Harry Partch's 43-tone scale: Difference between revisions

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See [[Partch 43]] for the scale as a scala file.

===Ratios of the 11 Limit===

==Ratios of the 11 Limit==

Here are all the ratios within the [[octave]] with odd factors up to and including 11, known as the 11-limit [[tonality diamond]]. Note that the [[Inversion (interval)|inversion]] of every interval is also present, so the set is symmetric about the octave.

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===Filling in the gaps===

==Filling in the gaps==

There are two reasons why the 11-limit ratios by themselves would not make a good scale. First, the scale only contains a complete set of chords ([[otonalities]] and [[utonalities]]) based on one [[tonic (music)|tonic]] pitch. Second, it contains large gaps, between the tonic and the two pitches to either side, as well as several other places. Both problems can be solved by filling in the gaps with "multiple-number ratios", or intervals obtained from the product or quotient of other intervals within the 11 limit.

@@ Line 4: / Line 4: @@
 See [[Partch 43]] for the scale as a scala file.
-===Ratios of the 11 Limit===
+==Ratios of the 11 Limit==
 Here are all the ratios within the [[octave]] with odd factors up to and including 11, known as the 11-limit [[tonality diamond]]. Note that the [[Inversion (interval)|inversion]] of every interval is also present, so the set is symmetric about the octave.
@@ Line 31: / Line 31: @@
 |}
-===Filling in the gaps===
+==Filling in the gaps==
 There are two reasons why the 11-limit ratios by themselves would not make a good scale. First, the scale only contains a complete set of chords ([[otonalities]] and [[utonalities]]) based on one [[tonic (music)|tonic]] pitch. Second, it contains large gaps, between the tonic and the two pitches to either side, as well as several other places. Both problems can be solved by filling in the gaps with "multiple-number ratios", or intervals obtained from the product or quotient of other intervals within the 11 limit.