Given a tonic, or starting note, and a set of intervals, generate the musical scale starting with the tonic and following the specified interval pattern.
Scales in Western music are based on the chromatic (12-note) scale.This scale can be expressed as the following group of pitches:
A, A#, B, C, C#, D, D#, E, F, F#, G, G#
A given sharp note (indicated by a #), can also be expressed as the flat of the note above it (indicated by a b), so the chromatic scale can also be written like this:
A, Bb, B, C, Db, D, Eb, E, F, Gb, G, Ab
The major and minor scale and modes are subsets of this twelve-pitch collection. They have seven pitches, and are called diatonic scales. The collection of notes in these scales is written with either sharps or flats, depending on the tonic. Here is a list of which are which:
No Accidentals: C major A minor
Use Sharps: G, D, A, E, B, F# major e, b, f#, c#, g#, d# minor
Use Flats: F, Bb, Eb, Ab, Db, Gb major d, g, c, f, bb, eb minor
The diatonic scales, and all other scales that derive from the chromatic scale, are built upon intervals. An interval is the space between two pitches.
The simplest interval is between two adjacent notes, and is called a "half step", or "minor second" (sometimes written as a lower-case "m"). The interval between two notes that have an interceding note is called a "whole step" or "major second" (written as an upper-case "M"). The diatonic scales are built using only these two intervals between adjacent notes.
Non-diatonic scales can contain the same letter twice, and can contain other intervals. Sometimes they may be smaller than usual (diminished, written "D"), or larger (augmented, written "A"). Intervals larger than an augmented second have other names.
Here is a table of pitches with the names of their interval distance from the tonic (A).
| A | A# | B | C | C# | D | D# | E | F | F# | G | G# | A |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Unison | Min 2nd | Maj 2nd | Min 3rd | Maj 3rd | Per 4th | Tritone | Per 5th | Min 6th | Maj 6th | Min 7th | Maj 7th | Octave |
| Dim 3rd | Aug 2nd | Dim 4th | Aug 4th | Dim 5th | Aug 5th | Dim 7th | Aug 6th | Dim 8ve | ||||
| Dim 5th |
Go through the project setup instructions for Xcode using Swift:
http://exercism.io/languages/swift
http://exercism.io/languages/swift/tests
Notably from the source directory:
swift test runs tests
swift package generate-xcodeproj creates an Xcode project
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
import XCTest
@testable import ScaleGeneratorTests
XCTMain([
testCase(ScaleGeneratorTests.allTests)
])import XCTest
@testable import ScaleGenerator
class ScaleGeneratorTests: XCTestCase {
func testNamingScale() {
let chromatic = ScaleGenerator(tonic: "c", scaleName: "chromatic")
XCTAssertEqual(chromatic.name, "C chromatic")
}
func testChromaticScale() {
let chromatic = ScaleGenerator(tonic: "C", scaleName: "chromatic")
XCTAssertEqual(chromatic.pitches(), ["C", "C#", "D", "D#", "E", "F", "F#", "G", "G#", "A", "A#", "B"])
}
func testAnotherChromaticScale() {
let chromatic = ScaleGenerator(tonic: "F", scaleName: "chromatic")
XCTAssertEqual(chromatic.pitches(), ["F", "Gb", "G", "Ab", "A", "Bb", "B", "C", "Db", "D", "Eb", "E"])
}
func testNamingMajorScale() {
let major = ScaleGenerator(tonic: "G", scaleName: "major", pattern: "MMmMMMm")
XCTAssertEqual(major.name, "G major")
}
func testMajorScale() {
let major = ScaleGenerator(tonic: "C", scaleName: "major", pattern: "MMmMMMm")
XCTAssertEqual(major.pitches(), ["C", "D", "E", "F", "G", "A", "B"])
}
func testAnotherMajorScale() {
let major = ScaleGenerator(tonic: "G", scaleName: "major", pattern: "MMmMMMm")
XCTAssertEqual(major.pitches(), ["G", "A", "B", "C", "D", "E", "F#"])
}
func testMinorScale() {
let minor = ScaleGenerator(tonic: "f#", scaleName: "minor", pattern: "MmMMmMM")
XCTAssertEqual(minor.pitches(), ["F#", "G#", "A", "B", "C#", "D", "E"])
}
func testAnotherMinorScale() {
let minor = ScaleGenerator(tonic: "bb", scaleName: "minor", pattern: "MmMMmMM")
XCTAssertEqual(minor.pitches(), ["Bb", "C", "Db", "Eb", "F", "Gb", "Ab"])
}
func testDorianMode() {
let dorian = ScaleGenerator(tonic: "d", scaleName: "dorian", pattern: "MmMMMmM")
XCTAssertEqual(dorian.pitches(), ["D", "E", "F", "G", "A", "B", "C"])
}
func testMixolydianMode() {
let mixolydian = ScaleGenerator(tonic: "Eb", scaleName: "mixolydian", pattern: "MMmMMmM")
XCTAssertEqual(mixolydian.pitches(), ["Eb", "F", "G", "Ab", "Bb", "C", "Db"])
}
func testLydianMode() {
let lydian = ScaleGenerator(tonic: "a", scaleName: "lydian", pattern: "MMMmMMm")
XCTAssertEqual(lydian.pitches(), ["A", "B", "C#", "D#", "E", "F#", "G#"])
}
func testPhrygianMode() {
let phrygian = ScaleGenerator(tonic: "e", scaleName: "phrygian", pattern: "mMMMmMM")
XCTAssertEqual(phrygian.pitches(), ["E", "F", "G", "A", "B", "C", "D"])
}
func testLocrianMode() {
let locrian = ScaleGenerator(tonic: "g", scaleName: "locrian", pattern: "mMMmMMM")
XCTAssertEqual(locrian.pitches(), ["G", "Ab", "Bb", "C", "Db", "Eb", "F"])
}
func testHarmonicMinor() {
let harmonicMinor = ScaleGenerator(tonic: "d", scaleName: "harmonic minor", pattern: "MmMMmAm")
XCTAssertEqual(harmonicMinor.pitches(), ["D", "E", "F", "G", "A", "Bb", "Db"])
}
func testOctatonic() {
let octatonic = ScaleGenerator(tonic: "C", scaleName: "octatonic", pattern: "MmMmMmMm")
XCTAssertEqual(octatonic.pitches(), ["C", "D", "D#", "F", "F#", "G#", "A", "B"])
}
func testHexatonic() {
let hexatonic = ScaleGenerator(tonic: "Db", scaleName: "hexatonic", pattern: "MMMMMM")
XCTAssertEqual(hexatonic.pitches(), ["Db", "Eb", "F", "G", "A", "B"])
}
func testPentatonic() {
let pentatonic = ScaleGenerator(tonic: "A", scaleName: "pentatonic", pattern: "MMAMA")
XCTAssertEqual(pentatonic.pitches(), ["A", "B", "C#", "E", "F#"])
}
func testEnigmatic() {
let enigmatic = ScaleGenerator(tonic: "G", scaleName: "enigma", pattern: "mAMMMmm")
XCTAssertEqual(enigmatic.pitches(), ["G", "G#", "B", "C#", "D#", "F", "F#"])
}
static var allTests: [(String, (ScaleGeneratorTests) -> () throws -> Void)] {
return [
("testNamingScale", testNamingScale),
("testChromaticScale", testChromaticScale),
("testAnotherChromaticScale", testAnotherChromaticScale),
("testNamingMajorScale", testNamingMajorScale),
("testMajorScale", testMajorScale),
("testAnotherMajorScale", testAnotherMajorScale),
("testDorianMode", testDorianMode),
("testMixolydianMode", testMixolydianMode),
("testLydianMode", testLydianMode),
("testPhrygianMode", testPhrygianMode),
("testLocrianMode", testLocrianMode),
("testHarmonicMinor", testHarmonicMinor),
("testOctatonic", testOctatonic),
("testHexatonic", testHexatonic),
("testPentatonic", testPentatonic),
("testEnigmatic", testEnigmatic)
]
}
}struct ScaleGenerator {
private let chromaticSharp = ["A", "A#", "B", "C", "C#", "D", "D#", "E", "F", "F#", "G", "G#"]
private let choromaticFlat = ["A", "Bb", "B", "C", "Db", "D", "Eb", "E", "F", "Gb", "G", "Ab"]
private let forSharp = ["C", "G", "D", "A", "E", "B", "F#", "a", "e", "b", "f#", "c#", "g#", "d#"]
private let intervals: [Character: Int] = ["m": 1, "M": 2, "A": 3]
var tonic: String
var scaleName: String
var pattern: String = "mmmmmmmmmmmm"
var name: String {
"\(tonic.normalized()) \(scaleName)"
}
private var chromaticScale: [String] {
forSharp.contains(tonic) ? chromaticSharp : choromaticFlat
}
func pitches() -> [String] {
var index = chromaticScale.firstIndex(of: tonic.normalized())!
return pattern.map {
let key = chromaticScale[index]
index = (index + (intervals[$0] ?? 0)) % 12
return key
}
}
}
extension String {
func normalized() -> String {
guard let first = first else { return "" }
return first.uppercased() + dropFirst()
}
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