S-expression: Difference between revisions

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All S-expressions have other equivalent S-expressions, however when the equivalence makes one comma a member of two of the infinite families discussed on this page, or otherwise makes it equal to a product or ratio between two such commas, this basically always means exceptional and nontrivial ("deep") tempering opportunities, usually leading to multiple of the most elegant and efficient temperaments that we know of depending how you temper further. Generally we exclude 1/n-square-particulars, only noting up to 1/3-square-particulars, because equivalent 1/n-square-particular expressions become very common as you allow higher n, but are still quite rare for small n.  
All S-expressions have other equivalent S-expressions, however when the equivalence makes one comma a member of two of the infinite families discussed on this page, or otherwise makes it equal to a product or ratio between two such commas, this basically always means exceptional and nontrivial ("deep") tempering opportunities, usually leading to multiple of the most elegant and efficient temperaments that we know of depending how you temper further. Generally we exclude 1/n-square-particulars, only noting up to 1/3-square-particulars, because equivalent 1/n-square-particular expressions become very common as you allow higher n, but are still quite rare for small n.  


=== Incomplete table ===
=== Examples ===
Here is an incomplete list of examples (feel free to expand with any equivalences you find that you think are valuable):
Here is an incomplete list of examples (feel free to expand with any equivalences you find that you think are valuable):


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! Comma
! Comma
! S-expressions
! S-expressions
|-
| [[25/24]]
| S2/(S3*S4<sup>2</sup>) = S5
|-
| [[49/48]]
| S3/(S5*S6<sup>2</sup>) = S7
|-
| [[64/63]]
| (S4*S5*S6)/S3 = S4/(S6*S7) = S8
|-
|-
| [[81/80]]
| [[81/80]]