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April 22, 2018 10:44
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"https://music.stackexchange.com/a/70189/932" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import Graphics.Dynamic.Plot.R2\n", | |
"import Data.Function\n", | |
"import Data.VectorSpace\n", | |
"import Data.Colour.Names" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"tone :: Double -> Double\n", | |
"tone t = case t - fromIntegral (round t::Int) of\n", | |
" φ | φ>0 -> φ\n", | |
" | otherwise -> φ^2" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"chordWvFormPlots :: [Double] -> [DynamicPlottable]\n", | |
"chordWvFormPlots freqs = [plotLatest\n", | |
" [ plotMultiple (\n", | |
" let sigs = [ tone . (ν*) | ν <- freqs ]\n", | |
" amplitudes = [if t > t₀ then min 1 $ t-t₀ else 0 | t₀<-[2,4..]]\n", | |
" in [ continFnPlot ((+y₀) . (*a) . sig . (t+)) & legendName (show ν++\" Hz\")\n", | |
" | ((ν, y₀), (a, sig)) <- zip (zip freqs [1..]) (zip amplitudes sigs) ]\n", | |
" ++ [continFnPlot (sumV (zipWith ((.).(*)) amplitudes sigs) . (t+))\n", | |
" & tint white]\n", | |
" ) & plotDelay 0.05\n", | |
" | t <- [0, 0.05 ..]\n", | |
" ]\n", | |
" , noDynamicAxes\n", | |
" , forceXRange (0,4) ]" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"> Are intervals like major 3rd, minor 3rd, and major 2nd all based on the scales, or are they based on how many semitones they have?\n", | |
"\n", | |
"Neither, really. They're based on _frequency ratios_. The consonant Western (Ptolemaic) intervals are defined as:\n", | |
"\n", | |
"- Octave (P8) = 2:1\n", | |
"- Perfect fifth (P5) = 3:2\n", | |
"- Perfect fourth (P4) = 4:3\n", | |
"- Major third (M3) = 5:4\n", | |
"- Major sixth (M6) = P4∗M3 = 5:3\n", | |
"- Minor third (m3) = P5 ⁄ M3 = 6:5\n", | |
"- Minor sixth (m6) = P8 ⁄ M3 = 8:5\n", | |
"\n", | |
"No semitones nor scales anywhere to be seen.\n", | |
"\n", | |
"The reason we chose _simple integer ratios_: frequencies that are at a small integer ratio give nice, consistent sound signals. For example, a major chord has the following waveform:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"GraphWindowSpecR2{lBound=0.0, rBound=4.0, bBound=-0.5, tBound=3.5, xResolution=640, yResolution=480}" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plotWindow $ chordWvFormPlots [4,5,6]" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"[![Waveform of a JI major chord composed of tweaked-triangular signals][1]][1]\n", | |
"[1]: https://i.stack.imgur.com/Wr4xT.gif\n", | |
"\n", | |
"\n", | |
"which is much richer than the individual components, but still has a clear repetitive structure that the ear can latch onto. Compare this to a chord composed of random-ish frequencies in a similar range:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"GraphWindowSpecR2{lBound=0.0, rBound=4.0, bBound=-0.5, tBound=3.5, xResolution=640, yResolution=480}" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plotWindow $ chordWvFormPlots [3.7,5.09,6.02]" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"[![Waveform of a detuned chord composed of tweaked-triangular signals][2]][2]\n", | |
"[2]: https://i.stack.imgur.com/XSJX5.gif" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"which is just a noisy mess.\n", | |
"\n", | |
"From these fundamental intervals, the Ptolemaic scale is constructed:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"{-# LANGUAGE FlexibleContexts #-}\n", | |
"import Diagrams.Prelude\n", | |
"import Diagrams.Backend.Cairo (Cairo)\n", | |
"import Control.Monad\n", | |
"type Dia = QDiagram Cairo V2 Double Any\n", | |
"import Data.Ratio" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"type Freq = Double -- relative to C" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"keyboard :: Dia\n", | |
"keyboard = hcat [ rect 1 7 & fc (c k) & opacity 0.1\n", | |
" | k <- \" ❚ ❚ ❚ ❚ ❚ \" ]\n", | |
" where c ' ' = white\n", | |
" c '❚' = black" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"labelFreq :: Freq -> String\n", | |
"labelFreq ν = noteNames!!s\n", | |
" where lν = logBase 2 ν\n", | |
" s = round $ lν * 12\n", | |
" noteNames = cycle $ words \"C C♯ D E♭ E F F♯ G G♯ A B♭ B\"\n", | |
"\n", | |
"showRatio :: Rational -> String\n", | |
"showRatio q = map toSup (show $ numerator q) ++ \"⁄\" ++ map toSub (show $ denominator q)\n", | |
" where toSup = (\"⁰¹²³⁴⁵⁶⁷⁸⁹\"!!) . subtract (fromEnum '0') . fromEnum\n", | |
" toSub = (\"₀₁₂₃₄₅₆₇₈₉\"!!) . subtract (fromEnum '0') . fromEnum\n", | |
"\n", | |
"showIntervalName :: Rational -> String\n", | |
"showIntervalName 1 = \"P1\"\n", | |
"showIntervalName q\n", | |
" | q < 1 = showIntervalName $ recip q\n", | |
" | q < 10/9 = \"m2\"\n", | |
" | q <= 9/8 = \"M2\"\n", | |
" | q <= 6/5 = \"m3\"\n", | |
" | q < 4/3 = \"M3\"\n", | |
" | q < 7/5 = \"P4\"\n", | |
" | q <= 3/2 = \"P5\"\n", | |
" | q < 5/3 = \"m6\"\n", | |
" | q < 7/4 = \"M6\"\n", | |
" | q < 15/8 = \"m7\"\n", | |
" | q < 2 = \"M7\"" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import Data.Monoid hiding ((<>))\n", | |
"import Data.Semigroup\n", | |
"data ScTree = ScNode\n", | |
" | ScBranches [(Rational, ScTree)] deriving (Show)\n", | |
"instance Semigroup ScTree where\n", | |
" ScNode<>a = a\n", | |
" a<>ScNode = a\n", | |
" ScBranches ol<>ScBranches or = ScBranches $ ol++or\n", | |
"instance Monoid ScTree where\n", | |
" mempty = ScNode\n", | |
" mappend = (<>)\n", | |
"instance Num ScTree where\n", | |
" fromInteger = fromRational . fromInteger\n", | |
" ScNode * a = a\n", | |
" ScBranches brs * c = ScBranches [(r, br*c) | (r,br)<-brs]\n", | |
"instance Fractional ScTree where\n", | |
" fromRational r = ScBranches [(r, ScNode)]\n", | |
" ScBranches brs / ScBranches [(d,ScNode)] = ScBranches [(r/d, br)|(r,br)<-brs]\n", | |
":opt no-lint" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"constructScale :: (Freq -> String) -> (Rational -> String) -> ScTree -> Dia\n", | |
"constructScale showFreq showIntv = go 1\n", | |
" where go _ ScNode = mempty\n", | |
" go ν₀ (ScBranches brs)\n", | |
" = mconcat\n", | |
" [ (fromVertices [ p₀^&2, pn^&0 ] # opacity 0.5 # lc col\n", | |
" <> circle 0.1 # moveTo (pn^&0)\n", | |
" <> text (showIntv qν) # scale 0.3 # moveTo ((p₀*η+pn*(1-η))^&(2*η)) # fc col\n", | |
" <> text (showFreq νn) # scale 0.4 # moveTo (pn^& 0.5) # opacity 0.4 )\n", | |
" === go νn br\n", | |
" | (qν, br) <- brs\n", | |
" , let νn = ν₀ * realToFrac qν\n", | |
" [p₀,pn] = (*12) . logBase 2 <$> [ν₀,νn]\n", | |
" η = cos (abs . logBase 2 $ fromRational qν) ^ 2 / 2\n", | |
" iname = showIntervalName qν\n", | |
" col = case iname of\n", | |
" \"P5\" -> blue\n", | |
" \"P4\" -> green\n", | |
" (_:'2':_) -> red\n", | |
" ('M':_) -> orange\n", | |
" ('m':_) -> purple\n", | |
" _ -> black\n", | |
" ]\n", | |
"\n", | |
"onKeyboard :: Dia -> Dia\n", | |
"onKeyboard pth\n", | |
" = strutX 2 ||| (pth # alignT <> keyboard # alignT) ||| strutX 2" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"onKeyboard $ constructScale labelFreq showIntervalName\n", | |
" ( 1 * 1\n", | |
" <> 5/4 * 1\n", | |
" <> 4/3 * (1 <> 5/4)\n", | |
" <> 3/2 * (1 <> 5/4 <> 3/4) )" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In this scale, there are now also other intervals apart from the consonant ones,\n", | |
"in particular, the intervals between neighbouring scale degrees, which are called\n", | |
"_seconds_." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"onKeyboard $ constructScale labelFreq showIntervalName\n", | |
" ( 1 * 1 * (9/8)\n", | |
" <> 5/4 * 1 * (16/15)\n", | |
" <> 4/3 * (1 * (9/8) <> 5/4 * (9/8))\n", | |
" <> 3/2 * (1 * (10/9) <> 5/4 * (16/15) <> 3/4 * (10/9)) )" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here it is obvious why we talk of _minor_ and _major_ seconds:\n", | |
"e.g. the distance (i.e. cross-ratio) between F and G is clearly much\n", | |
"more than the distance between E and F, but at first glance seems to\n", | |
"be at least similar to the distance between C and D, between D and E etc..\n", | |
"\n", | |
"Here are the numerical values:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 14, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"onKeyboard $ constructScale (show . round . (440*3/5*)) showRatio\n", | |
" ( 1 * 1 * (9/8)\n", | |
" <> 5/4 * 1 * (16/15)\n", | |
" <> 4/3 * (1 * (9/8) <> 5/4 * (9/8))\n", | |
" <> 3/2 * (1 * (10/9) <> 5/4 * (16/15) <> 3/4 * (10/9)) )" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Note that there are actually two different kinds of major second here: the _major tone_ ⁹⁄₈ and the\n", | |
"_minor tone_ ¹⁰⁄₉.\n", | |
"\n", | |
"They are similar enough that at least in a melody, the discrepancy is hardly noticed. In\n", | |
"[meantone temperaments](https://en.wikipedia.org/wiki/Meantone_temperament),\n", | |
"which include the [12-edo tuning](https://en.wikipedia.org/wiki/Equal_temperament) used\n", | |
"by modern pianos and guitars, minor and major tones are approximated by the same interval." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Haskell", | |
"language": "haskell", | |
"name": "haskell" | |
}, | |
"language_info": { | |
"codemirror_mode": "ihaskell", | |
"file_extension": ".hs", | |
"name": "haskell", | |
"version": "8.2.1" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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