Mode height: Difference between revisions
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'''Mode height''' is the average [[pitch]] height of a [[mode]] of a [[scale]]. It can take values between -1 and 1 exclusive, where [[symmetric mode]]s have a mode height of 0. | |||
Consider the [[diatonic scale]] in [[12edo]] as an example. | Consider the [[diatonic scale]] in [[12edo]] as an example. | ||
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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. | 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. | ||
== In equal tunings == | |||
The mode height of a scale in an [[equal tuning]] may instead be expressed in degrees of the tuning<ref>[[Hearne, Lillian M.]] (2020). [https://researchers-admin.westernsydney.edu.au/ws/portalfiles/portal/94900730/uws_58606.pdf "The Cognition of Harmonic Tonality in Microtonal Scales"], p. 171. ''Western Sydney University''. Retrieved 21 July 2025.</ref>. In that case, the values it can take are between -''N''/2 and -''N''/2 exclusive, where ''N'' is the number of degrees of the tuning spanned by the mode. | |||
== References == | |||
<references /> | |||
[[Category:Scale]] | [[Category:Scale]] | ||
[[Category:Terms]] | [[Category:Terms]] | ||