User:Holger Stoltenberg/sandbox: Difference between revisions

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 == A variety of projections of the model ==
-Keep in mind that Fig.3 is just one ''graphical representation of relationships'' between pitches, musical intervals and overtone scales. More specifically, Fig.3 shows one of many useful Cartesian projections of an abstract model onto a 2D-plane.
+Keep in mind that the ''Horizon Chart'' (Fig.3) is just one ''graphical representation of relationships'' between pitches, musical intervals and overtone scales. More specifically, Fig.3 shows one of many useful Cartesian projections of an abstract model onto a 2D-plane.
-This kind of Cartesian projection of tonal space (with a straight horizontal line for each mode of an overtone scale) can be easily handled in a programming environment.
+Nevertheless, this representation is the basis for a variety of ''realtime'' ''operations on chords'' that a future musical instrument can apply. In addition, the Cartesian projection of tonal space (with a straight horizontal line for each mode of an overtone scale) can be easily handled in a programming environment.
+== Polar projection of tonal space ==
+In polar projection of the model, the horizontal ''mode'' lines form circles:
+[[File:Fig-4 tonal space POLAR 149.png|458px|center]]