/**

uniqueremainders1(Divisor,Values,UniqueRemainders)
For a chord progression (Values), finds the unique intervals between consecutive base notes (Remainders1).
Where a (the dividend) and n (the divisor) are in a mod n.

For: versechorussoloprogression('C','D').
[[C,D]]
?- uniqueremainders1(12,[0,2],UniqueRemainders).
UniqueRemainders = [2].

For: versechorussoloprogression('C','D').
[[C,G,D]]
?- uniqueremainders1(12,[0,7,2],UniqueRemainders).
UniqueRemainders = [7].

For: versechorussoloprogression('C','E').
[[C,D,E]]
?- uniqueremainders1(12,[0,2,4],UniqueRemainders).
UniqueRemainders = [2].

For: versechorussoloprogression('C','E').
[[C,D,A,E]]
?- uniqueremainders1(12,[0,2,9,4],UniqueRemainders).
UniqueRemainders = [2, 7]

For: versechorussoloprogression('C','E').
[[C,G,A,E]]
?- uniqueremainders1(12,[0,7,9,4],UniqueRemainders).
UniqueRemainders = [7, 2]

For: versechorussoloprogression('C','E').
[[C,G,D,E]]
?- uniqueremainders1(12,[0,7,2,4],UniqueRemainders).
UniqueRemainders = [7, 2]

For: versechorussoloprogression('C','E').
[[C,G#,E]]
?- uniqueremainders1(12,[0,8,4],UniqueRemainders).
UniqueRemainders = [8]

For: versechorussoloprogression('C','D#').
[[C,G,D#]]
?- uniqueremainders1(12,[0,7,3],UniqueRemainders).
UniqueRemainders = [7, 8]

For: versechorussoloprogression('C','D#').
[[C,G#,D#]]
?- uniqueremainders1(12,[0,8,3],UniqueRemainders).
UniqueRemainders = [8, 7] 

**/

uniqueremainders1(Divisor,Values1,UniqueRemainders) :-
	Values1=[Value|Values2],
	uniqueremainders2(Divisor,Value,Values2,[],Remainders1),
	Remainders1=[Remainder|Remainders2],
	unique1(Remainders2,Remainder,[],UniqueRemainders).
uniqueremainders2(_Divisor,_Value,[],Remainders,Remainders) :- !.
uniqueremainders2(Divisor,Value1,Values1,Remainders1,Remainders2) :-
	Values1=[Value2|Values2],
	Dividend is Value2-Value1,
	Remainder is Dividend mod Divisor,
	append(Remainders1,[Remainder],Remainders3),
	uniqueremainders2(Divisor,Value2,Values2,Remainders3,Remainders2).

%% unique1(Remainders,Remainder,UniqueRemainders1,UniqueRemainders2)
%% Given the initial list of UniqueRemainders1, the first Remainder and the other Remainders, returns the remainders that are unique (UniqueRemainders2).

unique1(_Remainders,[],UniqueRemainders,UniqueRemainders) :- !.
unique1(Remainders1,Remainder,UniqueRemainders1,UniqueRemainders2) :-
	delete(Remainders1,Remainder,Remainders2),
        append([Remainder],Remainders2,Remainders3),
	unique2(Remainders3,Remainders4,Remainders5,UniqueRemainders1,UniqueRemainders3),
        unique1(Remainders5,Remainders4,UniqueRemainders3,UniqueRemainders2).
unique2(Remainders1,Remainder1,Remainders2,UniqueRemainders1,UniqueRemainders2) :-
        Remainders1=[Remainder2,Remainder1|Remainders2],
	append(UniqueRemainders1,[Remainder2],UniqueRemainders2).
unique2(Remainders1,_Remainder1,Remainder2,UniqueRemainders1,UniqueRemainders2) :-
        Remainders1=[Remainder2],
        append(UniqueRemainders1,[Remainder2],UniqueRemainders2).