Formulas & shortcuts
Music · 17
Every formula in this course and the easiest ways to remember them, on one page.
1Sound and musical instrumentsBeginner
Sound and its properties
Open lessonMusical instruments and the orchestra
Open lesson2Music literacy: notes, rhythm, scales and chordsIntermediate
Music notation: staff, clefs, note values and time signatures
Open lessonRhythm, metre and tempo
Open lessonScales, intervals and chords
Open lessonMajor: T – T – S – T – T – T – S
- Ttone (whole step) = 2 semitones
- Ssemitone (half step): the distance between neighbouring keys
C major uses only white keys: C – D – E – F – G – A – B – C.
Natural minor: T – S – T – T – S – T – T
A minor also uses only white keys: A – B – C – D – E – F – G – A.
3The history of world and Azerbaijani musicAdvanced
World music history: from Baroque to the 20th century
Open lessonAzerbaijani music: from mugham to jazz-mugham
Open lesson4Music theory and acousticsUniversity
Harmony, musical form and the physics of sound
Open lessonf = v / λf = v / λ
- ffrequency, in hertz (Hz)
- vwave speed, m/s (in air at 20 °C ≈ 343 m/s)
- λwavelength, m
In one second f waves pass, each λ long, so the wave travels f · λ = v per second.
f₁ = v / (2L), fₙ = n · f₁f₁ = v / (2L), fₙ = n · f₁
- Lvibrating length of the string, m
- vwave speed on the string (depends on its tension and mass), m/s
- nharmonic number: 1, 2, 3, …
Both ends of the string are fixed (nodes), so the longest standing wave is λ₁ = 2L and f₁ = v / λ₁ = v / (2L). Vibrating in halves gives 2f₁, in thirds 3f₁ — these are the overtones.
r¹² = 2 ⇒ r = 2^(1/12) ≈ 1.059463; f = f₀ · 2^(n/12)
- rthe frequency ratio of one semitone
- f₀reference frequency, e.g. A = 440 Hz
- nnumber of semitones from the reference (up +, down −)
Twelve equal steps must make an octave: r · r · … · r (12 times) = 2, so r = 2^(1/12) ≈ 1.059463.
c = 1200 · log₂(f₂ / f₁)c = 1200 · log₂(f₂ / f₁)
- cthe interval in cents; 1 equal semitone = 100 cents, an octave = 1200 cents