A4 Sine Waves and Additive Synthesis

Sine Wave Math

  1. Sine waves are important to electronic music, and music in general because: Sine waves, which describes displacement from equilibrium with a single frequency, can be used to describe any disturbances in the air (“sound waves”), or vibrations. Strings, air inside wind instruments, or the vocal folds in the human throat – all these sources of musical sound can be made to vibrate in sinusoidal motion with a single frequency. More complicated sources can be described using the superposition of several sine waves in the harmonic series of different frequencies. Pitch and timbre are decided by the strongest sine wave and the relative frequencies of all waves that are added together in the mix, respectively.
  2. y(x) = A*sin(2πft + ø) is used to calculate the displacement from equilibrium of a wave particle. A is the maximum displacement of the wave particle from the equilibrium (achieved when |sin(2πft + ø)| = 1), f is the frequency of the wave, which is the number of cycles per unit time, t is time/seconds, so ft is the total number of cycles travelled by the wave in time t. ø is the angle that the radius makes with the horizontal axis in the unit circle at t = 0. Assuming ø = 0, the cycle starts at an angle of 0, so the initial displacement is 0. This is not really a struggle for me as I learnt about this in high school physics.
  3. We have a unit circle with radius = 1. The right triangle is formed by the angle of the radius moving counterclockwise around the unit circle. Sine is opposite over hypotenuse, in this case the hypotenuse is the radius = 1. Thus sine is simply the length of the opposite side. This side varies in length as the angular displacement increases. For example, at 45º, the length of the opposite side, thus sin of 45º, is .707. At 90º the opposite side of the right triangle “disappears” and becomes equal to the length of the unit circle. Thus the sin of 90º is 1. The Max patch demonstrates how sine wave is formed as angle of the radius moves counterclockwise around the unit circle.sin45sin90
  4. This patch demonstrates the meaning of wave frequency. With the frequency of 1 Hz, wave particle travels a complete cycle in 1 second. When the frequency is changed to 2 Hz, wave particle travels a complete cycle in 1/2 = .5 second, meaning it travels 2 complete cycles in 1 second.
  5. An example of equal musical interval would be octaves. Different frequencies that demonstrate the same note but one octave apart are in ratio of 2:1. (The same note in one octave higher are double the same note one octave lower). For example, G2’s frequency is at 100 Hz, G3’s frequency is double of G2 at 200Hz, a difference of 100 Hz from G2’s frequency, G4’s frequency is double of G3 at 400Hz, instead of 100 Hz from G3’s frequency which is at 300 Hz. Thus, equal music intervals do not mean equal differences, but equal ratios of frequencies.
  6. Any two of the lower few frequencies in a harmonic series sound good together.  For example, harmonics 2 and 3 form a “perfect fifth.”  Harmonics 3 and 4 form a “perfect fourth”; 4 and 5 form a “major third,” etc. Any repeating wave shape of frequency f can be created by adding together sine waves of frequency f, 2*f, 3*f, 4*f, …  That means we can create any wave shape by using only the sine waves in the harmonic series for that pitch. So when we “mess around with ” the relationship of the partials by adding them to the sine wave with fundamental frequency, we can create harmonies and different timbres and amplitudes.
  7. Sine wave possesses only a fundamental frequency, with no additional harmonic content. Triangle contains partials at the odd frequencies, with amplitudes at the inverse of the square of the harmonic number. Square wave contains odd partials with amplitudes at the inverse of the partial number. Sawtooth contains all harmonics, with amplitudes as the inverse of the harmonic number. The upper partials have increasingly greater than the fundamental wave while their amplitudes decrease due to them being the inverse of the partials.

A2 MIDI Questions

  1. MIDI is a communications protocol established in 1984, in order to allow one keyboard to serve the master keyboard for controlling various synthesizers in a performance, saving the performers from jumping around different synthesizers to create different sounds. MIDI captures performance gestures such as the note, the volume of the note (expressed by the velocity of the hammer hitting the piano string), the channel in which the note is played, whether foot pedal is used on the note, possible modulations of the note and the timbre of the sounds.
  2. MIDI is an 8-bit system that has two types of data: Status Byte and Data Byte. Status Byte’s MSB is a 1, while Data Byte’s MSB is a 0. The highest and lowest possible status byte is 255 and 128 respectively, while the highest and lowest possible data byte is 127 and 0 respectively.
  3. In a complete Note On message, the status byte, between 144 and 159, represents ‘note-on, on channel 1 to 16’, and 2 data bytes representing the note and velocity of the note, each of which ranges from 0 to 127.
  4. Controller message represents the control aspects of the sounds decided by a performer’s use of foot pedal, modulation wheel or any other sliders that affect the sounds. In a complete Controller message, the status byte represents, between 176 and 191, means ‘controller message, on channels 1 to 16’, and 2 data bytes representing the type of controller moved and the extent and how far was it moved, each of which ranges from 0 to 127.
  5. There is only one data byte to represent the type of patch used as a timbre is absolute and cannot be variated further.
  6. MIDI notes can be turned off when data byte for velocity of the note is set to 0, even though there is a MIDI note off message as it is more efficient to use the former method.
  7. MIDI can send multiple messages of Note on and Controller message to 16 different channels at the same time. For example, Note On Status Byte ranges from 144 to 159, in which 144 means ‘note on, channel one’, 159 means ‘note on, channel 16’; Controller message ranges from 176 to 191, in which 180 means ‘controller message, channel five’.
  8. MIDI timing is executed against a time stamp from time zero and encoded in a MIDI file. For example, a MIDI file starts with a note-on message, followed by a note-off message 1000 milliseconds later: 0 144 60 96 (time 0, note on, channel 1, note C, velocity 96) / 1000 144 60 96 (time 1000, note on, channel 1, note C, velocity 0). A MIDI file can also have controller message that looks like this: 0 176 1 1 (time 0, controller message, channel 1, modulation, value 1) / 20 176 1 15 (time 20, controller message, channel 1, value 150), meaning that in 20 milliseconds, the modulation wheel has moved to a value of 15.
  9. Construct a MIDI note-on message that lasts for 1000 milliseconds by sending, for example, note 35 and velocity 100, to ‘makenote’ object. These are sent out to ‘noteout’ object on channel 10 (which is preserved for percussion instruments) to device number 1, which is the computers’ internal synth. A bass drum sound then can be heard from the computer’s speaker. We can choose other note value from 35 to 81 to trigger different drum sounds, such as hi-hats and snare drums. Velocities represent how hard the drum pad is pressed and thus determines the loudness of the sound.

A1 Listening Assignment

  1. John Cage Williams Mix: This piece defies my expectation of music as it lacks a clear-cut rhythms and tempo, which are criteria that I expected to consider something as music. But looking at the composer’s intention, which is to produce and organize short jumps of a wide range of tape sounds ranging from city, country,… to wind sounds, I can see the work’s influence on the modern music production, which now widely incorporates short samples of sounds layered on top of one another and repeated in a certain pattern. As strange as it may sound, while listening to the song, I can imagine myself as someone who just loses memory and suddenly remembers short flashes of memory. It was a goosebumps-inducing and a bit uncomfortable piece for me.
  2. Stockhausen “Gesang der Junglinge” (Voices of Children): This piece totally sounds like a cacophony to me from start to finish as the vocals seems to be  randomly interspersed with some computer-generated sounds. I keep expecting for it to have some kind of climax or dynamics somewhere in the song for it is a bit long, but the energy seems to not fluctuate a lot. Without its context, I would not consider this piece as music at all. Knowing its context and author’s intention, which is to “integrate electronic sounds with the human voice by means of matching voice resonances with pitch and creating sounds of phonemes electronically”, I can appreciate the fact that there is a relationship between the human vocals and the electronic sounds even though I couldn’t figure that out just by my own hearing. This piece gives me the feeling that I gained the magical power of seeing ghosts. Overall, to me it was a creepy-sounding piece.
  3. Luciano Berio Ommagio (homage) a Joyce: Even though I’m a bit uncomfortable listening to the piece at first, I like how the woman’s voice is at times sped up, at times slowed down and layered. It was closer to what I expect from hearing music, especially electronic music or remixes by DJs, where sounds are often mixed, sped up and slowed down in some parts while maintaining a coherency. The piece, which classified the recorded words included in the poem “Sirens” according to their resonance colors, in relation to the resonance point of the vocal apparatus”, is used to study the relationships between different European languages and pure vocalism from several points of view. While it serves such an interesting academic purpose, the piece, to my untrained ears, sounds like a cassette tape of an audio book which is sometimes fast-forwarded or slowed down.
  4. Milton Babbitt Ensembles for Synthesizer: Surprisingly, these pieces of music have certain melodies and rhythms that I can follow, and are just really entertaining to hear. Since the author focused in the rhythmic precision he could achieve using the Mark II synthesizer rather than producing new timbres, the piece sounds diverse but coherent. These pieces remind me of video games tunes.
  5. Morton Subotnick Silver Apples of the Moon:  This piece has dynamics and builds up gradually to a climax towards the end, which is what I usually expect from music, and there are also a lot of cool effects that are nice to hear. There are even parts that sounds funky and rhythmic.It gives me the feeling that aliens and spaceships are descending to earth and soon destroying human kind. The fact that this piece is composed in a way that included “sections with metric rhythms” at a time when “rhythm might be an afterthought or of no consequence, and simple patterned structures were largely avoided” elevated its value further.
  6. Alvin Lucier I am Sitting in a Room: I think this is a physics experiment that unintentionally becomes music over time. Certain frequencies are emphasized as they resonate in the rooms with different characteristic resonance frequencies until words become tunes. I don’t think the author meant for this to become a musical composition but to test how sounds are picked up by sound-generating machine (loudspeaker) and manipulated in different settings/medium.
  7. Terry Riley A Rainbow in Curved Air: This piece’s use of overdubbing of various instruments like electric organ, harpsichords, dumbec and tambourine gives itself a rich feeling. The drums towards the third section of the piece were the highlight for me. Overall, this piece gives me a happy and therapeutic feeling.
  8. Steve Reich Come Out: The fragment “come out to show them” was played in unison and then slip out of sync to produce a phase shifting effect, then gradually only become a reverberation. This technique used in this piece reminds me of the technique a DJ uses to remix a song to play in an electronic music festival.
  9. Brian Eno Atmospheres: The music has a relaxing and chill vibe. Ambient music’s purpose is “to modify the listener’s perception of the surrounding environment”. I think it achieves its purpose quite well, as ambient music makes me feel at peace with my surroundings and help me focus on whatever I’m doing at the moment.
  10. Beatles Tomorrow Never Knows (1966): The electronic ‘skrr’ (?) sound effects and the introspective lyrics add so much spice to the otherwise repetitive piece of music. It’s probably the closest piece that I would consider music in today’s context. I’m quite surprised that the Beatles actually had these kinds of songs where they can go full-on experimental like this.
  11. Afrika Bambaataa Looking for the Perfect Beat: The beat starts out simple and layers of different instruments and vocals come later to form a great harmony, becoming the “near-perfect homage to digital-era technology”. This piece is so fun to listen and dance to.