Music

Music

• Just any ol' sounds people find pleasing

• We will work in the "classical" realm of notes and note combinations

• Further, we will work in the "western" paradigm with particular "scales" and "chords" and stuff

Review: Notes

• A note is a sound with a perceived frequency and duration

• 440Hz is A above middle C (MIDI key 69)

• Split the octave between 440Hz and 880Hz into 12 equal parts with the same ol' identity

  $$ f = 440 \cdot 2^{(k - 69)/12} $$

• Formula holds down to near 0Hz and up to infinity

Review: Relative Pitch

• The ear (usually) only hears relative pitch

• We could have started with any base frequency rather than 440 and done the same thing

• For example, we could have chosen

  $$ 440 \cdot 2^{(k - 71)/12} \approx 493.88 \cdot 2^{(k - 69)/12} $$

• Then we would have a scale "two half-steps up" from 440

The Piano Keyboard Is Special

• White keys going from middle C to next C up define a "C major scale"

• A scale is a set of notes within an octave

• The C major scale has eight notes: MIDI key numbers

  60, 62, 64, 65, 67, 69, 71
  

• The pattern here is in "half-steps":

  0, +2, +2, +1, +2, +2, +2 (, +1)
  

• If we repeat this same pattern of half-steps starting from any key on the keyboard, we get a major scale

• All major scales sound alike: "happy", "default"

Stupid Note Names

• We name the white keys on the piano by letter. We use A for key 69, and go up/down by eights

• This means that our C-major scale is

  C, D, E, F, G, A, B, C

• A black key can be thought of as a half-step up from the white key just to its left, or a half-step down from the white key just to its right

• Each black key gets two names: a "sharp" name ♯ for the "half-step-up" case, and a "flat" name ♭ for the "half-step-down" case

• Thus key number 70, a black key, can be thought of as A♯ or B♭

• In textual notation, you'll often see # for ♯ and b for ♭

• (In general, "sharp" means "toward higher frequencies" and "flat" means "toward lower frequencies")

Example: Relative Major Scales

• Let's work out the D major scale

  • start with D (key 62)

  • Then go +2, +2, +1, +2, +2, +2 (, +1)

  • So D, E, F# (Gb), G, A, B, C# (Db), D

Note Duration

• Divide music into "beats": typically 45-130 bpm (classical beat rates)

• If a note's duration is a single beat, it is usually a "quarter note" (because reasons, see below)

• Note duration is typically 1/16 to 4 beats but can vary outside that range: mostly "snap-quantized" to the beats

Beat Groupings — Time Signature

• Group up beats into collections usually of 4, sometimes of 3, occasionally others

• This defines the "time signature" of a piece of music: this is usually written as a fraction

• For example, a time signature of 4/4 says that the music will be grouped into 4-beat sections, with each beat a quarter note

• 4/4 is known as "common time" ?, because it is… well, common

Make "A Piece Of Music"

• Pick a beat rate

• Pick a time signature

• Pick notes and note durations

  • (They can overlap)

• But probably don't want to memorize it, so need to record somehow

  • Record audio performance (but how to repeat it?)

  • Record MIDI key down/up events (but how to read/analyze it?)

  • Some kind of "music notation"