CMC is not a colour space but rather a tolerancing system.
CMC tolerancing is based on CIELAB (L*C*h) and provides better agreement between visual assessment and measured colour difference. CMC tolerancing was developed by the Colour Measurement Committee of the Society of Dyers and Colourists in Great Britain and became public domain in 1988.
The CMC calculation mathematically defines an ellipsoid around the standard colour with semi-axis corresponding to hue, chroma and lightness. The ellipsoid represents the volume of acceptable colour and automatically varies in size and shape depending on the position of the colour in colour space.
The ellipsoids in the orange area of colour space are longer and narrower than the broader and rounder ones in the green area. The size and shape of the ellipsoids also change as the colour varies in chroma and/or lightness.
The CMC equation allows you to vary the overall size of the ellipsoid to better match what is visually acceptable. By varying the commercial factor (cf), the ellipsoid can be made as large or small as necessary to match visual assessment. The cf value is the tolerance, which means that if cf=1.0, then Delta E CMC less than 1.0 would pass, but more than 1.0 would fail.
Since the eye will generally accept larger differences in lightness (l) than in chroma (c), a default ratio for (l:c) is 2:1. A 2:1 ratio will allow twice as much difference in lightness as in chroma. The CMC equation allows this ratio to be adjusted to achieve better agreement with visual assessment.