Amplitude values in Csound
The 0dbfs value sets the full-scale amplitude. Csound defaults to 32768 for compatibility with older orchestras. The manual examples use 0dbfs = 1, so full-scale output ranges from -1 to 1. An older amplitude of 10000 becomes about 0.3 on this scale.
The 0dbfs value enables Csound to produce appropriately scaled values to whatever output format is being used, whether 24bit integer, 32bit floats, or even 32bit integers. Put another way, the literal amplitude values you write in a Csound instrument only match those written literally to the file if the 0dbfs value in Csound corresponds exactly to that of the output sample format. The consequence of this approach is that you can write a piece with a certain amplitude and have it render correctly and identically (setting aside of course the better dynamic range of the high-res formats) whether written to an integer or floats file, or rendered in real-time.
Note
The one exception to this is if you choose to write to a "raw" (headerless) file format. In such cases the internal 0dbfs value is meaningless, and whatever values you use are written unmodified. This does enable arbitrary data to be generated or processed by Csound. It is a relatively exotic thing to do, but some users need it.
You can choose to redefine the 0dbfs value in the orchestra header, purely for your own convenience or preference. Many people will choose 1.0 (the standard for SAOL, other software like Pure Data, and for many plugin standards such as VST, LADSPA, CoreAudio AudioUnits, etc), but any value is possible.
The common factor in defining amplitudes is the decibel (dB) scale, with 0dBFS always understood as digital peak; hence "0dbfs" means "0dB Full-Scale value". This measure is different to actual amplitude values, since amplitude values are a linear scale which show the actual oscillation around 0, so they can be positive or negative. Decibel values are an absolute logarithmic scale, but can be useful for most opcodes as well. You can convert amplitude to and from decibels using the ampdb, ampdbfs, dbamp and dbfsamp functions. This way, Csound enables the programmer to express all amplitudes in dB - lower amplitudes will then be represented by negative dB values. This reflects industry practice (e.g. in level meters in mixers, etc).
The same level in dBFS gives different amplitude values for each 0dbfs setting. A level of -6 dBFS is about half the full-scale amplitude.
dBFS in relation to amplitude
| dBFS | 0dbfs = 32768 (default) | 0dbfs = 1 | 0dbfs = 1000 (unusual) |
|---|---|---|---|
| 0 dB | 32768 | 1 | 1000 |
| -6 dB | 16422.904 | 0.501187 | 501.187 |
| -20 dB | 3276.8 | 0.1 | 100 |
Some Csound users might therefore be minded to express all levels in dBFS, and obviate any confusion or ambiguity of level that may otherwise arise when using explicit amplitude values. The decibel scale reflects the response of the ear pretty closely, and that when you want to express a really quiet level, it might be easier and more expressive to write "-46dB" than "0.005" or "163.8".
The reason for using 0dbfs is very simple: digital peak equates to maximum level regardless of sample resolution. If you then define a signal at -110dB you will lose it if rendering to a 16bit file, but retain it (audibly or not) if rendering to 24bit or better. In other words, there is a fixed ceiling, but a moveable floor - you can define sounds as quietly as you like (e.g. envelope tails), in a predictable way, and preserve them or not (without changing the orch code at all), depending on the resolution (file or audio i/o) you render to.