We propose a new sensing technique for one-dimensional touch input workable on an interactive thread of less than 0.4 mm thick. Our technique locates up to two touches using impedance sensing with a spacing resolution unachievable by the existing methods. Our approach is also unique in that it locates a touch based on a mathematical model describing the change in thread impedance in relation to the touch locations. This allows the system to be easily calibrated by the user touching a known location(s) on the thread. The system can thus quickly adapt to various environmental settings and users. A system evaluation showed that our system could track the slide motion of a finger with an average error distance of 6.13 mm and 4.16 mm using one and five touches for calibration, respectively. The system could also distinguish between single touch and two concurrent touches with an accuracy of 99% and could track two concurrent touches with an average error distance of 8.55 mm. We demonstrate new interactions enabled by our sensing approach in several unique applications.