Intervals
Intervals are generated by frequency ratios. All intervals comes from ratio 2^(n/12).
n = 0 => Frequency Ratio: 1.000
n = 1 => Frequency Ratio: 1.059
n = 2 => Frequency Ratio: 1.122
n = 3 => Frequency Ratio: 1.189 (1.200) Minor 3rd
n = 4 => Frequency Ratio: 1.260 (1.250) Major 3rd
n = 5 => Frequency Ratio: 1.335 (1.333) Perfect 4th
n = 6 => Frequency Ratio: 1.414
n = 7 => Frequency Ratio: 1.498 (1.500) Perfect 5th
n = 8 => Frequency Ratio: 1.587
n = 9 => Frequency Ratio: 1.682
n = 10 => Frequency Ratio: 1.782
n = 11 => Frequency Ratio: 1.888
n = 12 => Frequency Ratio: 2.000
For example, if we start from note from A at frequency 440 Hz, then we got:
The Minor Third Interval ( n = 3 ) will be note from C at frequency 523 Hz; the frequency ratio between notes is 1.200 or 6/5; the number of semitones in this interval is 3.
The Major Third Interval ( n = 4 ) will be note from C# at frequency 554 Hz; the frequency ratio between notes is 1.250 or 5/4; the number of semitones in this interval is 4.
The Perfect Fourth Interval ( n = 5 ) will be note from D at frequency 587 Hz; the frequency ratio between notes is 1.333 or 4/3; the number of semitones in this interval is 5.
The Perfect Fifth Interval ( n = 7 ) will be note from E at frequency 659 Hz; the frequency ratio between notes is 1.500 or 3/2; the number of semitones in this interval is 7.
Harmonics (Fundamentals and Overtones)
The fundamental, or first harmonic, is the lowest frequency in a given signal.
The overtones (second harmonic, third harmonic, etc.) have frequencies that are integer multiples of the fundamental frequency f (second harmonic has frequency 2f, third harmonic has frequency 3f, ...).