Make a program the takes 3 notes and builds the possible chords out of the combination of the three notes, including the root.

Description:

Most Western music is based on the chromatic scale: a series of 12 pitches, represented as notes, each a semitone apart. Notes are named with the letters A-G. Some notes are named just a letter, while some have a suffix called an accidental meaning a semitione above or below the note with the letter-name.

Starting from A, the 12 tones can be named

0

1

2

3

4

5

6

7

8

9

10

11

With #'s

A

A#

B

C

C#

D

D#

E

F

F#

G

G#

With b' s

A

Bb

B

C

Db

D

Eb

E

F

Gb

G

Ab

Other names

Cb

B#

Fb

E#

The difference between two successive notes is called a half-step. The order of notes is cyclic. That is, the note one half-step higher than G#/Ab is again A, and the note one half-step lower than A is Ab/G#. Notes that are a multiple of 12 half-steps apart have the same name, and for our purposes we will consider them equivalent.

Each pitch may have multiple names: A# is the same as Bb, C# is the same as Db, etc. The alternate names of a pitch is called an enharmonic.

Intervals

The distance between two notes is called an interval. The names of the intervals are:

Distance in Half-Steps	Name of Interval
0	Perfect unison
1	Minor second
2	Major second
3	Minor third
4	Major third
5	Perfect fourth
6	Diminished fifth
7	Perfect fifth
8	Augmented fifth
9	Major sixth
10	Minor seventh
11	Major seventh

Chords

A chord in music is made of three or more notes that is heard as if sounding simultaneously. A three-note chord, called a triad is named made from a 7-note subset of the chromatic scale, called the diatonic scale. Each note is mapped to each of the letters A-G with potentially an accidental.

Chord Spelling

Chords are spelled by identifying the notes. For example

G B D

C Eb G

B D# G

Note: (no pun intended) the note might not be in order, that is, the first note might not be the root of the chord.

Chord Quality

The chord quality is determined by the interval between the root and the third note of the diatonic scale. When the third is 4 semi-tones from the root, it's a major chord; if it is 3 semi-tones, it is a minor chord.

The Altered 5^th

The distance between the root and the fifth note of the diatonic scale is normally 7 semi-tones from the root. If the fifth is a semi-tone higher the chord is augmented, if a semi-tone lower, it is diminished.

Chord Name

A chord is named based on

The root note (e.g. C)

The chord quality(e.g. major or minor).

The alteration of fifth note of the diatonic scale (e.g. diminished or augmented).

The chord name can be determined two ways:

Method 1: by measuring the interval between the root and third, and then the interval between the third and fifth or,

Method 2: by measuring the interval between the root and third, then the interval between the root and the fifth.

Method 1			Method 2
Root-->Third	Third-->Fifth	Chord Name	Root-->Third	Root-->Fifth
Major third	Minor third	Major (maj)	Major third	Perfect fifth
Minor third	Major third	Minor (min)	Minor third	Perfect fifth
Major third	Major third	Augmented (aug)	Major third	Augmented fifth
Minor third	Minor third	Diminished (dim)	Minor third	Diminished fifth

Assignment:

Create a class named ChordFinder with the following features:

Feature	Signature	Requirement
Constructors
	N/A	Will be a utility classwith just a static public method
Methods
	static Set getChordName(String notes)	Input: Valid input must have exactly three discrete notes separated by whitespace Accidentals will use # for sharp and b for flats. too many or too few notes should throw an IllegalArgumentException an invalid note, e.g. Zb, should throw an IllegalArgumentException Output: A set that containing the names of possible chords names of the given notes The format must be where is the root note, A G optionally followed by a b or # representing a sharp or flat respectively. The note must be upper-case a space is one of maj,min,aug,dim; the name must be lower case Precondition: Notes are recognized (character A-Goptionally followed by a b for flats or # for sharps). Note: while double sharps and flats exist, they are not within scope.

Example Test Cases

Scenario	Expected results
getChordName("D G B")	[G maj] Root : G Interval G-->B : major third Interval B-->D: minor third
getChordName(C Eb G )	[C min] Root: C Interval C--> Eb : minor third Interval C--> G : perfect fifth
getChordName(B D# G)	[B aug, D# aug, G aug] Roots : B, D#, or G Intervals (B>D#, D#-->G, and G-->B) : major third Intervals (B-->G , D#-->B, G-->D#) : augmented fifth