For theoretical purposes, the absolute model is usually too specific. Perceptually, most of a tuning's identity comes from the ratios between its frequencies rather than the exact values of the frequencies themselves. For example, even if the frequencies of one piano's strings are 1.01 times higher than those of another piano, they can both be said to be tuned in 12TET. This motivates the definition of a relative tuning as a map from a set of pitches to frequency ratios that are understood to share an implicit undefined reference. For example, a relative tuning of the pitches {C3, E3, G3} might map them to the ratios {1, 1.26, 1.5}.
A relative tuning's frequency ratios can be interpreted as frequencies
with undefined units, or relative frequencies. Note that a frequency
ratio does not have to be a ratio of integers: it can be any real
number. Figure 3.2 is a block diagram of a relative
tuning.
In order to understand the idea of a relative tuning, it may be
helpful to think about how one could be used to build an absolute
tuning. To build an absolute tuning from the example relative tuning
above, a reference frequency x must be chosen and each element of
the ratio set multiplied by it to yield the frequency set {x,
1.26x, 1.5x}. If x is chosen to be 261 Hz, the resulting absolute
tuning is {261 Hz, 329 Hz, 391 Hz}. Figure 3.3 is a block
diagram of an absolute tuning built using a relative tuning, a
reference frequency, and a multiplier (symbolized by `
').
