Diatonic Scale Steps

In the same way that the tuning of triads changes according to the position of the tuning slider, so does the tuning of the scales in which these triads are embedded. For example, the recognisable diatonic scale contains five large steps (major seconds) and two small steps (minor seconds) in the characteristic pattern LLSLLLS. Assuming a pure octave of 1200 cents:

When beta = 700 cents, the large steps are exactly twice the size of the small steps. This tuning is 12-TET, where the major second is two 12-TET steps, and the minor second is one 12-TET step.

As beta is increased, the large steps get larger and the small steps get smaller. For example, when beta = 705.88 cents (which is equivalent to 17-TET), the large steps are three times the size of the small steps.

When beta = 720 cents, the small steps shrink to zero, leaving five equally sized large steps. This tuning is called 5-TET, and is very close ot the tradition slendro scale of the Indonesian gamelon.

As beta is decreased below 700 cents, the large intervals get smaller and the small intervals get larger. For example, when beta = 694.74 cents (which is equivalent to 19-TET), the large steps are 1.5 times greater than the small steps.

When beta = 685.71 cents, the "large" steps and the "small" steps become the same size. This tuning is called 7-TET, and forms the scalic structure used in traditional Thai music and in the balafon music of Mandinka in West Africa.

The above tuning range of 685.71 to 720 cents is called the 5-limit ordinal tuning range of the syntonic continuum, and it is the tuning range over which this particular scale form (the seven-note diatonic) is recognisably diatonic because they consist of five large steps evenly interspersed by two small steps. Within this range there are many useful tunings such as the purer-tunings (indicated on the left of the tuning slider) and many notable equal temperaments (indicated on the right of the slider).

Each of the above tunings can be explored by setting the tuning slider to the relevant n-TET positions indicated to the right of the Syntonic slider. For extreme tunings like 7-TET and 5-TET at the ends of the slider, it is advisable to set the tone diamond to its right-most position.