Wolfram CDF Player
Mathematica is the signature product of Wolfram, Inc. It is extremely powerful, expensive, and flexible, with a steep learning curve and an unforgiving syntax. However Wolfram provides a free CDF Player, that allows interactive exploration of thousands of programs others have written on the full version of Mathematica. The multiplatform Player can be downloaded at http://www.wolfram.com/cdf-player/, and then housands of pre-made demonstrations are easily run. Of these, perhaps 5 or 10 are of high value to us, although that can change as more are being added every day. Some of these should not be missed, such as Pythagorean, Meantone, and Equal Temperament Musical Scales,
that makes an appearance in Chapter 26:
and Shepard Tones, http://demonstrations.wolfram.com/ShepardTones/, a surprising pitch "illusion". The pitch rises from one note to the next but after 12 notes it is back where it started! I put illusion in quotes because the pitch really does rise according to our internal algorithms, showing that pitch is a qualitative impression like taste, not a quantitative measure of frequency. In other words, the Shepard tones are not an illusion, but rather a direct consequence of a central property of our perception of pitch. See Chapter 23.
If you happen to own and use Mathematica, you can download the source code instead.
The author finds Amadeus Pro very useful, though it lacks autocorrelation computation. It also costs $59.95; there is a 25% discount available for students. The fully functional program may be freely downloaded with a 30 day trial period.
SignalSuite makes signal generation much easier, suitable for driving experiments incuding studies of phantom tones (Chapter 25). Not cheap for such a limited purpose product at $29.95, it is very capable at what it does, that includes predetermined ramping of the frequency of two tones. The general purpose ElectroAcoustics Toolbox includes an FFT and impulse response analysis, plus much more signal analysis and signal generation, but is sold as a professional tool at $499.
WaveSurfer is a free and capable waveform-sonogram analyzer; the graphics is quite good but the program lacks some of the sound generation and transformation tools available in Amadeus Pro for example.
Audacity is available free for Mac OS X, Microsoft Windows, GNU/Linux, and other operating systems. It records and plays back sounds, does a spectral analysis of recorded sounds, processes sound clips with dozens of tools, generates standard tones, computes the sonogram with adjustable parameters, and much more.
Sonogram Visible Speech has useful features such as autocorrelation, and nice graphics. It seems to be losing its presence on the web, unfortunately. Try your own search for it; the developer is Christoph Lauer.
RavenPro is a full featured sound capture and analysis program originally developed for bird calls and songs, by the Cornell Laboratory of Ornithology. It includes autocorrelations analysis, sonograms, power spectra, etc. The graphics is good but user interface is a bit compex. Unfortunately Cornell has opted in favor of making money rather than spreading science: a standard academic license is $400 and a student one semester license is $50. These prices are not justified in view of the close approximation of competing software for free or much less, including Praat.
RavenLite is free, but less capable than other freely available sound analysis programs.
Praat is a powerful (in fact professional level), free, multiplatform sound analysis program developed in the Netherlands for phonetics analysis. Along the way it does most of what the most capable programs do, plus things like formant analysis, pitch analysis, and "Gender transformation," that works really well, if carefully applied. The Achilles heel is that the interface is klunky and takes some getting used to, but it is not ultimately difficult. Hats off to the developers (and scientists) Paul Boersma and David Weenink for doing such a good job and making it available.
Sonic Visualizer is free and is based on plugins, that are expanding in capability. It is aimed especially at music analysis.
Tone Generator allows flexible production of fixed and swept tones, suitable for hearing analysis, driving experiments (e.g. measuring frequency response), etc. $29.99 or $59.95 for the professional version.
Wavosaur (Windows) Free sound editor with VST support
Android apps are coming fast and users with Android phones or tablets may want to check out Google play, for example Audio Test Tone Generator (and other apps listed there)
All the packages perform a spectrum analysis of a sound file that is either recorded using the package or stored on disk, and most make sonograms. A partial list of other features is: display the waveform real time, display a sonogram real-time, play the sound backwards, provide the statistics of the sound file (e.g. loudness in decibels), change the pitch and the speed of playback independently (quite a trick, wherein you avoid a Donald Duck effect if you speed the sound up by 50% but leave the pitch the same), de-noise the sound according to various criteria, create multitrack files, work with tracks independently, gender shift speech, analyze pitch and formants. In addition, the software package may be able to access hundreds of cross package and platform specialty transformations and filters, such as the VST set. Most packages will allow generation of periodic tones such as sinusoids, square waves, triangle waves, and sawtooth waves. They are usually not flexible enough to independently control the phase and amplitude of many partials, that is why MAX Partials was created.
We could not possibly be comprehensive here. A long list with some comparasons is available on Wikipedia here.