[UVA] 10528 - Major Scales
Problem C: Major Scales
In music, the range of audible frequencies is divided into octaves, where each octave spans frequencies within factor of 2 of one another. For example, the note called middle C corresponds to an audio frequency of 263 Hz. The octave below middle C spans the frequency range from 131.5 Hz to 263 Hz while the octave above middle C spans the range from 263 Hz to 526 Hz.An octave contains 13 chromatic notes whose frequencies differ by a common ratio. The separation between two adjacent chromatic notes is called a half-step or semi-tone. Note that there are 12 semi-tones in an octave and therefore the frequency ratio represented by a semi-tone is 1.0593 (since 1.059312 = 2). A tone is two semi-tones.
While it might be convenient to use frequencies to describe musical notes, historical tradition demands that we name the notes of the chromatic scale, in order: C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C, and so on, repeating the same names for each new octave.
Western music rarely uses all the notes in the chromatic scale. Instead, 8 of the 13 chromatic notes are commonly used a composition. The most common such set of 8 notes is the major scale. The 8 notes of a major scale, in order, are separated by: tone, tone, semi-tone, tone, tone, tone, semi-tone. A major scale can begin with any of the chromatic notes; this note defines the key of the scale. Coincidentally, in the key of C, the major scale consists of the notes: C, D, E, F, G, A, B, C. On the other hand, in the key of F, the major scale is: F, G, A, A#, C, D, E, F.
There are other scales, notably the minor scale, and music composed in a particular scale sometimes uses notes that are not within the scale, caled accidentals. We shall concern ourselves only with music composed in a major scale with no accidentals.
Your job is to read a sequence of notes and to identify all the keys that the music might have been composed in. Your program need not have any musical ear: report a particular key if and only if all the notes come from the major scale in that key.
Input contains several test cases. Each test case consists of a single line of input, containing a sequence of chromatic notes separated by white space. No input line exceeds 1000 characters. The last line of input contains the word "END".
For each test case, output a line giving the possible keys, in the order given above.
Sample Input
C C D F E G A A F G B A B C D E F G C# C C D F E G A A F G C C C C C END
Output for Sample Input
C C F C C# D# F G G# A#
G. Cormack
對於每個主旋律，什麼大調，都是按照全全半全全全半的方式去分布。
藉此得到每個大調分別存在的七個音，然後窮舉所有可能去檢查，是否存在。
#include <stdio.h>
#include <string.h>
#include <set>
#include <iostream>
#include <sstream>
using namespace std;
int main() {
char s[12][10] = {"C","C#","D","D#","E",
"F","F#","G","G#","A","A#","B"};
int cross[7] = {2,2,1,2,2,2,1};
int i, j;
set<string> S[12];
for(i = 0; i < 12; i++) {
int pos = i;
for(j = 0; j < 7; j++) {
pos += cross[j];
pos %= 12;
S[i].insert(s[pos]);
}
}
string line;
while(getline(cin, line)) {
if(line == "END") break;
stringstream sin(line);
string A[1005];
int n = 0;
while(sin >> A[n])
n++;
int first = 0;
for(i = 0; i < 12; i++) {
int ok = 1;
for(j = 0; j < n && ok; j++) {
if(S[i].find(A[j]) == S[i].end())
ok = 0;
}
if(ok) {
if(first) putchar(' ');
first = 1;
printf("%s", s[i]);
}
}
puts("");
}
return 0;
}