equal temperament

It turns out what I've been calling the 12-step rational scale is the scale used in the system called 'equal temperament.' And equal temperament is the main system used in western music. (Temperament is an archaic term meaning tuning.)

In equal temperament, the scale I've been calling the 12-step rational scale is called the 'chromatic' scale. And the scale I've been calling the 7-step rational scale is called the 'diatonic' scale.

The tuning - the set of pitches - used in the natural scale is called 'just intonation.' (Intonation is another way of saying tuning.)

Most modern western instruments are tuned using equal temperament.

Here's a graphic of a part of the modern keyboard (i.e., the keyboard used in a modern keyboard instrument, like the piano or the synthesizer):

_____________________________________________________________________
   |  |/|  |/|  |  |/|  |/|  |/|  |  |/|  |/|  |  |/|  |/|  |/|  |
   |  |/|  |/|  |  |/|  |/|  |/|  |  |/|  |/|  |  |/|  |/|  |/|  |
   |  |/|  |/|  |  |/|  |/|  |/|  |  |/|  |/|  |  |/|  |/|  |/|  |
   |  |/|  |/|  |  |/|  |/|  |/|  |  |/|  |/|  |  |/|  |/|  |/|  |
   |   |    |   |   |    |    |   |   |    |   |   |    |    |   |
   |   |    |   |   |    |    |   |   |    |   |   |    |    |   |
   |   |    |   |   |    |    |   |   |    |   |   |    |    |   |
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

• the pattern
  • 7 white keys[1], interspersed with 5 black keys

the full set of 12 pitches (both white and black keys) is the chromatic scale

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footnotes

1. In western music theory, there are two terms named 'key,' with very different meanings. In this context, a key is a user interface device, pushed/struck by the user's finger.