7edo: Difference between revisions

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Observations: Add observations about stretched octave
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7edo is the unique intersection of the temperaments of [[meantone]] (specifically [[3/4-comma meantone]]) and [[porcupine]].
7edo is the unique intersection of the temperaments of [[meantone]] (specifically [[3/4-comma meantone]]) and [[porcupine]].


The [[Octave stretch|stretched-octaves]] tuning [[Ed258/128#7ed257/128|7ed257/128]] greatly improves 7edo’s approximation of 3/1, 5/1 and 11/1, at the cost of slightly worsening 2/1 and 7/1, and greatly worsening 13/1. If one is hoping to use 7edo for [[11-limit]] harmonies, then 7ed257/128 is a good choice to make that easier.
The [[Octave stretch|stretched-octaves]] tuning [[Ed257/128#7ed257/128|7ed257/128]] greatly improves 7edo’s approximation of 3/1, 5/1 and 11/1, at the cost of slightly worsening 2/1 and 7/1, and greatly worsening 13/1. If one is hoping to use 7edo for [[11-limit]] harmonies, then 7ed257/128 is a good choice to make that easier.


The stretched 7edo tuning [[zpi|15zpi]] can also be used to improve 7edo’s approximation of JI in the same way.
The stretched 7edo tuning [[zpi|15zpi]] can also be used to improve 7edo’s approximation of JI in the same way.