# Mode height

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The average pitch height of a mode. It can take values between -1 and 1 exclusive, where symmetric modes have a mode height of 0.

Consider the diatonic scale in 12edo as an example.

We may write the Ionian (major) as 0 200 400 500 700 900 1100 1200.

We don't have to consider 0 and 1200 in calculating the mode height, as those notes are on either end and cancel each other out. To calculate the mode height we first shift the scale so that 0 cents is in the middle of the period, so we take away 600c from every interval. The mode height of the Ionian mode is then (-400 + (-200) + (-100) + 100 + 300 + 500) / (1200*6) = 0.02778.