ChenYN Piano Tuner 陈师傅调音-佩卓夫（PETROF）钢琴的平均律与“狼音”之间隔

佩卓夫（PETROF）钢琴的平均律与“狼音”之间隔

In a Petrof piano, this refers to the interval between equal temperament and the "wolf tone."

检查一架十多年没有调律的佩卓夫PETROF三角钢琴骤然发现了狼音音程Wolf Interval，无法确认当年的调律师是如何为了保证五度纯净，把这误差24 音分全部“塞进”最后一个五度导致其产生狼音的。狼音的产生也是因为数学上12个纯五度不等于 7个纯八度，两者之间存在约 23.46 音分的余数（称为毕达哥拉斯增差）。 

很久没有谈及十二平均律的比例与五度音程，如何达到物理上的“完美纯净”。特别是让所有半音之间的比例完全相等（约1.05946），其奥秘在于将这 24 音分的误差被平均分成了 12 份，每个五度音程只分担约 2 音分的极小偏差，从而实现了自由转调。十二平均律通过均匀分配误差，彻底消除了狼音音程Wolf Interval。

感恩早年母亲的教诲让我学习了音乐且多次弹奏舒曼的《梦幻曲》记忆犹新，然早年狼音的存在大多与乐器的构造及局限性有关，特别是大提琴等弦乐器。多年后的理论与实践，特别是琴体共振频率与琴弦频率冲突等物理杂音与律法等受益匪浅。此次调整非常成功且主人欣赏之余额外小费$88红包！

祝各位节日快乐！

2025-12-16于纽约

 

In a Petrof piano, this refers to the interval between equal temperament and the "wolf tone."

Inspecting a Petrof grand piano that hadn't been tuned for over ten years, I suddenly discovered a wolf interval.  It was impossible to determine how the tuner from years ago managed to "stuff" all 24 cents of error into the last perfect fifth to maintain the purity of the other fifths, thus creating the wolf interval. The wolf interval arises because mathematically, twelve perfect fifths do not equal seven perfect octaves; there is a remainder of approximately 23.46 cents between them (known as the Pythagorean comma).