With the increasing importance of smart gadgets in our daily lives, there is a need for an automatic piano transcription system in various multimedia services. For automatic piano transcription, the string inharmonicity coefficient (B) and fundamental frequency (f(0)) should be detected robustly and accurately. The proposed triplet-sequentially additive partial (SAP) algorithm improves the current estimation algorithm in terms of both performance and speed with less prior knowledge. Additionally, this joint (B,f(0)) estimation algorithm is applied directly to the transcription of real piano recordings, and the 4.41% improvement of accuracy was achieved over another transcription system that had both similar processing steps and feature extraction method.