Just intonation point: Difference between revisions
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The '''JIP''' ('''just intonation point''') is a special tuning map that maps every monzo in some subgroup to its | The '''JIP''' ('''just intonation point''') is a special tuning map that maps every monzo in some subgroup to its span in cents (or any other unit), relative to the point 1/1 (which maps to 0 cents). | ||
For instance, in 5-limit JI, the JIP is {{val | 1200.000 1901.955 2786.314 }}; if we take the bracket product of this tuning map with any monzo, we get its size in cents. | For instance, in 5-limit JI, the JIP is {{val | 1200.000 1901.955 2786.314 }}; if we take the bracket product of this tuning map with any monzo, we get its size in cents. Of course, one can always build the JIP using different units than cents. | ||
For prime limits, the JIP has a particularly simple definition in Tenney-weighted coordinates, where it is always the all-ones vector or {{val | 1 1 1 ...}}. | For prime limits, the JIP has a particularly simple definition in Tenney-weighted coordinates, where it is always the all-ones vector or {{val | 1 1 1 ...}}. | ||