Vals and tuning space: Difference between revisions
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A '''val''' "maps" [[just intonation]] to a certain number of steps in a chain of [[generator]]s; by putting vals together we can define the mapping of a [[regular temperament]] and thereby define the temperament. A val is written in the form {{val| ''a''<sub>1</sub> ''a''<sub>2</sub> ''a''<sub>3</sub> … ''a''<sub>''k''</sub> }}, where the numbers ''a''<sub>1</sub> ''a''<sub>2</sub> ''a''<sub>3</sub> … are the number of steps along the chain that the first ''k'' [[prime]]s are mapped to. This can be generalized so that ''a''<sub>1</sub> ''a''<sub>2</sub> ''a''<sub>3</sub> … represent the number of steps any JI [[basis]] is mapped to, whereas a JI basis for a [[just intonation subgroup]] is an independent collection of just intonation intervals, meaning that no one of them is a product of the rest. | A '''val''' "maps" [[just intonation]] to a certain number of steps in a chain of [[generator]]s; by putting vals together we can define the mapping of a [[regular temperament]] and thereby define the temperament. A val is written in the form {{val| ''a''<sub>1</sub> ''a''<sub>2</sub> ''a''<sub>3</sub> … ''a''<sub>''k''</sub> }}, where the numbers ''a''<sub>1</sub> ''a''<sub>2</sub> ''a''<sub>3</sub> … are the number of steps along the chain that the first ''k'' [[prime]]s are mapped to. This can be generalized so that ''a''<sub>1</sub> ''a''<sub>2</sub> ''a''<sub>3</sub> … represent the number of steps any JI [[basis]] is mapped to, whereas a JI basis for a [[just intonation subgroup]] is an independent collection of just intonation intervals, meaning that no one of them is a product of the rest. | ||