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'''), also known as '''just tuning map''', 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 ~~[[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 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 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 … }}.

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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'''), also known as '''just tuning map''', 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 [[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 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 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 … }}.