Changes

whole/half |--w--|--w--|-h|--w--|--w--|--w--|-h| note name C D E F G A B C fret on 1st 8 10 12 13 15 17 19 20 0 1 3 5 7 8 stretch whole, whole 8-----10----12 3-----5-----7 ring whole, half 10----12-13 5-----7--8 middle half, whole 12-13----15 7--8-----10 stretch2 whole, whole2 13----15----17

The 4-note whole/whole/half tetrachord is present twice in the major scale (C D E F, G A B C). We can see above that This combines a stretch pattern will cover the whole/whole, pattern ((C D E) and (G A B)) and a ring pattern will cover the whole/half((D E F) and (A B C)). Each The first tetrachord is always followed by connected to the second with a whole tone(F G). That This gives us a half/whole sequence is covered by the middle pattern(E F G). This gives us a stretchIf we reverse the order of tetrachords (G A B C, ringC D E F), and middle pattern for each tetrachordthey share the tonic note as an ending/starting point (C C). So we have 2 each Since the tonic note to the 2nd note in the scale is also a whole tone, this gives us the same pattern of those patterns for 2 tetrachordshalf/whole (B C D).  All that remains is the initial whole tone that bridges the two tetrachords(F G A). This is represented by "stretch2whole, whole2" above. If we reverse the order of tetrachords (G A B C, C D E F) we notice they overlap on the C - there is no whole or semitone between them - one goes right into the other. Thus, there is no additional 3 note pattern((C D E) is already covered in the first tetrachord).  We have 2 middle, 2 ring, and 3 stretch patterns per scale per octave (given that we need to extend one note past the octave to get the last 3 note pattern - see how the last middle pattern extends nowhere above). {|class="wikitable"! Pattern !! Tetrachord 1 !! Tetrachord 2 !! Tetrachord bridge |-| whole/whole || (C D E) || (G A B) || (F G A)|-| whole/half || (D E F) || (A B C)|-| half/whole || (E F G) || (B C D)|}

# whole/whole(stretch)# whole/half(ring)# half/whole(middle)# whole/whole(stretch2)# whole/whole(stretch)# whole/half(ring)# half/whole(middle)