Just intonation point: Difference between revisions
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The '''just intonation point''' ('''JIP''') is a special [[tuning map]] that maps every [[monzo]] in some [[subgroup]] to its [[span]] in [[cent]]s (or any other logarithmic [[interval size unit]]), relative to the point 1/1 (which maps to 0 cents). | The '''just intonation point''' ('''JIP''') is a special [[tuning map]] that maps every [[monzo]] in some [[subgroup]] to its [[span]] in [[cent]]s (or any other logarithmic [[interval size 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 {{w|dot 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 instance, in 5-limit JI, the JIP is {{val | 1200.000 1901.955 2786.314 }}; if we [[Mathematical guide/Matrix operations#Dot product|take]] the {{w|dot 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, {{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, {{val | 1 1 1 … }}. | ||