Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

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;
}