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" caseThus key number 70, a black key, can be thought of as A♯ or B♭
In textual notation, you'll often see
#
for♯
andb
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