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* @file 调号工具函数
* @description 提供调号相关的计算和转换
*/
import { StepName, KeyMode } from '../models/types';
import { getKeyTonic, getKeyAlterations, getMidiPitch } from './PitchUtils';
/**
* 调号信息
*/
export interface KeyInfo {
/** 五度圈位置 */
fifths: number;
/** 调式 */
mode: KeyMode;
/** 主音 */
tonic: { step: StepName; alter?: number };
/** 调号中的升降音 */
alterations: { step: StepName; alter: number }[];
/** 调号名称（中文） */
name: string;
/** 关系大小调 */
relative?: { fifths: number; mode: KeyMode };
}
/**
* 大调名称映射
*/
const MAJOR_KEY_NAMES: Record<number, string> = {
[-7]: 'Cb大调', [-6]: 'Gb大调', [-5]: 'Db大调', [-4]: 'Ab大调',
[-3]: 'Eb大调', [-2]: 'Bb大调', [-1]: 'F大调', [0]: 'C大调',
[1]: 'G大调', [2]: 'D大调', [3]: 'A大调', [4]: 'E大调',
[5]: 'B大调', [6]: 'F#大调', [7]: 'C#大调'
};
/**
* 小调名称映射
*/
const MINOR_KEY_NAMES: Record<number, string> = {
[-7]: 'ab小调', [-6]: 'eb小调', [-5]: 'bb小调', [-4]: 'f小调',
[-3]: 'c小调', [-2]: 'g小调', [-1]: 'd小调', [0]: 'a小调',
[1]: 'e小调', [2]: 'b小调', [3]: 'f#小调', [4]: 'c#小调',
[5]: 'g#小调', [6]: 'd#小调', [7]: 'a#小调'
};
/**
* 简谱调号名称（1=X）
*/
const JIANPU_KEY_NAMES: Record<number, string> = {
[-7]: '1=Cb', [-6]: '1=Gb', [-5]: '1=Db', [-4]: '1=Ab',
[-3]: '1=bE', [-2]: '1=bB', [-1]: '1=F', [0]: '1=C',
[1]: '1=G', [2]: '1=D', [3]: '1=A', [4]: '1=E',
[5]: '1=B', [6]: '1=#F', [7]: '1=#C'
};
/**
* 获取调号的完整信息
* @param fifths 五度圈位置
* @param mode 调式（默认大调）
* @returns 调号信息
*/
export function getKeyInfo(fifths: number, mode: KeyMode = 'major'): KeyInfo {
const tonic = getKeyTonic(fifths);
const alterations = getKeyAlterations(fifths);
let name: string;
let relative: { fifths: number; mode: KeyMode } | undefined;
if (mode === 'major') {
name = MAJOR_KEY_NAMES[fifths] ?? `${fifths}个升降号大调`;
relative = { fifths, mode: 'minor' }; // 关系小调
} else if (mode === 'minor') {
name = MINOR_KEY_NAMES[fifths] ?? `${fifths}个升降号小调`;
relative = { fifths, mode: 'major' }; // 关系大调
} else {
// 其他调式
name = `${tonic.step}${tonic.alter === 1 ? '#' : tonic.alter === -1 ? 'b' : ''} ${mode}`;
}
return {
fifths,
mode,
tonic,
alterations,
name,
relative
};
}
/**
* 获取简谱调号标记
* @param fifths 五度圈位置
* @returns 如 "1=C", "1=G", "1=bB"
*/
export function getJianpuKeyName(fifths: number): string {
return JIANPU_KEY_NAMES[fifths] ?? `1=${getKeyTonic(fifths).step}`;
}
/**
* 从调名获取五度圈位置
* @param keyName 调名（如 "C", "G", "Bb", "F#"）
* @param mode 调式
* @returns 五度圈位置
*/
export function getKeyFifths(keyName: string, mode: KeyMode = 'major'): number {
// 解析调名
const match = keyName.match(/^([A-G])([#b])?$/i);
if (!match) {
throw new Error(`Invalid key name: ${keyName}`);
}
const step = match[1].toUpperCase() as StepName;
const alter = match[2] === '#' ? 1 : match[2] === 'b' ? -1 : 0;
// 根据主音找五度圈位置
for (let fifths = -7; fifths <= 7; fifths++) {
const tonic = getKeyTonic(fifths);
if (tonic.step === step && (tonic.alter ?? 0) === alter) {
return fifths;
}
}
throw new Error(`Key not found: ${keyName}`);
}
/**
* 获取调内音阶（大调）
* @param fifths 五度圈位置
* @param octave 起始八度
* @returns 音阶音符数组
*/
export function getMajorScale(
fifths: number,
octave: number
): { step: StepName; octave: number; alter: number }[] {
const scale: { step: StepName; octave: number; alter: number }[] = [];
const tonic = getKeyTonic(fifths);
const alterations = getKeyAlterations(fifths);
const alterMap = new Map(alterations.map(a => [a.step, a.alter]));
// 大调音阶：全全半全全全半
const steps: StepName[] = ['C', 'D', 'E', 'F', 'G', 'A', 'B'];
const tonicIndex = steps.indexOf(tonic.step);
let currentOctave = octave;
for (let i = 0; i < 8; i++) {
const stepIndex = (tonicIndex + i) % 7;
const step = steps[stepIndex];
if (i > 0 && stepIndex === 0) {
currentOctave++;
}
const alter = alterMap.get(step) ?? 0;
scale.push({ step, octave: currentOctave, alter });
}
return scale;
}
/**
* 获取调内音阶（自然小调）
* @param fifths 五度圈位置
* @param octave 起始八度
* @returns 音阶音符数组
*/
export function getNaturalMinorScale(
fifths: number,
octave: number
): { step: StepName; octave: number; alter: number }[] {
// 自然小调 = 关系大调从第6级开始
const scale = getMajorScale(fifths, octave);
// 重新排列，从第6级开始（la = 6）
const minorScale = [];
for (let i = 5; i < 5 + 8; i++) {
const note = scale[i % 7];
minorScale.push({
...note,
octave: note.octave + (i >= 7 ? 1 : 0)
});
}
return minorScale;
}
/**
* 判断两个调是否为关系大小调
* @param fifths1 调1的五度圈位置
* @param mode1 调1的调式
* @param fifths2 调2的五度圈位置
* @param mode2 调2的调式
* @returns 是否为关系大小调
*/
export function areRelativeKeys(
fifths1: number, mode1: KeyMode,
fifths2: number, mode2: KeyMode
): boolean {
// 关系大小调有相同的五度圈位置，但调式不同
return fifths1 === fifths2 && mode1 !== mode2 &&
((mode1 === 'major' && mode2 === 'minor') ||
(mode1 === 'minor' && mode2 === 'major'));
}
/**
* 判断两个调是否为同主音大小调
* @param fifths1 调1的五度圈位置
* @param mode1 调1的调式
* @param fifths2 调2的五度圈位置
* @param mode2 调2的调式
* @returns 是否为同主音大小调
*/
export function areParallelKeys(
fifths1: number, mode1: KeyMode,
fifths2: number, mode2: KeyMode
): boolean {
// 同主音大小调有相同的主音，但调式不同
const tonic1 = getKeyTonic(fifths1);
const tonic2 = getKeyTonic(fifths2);
return tonic1.step === tonic2.step &&
(tonic1.alter ?? 0) === (tonic2.alter ?? 0) &&
mode1 !== mode2;
}
/**
* 计算两个调之间的转调关系
* @param fromFifths 起始调
* @param toFifths 目标调
* @returns 转调信息
*/
export function getModulationInfo(
fromFifths: number,
toFifths: number
): { distance: number; direction: 'sharp' | 'flat' | 'none'; isNear: boolean } {
const distance = toFifths - fromFifths;
const direction = distance > 0 ? 'sharp' : distance < 0 ? 'flat' : 'none';
// 近关系调：五度圈上相差 ±1
const isNear = Math.abs(distance) <= 1;
return { distance, direction, isNear };
}
/**
* 获取调内和弦（大调）
* @param fifths 五度圈位置
* @returns 级数和弦数组
*/
export function getDiatonicChords(fifths: number): {
degree: number;
root: { step: StepName; alter: number };
quality: 'major' | 'minor' | 'diminished';
romanNumeral: string;
}[] {
const scale = getMajorScale(fifths, 4);
const qualities: ('major' | 'minor' | 'diminished')[] =
['major', 'minor', 'minor', 'major', 'major', 'minor', 'diminished'];
const romanNumerals = ['I', 'ii', 'iii', 'IV', 'V', 'vi', 'vii°'];
return scale.slice(0, 7).map((note, i) => ({
degree: i + 1,
root: { step: note.step, alter: note.alter },
quality: qualities[i],
romanNumeral: romanNumerals[i]
}));
}
/**
* 检查音符是否需要临时记号
* @param step 音名
* @param alter 升降
* @param fifths 调号
* @returns 是否需要临时记号
*/
export function needsAccidental(step: StepName, alter: number, fifths: number): boolean {
const keyAlterations = getKeyAlterations(fifths);
const keyAlterMap = new Map(keyAlterations.map(a => [a.step, a.alter]));
const expectedAlter = keyAlterMap.get(step) ?? 0;
return alter !== expectedAlter;
}
/**
* 获取移调后的调号
* @param fifths 原调号
* @param semitones 移调半音数
* @returns 新调号的五度圈位置
*/
export function transposeKey(fifths: number, semitones: number): number {
// 半音与五度圈的关系：每上升7个半音 = 五度圈+1
// 简化：半音数 % 12，然后找对应的五度圈变化
const semitoneToFifths: Record<number, number> = {
0: 0, 1: 7, 2: 2, 3: -3, 4: 4, 5: -1,
6: 6, 7: 1, 8: -4, 9: 3, 10: -2, 11: 5
};
const normalizedSemitones = ((semitones % 12) + 12) % 12;
const fifthsChange = semitoneToFifths[normalizedSemitones];
let newFifths = fifths + fifthsChange;
// 保持在 -7 到 +7 范围内
while (newFifths > 7) newFifths -= 12;
while (newFifths < -7) newFifths += 12;
return newFifths;
}
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