Wedgie: Difference between revisions

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== How to read a wedgie ==

~~Following intuitions from [[ploidacot]], one~~ way to characterize temperaments is by how many parts they split important intervals into – for example, the perfect fifth and the ~~octave~~.

One way to characterize temperaments is by how many parts they split important intervals into – for example, the octave and the perfect fifth. The [[ploidacot]] system works under this principle, and the reader is encouraged to be familiarized with it.

For any ''n''-prime subgroup of a rank-''n'' temperament, there exist a finite number (1 or more) of copies of that subgroup within the temperament. Think of these as "universes" that are connected exclusively by intervals of that subgroup and may be travelled between by using intervals outside the subgroup. For example, a temperament that is [[Ploidacot/Diploid dicot|diploid dicot]] – dividing the octave into two parts and also dividing the perfect fifth into two parts – will have a 2.3 wedgie entry of 4 (since there are four distinct copies of the 3-limit – the basic 3-limit, offset by a neutral third, offset by a semioctave, and offset by both). Each wedgie entry counts the number of copies of its corresponding subgroup. Because any temperament can be defined by splitting some interval and assigning the parts just interpretations, this is enough to uniquely characterize the temperament.

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 == How to read a wedgie ==
-Following intuitions from [[ploidacot]], one way to characterize temperaments is by how many parts they split important intervals into – for example, the perfect fifth and the octave.
+One way to characterize temperaments is by how many parts they split important intervals into – for example, the octave and the perfect fifth. The [[ploidacot]] system works under this principle, and the reader is encouraged to be familiarized with it.
 For any ''n''-prime subgroup of a rank-''n'' temperament, there exist a finite number (1 or more) of copies of that subgroup within the temperament. Think of these as "universes" that are connected exclusively by intervals of that subgroup and may be travelled between by using intervals outside the subgroup. For example, a temperament that is [[Ploidacot/Diploid dicot|diploid dicot]] – dividing the octave into two parts and also dividing the perfect fifth into two parts – will have a 2.3 wedgie entry of 4 (since there are four distinct copies of the 3-limit – the basic 3-limit, offset by a neutral third, offset by a semioctave, and offset by both).  Each wedgie entry counts the number of copies of its corresponding subgroup. Because any temperament can be defined by splitting some interval and assigning the parts just interpretations, this is enough to uniquely characterize the temperament.