Most of you probably know the C major scale:
C D E F G A B C
2 2 1 2 2 2 1
From these intervales, we can construct any major scale starting in any note (the key of the scale). The 12 notes in our 12-tone equal temperament tuning system are:
C C♯ D D♯ E F F♯ G G♯ A A♯ B
equivalently (substituting some enharmonic equivalents):
C D♭ D E♭ E F G♭ G Ab A B♭ B
with a semitone between each pair of adjacent notes.
Each scale has to have the seven notes in order, starting from the key. Otherwise, you could have two notes in the same line of the pentagram, which would be confusing. So, in G# major/ionian, you have F## instead of G; musicians will just look at where in the pentagram is the note, they already have learned the accidentals for each scale. Indeed, in G# major, F## is represented in the line of F## without accidentals, the accidentals are in the key signature - but since that key signature would require 2 sharps for F, usually this is notated as Ab major.
2 2 1 2 2 2 1 intervals, we arrive at seven different modes of the diatonic scale:
2 2 1 2 2 2 1- corresponds to the major scale
2 1 2 2 2 1 2
1 2 2 2 1 2 2
2 2 2 1 2 2 1
2 2 1 2 2 1 2
2 1 2 2 1 2 2- corresponds to the natural minor scale, and to the melodic minor scale when descending (when ascending, the melodic minor scale has raised 6th and 7th degrees. There is also a harmonic minor scale, with a raised 7th degree compared to the natural minor).
1 2 2 1 2 2 2
So, the challenge is to write a program that takes as input (via stdin) a key and a mode and outputs (via stdout) the corresponding scale. Some test cases (stdin(
mode) => stdout(
Input: Output: C mixolydian => C D E F G A Bb F mixolydian => F G A Bb C D Eb G mixolydian => G A B C D E F G# ionian => G# A# B# C# D# E# F## Bb aeolian => Bb C Db Eb F Gb Ab
How many (major and minor) keys are there? Why?