• 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"

Last modified: Tuesday, 18 May 2021, 2:13 PM