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* @file 音高工具函数
* @description 提供音高相关的计算和转换
*/
import { StepName, AlterationType } from '../models/types';
/**
* 音名到半音的映射（以 C 为 0）
*/
const STEP_TO_SEMITONE: Record<StepName, number> = {
'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11
};
/**
* 半音到音名的映射（只考虑自然音）
*/
const SEMITONE_TO_STEP: StepName[] = ['C', 'C', 'D', 'D', 'E', 'F', 'F', 'G', 'G', 'A', 'A', 'B'];
/**
* 半音到音名是否需要升号
*/
const SEMITONE_NEEDS_SHARP: boolean[] = [false, true, false, true, false, false, true, false, true, false, true, false];
/**
* 简谱数字到音名的映射（C大调）
*/
const JIANPU_TO_STEP: StepName[] = ['C', 'D', 'E', 'F', 'G', 'A', 'B'];
/**
* 音名到简谱数字的映射
*/
const STEP_TO_JIANPU: Record<StepName, number> = {
'C': 1, 'D': 2, 'E': 3, 'F': 4, 'G': 5, 'A': 6, 'B': 7
};
/**
* 计算 MIDI 音高值
* @param step 音名
* @param octave 八度
* @param alter 升降
* @returns MIDI 音高 (0-127)
*/
export function getMidiPitch(step: StepName, octave: number, alter: number = 0): number {
return (octave + 1) * 12 + STEP_TO_SEMITONE[step] + alter;
}
/**
* 从 MIDI 音高获取音名和八度
* @param midi MIDI 音高
* @param preferSharp 优先使用升号（否则用降号）
* @returns 音名、八度、升降
*/
export function fromMidiPitch(
midi: number,
preferSharp: boolean = true
): { step: StepName; octave: number; alter: AlterationType } {
const octave = Math.floor(midi / 12) - 1;
const semitone = midi % 12;
const step = SEMITONE_TO_STEP[semitone];
let alter: AlterationType = 0;
if (SEMITONE_NEEDS_SHARP[semitone]) {
if (preferSharp) {
alter = 1;
} else {
// 使用降号，音名需要往上一个
const nextStep = SEMITONE_TO_STEP[(semitone + 1) % 12];
return { step: nextStep, octave, alter: -1 };
}
}
return { step, octave, alter };
}
/**
* 计算两个音高之间的半音距离
* @param step1 音名1
* @param octave1 八度1
* @param alter1 升降1
* @param step2 音名2
* @param octave2 八度2
* @param alter2 升降2
* @returns 半音距离（正数表示 2 比 1 高）
*/
export function getSemitoneDistance(
step1: StepName, octave1: number, alter1: number,
step2: StepName, octave2: number, alter2: number
): number {
const midi1 = getMidiPitch(step1, octave1, alter1);
const midi2 = getMidiPitch(step2, octave2, alter2);
return midi2 - midi1;
}
/**
* 移调
* @param step 音名
* @param octave 八度
* @param alter 升降
* @param semitones 半音数（正数升调，负数降调）
* @param preferSharp 优先使用升号
* @returns 新的音高
*/
export function transpose(
step: StepName,
octave: number,
alter: number,
semitones: number,
preferSharp: boolean = true
): { step: StepName; octave: number; alter: AlterationType } {
const midi = getMidiPitch(step, octave, alter) + semitones;
return fromMidiPitch(midi, preferSharp);
}
/**
* 获取简谱数字（固定调）
* @param step 音名
* @returns 1-7
*/
export function getJianpuNumberFixed(step: StepName): number {
return STEP_TO_JIANPU[step];
}
/**
* 获取简谱数字（首调）
* @param step 音名
* @param alter 升降
* @param keyFifths 调号的五度圈位置
* @returns 1-7
*/
export function getJianpuNumberMovable(
step: StepName,
alter: number,
keyFifths: number
): number {
// 获取调号的主音
const keyTonic = getKeyTonic(keyFifths);
// 计算当前音相对于主音的半音数
const currentSemitone = STEP_TO_SEMITONE[step] + alter;
const tonicSemitone = STEP_TO_SEMITONE[keyTonic.step] + (keyTonic.alter ?? 0);
// 相对半音数（0-11）
let relativeSemitone = (currentSemitone - tonicSemitone + 12) % 12;
// 半音到简谱的映射（大调音阶）
const semitoneToJianpu: Record<number, number> = {
0: 1, 2: 2, 4: 3, 5: 4, 7: 5, 9: 6, 11: 7
};
// 如果不在大调音阶上，找最近的
if (semitoneToJianpu[relativeSemitone] !== undefined) {
return semitoneToJianpu[relativeSemitone];
}
// 变化音，返回相邻的自然音
const lowerSemitones = [0, 0, 2, 2, 4, 5, 5, 7, 7, 9, 9, 11];
return semitoneToJianpu[lowerSemitones[relativeSemitone]];
}
/**
* 获取调号的主音
* @param fifths 五度圈位置 (-7 到 +7)
* @returns 主音的音名和升降
*/
export function getKeyTonic(fifths: number): { step: StepName; alter?: number } {
// 五度圈顺序
const fifthsToTonic: Record<number, { step: StepName; alter?: number }> = {
[-7]: { step: 'C', alter: -1 }, // Cb
[-6]: { step: 'G', alter: -1 }, // Gb
[-5]: { step: 'D', alter: -1 }, // Db
[-4]: { step: 'A', alter: -1 }, // Ab
[-3]: { step: 'E', alter: -1 }, // Eb
[-2]: { step: 'B', alter: -1 }, // Bb
[-1]: { step: 'F' }, // F
[0]: { step: 'C' }, // C
[1]: { step: 'G' }, // G
[2]: { step: 'D' }, // D
[3]: { step: 'A' }, // A
[4]: { step: 'E' }, // E
[5]: { step: 'B' }, // B
[6]: { step: 'F', alter: 1 }, // F#
[7]: { step: 'C', alter: 1 }, // C#
};
return fifthsToTonic[fifths] ?? { step: 'C' };
}
/**
* 获取调号中的升降号音名
* @param fifths 五度圈位置
* @returns 带升降号的音名数组
*/
export function getKeyAlterations(fifths: number): { step: StepName; alter: number }[] {
const result: { step: StepName; alter: number }[] = [];
if (fifths > 0) {
// 升号调，按 F C G D A E B 顺序
const sharpOrder: StepName[] = ['F', 'C', 'G', 'D', 'A', 'E', 'B'];
for (let i = 0; i < fifths && i < 7; i++) {
result.push({ step: sharpOrder[i], alter: 1 });
}
} else if (fifths < 0) {
// 降号调，按 B E A D G C F 顺序
const flatOrder: StepName[] = ['B', 'E', 'A', 'D', 'G', 'C', 'F'];
for (let i = 0; i < -fifths && i < 7; i++) {
result.push({ step: flatOrder[i], alter: -1 });
}
}
return result;
}
/**
* 检查音符是否在调内
* @param step 音名
* @param alter 升降
* @param fifths 五度圈位置
* @returns 是否在调内
*/
export function isInKey(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;
}
/**
* 获取调内某个音级的音符
* @param scaleDegree 音级 (1-7)
* @param fifths 五度圈位置
* @param octave 八度
* @returns 音名、八度、升降
*/
export function getScaleDegree(
scaleDegree: number,
fifths: number,
octave: number
): { step: StepName; octave: number; alter: number } {
const tonic = getKeyTonic(fifths);
const tonicIndex = ['C', 'D', 'E', 'F', 'G', 'A', 'B'].indexOf(tonic.step);
// 计算音名
const degreeIndex = (tonicIndex + scaleDegree - 1) % 7;
const step = ['C', 'D', 'E', 'F', 'G', 'A', 'B'][degreeIndex] as StepName;
// 计算八度偏移
let oct = octave;
if (tonicIndex + scaleDegree - 1 >= 7) {
oct += 1;
}
// 获取调内升降号
const keyAlterations = getKeyAlterations(fifths);
const alter = keyAlterations.find(a => a.step === step)?.alter ?? 0;
return { step, octave: oct, alter };
}
/**
* 比较两个音高
* @param a 音高 a
* @param b 音高 b
* @returns 负数表示 a < b，0 表示相等，正数表示 a > b
*/
export function comparePitch(
a: { step: StepName; octave: number; alter?: number },
b: { step: StepName; octave: number; alter?: number }
): number {
const midiA = getMidiPitch(a.step, a.octave, a.alter ?? 0);
const midiB = getMidiPitch(b.step, b.octave, b.alter ?? 0);
return midiA - midiB;
}
/**
* 获取音高的字符串表示
* @param step 音名
* @param octave 八度
* @param alter 升降
* @returns 如 "C4", "F#5", "Bb3"
*/
export function pitchToString(step: StepName, octave: number, alter: number = 0): string {
let alterStr = '';
if (alter === 1) alterStr = '#';
else if (alter === -1) alterStr = 'b';
else if (alter === 2) alterStr = '##';
else if (alter === -2) alterStr = 'bb';
return `${step}${alterStr}${octave}`;
}
/**
* 从字符串解析音高
* @param str 如 "C4", "F#5", "Bb3"
* @returns 音名、八度、升降
*/
export function parsePitchString(str: string): { step: StepName; octave: number; alter: number } {
const match = str.match(/^([A-G])(#{1,2}|b{1,2})?(-?\d+)$/i);
if (!match) {
throw new Error(`Invalid pitch string: ${str}`);
}
const step = match[1].toUpperCase() as StepName;
const alterStr = match[2] || '';
const octave = parseInt(match[3], 10);
let alter = 0;
if (alterStr === '#') alter = 1;
else if (alterStr === '##') alter = 2;
else if (alterStr === 'b') alter = -1;
else if (alterStr === 'bb') alter = -2;
return { step, octave, alter };
}
/**
* 获取音程名称
* @param semitones 半音数
* @returns 音程名称
*/
export function getIntervalName(semitones: number): string {
const intervals: Record<number, string> = {
0: '纯一度', 1: '小二度', 2: '大二度', 3: '小三度',
4: '大三度', 5: '纯四度', 6: '增四度/减五度', 7: '纯五度',
8: '小六度', 9: '大六度', 10: '小七度', 11: '大七度',
12: '纯八度'
};
const absSemitones = Math.abs(semitones);
const octaves = Math.floor(absSemitones / 12);
const remainder = absSemitones % 12;
let name = intervals[remainder] ?? `${remainder}半音`;
if (octaves > 0) {
name = `${octaves}个八度 + ${name}`;
}
return semitones < 0 ? `下行${name}` : name;
}
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