The Interpretation of MIDI Velocity

The MIDI standard does not specify how MIDI key velocity is to be interpreted. Of course, individual synthetic instruments respond differently, but one would expect that on average, instruments will respond about the same. This study aims to determine empirically how hardware and software MIDI synthesizers translate velocity to peak RMS amplitude. Analysis shows synthesizers roughly follow an xsquared rather than exponential mapping. Given a desired dynamic range (from velocity 1 to 127), a square-law mapping from velocity to RMS is uniquely determined, making dynamic range a convenient way to summarize behavior. Surprisingly, computed values of dynamic range for commercial synthesizers vary by more than 60dB. 1 Technical Introduction MIDI key velocity (Rothstein 1995) is normally an indication of dynamic level or loudness, but the MIDI standard (MMA 1996) does not specify exactly how velocity should be interpreted. In synthesizers, key velocity can control many parameters, including amplitude, FM modulation depth, and sample selection. Even when velocity is used simply to scale audio amplitude, it is unclear how to map MIDI velocity to amplitude. In order to create a truly “MIDI compatible” system, one should try to be consistent with existing implementations so that similar key velocity values result in similar output levels. Lacking any published recommendations or specifications, I measured many programs (instruments) on a handful of synthesizers to determine how key velocity maps to peak RMS amplitude. At the outset of this work, I assumed that MIDI velocity would be logarithmically related to amplitude since it is well known that perceived loudness is also quasi-logarithmic. A logarithmic scale would allow a wide dynamic range to be represented efficiently by the 7-bit velocity value in MIDI messages. One finding is that a logarithmic relationship is not a good fit to a variety of commercial synthesizers and patches. Overall, a square-root function is a better, and in some cases nearly exact, model of MIDI velocity as a function of RMS amplitude. However, synthesizers and programs appear to be quite inconsistent. We can make recommendations for MIDI-controlled instruments, but there is hardly a de facto standard. The next section expands upon the motivation as well as some musical and esthetic concerns relating to this work. Section 3 describes what I measure to study velocity, and Section 4 describes how I measure it. Section 5 introduces a model for sound variation as a function of velocity, and Section 6 fits this model to actual synthesizers. This is followed by some discussion and conclusions. 2 A Broader Introduction MIDI seems to be a permanent fixture on the computer music landscape. It has been used for more than twenty years almost without change, and it has survived a major transition from serving as a real-time hardware control protocol to a data format for music that is realized entirely in software. MIDI is even used to specify ring tones for cell phones, possibly the largest application of music synthesis technology to date. MIDI is not without shortcomings, and the limitations of MIDI have been lamented by more than one author. (Moore 1988, Wessel and Wright 2002) Various proposals to extend or replace MIDI have also appeared. (McMillen 1994, Wright 1997) Nevertheless, MIDI has proven to be resilient, durable, and well understood. The perceived benefits of MIDI compatibility usually outweigh any implementation difficulty, so most computer music systems handle MIDI messages and standard MIDI files. One of the features of MIDI is that it supports the notion of the music score (or sequence of MIDI messages) as an abstract specification that can be “performed” by a variety of synthesizers. This has roots in Western music, common practice notation, and music performance practice – music scores can be played by different performers using different instrumentation. Many computer musicians have rejected this notion outright, replacing vague sequences of MIDI messages with precise specifications of the entire sound production process using software synthesis. In this approach, the “instrument,” its control, and even the notion of score are often integrated into a single software program, patch, or configuration, giving precise control of sound from human gesture all the way down to the details of sample-by-sample computation. Now that we have experienced music making with MIDI-based systems and more general software-based systems, we can observe that these two approaches naturally Originally published as: Roger B. Dannenberg, “The Interpretation of MIDI Velocity,” in Proceedings of the 2006 International Computer Music Conference, San Francisco, CA: The International Computer Music Association, 2006, pp. 193-196. Copyright © 1996 by Roger B. Dannenberg