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Encyclopedia of Microtonal Music Theory

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unique

[Paul Erlich]

An equal temperament uniquely articulates just intonation in some odd limit if all just intervals of that odd limit are approximated by different numbers of steps in the ET.

For example, 12-tET does not uniquely articulate the 7-limit because 7:5 and 10:7 are both approximated by 6 steps and 6:5 and 7:6 are both represented by 3 steps. The data for this case are tabulated in the last column of this table.

Although this definition is perfectly applicable to non-octave equal temperaments, uniqueness may also be defined with respect to an "integer limit". The data for this case are tabulated in the second-to-last column of this table.

[Joe Monzo]

The data for ETs thru 72 are plotted on the following chart:

unique
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