Geometric mean: Difference between revisions

(2 intermediate revisions by one other user not shown)

Line 1:

: ''"Mean" redirects here. For other types, see [[Pythagorean means]].''

In tuning, the '''geometric mean''', '''pitch mean''', or simply '''mean''' generates new pitch materials by taking the mean in the [[Wikipedia: Logarithmic scale|logarithmic scale]] of pitch i.e. the scale proportional to the logarithm of frequency. It can be said with respect to ~~frequencies or~~ frequency ratios on a certain common fundamental. The idea of treating [[quarter-comma meantone]] as the "strict" meantone is backed by this type of mean.

In tuning, the '''geometric mean''', '''pitch mean''', or simply '''mean''' generates new pitch materials by taking the mean in the [[Wikipedia: Logarithmic scale|logarithmic scale]] of pitch i.e. the scale proportional to the logarithm of frequency, such as [[cent]]s. It can be said with respect to pitches in frequency as well as intervals in frequency ratios on a certain common fundamental. The idea of treating [[quarter-comma meantone]] as the "strict" meantone is backed by this type of mean.

The geometric mean ''f'' of two frequencies ''f''<sub>1</sub> and ''f''<sub>2</sub> is

Line 54:

* [[Mediant]]

[[Category:~~Theory~~]]

[[Category:Pythagorean means]]

[[Category:Terms]]

[[Category:Elementary math]]

@@ Line 1: / Line 1: @@
 : ''"Mean" redirects here. For other types, see [[Pythagorean means]].''
-In tuning, the '''geometric mean''', '''pitch mean''', or simply '''mean''' generates new pitch materials by taking the mean in the [[Wikipedia: Logarithmic scale|logarithmic scale]] of pitch i.e. the scale proportional to the logarithm of frequency. It can be said with respect to frequencies or frequency ratios on a certain common fundamental. The idea of treating [[quarter-comma meantone]] as the "strict" meantone is backed by this type of mean.
+In tuning, the '''geometric mean''', '''pitch mean''', or simply '''mean''' generates new pitch materials by taking the mean in the [[Wikipedia: Logarithmic scale|logarithmic scale]] of pitch i.e. the scale proportional to the logarithm of frequency, such as [[cent]]s. It can be said with respect to pitches in frequency as well as intervals in frequency ratios on a certain common fundamental. The idea of treating [[quarter-comma meantone]] as the "strict" meantone is backed by this type of mean.
 The geometric mean ''f'' of two frequencies ''f''<sub>1</sub> and ''f''<sub>2</sub> is
@@ Line 54: / Line 54: @@
 * [[Mediant]]
-[[Category:Theory]]
+[[Category:Pythagorean means]]
 [[Category:Terms]]
 [[Category:Elementary math]]