Originally scale intervals were define by the ratios between the tones and were derived from ratios found in overtones. These are called natural scales. A capella groups sometimes sing in these natural scales. However, they do not allow composers much freedom to change keys in the middle of a piece and could even required retuning of instruments between pieces if the keys were different.
During the 18th century muscicians figured out a new way of tuning where the intervals were averaged between all the possible values, this was called equal-tempered scales. Johann Sebastian Bach wrote a famous set of keyboard pieces taking advantage of this new way of doing scales, The Well-Tempered Klavier.
In this illustration, you can play several scales both with natural tuning and with well-tempered tuning.
To see the illustration in full screen, which is recommended, press the Full Screen button, which appears at the top of the page.
Below is a list of the ways that you can alter the illustration. The settings include the following:
Keyboard: click or touch a key to play the tone associated
with that key. The tone lasts as long as the click or touch. The graph will
plot that frequency until the next tone is played.
Play Major: Press to have a C major scale played up and then down.
Play Minor: Press to have a c minor scale played up and then down.
Play Chromatic: Press to have a chromatic scale played up and then down.
Play Pentatonic: Press to have a pentatonic scale played up and then down.
Type of Scale: select which type of tuning you wish to use, natural or equal tempered.
Pressing this button restores the settings to their default values.