Musical Phantoms

Slides from my NSSpain 2016 talk

Transcript

1. Musical Phantoms © TJ Usiyan, 2016 1
2. Caveats 4 Details omitted 4 More Signals, Less Types 4 This is all exploratory © TJ Usiyan, 2016 2
3. This is All Exploratory 4 Problems of Interest 4 Semantics 4 Sample Rate 4 Infinite Sequences 4 User Input © TJ Usiyan, 2016 3
4. This is All Exploratory 1. Make it work 2. Make it fast 3. Make it pretty © TJ Usiyan, 2016 4
5. This is All Exploratory 1. Make it work 2. Make it pretty 3. Could it be prettier? 4. Make it prettier 5. Make it fast © TJ Usiyan, 2016 5
6. Stay Calm and Let It Wash Over You © TJ Usiyan, 2016 6
7. The Plan 4 Math 4 Audio 4 Types 4 Phantom Types © TJ Usiyan, 2016 7
8. Unit Circle1 1 from: Wikipedia, LucasVB Circle_cos_sin © TJ Usiyan, 2016 8
9. © TJ Usiyan, 2016 9
10. © TJ Usiyan, 2016 10
11. Hertz.swift typealias Samples = Int typealias Seconds = Double /// Cycles (or periods) per second typealias Hertz = Double © TJ Usiyan, 2016 11
12. SampleRateType.swift public protocol SampleRateType { static var hertz: Hertz { get } init() } © TJ Usiyan, 2016 12
13. SampleRateType.swift extension SampleRateType { var frameDuration: Seconds { return 1.0 / Self.value } func convert(samples: Samples) -> Seconds { return frameDuration * Double(samples) } func convertToSamples(seconds: Seconds) -> Samples { return Int(Self.value * seconds) } } © TJ Usiyan, 2016 13
14. public struct SampleRate_44100 : SampleRateType { public static let hertz: Hertz = 44100.0 public init() {} } public struct SampleRate_50 : SampleRateType { public static let hertz: Hertz = 50.0 public init() { } } public struct SampleRate_100 : SampleRateType { public static let hertz: Hertz = 100.0 public init() { } } public struct SampleRate_500 : SampleRateType { public static let hertz: Hertz = 500.0 public init() { } } public struct SampleRate_1000 : SampleRateType { public static let hertz: Hertz = 1000.0 public init() { } } © TJ Usiyan, 2016 14
15. Signals © TJ Usiyan, 2016 15
16. public protocol SignalType : Sequence { associatedtype SampleRate : SampleRateType associatedtype Iterator : SignalGeneratorType } public protocol SignalGeneratorType : IteratorProtocol { associatedtype SampleRate : SampleRateType } © TJ Usiyan, 2016 16
17. Constant Return an unchanging value © TJ Usiyan, 2016 17
18. Constant.swift public struct Constant<T, SR : SampleRateType> { public let value:T public init(value:T) { self.value = value } } © TJ Usiyan, 2016 18
19. Constant.swift extension Constant : SignalType { public typealias SampleRate = SR public typealias Iterator = ConstantGenerator<T, SR> public func makeIterator() -> Iterator { return Iterator(signal: self) } } © TJ Usiyan, 2016 19
20. Constant.swift public struct ConstantGenerator<T, SR : SampleRateType> { fileprivate let value:T fileprivate init(value:T) { self.value = value } fileprivate init(signal:Constant<T, SR>) { self.init(value: signal.value) } } © TJ Usiyan, 2016 20
21. SR? © TJ Usiyan, 2016 21
22. Oscillators © TJ Usiyan, 2016 22
23. Oscillators Sine(x) © TJ Usiyan, 2016 23
24. TimeSignal.swift struct TimeSignal<SR : SampleRateType> { init() { } } © TJ Usiyan, 2016 24
25. TimeSignal.swift extension TimeSignal : SignalType { typealias SampleRate = SR typealias Iterator = TimeSignalGenerator<SR> func makeIterator() -> Iterator { return Iterator(index: 0) } } © TJ Usiyan, 2016 25
26. TimeSignal.swift public struct TimeSignalGenerator<SR : SampleRateType> { fileprivate var index:Index internal init(index:Index) { self.index = index } } © TJ Usiyan, 2016 26
27. TimeSignal.swift extension TimeSignalGenerator : SignalGeneratorType { public typealias SampleRate = SR public typealias Element = (frame:Int, seconds:Double) public typealias Index = Int public mutating func next() -> Element? { let value = (frame:index, seconds:Double(index) / SR.hertz) index += 1 return value } } © TJ Usiyan, 2016 27
28. TimeSignal.swift extension TimeSignal : SignalType { typealias SampleRate = SR typealias Iterator = TimeSignalGenerator<SR> func makeIterator() -> Iterator { return Iterator(index: 0) } } © TJ Usiyan, 2016 28
29. Oscillators are Continuous Functions of Time struct ContinuousTimeFunction<OutputType, SR : SampleRateType> { let function:(_ time:Double) -> OutputType init(function:@escaping (_ time:Double) -> OutputType) { self.function = function } } © TJ Usiyan, 2016 29
30. Continuous Functions of Time public struct ContinuousTimeFunctionGenerator<OutputType, SR : SampleRateType> { public typealias Index = Int public typealias Function = (_ time:Double) -> OutputType fileprivate var clock:TimeSignal<SR>.Iterator fileprivate let function:Function public init(index:Index, function:@escaping Function) { self.clock = TimeSignalGenerator<SR>(index:index) self.function = function } fileprivate init(clock:TimeSignalGenerator<SR>, function:@escaping Function) { self.clock = clock self.function = function } } © TJ Usiyan, 2016 30
31. Sine let contFnSin: ContinuousTimeDoubleSignal = { let frequency: Hertz = 2 let period: Second = twoPi let initialPhase: Double = 0 let fn = { sample in return sin(initialPhase + sample * frequency * period) } return ContinuousTimeFunction(function: fn) }() © TJ Usiyan, 2016 31
32. Phase class Phase<SR : SampleRateType> { var value: Seconds { didSet { if value >= period { value = value.truncatingRemainder(dividingBy: period) } } } let period: Seconds init(value: Seconds, period: Seconds) { self.value = fabs(value).truncatingRemainder(dividingBy: period) self.period = period } } © TJ Usiyan, 2016 32
33. Playground © TJ Usiyan, 2016 33
34. Drawbacks 4 Lock in to sample rate 4 Limitations with generics 4 Inference. So much inference. © TJ Usiyan, 2016 34
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39. © TJ Usiyan, 2016 39
40. Based on "Audio Processing and Sound Synthesis in Haskell" by Eric Cheng and Paul Hudak © TJ Usiyan, 2016 40
41. Thank you Questions @griotspeak © TJ Usiyan, 2016 41