### Understanding Machine[6]

Machine[6] is a 6 (unique) note per octave tuning. In 11-equal (11edo), it can be described as "Moment of symmetry" scale (MOS) where we are stacking every 2 steps of 11-edo ("using 2\11 as a generator") and taking the clock-arithmetic remainder (modulus) if & when we pass the octave (step #11 of 11-edo).

### Recipe:

- Create a stack of 6 notes from a given starting note; make them 2\11 (or 2deg11 or "2 degrees of 11-edo") apart:

**0 2 4 6 8 10**("0" represents the starting pitch) - Sort the list in order, add the octave (in this case, no sorting required, because we haven't had to do any clock-wrapping:

**0 2 4 6 8 10 (11)**("0" and "11" represent the same starting pitch) - If we measure the "gaps" between the neighboring pitches in the series above, we get another way of representing the series:

**2 2 2 2 2 1**

Notice it confirms to the definition of a MOS scale, it only has 2 sizes of gap, an 'L' and an 'S' (large and small, and we don't care what the relative size of 'L' and 'S' are, as long as there are only 2 sizes. Any scale with 2 step sizes is called a MOS, for "Moment of Symmetry". You can play around with a MOS JavaScript app here.

In cents, the scale would look like so:

0.0

218.181818182 (2 steps of 11-edo)

436.363636364 (another 2 steps up, etc.)

654.545454545

872.727272727

1090.90909091

1200.0 (1 step from the previous position)

Just like any other scale, we can rotate the list of inter-note distances and get a different "mode", e.g. **2 2 1 2 2 2** instead of **2 2 2 2 2 1**.