Just intonation point: Difference between revisions
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The JI point, or '''JIP''', commonly denoted "J", is a point in ''p''-limit tuning space {{val|log<sub>2</sub>2 log<sub>2</sub>3 log<sub>2</sub>5 … log<sub>2</sub>''p''}}. If M is a monzo, then <J|M> is M evaluated in terms of octaves. If we shift to weighted coordinates, so that M = {{monzo|''m''<sub>2</sub> ''m''<sub>3</sub> ''m''<sub>5</sub> … ''m''<sub>''p''</sub>}} is represented by the ket vector {{monzo|e<sub>2</sub>log<sub>2</sub>2 e<sub>3</sub>log<sub>2</sub>3 e<sub>5</sub>log<sub>2</sub>5 … e<sub>''p''</sub>log<sub>2</sub>''p''}}, then J becomes correspondingly the bra vector {{val|1 1 1 … 1}}. | The JI point, or '''JIP''', commonly denoted "J", is a point in ''p''-limit tuning space {{val|log<sub>2</sub>2 log<sub>2</sub>3 log<sub>2</sub>5 … log<sub>2</sub>''p''}}. If M is a monzo, then <J|M> is M evaluated in terms of octaves. If we shift to weighted coordinates, so that M = {{monzo|''m''<sub>2</sub> ''m''<sub>3</sub> ''m''<sub>5</sub> … ''m''<sub>''p''</sub>}} is represented by the ket vector {{monzo|e<sub>2</sub>log<sub>2</sub>2 e<sub>3</sub>log<sub>2</sub>3 e<sub>5</sub>log<sub>2</sub>5 … e<sub>''p''</sub>log<sub>2</sub>''p''}}, then J becomes correspondingly the bra vector {{val|1 1 1 … 1}}. | ||
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Revision as of 03:14, 26 July 2020
The JI point, or JIP, commonly denoted "J", is a point in p-limit tuning space ⟨log22 log23 log25 … log2p]. If M is a monzo, then <J|M> is M evaluated in terms of octaves. If we shift to weighted coordinates, so that M = [m2 m3 m5 … mp⟩ is represented by the ket vector [e2log22 e3log23 e5log25 … eplog2p⟩, then J becomes correspondingly the bra vector ⟨1 1 1 … 1].