Mathematics Page

Questions on the Mathematics of Computer Music, part 1


  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.


  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)


  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.

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