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A toolkit for computer-aided musicology, Javascript version
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<h1 class="page-title">Source: music21/roman.js</h1>
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<pre
class="sunlight-highlight-javascript linenums">/**
* music21j -- Javascript reimplementation of Core music21p features.
* music21/roman -- roman.RomanNumberal -- Chord subclass
*
* Copyright (c) 2013-17, Michael Scott Cuthbert and cuthbertLab
* Based on music21 (=music21p), Copyright (c) 2006–17, Michael Scott Cuthbert and cuthbertLab
*
*/
import { Music21Exception } from './exceptions21.js';
import { chord } from './chord.js';
import { common } from './common.js';
// import { debug } from './debug.js';
import { figuredBass } from './figuredBass.js';
import { harmony } from './harmony.js';
import { interval } from './interval.js';
import { key } from './key.js';
import { pitch } from './pitch.js';
import { scale } from './scale.js';
/**
* Roman numeral module. See {@link music21.roman} namespace
*
* @exports music21/roman
*/
/**
* music21.roman -- namespace for dealing with RomanNumeral analysis.
*
* @namespace music21.roman
* @memberof music21
* @requires music21/chord
* @requires music21/common
* @requires music21/figuredBass
* @requires music21/harmony
* @requires music21/key
* @requires music21/pitch
* @requires music21/interval
*/
export const roman = {};
roman.figureShorthands = {
'53': '',
'3': '',
'63': '6',
'753': '7',
'75': '7', // controversial perhaps
'73': '7', // controversial perhaps
'9753': '9',
'975': '9', // controversial perhaps
'953': '9', // controversial perhaps
'97': '9', // controversial perhaps
'95': '9', // controversial perhaps
'93': '9', // controversial perhaps
'653': '65',
'6b53': '6b5',
'643': '43',
'642': '42',
bb7b5b3: 'o7',
bb7b53: 'o7',
// '6b5bb3': 'o65',
b7b5b3: '/o7',
};
roman.functionalityScores = {
I: 100,
i: 90,
V7: 80,
V: 70,
V65: 68,
I6: 65,
V6: 63,
V43: 61,
I64: 60,
IV: 59,
i6: 58,
viio7: 57,
V42: 55,
viio65: 53,
viio6: 52,
'#viio65': 51,
ii: 50,
'#viio6': 49,
ii65: 48,
ii43: 47,
ii42: 46,
IV6: 45,
ii6: 43,
VI: 42,
'#VI': 41,
vi: 40,
viio: 39,
'#viio': 39,
iio: 37, // common in Minor
iio42: 36,
bII6: 35, // Neapolitan
iio43: 32,
iio65: 31,
'#vio': 28,
'#vio6': 28,
III: 22,
v: 20,
VII: 19,
VII7: 18,
IV65: 17,
IV7: 16,
iii: 15,
iii6: 12,
vi6: 10,
};
/**
* expandShortHand - expand a string of numbers into an array
*
* N.B. this is NOT where abbreviations get expanded
*
* @memberof music21.roman
* @param {string} shorthand string of a figure w/o roman to parse
* @return {Array<string>} array of shorthands
*/
roman.expandShortHand = function expandShortHand(shorthand) {
shorthand = shorthand.replace('/', '');
if (shorthand.match(/[b-]$/)) {
shorthand += '3';
}
shorthand = shorthand.replace('11', 'x');
shorthand = shorthand.replace('13', 'y');
shorthand = shorthand.replace('15', 'z');
const rx = new RegExp('#*-*b*o*[1-9xyz]', 'g');
let shorthandGroups = [];
let match = rx.exec(shorthand);
while (match !== null) {
shorthandGroups.push(match[0]);
match = rx.exec(shorthand);
}
if (shorthandGroups.length === 1 && shorthandGroups[0].endsWith('3')) {
shorthandGroups = ['5', shorthandGroups[0]];
}
const shGroupOut = [];
for (let sh of shorthandGroups) {
sh = sh.replace('x', '11');
sh = sh.replace('y', '13');
sh = sh.replace('z', '15');
shGroupOut.push(sh);
}
return shGroupOut;
};
/**
* correctSuffixForChordQuality - Correct a given inversionString suffix given a
* chord of various qualities.
*
* @memberof music21.roman
* @param {music21.chord.Chord} chordObj
* @param {string} inversionString a string like '6' to fix.
* @return {string} corrected inversionString
*/
roman.correctSuffixForChordQuality = function correctSuffixForChordQuality(
chordObj,
inversionString
) {
const fifthType = chordObj.semitonesFromChordStep(5);
let qualityName = '';
if (fifthType === 6) {
qualityName = 'o';
} else if (fifthType === 8) {
qualityName = '+';
}
if (
inversionString !== undefined
&& (inversionString.startsWith('o') || inversionString.startsWith('/o'))
) {
if (qualityName === 'o') {
// don't call viio7, viioo7.
qualityName = '';
}
}
const seventhType = chordObj.semitonesFromChordStep(7);
if (seventhType !== undefined && fifthType === 6) {
// there is a seventh and this is a diminished 5
if (seventhType === 10 && qualityName === 'o') {
qualityName = '/o';
} else if (seventhType !== 9) {
// do something for very odd chords built on diminished triad.
}
}
return qualityName + inversionString;
};
/**
* maps an index number to a roman numeral in lowercase
*
* @memberof music21.roman
* @example
* music21.roman.romanToNumber[4]
* // 'iv'
*/
roman.romanToNumber = [undefined, 'i', 'ii', 'iii', 'iv', 'v', 'vi', 'vii'];
/**
* Represents a RomanNumeral. By default, capital Roman Numerals are
* major chords; lowercase are minor.
*
* @class RomanNumeral
* @memberof music21.roman
* @extends music21.chord.Chord
* @param {string} figure - the roman numeral as a string, e.g., 'IV', 'viio', 'V7'
* @param {string|music21.key.Key} [keyStr='C']
* @property {Array<music21.pitch.Pitch>} scale - (readonly) returns the scale associated with the roman numeral
* @property {music21.key.Key} key - the key associated with the RomanNumeral (not allowed to be undefined yet)
* @property {string} figure - the figure as passed in
* @property {string} degreeName - the name associated with the scale degree, such as "mediant" etc., scale 7 will be "leading tone" or "subtonic" appropriately
* @property {int} scaleDegree
* @property {string} impliedQuality - "major", "minor", "diminished", "augmented"
* @property {Array<music21.pitch.Pitch>} pitches - RomanNumerals are Chord objects, so .pitches will work for them also.
*/
export class RomanNumeral extends harmony.Harmony {
constructor(figure = '', keyStr, keywords) {
const params = { updatePitches: false, parseFigure: false };
common.merge(params, keywords);
super(figure, params);
this._parsingComplete = false;
// not yet used...
this.primaryFigure = undefined;
this.secondaryRomanNumeral = undefined;
this.secondaryRomanNumeralKey = undefined;
this.pivotChord = undefined;
this.scaleCardinality = 7;
this._figure = undefined;
this.caseMatters = true;
if (typeof figure === 'number') {
this.caseMatters = false;
}
this.scaleDegree = undefined;
this.frontAlterationString = undefined;
this.frontAlterationTransposeInterval = undefined;
this.frontAlterationAccidental = undefined;
this.romanNumeralAlone = undefined;
this.impliedQuality = undefined;
this.impliedScale = undefined;
this.scaleOffset = undefined;
this.useImpliedScale = false;
this.bracketedAlterations = [];
this.omittedSteps = [];
this.followsKeyChange = false;
this._functionalityScore = undefined;
this._scale = undefined; // the key
this.figure = figure;
this.key = keyStr;
// to remove...
this.numbers = '';
if (figure !== '') {
this._parseFigure();
this._parsingComplete = true;
this._updatePitches();
}
}
_parseFigure() {
let workingFigure = this.figure;
let useScale = this.impliedScale;
if (!this.useImpliedScale) {
useScale = this.key;
}
[workingFigure, useScale] = this._correctForSecondaryRomanNumeral(
useScale
);
this.primaryFigure = workingFigure;
workingFigure = this._parseOmittedSteps(workingFigure);
workingFigure = this._parseBracketedAlterations(workingFigure);
workingFigure = workingFigure.replace(/^N6/, 'bII6');
workingFigure = workingFigure.replace(/^N/, 'bII6');
workingFigure = this._parseFrontAlterations(workingFigure);
[workingFigure, useScale] = this._parseRNAloneAmidstAug6(
workingFigure,
useScale
);
workingFigure = this._setImpliedQualityFromString(workingFigure);
this._tempRoot = useScale.pitchFromDegree(this.scaleDegree);
this._fixMinorVIandVII(useScale);
const expandedFigure = roman.expandShortHand(workingFigure);
this.figuresNotationObj = new figuredBass.Notation(
expandedFigure.toString()
);
const numbersArr = workingFigure.match(/\d+/);
if (numbersArr != null) {
workingFigure = workingFigure.replace(/\d+/, '');
this.numbers = parseInt(numbersArr[0]);
}
}
_parseFrontAlterations(workingFigure) {
let frontAlterationString = '';
let frontAlterationTransposeInterval;
let frontAlterationAccidental;
const _alterationRegex = new RegExp('^(b+|-+|#+)');
const match = _alterationRegex.exec(workingFigure);
if (match != null) {
const group = match[1];
let alteration = group.length;
if (group[0] === 'b' || group[0] === '-') {
alteration *= -1;
}
frontAlterationTransposeInterval = interval.intervalFromGenericAndChromatic(
1,
alteration
);
frontAlterationAccidental = new pitch.Accidental(alteration);
frontAlterationString = group;
workingFigure = workingFigure.replace(_alterationRegex, '');
}
this.frontAlterationString = frontAlterationString;
this.frontAlterationTransposeInterval = frontAlterationTransposeInterval;
this.frontAlterationAccidental = frontAlterationAccidental;
return workingFigure;
}
_correctBracketedPitches() {
for (const innerAlteration of this.bracketedAlterations) {
const [alterNotation, chordStep] = innerAlteration;
const alterPitch = this.getChordStep(chordStep);
if (alterPitch === undefined) {
continue;
}
const newAccidental = new pitch.Accidental(alterNotation);
if (alterPitch.accidental === undefined) {
alterPitch.accidental = newAccidental;
} else {
alterPitch.accidental.set(
alterPitch.accidental.alter + newAccidental.alter
);
}
}
}
_setImpliedQualityFromString(workingFigure) {
let impliedQuality = '';
if (workingFigure.startsWith('o')) {
impliedQuality = 'diminished';
workingFigure = workingFigure.replace(/^o/, '');
} else if (workingFigure.startsWith('/o')) {
impliedQuality = 'half-diminished';
workingFigure = workingFigure.replace(/^\/o/, '');
} else if (workingFigure.startsWith('+')) {
impliedQuality = 'augmented';
workingFigure = workingFigure.replace(/^\+/, '');
} else if (workingFigure.endsWith('d7')) {
impliedQuality = 'dominant-seventh';
workingFigure = workingFigure.replace(/d7$/, '7');
} else if (
this.caseMatters
&& this.romanNumeralAlone.toUpperCase() === this.romanNumeralAlone
) {
impliedQuality = 'major';
} else if (
this.caseMatters
&& this.romanNumeralAlone.toLowerCase() === this.romanNumeralAlone
) {
impliedQuality = 'minor';
}
this.impliedQuality = impliedQuality;
return workingFigure;
}
_fixMinorVIandVII(useScale) {
if (useScale.mode !== 'minor') {
return;
}
if (!this.caseMatters) {
return;
}
if (this.scaleDegree !== 6 && this.scaleDegree !== 7) {
return;
}
if (
!['minor', 'diminished', 'half-diminished'].includes(
this.impliedQuality
)
) {
return;
}
const fati = this.frontAlterationTransposeInterval;
if (fati !== undefined) {
const newFati = interval.add([fati, new interval.Interval('A1')]);
this.frontAlterationTransposeInterval = newFati;
this.frontAlterationAccidental.alter
= this.frontAlterationAccidental.alter + 1;
} else {
this.frontAlterationTransposeInterval = new interval.Interval('A1');
this.frontAlterationAccidental = new pitch.Accidental(1);
}
this._tempRoot = this.frontAlterationTransposeInterval.transposePitch(
this._tempRoot
);
return;
}
_parseRNAloneAmidstAug6(workingFigure, useScale) {
let romanNumeralAlone = '';
const _romanNumeralAloneRegex = new RegExp(
'(IV|I{1,3}|VI{0,2}|iv|i{1,3}|vi{0,2}|N)'
);
const _augmentedSixthRegex = new RegExp('(It|Ger|Fr|Sw)');
const rm = _romanNumeralAloneRegex.exec(workingFigure);
const a6match = _augmentedSixthRegex.exec(workingFigure);
if (rm === null && a6match === null) {
throw new Music21Exception(
`No roman numeral found in ${workingFigure}`
);
}
if (a6match !== null) {
if (useScale.mode === 'major') {
useScale = new key.Key(useScale.tonic.name, 'minor');
this.impliedScale = useScale;
this.useImpliedScale = true;
}
romanNumeralAlone = a6match[1];
if (['It', 'Ger'].includes(romanNumeralAlone)) {
this.scaleDegree = 4;
} else {
this.scaleDegree = 2;
}
workingFigure = workingFigure.replace(_augmentedSixthRegex, '');
this.romanNumeralAlone = romanNumeralAlone;
if (romanNumeralAlone !== 'Fr') {
this.bracketedAlterations.push(['#', 1]);
}
if (romanNumeralAlone === 'Fr' || romanNumeralAlone === 'Sw') {
this.bracketedAlterations.push(['#', 3]);
}
} else {
romanNumeralAlone = rm[1];
this.scaleDegree = common.fromRoman(romanNumeralAlone);
workingFigure = workingFigure.replace(_romanNumeralAloneRegex, '');
this.romanNumeralAlone = romanNumeralAlone;
}
return [workingFigure, useScale];
}
/**
* get romanNumeral - return either romanNumeralAlone (II) or with frontAlterationAccidental (#II)
*
* @return {string} new romanNumeral;
*/
get romanNumeral() {
if (this.frontAlterationAccidental === undefined) {
return this.romanNumeralAlone;
} else {
return (
this.frontAlterationAccidental.modifier + this.romanNumeralAlone
);
}
}
get scale() {
if (this._scale !== undefined) {
return this._scale;
} else {
this._scale = this.key.getScale();
return this._scale;
}
}
get key() {
return this._scale;
}
set key(keyOrScale) {
if (typeof keyOrScale === 'string') {
this._scale = new key.Key(keyOrScale);
} else if (typeof keyOrScale === 'undefined') {
this._scale = new key.Key('C');
} else {
this._scale = keyOrScale;
}
if (keyOrScale === undefined) {
this.useImpliedScale = true;
this.impliedScale = new scale.MajorScale('C');
} else {
this.useImpliedScale = false;
this.impliedScale = false;
}
if (this._parsingComplete) {
this._updatePitches();
}
}
get figure() {
return this._figure;
}
set figure(newFigure) {
this._figure = newFigure;
if (this._parsingComplete) {
this._parseFigure();
this._updatePitches();
}
}
get figureAndKey() {
let tonicName = this.key.tonic.name;
let mode = '';
if (this.key.mode !== undefined) {
mode = ' ' + this.key.mode;
}
if (mode === ' minor') {
tonicName = tonicName.toLowerCase();
} else if (mode === ' major') {
tonicName = tonicName.toUpperCase();
}
return this.figure + ' in ' + tonicName + mode;
}
get degreeName() {
if (this.scaleDegree < 7) {
return [
undefined,
'Tonic',
'Supertonic',
'Mediant',
'Subdominant',
'Dominant',
'Submediant',
][this.scaleDegree];
} else {
const tonicPitch = this.key.tonic;
let diffRootToTonic = (tonicPitch.ps - this.root().ps) % 12;
if (diffRootToTonic < 0) {
diffRootToTonic += 12;
}
if (diffRootToTonic === 1) {
return 'Leading-tone';
} else {
return 'Subtonic';
}
}
}
/**
* Update the .pitches array. Called at instantiation, but not automatically afterwards.
*
* @memberof music21.roman.RomanNumeral
*/
_updatePitches() {
let useScale;
if (this.secondaryRomanNumeralKey !== undefined) {
useScale = this.secondaryRomanNumeralKey;
} else if (!this.useImpliedScale) {
useScale = this.key;
} else {
useScale = this.impliedScale;
}
this.scaleCardinality = 7; // simple speedup;
const bassScaleDegree = this.bassScaleDegreeFromNotation(
this.figuresNotationObj
);
const bassPitch = useScale.pitchFromDegree(
bassScaleDegree,
'ascending'
);
const pitches = [bassPitch];
let lastPitch = bassPitch;
const numberNotes = this.figuresNotationObj.numbers.length;
for (let j = 0; j < numberNotes; j++) {
const i = numberNotes - j - 1;
const thisScaleDegree
= bassScaleDegree + this.figuresNotationObj.numbers[i] - 1;
const newPitch = useScale.pitchFromDegree(
thisScaleDegree,
'ascending'
);
const pitchName = this.figuresNotationObj.modifiers[
i
].modifyPitchName(newPitch.name);
const newNewPitch = new pitch.Pitch(pitchName);
newNewPitch.octave = newPitch.octave;
if (newNewPitch.ps < lastPitch.ps) {
newNewPitch.octave += 1;
}
pitches.push(newNewPitch);
lastPitch = newNewPitch;
}
if (this.frontAlterationTransposeInterval !== undefined) {
const newPitches = [];
for (const thisPitch of pitches) {
const newPitch = this.frontAlterationTransposeInterval.transposePitch(
thisPitch
);
newPitches.push(newPitch);
}
this.pitches = newPitches;
} else {
this.pitches = pitches;
}
this._matchAccidentalsToQuality(this.impliedQuality);
this.scaleOffset = this.frontAlterationTransposeInterval;
if (this.omittedSteps.length) {
const omittedPitches = [];
for (const thisCS of this.omittedSteps) {
const p = this.getChordStep(thisCS);
if (p !== undefined) {
omittedPitches.push(p.name);
}
}
const newPitches = [];
for (const thisPitch of pitches) {
if (!omittedPitches.includes(thisPitch.name)) {
newPitches.push(thisPitch);
}
}
this.pitches = newPitches;
// do something...
}
this._correctBracketedPitches();
}
bassScaleDegreeFromNotation(notationObject) {
const c = new pitch.Pitch('C3');
const cDNN = c.diatonicNoteNum; // always 22
const pitches = [c];
for (const i of notationObject.numbers) {
const distanceToMove = i - 1;
const newDiatonicNumber = cDNN + distanceToMove;
const [newStep, newOctave] = interval.convertDiatonicNumberToStep(
newDiatonicNumber
);
const newPitch = new pitch.Pitch('C3');
newPitch.step = newStep;
newPitch.octave = newOctave;
pitches.push(newPitch);
}
const tempChord = new chord.Chord(pitches);
const rootDNN = tempChord.root().diatonicNoteNum;
const staffDistanceFromBassToRoot = rootDNN - cDNN;
let bassSD = common.posMod(
this.scaleDegree - staffDistanceFromBassToRoot,
7
);
if (bassSD === 0) {
bassSD = 7;
}
return bassSD;
}
_matchAccidentalsToQuality(impliedQuality) {
const correctSemitones = this._findSemitoneSizeForQuality(
impliedQuality
);
const chordStepsToExamine = [3, 5, 7];
for (let i = 0; i < chordStepsToExamine.length; i++) {
const thisChordStep = chordStepsToExamine[i];
const thisCorrect = correctSemitones[i];
const thisSemis = this.semitonesFromChordStep(thisChordStep);
if (thisCorrect === undefined) {
continue;
}
if (thisSemis === undefined) {
continue;
}
if (thisSemis === thisCorrect) {
continue;
}
let correctedSemis = thisCorrect - thisSemis;
if (correctedSemis >= 6) {
correctedSemis = -1 * (12 - correctedSemis);
} else if (correctedSemis <= -6) {
correctedSemis += 12;
}
const faultyPitch = this.getChordStep(thisChordStep);
// TODO: check for faultyPitch is undefined
if (faultyPitch.accidental === undefined) {
faultyPitch.accidental = new pitch.Accidental(correctedSemis);
} else {
const acc = faultyPitch.accidental;
correctedSemis += acc.alter;
if (correctedSemis >= 6) {
correctedSemis = -1 * (12 - correctedSemis);
} else if (correctedSemis <= -6) {
correctedSemis += 12;
}
acc.set(correctedSemis);
}
}
}
_correctForSecondaryRomanNumeral(useScale, figure) {
if (figure === undefined) {
figure = this._figure;
}
let workingFigure = figure;
const rx = new RegExp('(.*?)/([#a-np-zA-NP-Z].*)');
const match = rx.exec(figure);
if (match !== null) {
const primaryFigure = match[1];
const secondaryFigure = match[2];
const secondaryRomanNumeral = new RomanNumeral(
secondaryFigure,
useScale,
this.caseMatters
);
this.secondaryRomanNumeral = secondaryRomanNumeral;
let secondaryMode;
if (secondaryRomanNumeral.quality === 'minor') {
secondaryMode = 'minor';
} else if (secondaryRomanNumeral.quality === 'major') {
secondaryMode = 'minor';
} else if (secondaryRomanNumeral.semitonesFromChordStep(3) === 3) {
secondaryMode = 'minor';
} else {
secondaryMode = 'major';
}
this.secondaryRomanNumeralKey = new key.Key(
secondaryRomanNumeral.root().name,
secondaryMode
);
useScale = this.secondaryRomanNumeralKey;
workingFigure = primaryFigure;
}
return [workingFigure, useScale];
}
_parseOmittedSteps(workingFigure) {
const omittedSteps = [];
const rx = new RegExp(/\[no(\d+)\]s*/);
let match = rx.exec(workingFigure);
while (match !== null) {
let thisStep = match[1];
thisStep = parseInt(thisStep);
thisStep = thisStep % 7 || 7;
omittedSteps.push(thisStep);
workingFigure = workingFigure.replace(rx, '');
match = rx.exec(workingFigure);
}
this.omittedSteps = omittedSteps;
return workingFigure;
}
_parseBracketedAlterations(workingFigure) {
const bracketedAlterations = this.bracketedAlterations;
const rx = new RegExp(/\[(b+|-+|#+)(\d+)\]/);
let match = rx.exec(workingFigure);
while (match !== null) {
const matchAlteration = match[1];
const matchDegree = parseInt(match[2]);
bracketedAlterations.push([matchAlteration, matchDegree]);
workingFigure = workingFigure.replace(rx, '');
match = rx.exec(workingFigure);
}
return workingFigure;
}
_findSemitoneSizeForQuality(impliedQuality) {
let correctSemitones;
if (impliedQuality === 'major') {
correctSemitones = [4, 7];
} else if (impliedQuality === 'minor') {
correctSemitones = [3, 7];
} else if (impliedQuality === 'diminished') {
correctSemitones = [3, 6, 9];
} else if (impliedQuality === 'half-diminished') {
correctSemitones = [3, 6, 10];
} else if (impliedQuality === 'augmented') {
correctSemitones = [4, 8];
} else if (impliedQuality === 'dominant-seventh') {
correctSemitones = [4, 7, 10];
} else {
correctSemitones = [];
}
return correctSemitones;
}
/**
* Gives a string display. Note that since inversion is not yet supported
* it needs to be given separately.
*
* Inverting 7th chords does not work.
*
* @memberof music21.roman.RomanNumeral
* @param {string} displayType - ['roman', 'bassName', 'nameOnly', other]
* @param {int} [inversion=0]
* @returns {String}
*/
asString(displayType, inversion) {
const keyObj = this.key;
const tonicName = keyObj.tonic.name;
const mode = keyObj.mode;
// specifying inversion is for backwards compatibility only.
if (inversion === undefined) {
inversion = 0;
}
let inversionName = '';
if (inversion === 1) {
if (displayType === 'roman') {
inversionName = '6';
} else {
inversionName = ' (first inversion)';
}
} else if (inversion === 2) {
if (displayType === 'roman') {
inversionName = '64';
} else {
inversionName = ' (second inversion)';
}
}
let fullChordName;
let connector = ' in ';
let suffix = '';
if (displayType === 'roman') {
fullChordName = this.figure;
fullChordName = fullChordName.replace('/o', 'ø');
} else if (displayType === 'nameOnly') {
// use only with only choice being tonicName
fullChordName = '';
connector = '';
suffix = ' triad';
} else if (displayType === 'bassName') {
fullChordName = this.bass().name.replace(/-/, 'b');
} else {
// "default" submediant, etc...
fullChordName = this.degreeName;
if (this.numbers !== undefined) {
fullChordName += ' ' + this.numbers.toString();
}
}
let tonicDisplay = tonicName.replace(/-/, 'b');
if (mode === 'minor') {
tonicDisplay = tonicDisplay.toLowerCase();
}
const chordStr
= fullChordName
+ inversionName
+ connector
+ tonicDisplay
+ ' '
+ mode
+ suffix;
return chordStr;
}
}
roman.RomanNumeral = RomanNumeral;
</pre>
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