Major refactor of internal note storage to better support transposition.

Refactor to store notes as key-agnostic scale degrees + alterations
(flat, sharp, etc.).

We now think of a pitch in different ways:
- *Note*: the 7 notes diatonic to C major. Notes capture the principle
  in western harmony of the common scales having seven distinct diatonic
  "notes" and allows us to do arithmetic with them (do up three scale
  degrees).
- *Pitch*: the 12 chromatic pitches, regardless key. Pitch allows us to
  assign unique names and ordinal values to each note of the chromatic
  scale, allowing us to do arithmetic with them.
- *SpelledPitch*: a unique spelling of one of the chromatic pitches
  (*Note* + alteration) allowing the stylistic choice to use
  different *Notes* to describe a single *Pitch*.
- *ScaleDegree*: a variant of *SpelledPitch* that uses the scale degree
  instead of the *Pitch* to store a pitch in a key-agnostic manner.

To illustrate, the difference, consider the flat-six in the key of Eb.
- *Note*: The 6th scale degree in Eb is C (1-E 2-F 3-G 4-A 5-B 6-C).
- *Pitch*: In the chromatic scale, ignoring the key, this is the *Pitch*
  called B.
- *SpelledPitch*: In the context of the key of Eb, because this is the
  *Note* C, we should spell this as Cb, not B. So the spelled pitch is
  *Note*(C), *Alteration*(flat).
- *ScaleDegree*: This captures the key-agnostic representation that we
  used in the begining: *Number*(6) and *Alteration*(flat)

With these four ways of representing a note, we can transpose any
pitches that follow western 12-tone harmony arbitrarily between keys
preserving the author's choice of chord function (remembering that this
is the b6 and not the #5, in our example).

Building on this new notational data model, the AST now uses the
*ScaleDegree* relative to the provided key as the internal
representation of a pitch. Formatting of a *ScaleDegree* always requires
the key in which it is being rendered. Transposition is now only a
matter or updating the current key.

src/pco_chordspkg/html.nim

@@ -1,13 +1,13 @@
 import std/[logging, options, os, strutils]
 import zero_functional
 
-import ./ast
+import ./[ast, notation]
 
 type
   FormatContext = ref object
     chart: ChordChart
-    currentKey: ChordChartPitch
-    sourceKey: ChordChartPitch
+    currentKey: Key
+    sourceKey: Key
     currentSection: ChordChartNode
     numberChart: bool
     transposeSteps: int
@@ -80,7 +80,7 @@ h3 .section-text {
   height: 1.2em;
 }
 
-.chord .flavor {
+.number-chart .chord .flavor {
   font-variant-position: super;
 }
 
@@ -175,7 +175,7 @@ h3 .section-text {
   height: 1.2em;
 }
 
-.chord .flavor {
+.number-chart .chord .flavor {
   font-variant-position: super;
 }
 
@@ -197,62 +197,23 @@ h3 .section-text {
 </style>
 """
 
-func scaleDegree(root: ChordChartPitch, p: ChordChartPitch): string =
-  let distance = p - root
-  case distance:
-  of 0: "1"
-  of 1: "♭2"
-  of 2: "2"
-  of 3: "♭3"
-  of 4: "3"
-  of 5: "4"
-  of 6: "♭5"
-  of 7: "5"
-  of 8: "♭6"
-  of 9: "6"
-  of 10: "♭7"
-  of 11: "7"
-  else: raise newException(Exception, "Impossible")
-
 func format(ctx: FormatContext, chord: ChordChartChord, useNumber = false): string =
   ##if not useNumber and chord.original.isSome: return chord.original.get
 
-  if useNumber:
-    result = "<span class=root>" &
-      ctx.currentKey.scaleDegree(chord.rootPitch) & "</span>"
+  result = "<span class=root>"
+  if useNumber: result &= $chord.root
+  else: result &= $ctx.currentKey.spellPitch(chord.root)
+  result &= "</span>"
 
-    if chord.flavor.isSome:
+  if chord.flavor.isSome:
       result &= "<span class=flavor>" & chord.flavor.get & "</span>"
 
-    if chord.bassPitch.isSome:
-      result &= "<span class=bass>/" &
-        ctx.currentKey.scaleDegree(chord.bassPitch.get) & "</span>"
+  if chord.bass.isSome:
+    result &= "<span class=bass>/"
+    if useNumber: result &= $chord.bass.get
+    else: result &= $ctx.currentKey.spellPitch(chord.bass.get)
+    result &= "</span>"
 
-  else:
-    result = "<span class=root>" &
-      renderPitchInKey(chord.rootPitch, ctx.currentKey) & "</span>"
-
-    if chord.flavor.isSome:
-      result &= "<span class=flavor>" & chord.flavor.get & "</span>"
-
-    if chord.bassPitch.isSome:
-      result &= "<span class=bass>/" &
-        renderPitchInKey(chord.bassPitch.get, ctx.currentKey) & "</span>"
-
-proc transpose(ctx: FormatContext, chord: ChordChartChord): ChordChartChord =
-  result = chord
-
-  let distance = ctx.currentKey - ctx.sourceKey
-  if distance != 0:
-    result = ChordChartChord(
-      original: none[string](),
-      rootPitch: chord.rootPitch + distance,
-      flavor:
-        if chord.flavor.isSome: some(chord.flavor.get)
-        else: none[string](),
-      bassPitch:
-        if chord.bassPitch.isSome: some(chord.bassPitch.get + distance)
-        else: none[ChordChartPitch]())
 
 func makeSongOrder(songOrder, indent: string): string =
   result = indent & "<section class=song-order>\p" &
@@ -298,7 +259,7 @@ proc toHtml(ctx: var FormatContext, node: ChordChartNode, indent: string): strin
 
     if node.chord.isSome:
       result &= "<span class=chord>" &
-        ctx.format(ctx.transpose(node.chord.get), ctx.numberChart) & "</span>"
+        ctx.format(node.chord.get, ctx.numberChart) & "</span>"
 
     result &= "<span class=lyric>"
     if node.word.isSome: result &= node.word.get
@@ -317,13 +278,13 @@ proc toHtml(ctx: var FormatContext, node: ChordChartNode, indent: string): strin
     result &= "</div><div class=page-contents>"
 
   of ccnkTransposeKey:
-    ctx.currentKey = ctx.currentKey + node.transposeSteps
+    ctx.currentKey = ctx.currentKey.transpose(node.transposeSteps)
     result &= indent & "<h4 class=note>Key Change: " & $ctx.currentKey & "</h4>"
 
   of ccnkRedefineKey:
     let oldKey = ctx.currentKey
-    ctx.sourceKey = node.newKey + ctx.transposeSteps
-    ctx.currentKey = ctx.sourceKey
+    ctx.sourceKey = node.newKey
+    ctx.currentKey = ctx.sourceKey.transpose(ctx.transposeSteps)
 
     if oldKey != ctx.currentKey:
       let headingVal = indent & "<h4 class=note>Key Change: " & $ctx.currentKey & "</h4>"
@@ -342,8 +303,8 @@ proc toHtml*(
 
   var ctx = FormatContext(
     chart: cc,
-    currentKey: cc.metadata.key.rootPitch + transpose,
-    sourceKey: cc.metadata.key.rootPitch,
+    currentKey: cc.metadata.key.transpose(transpose),
+    sourceKey: cc.metadata.key,
     currentSection: EMPTY_CHORD_CHART_NODE,
     numberChart: numberChart,
     transposeSteps: transpose)
@@ -368,17 +329,19 @@ proc toHtml*(
 
   result &= "  </head>\p"
 
+  var bodyClasses = newSeq[string]()
+  if numberChart: bodyClasses.add("number-chart")
   if cc.metadata.contains("columns") and cc.metadata["columns"] == "1":
-    result &= "  <body class='one-column'>"
-  else:
-    result &= "  <body class='two-column'>"
+    bodyClasses.add("one-column")
+  else: bodyClasses.add("two-column")
+  result &= "  <body class='" & bodyClasses.join(" ") & "'>"
 
   var indent = "      "
 
   # Title
   result &= indent & "<h1>" & cc.metadata.title & "</h1>\p"
 
-  var metadataPieces = @["Key: " & ctx.format(ctx.transpose(cc.metadata.key))]
+  var metadataPieces = @["Key: " & $ctx.currentKey]
   if cc.metadata.contains("time signature"):
     metadataPieces.add(cc.metadata["time signature"])
   if cc.metadata.contains("bpm"):