Audacity to generate a sound containing 300, 600, 900, 1200, 1800Hz pure tones. (I tried lower frequency but found my tiny loud speaker incapable of producing sound <200Hz) Then I subtracted 300, 600, 900 each time. The subtraction, however, didn't affect the pitch I perceived. Then I played 300 alone, which is the pitch. Sound you will hear in sequence: 300Hz 300+600+900+1200+1500+1800 600+900+1200+1500+1800 900+1200+1500+1800 1200+1500+1800 (notice that pitch begins to shift)

Name: Alex Barnett
Date: October 07, 2011 (11:34)
File uploaded: challoct.mp3
Comment: This is the stretched partial example I played in class. It is really enlightening to use praat to look at its spectrogram while it plays (use time window of around 0.1 sec). The first 3 sounds are the bell-like stretched instrument followed by it doubled in pitch then the two together (dissonant! Look at partials to see the misaligned ones). The next three sounds are the case where the "octave" is stretched to a factor 2.1, and it becomes consonant again. This comes from Bill Sethares here

Name: Katelyn Onufrey
Date: October 06, 2011 (19:36)
File uploaded: aural_illusion.wav
Comment: Using audacity, i generated tones of 100 Hz, 200 Hz, 300 Hz, 400 Hz, and 500 Hz. When you play all of these tones together, however, it does not sound like 5 different tones. It sounds like one pitch. This is an aural illusion and the pitch sounds like the GCD of these tones, which is 100 Hz. One explanation to this is that the human eat detects period.

Name: Evan Griffith
Date: October 03, 2011 (02:10)
File uploaded:
Comment: Correction to typo in the first sentence! It should read: "Here I have used Praat to create a spectrogram of the tone made by pressing the number 0 on my iPhone."

Name: Evan Griffith
Date: October 03, 2011 (02:06)
File uploaded:
Comment: Here I have used Praat to create a spectrogram have the tone made by pressing the number 0 on my iPhone. Two files are in the ZIP folder. The OGG file is the sound produced. The image file is the spectrogram. How many tones do you hear? You can see on the spectrogram that a lower tone is louder and hence it produces a darker strip. The interval between the two tones we can easily hear when we push the 0 key form an Augmented 4th which is 6 semitones.

Name: Michael Blum
Date: October 01, 2011 (21:22)
File uploaded:
Comment: An electronic organ has controls that allow the user to modify the harmonic content of the instrument. In the attached audio file, a note is played on an electronic organ (Logic Pro software instrument). The successive sounds are recordings of each individual component of the first organ sound recorded. In Audacity, you can see how each of the individual waveforms adds up to the full organ sound, placed at the beginning and end of the .ogg file. By this demonstration, we see that the partials of this signal only occur at f, 2f, 3f, etc. The first individual tone’s peak is measured at ~131 Hz (let us call this “f”); the next, ~392 Hz (3f); the next, ~261 Hz (2f); the next, ~529 Hz (4f); the next, ~799 Hz (6f); ~1061 Hz (8f); the next, 1334 Hz (10f); the next, ~1569 Hz (12f); the last, ~2097 Hz (16f). When the full organ sound is analyzed in Praat or Audacity, all of these tones exist on the spectrogram. To do this, I recorded each tone by isolating each individual upper drawbar (see attached .png file) on the electronic instrument.

Name: Zoë Furlong
Date: September 29, 2011 (13:49)
File uploaded: Twist_Keyboard.mp3
Comment: Twist part 2: After investigating my last audio sample further, I have found that the Fab Four may have been a little off-key (according to audacity)! The first note of the 4-part harmony, A4, was read as 437 Hz by audacity. As we all know, A4 is really 440 Hz so they were flat by 3 Hz, or about 12 cents. Their C#5 was read as 543 Hz, which is flat by 12.37 Hz, or about 36 cents. The E5 was 667 Hz, which is 7.74 Hz and 20 cents sharp. The last note, G5, was better: only .99 Hz flat, or 2.18 cents flat. Paul’s falsetto scream went up to 1772 Hz, which is actually 12 Hz/11.8 cents higher than A6, 1760 Hz! I played all of these notes on a keyboard in GarageBand in an attempt to replicate the most "in-key" version of the notes they sang.

Name: David Jiang
Date: September 28, 2011 (09:48)
File uploaded: phone ringer.ogg
Comment: This is a cell phone ring tone. It has two distinct pitches that repeat at a constant frequency. The period is approximately 3 seconds.

Name: Zoë Furlong
Date: September 28, 2011 (09:18)
File uploaded: Twist.ogg
Comment: This is a sample from the Beatles' recording of “Twist and Shout”. During this selection, the four all seem to contribute a different, harmonizing note to create a full chord. I was curious to see what notes and chord they actually were singing, and how in tune they were. Also, someone (probably Paul) does a full octave falsetto slide up to a very high note at the end of this file. The first note that is sung is A4, then C#5, then E5, then G5. The high falsetto scream goes up to A6. I hope to analyze this more and find exactly how off-key these notes were (if at all) and learn more about this specific chord.

Name: Austin Greenfield
Date: September 28, 2011 (02:34)
File uploaded: Whistle.ogg
Comment: (and now with the file attached) I recorded myself whistling a single note and then slowed down the recording numerous times. I chose to reduce the speed of the whistle each time by half, representing how by halving the frequency you attain the same note an octave lower.

Name: Austin Greenfield
Date: September 28, 2011 (02:33)
File uploaded:
Comment: I recorded myself whistling a single note and then slowed down the recording numerous times. I chose to reduce the speed of the whistle each time by half, representing how by halving the frequency you attain the same note an octave lower.

Name: Chloe Teeter
Date: September 28, 2011 (01:41)
File uploaded: is it an octave.ogg
Comment: I recorded myself attempting to sing an octave of no specific note. The frequency of the first, lower note is 191 Hz and the second, higher note is 387 Hz. By using n = 12 ( log(f/440) / log(2) ), I figured out that the first note is 44 cents flat of G3 and the second note is 22 cents flat of G4. So the interval is larger than an octave.

Name: Katelyn Onufrey
Date: September 28, 2011 (01:25)
File uploaded: tones.ogg
Comment: I created two sinusoidal tones on audacity with frequencies of 550 Hz and 552 Hz. They are both being played together with an amplitude of 1. In the recording, you can hear a pulsating tone with beats. The beats are caused when either the cos or sin part of the equation 2[cos(2pi(200-201/2)t]*[sin(2pi(200+201/2)t] equals zero because that interrupts the natural frequency.

Name: Xander Arnold
Date: September 28, 2011 (00:47)
File uploaded: untitled
Comment: The zip folder above contains audio of a recording of an "ah" sound and an "ee" sound at roughly the same volume and pitch, and a picture of the frequency analysis of them both. Looking at the analysis you can see that the frequencies of the partials are the same but the individual amplitudes of each partial vary between the "ah" and "ee." This relates to our discussion on how the transmission of a signal changes its sound. In this case, rather than the acoustics of a room changing the signal, it is the size and shape of my mouth, functioning as a resonating chamber. By making a different vowel shape with my mouth I have changed the amplitudes of different partials and therefore acted as a sort of pseudo-filter even though the overall pitch and amplitude are constant.

Name: Yoo Jung Kim
Date: September 28, 2011 (00:19)
File uploaded: phone.ogg
Comment: I recorded the my phone's ringback tone, a sound heard on the telephone line by the caller to signal that the called party's line is ringing. The tone increases in amplitude and is abruptly cut off at the end. Through audacity, I found the two peak frequency to be 445 and 484. When the two tones were played together, the sound generated was extremely similar to that of my ringback tone--albeit without the gradual increase in intensity. Judging by the wave of the graph, I estimated the frequency to be ~0.025 sec.

Name: Michael Blum
Date: September 28, 2011 (00:13)
File uploaded: Week 1.ogg
Comment: The attached file is a recording of my finger tapping the internal microphone on my computer. The first part of the recording is at actual speed, with a period of ~0.185 s (~5.4 Hz). I recorded myself tapping the microphone for about 1.5 minutes, but omitted the audio of part 1 after 12 seconds. I then sped up the recording by 5000%. This produced a sound that I perceived as a pitch. The period of the recording when sped up is ~1/270 seconds, and the frequency is ~270 Hz (although, since my tapping was not perfect, the frequency and period vary). The third sound in the attached file is a sine wave at 270 Hz, which serves as a comparison to the tone generated by the recording at 5000%. The attached file demonstrates that when periodic sounds are sped up to a certain degree, the individual sounds become indistinguishable and the human brain perceives them as pitch.

Name: Yichuan Wang
Date: September 27, 2011 (23:34)
File uploaded: 09-22-2011_Rain in East Wheelock.mp3
Comment: I recorded the sound of pouring rain at East Wheelock on the afternoon of 09-22-2011. There are times that periodicity can be observed (e.g. in the very beginning). In such segments, T= 0.002~0.003 s. Although the rain sounded mostly percussive, using Audacity, I found Peak Freq: 197 Hz at −60.0 dB The frequency of the sound of rain at East Wheelock is very close to (9 cents sharp of) G3.

Name: Chuanqi Sun
Date: September 27, 2011 (10:20)
File uploaded:
Comment: Recently, there has been a ghostly high-pitch noise annoying Eastwheelock residents. I recorded the mystery sound and analyzed it with Audacity. I found two peak frequencies of 1045Hz and 923Hz, and thus generated two pure tones with such frequencies to verify my idea. Amazingly, it worked! Files included: 1. Recording NOISE_Eastwheelock.mp3 (note a change of the tone) 2. Four spectrum graphs analyzing samples my records 1045 NOISE_1.png 1045 NOISE_2.png 923 NOISE_3.png (also note in the audio that tone changes ) 1045 NOISE_4.png 3. Computer Generated Noise Computer simulated noise.mp3

Name: Yoo Jung Kim
Date: September 27, 2011 (00:01)
File uploaded: tardis.mp3
Comment: This mp3 is the sound effect used in the decades-old cult British TV Series, Doctor Who. The effect is specifically used as a sound emitted in the dematerialization of the TARDIS--a time/dimensional travel machine and a critical plot device within the show. I found that the distinctive sound has been dubbed "vworp vworp." I also discovered that the that the effect was created within the BBC Radiophonic Workshop by Brian Hodgson as he dragged keys along the piano springs. The sound was then recorded and electronically processed to give rise to the sound recognized by Doctor Who fans of all ages. I wonder how the contact between two solid objects (e.g. the piano string and the keys) cause the phenomena that we perceive as sound.

Name: Blair Bandeen
Date: September 26, 2011 (20:31)
File uploaded: Phone.ogg
Comment: In this file is a recording I made of the sound of the "2" key on my phone's keyboard. After recording the sound I did some research online and learned that what is called dual-tone multi-frequency signaling was developed for telephone keypads when rotary dialing ended. It turns out every time you press a number on your phone you are hearing the combination of two pure tones. The system uses eight different signals in pairs to create the different numbers/symbols you see on your keypad.

Name: Evan Griffith
Date: September 24, 2011 (16:00)
File uploaded:
Comment: The attached ZIP file contains two items, an mp3 clip and a photo capture of the sound wave from the file. In the file, I play a very low C on my keyboard (2 octaves below C1) and then I play a C4 ("middle c") right after. Notice the changes in the wave as I switch from the lower C to the higher C. The sound I am using is the "Sawtooth synth." Similar to the Frac waves we studied in class, you can see the tooth-like structure of the wave's periods. Due to the higher frequency of the higher c, there are more repetitions per second and so the pattern is less distinguishable than that of the lower C without zooming in.

Name: alex barnett
Date: September 20, 2011 (19:52)
File uploaded: ACDC-Bells.mp3
Comment: The attached is the sound of the Denison bell, manufactured in 1923, in Leicestershire, UK. It was used as the opening of AC/DC's Hell's Bells. Is the signal periodic? Zoom into the waveform using audacity or praat and you'll see it's not. However, it does contain strong partials, the lowest being at 82 Hz. More about that later!

Name: alex barnett
Date: September 20, 2011 (19:50)
File uploaded:
Comment: test