Mathematics Page

Questions on the Mathematics of Computer Music, part 1

MIDI PAGE

  1. Explain the historical background of the MIDI protocol. When was it established, and what type of “performance gesture” was it first designed to capture?

It began in the 1970s and 1980s and was codified in 1984 as a way to allow a performer to control multiple synths at once via a keyboard.

  1. Explain MIDI as an 8 bit system. How do Status Byte and Data Bytes differ as regards the MSB (most significant bit). What is the lowest possible status byte (expressed as base 10 number?) What is the highest possible data byte (expressed as a base 10 number?).

An 8-bit system possesses 8 binary gates that can be closed and is able to represent a numerical value between 0 and 255. Status Bytes are the MSBs. SB: 144 DB: 127

  1. Explain the configuration of a Note On message. What does the status byte represent, and how many data bytes are necessary for a complete Note On message?

Three events, one status byte between 144 and 159 meaning “note-on, on channel 1-16”, and two data bytes (note number and velocity, 0-127).

  1. Similarly, explain the configuration of a Controller message (messages from sliders, joysticks, buttons, food pedals, wind controllers, etc.) What does the status byte represent, and how many data bytes are necessary for a complete Controller message.

Same idea as Note-On, controller message on channel 1-16 (176-191) and two data bytes (which controller/which value? 0-127)

  1. Why is the status byte of a patch change message followed by only one data byte?

There is only one parameter, which patch, that is needed to do this.

  1. How are MIDI notes turned off? Is there a separate note off message, or is this managed in a different (and somewhat musically unintuitive!) way?

Velocity of 0 is received by the release of a key.

  1. Explain how MIDI channels work in relationship to Note on and Controller messages.

CMs range from 176-191 and PCs run 192-207. PB runs 224-239. This allows the message/messages to be carried out by multiple other programs/pieces of hardware with one depression.

  1. How is a midi file structured in relationship to a millisecond time stamp?

1 message per millisecond.

 

  1. Imagine a drum pad trigger, where each pad triggers a different MIDI note. How would you set up a patch that would play different instruments on a drum kit? What would the velocities represent?

Each pad would be a separate channel; each channel would correspond to an instrument that could have a patch change applied. Velocities would represent loudness and timbre based upon the force with which the pad was hit.

MATHEMATICS OF SINE WAVE PAGE

  1. The Mathematics of the Sine Wave. Read through this page and try to explain what this is saying in your own words. Those of you working regularly with mathematical concepts will likely find this relatively simple. If your major or area of study is not so mathematical, it has maybe been awhile sine you’ve done trigonometry! Do your best to either explain what you read here, or write down questions for Tuesday’s class. You will not yet be able to run the Max demos, be we will look at these on Tuesday.

Sin waves are the most basic form of waveform and every single frequency sound can be represented by them and more complex sounds can be broken down into or are modified versions of them (i.e. square waves are hard-clipped sin waves)

ADDITIVE SYNTHESIS/HARMONIC SERIES PAGE

  1. Similarly, read through the page on Harmonics and Additive Synthesis. Part of Tuesday’s assignment will be to create a simple four-step additive synthesizer. Explain this page as best you can in your own words.

Note intervals are ratios and are exponential in growth. Adding harmonics modifies how these will sound.

  1. Conclude with describing the spectral content of a sine, triangle, square and sawtooth wave. How much energy (or amplitude) is present for each integer multiple of a fundamental tone, and how would you succinctly summarize that?

No idea.

Listening Assignment

I will answer the first question for all of these. I do not have an expectation or a standard for what music “should” be. I like all kinds of music, from EDM to Classical to Neo-Dadaist compositions and A-tonal orchestral pieces (I’ve actually heard all of these pieces before). On a side note, I’m not entirely sure as to what is meant by the third question, so I will attempt to answer it as best as I can with limited understanding.

I think the purpose of the William’s Project was to experiment with new technologies. It communicates with the listener by creating an ambient soundscape which permits the listener to fill in gaps and orchestrate his or her own narrative. It does not personally communicate with me, but it makes for good background noise.

I feel that Stockhausen was attempting to express an abstract concept via abstract and experimental use of sound to create patterned textures. This piece invokes many nature scenes with occasional visits by the paranormal.

I feel that Thema was attempting to capture the theme and moods expressed in the poem it is based off of. It seems discombobulated and sounds as if it is trying to cast the listener in any direction but the right one.

Babbit’s purpose is clearly the same as it is in many of his other works. To prove that music does not have to be melodic or consonant to be music. He wanted to experiment with the bounds of what music “can be” with the newest technology. This piece seems like frantic dabbling that was then arranged into patterns. Parts of it are almost danceable.

Morton, like many other electronic composers of his time, seems to want to experiment with what music “can be” and with the most recent technology. I feel the purpose of this piece was to create an a-tonal soundscape focussed heavily on rhythm. It makes me think of whale song fed through a bitcrusher.

Alvin seems to have set out to experiment with the idea of re-sampling and to show how anything can become musical. It also seems like he desired to see how far the human voice could be manipulated before it stopped sounding at all like a voice. It does not speak to me in any way.

Steve seems to desire to create a fitting tribute to this group of boys (I’m not sure how this was it at all or why he chose to use only one sample from the various ones he was given, but he did). I also think he was trying to show that, if altered through the right processes, even spoken words were very musical and could build not only rhythms but also musical lines. I personally find this work redundant and annoying, but musical all the same, just as a lot of pop music is.

Brian Eno is a well known composer of film scores and soundscapes. The collections on this album are no different and have the intended purpose of adding an atmosphere to a film or creating an emotional response in the listener. It makes me feel tense for the most part.

The purpose of the Beatles with this song was to sell massive quantities of it as all boy-bands do. It sounds sort of musically cool, I suppose. But to me it’s just like a lot of work done by Urban-Pop groups of the 90s but with more guitar.

The purpose of Afrika Bambaataa was to create a danceable, commercial beat. They succeeded. It does not speak to me in any way.

 

.nmsv and LogicX

Hey guys, this one is actually only sort of related to class. Anyways, I work with Massive and Logic Pro X and I design my own synth presets for them, so I thought I’d upload them and anyone in the class that wants to download them is more than welcome to take them and use them royalty free. So if you are interested in that, check out my categories and go to Native Instruments Massive or LogicX depending on what you are looking for. 🙂