Scales of chemical shifts:

Usually, the δ scale ranges from 0 to 12 ppm. A higher value of δ denotes the signal to be more downfield from the reference while a high field signal will correspond to a lower δ value.

This makes the shift dimensionless, other than a problem still keep. The value of the ratio is very small because the shift in field or frequency is nearly 10⁶ times smaller than the measuring field or frequency. Thus, we multiply this dimensionless quantity by 10⁶ and express it in terms of parts per million (ppm). Thus, the chemical shift, δ, is mathematically defined as follows:

δ =   ((v_Test  - v_TMS )/v_op )×10⁶

In sequence to circumvent this problem another scale called τ scale has been proposed. It is described as

τ = 10 - δ

Here the TMS is arbitrarily assigned a value of 10 τ. The unit is still in ppm with only difference in scale. The two scales are related as shown in Figure.

Figure: Schematic representation of δ the relationship between the δ and τ scales of chemical shifts

The classic chemical shift positions of some generally encountered function groups are given in Figure.

Figure: Range of chemical shift values for different types of protons