DAGA 2014 40TH GERMAN ANNUAL CONFERENCE ON ACOUSTICS Oldenburg, Germany March 10–14, 2014 How Microtonal is a Well-Tuned Concert Grand Piano? Timour Klouche Staatliches Institut für Musikforschung PK, Berlin, Germany Introduction The core question of this paper is how accurate the tun- ing of a well-tuned concert grand piano is. The underly- ing experiment is a direct extension of previous studies [1] [2] centering on methodological issues concerning validating tuning accuracy [1], and measuring micro- tonal accuracy of virtual instruments respectively [2]. After first presenting a series of measurements, we focus on exemplary details and relate the final outcome to that of the virtual piano presented at DAGA 2013. A more de- tailed version of the paper will be available online [3]. Setup and Methods The minimization of external influences to the mea- surements has been given high priority throughout the inception of our microtonal validation series [1]. We thus applied the very same, already validated and tested ex- perimental setup. That in turn makes a direct compar- ison with last years’ virtual piano (Pianoteq software synthesizer) tuning measurements possible. The inter- ested reader is directed to the publication [2] for details of the setup incl. all measurement and preprocessing parameters. Following is a very brief summary of the steps involved: The complete pitch gamut of a Steinway D concert grand piano is recorded directly after the tun- ing process preparing public concerts in the Curt-Sachs Saal of the Staatliches Institut für Musikforschung. Each recording consists of 88 piano pitches in the way that each key is depressed for 6s followed by 6s silence, cap- tured by ORTF condenser microphones. Subsequently the sound file (2 channel 192 kHz, 24 bit) is monoized, segmented with a MATAB rms-dependent script and analyzed via Praat. The fundamental frequency is calcu- lated with the F0 autocorrelation function of Praat (for all details see [2]). Two aspect are changed in comparison to the setup used in the last publication: Firstly, we had to include a recording chain to the measuring setup prior to the analyzing procedure, and secondly, a human player is added. How both factors are influencing the results will be analyzed in later experiments as are perceptive and cognitive implications. Here we focus deliberately on the signal description layer with measuring the funda- mental frequencies of piano tones. Results Results A: Measurements of 16 fresh tunings The analysis of the series of measurements (n=16) is de- picted in Fig. 1 and 2. Interestingly, outliers (up to roughly 3000 cents) are not everywhere and seem to be not equal- ly distributed (Fig. 1). Remarkable areas are the smooth re- gions around A4 and A5-A6 and the downturn from A6 on associated with large ranges but within also a zone with notably small measuring ranges. The downturn area is possibly indicating a measuring- or stimuli related artifact leading to a result approx. one oc- tave (but notably less than; cf. Results D) below the ex- pectancy value. Figure 2 depicts a zoomed window illus- trating how most values average around the expectancy value within 10 cents deviation with outliers not exceed- ing 40 cents in the mid frequencies. Results B: Selection of the best-fit piano tuning The single tuning with statistically least deviation to the expectancy had been chosen for further examination and later reprocessing (see Results C). Figure 3 shows a smooth fluctuation around 5 cents (indicating an offset) with out- lier areas below A1 and over A6. Intra-note ranges are de- picted in Fig. 4 that exhibits a similar picture with fluctua- tions around 5 cents and respective outliers. The ranges’ outliers are excessive only in the lows, likely indicating more plausible measuring errors in that area and a stimuli related problem in the highs (with below 30 cents ranges). Results C: Data reprocessing & comparison with a virtual piano Three aspects were c