We talk about pitch and interval in music... when we play a note on our instruments, the strings or lips or reeds on our instruments vibrate. That vibration causes air to move and the air movement is picked up by our ears. It's how we hear. As long as we play the same note, the pitch of the sound we make remains constant and this constant pitch is called frequency. Frequency is the rate of speed that the air vibrates. It basically means vibrations per second, but we call it Hertz (Hz) after the person that figured it out. A4 (the A key in the fourth octave on a piano) is 440 vibrations per second or 440 Hz.
The interval is the distance between two different pitches. There are twelve half-tones or steps (white and black piano keys) in an octave. The pitch (or frequency) difference between any two half-tones is a factor of the twelfth root of 2 or 1.05946309436.... a bunch of math that means that if you multiply or divide the frequency of any note by 1.0546309436, you'll have the frequency of the note next to it. Let's try it...
We know that A4 is 440 Hz.
A#4 is 440 * 1.05946309436 OR 466.16 Hz.
G#4 is 440 / 1.05946309436 OR 415.30 Hz.
If you jump through those hoops twelve times, you've got yourself an octave. Another (shorter) way to do it is just to raise that twelfth root of 2 to the x power, where x equals the number of notes separation. Let's look at an octave...
Again, we know that A4 is 440 Hz, but we also know there are
twelve notes between any octave.
A5 is 440 * 1.05946309436 ^ 12 OR 880 Hz.
A5 is 440 / 1.05946309436 ^ 12 OR 220 Hz.
A non octave example is:
G5 is 440 * 1.05946309436 ^ 10 OR 783.990 Hz.
If you'll look close, any octave doubles (or halves) the pitch you start out with. Look at the chart below... it's easy to see in the octaves of A, but it works the same way for all notes. Beyond that, the math (actually physics) of music can get pretty involved; so much so that beyond what we've already done, we aren't even going to get into it here.
Middle C (C4) is 261.63 Hz.
American Standard Pitch is A4 at 440 Hz.
International Standard Pitch is A4 at 435 Hz.
| Octave | C | C# | D | D# | E | F | F# | G | G# | A | A# | B |
| 0 | 27.500 | 29.135 | 30.868 | |||||||||
| 1 | 32.703 | 34.648 | 36.708 | 38.891 | 41.203 | 43.654 | 46.249 | 48.999 | 51.913 | 55.000 | 58.270 | 61.735 |
| 2 | 65.406 | 69.296 | 73.416 | 77.782 | 82.407 | 87.307 | 92.499 | 97.999 | 103.83 | 110.00 | 116.54 | 123.47 |
| 3 | 130.81 | 138.59 | 146.83 | 155.56 | 164.81 | 174.61 | 185.00 | 196.00 | 207.65 | 220.00 | 233.08 | 246.94 |
| 4 | 261.63 | 277.18 | 293.66 | 311.13 | 329.63 | 349.23 | 369.99 | 392.00 | 415.30 | 440.00 | 466.16 | 493.88 |
| 5 | 523.25 | 554.37 | 587.33 | 622.25 | 659.26 | 698.46 | 739.99 | 783.99 | 830.61 | 880.00 | 932.33 | 987.77 |
| 6 | 1046.5 | 1108.7 | 1174.7 | 1244.5 | 1318.5 | 1396.9 | 1480.0 | 1568.0 | 1661.2 | 1760.0 | 1864.7 | 1975.5 |
| 7 | 2093.0 | 2217.5 | 2349.3 | 2489.0 | 2637.0 | 2793.8 | 2960.0 | 3136.0 | 3322.4 | 3520.0 | 3729.3 | 3951.1 |
| 8 | 4186.0 | 4434.9 | 4698.6 | 4978.0 | 5274.0 | 5587.7 | 5919.9 | 6271.9 | 6644.9 | 7040.0 | 7458.6 | 7902.1 |