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Figures 9 Starting from 0 and using only major third and minor third you create this matrix and then locate in the MEUYAN all the pitch classes of a GIVEN SCALE AND ALL THE TRIADS OF THIS SCALE In this way you can locate all scales and their triads I think that it is something you can find only in the western music there are no other pitch collections with such properties in The meuyan From the article Balzano s direct product group Single steps are minor thirds in the y dimension and major thirds in the x dimension A diatonic major set is shown based around C as an asymmetrical region Note that this two dimensional representation constitutes an unrolling of a toroidal structure on the surface of which all points of the same integer are coincident ABOUT CIRCLE OF FIFHT Take a look at the down left circle if you start from any note and go in the watch direction 5 steps and add to this pitch classes collection the pitch class that stands one step downward you will see that you have all the pitch classes of the scale of the one you start but not in order in a terminology I learned from you we got the set of 7 but not as an order list It sounds a little complicated but if you ll try it on the circle its very easy For example lets start from A and then going in the circle we got E B F C G the one downward A D D A E B F C G The pitch classes of the scale A Major as you know you can build the same circle going down fifths for the Bemol scales Figure 8 FROM THE ARTICLE Upper two circles show the chroma circle as note names and as integers lower two circles show the circle of fifths as note names and as integers



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