Examine (Public Domain Classical Music) Recordings With the Score At Hand:
using the Petrucci Music Archive of 200,000+ free public domain scores.
Sites About the Ear and the Basilar Membrane:
OpenLearn LabSpace on Hearing. Wonderful exposition on the mechanics of hearing, with nice illustrations. I've pointed you to the page on the basilar membrane, because that's the part of the ear whose vibration levels are represented by the SpectratunePlus spectrograms, but you will likely want to check the prior and subsequent pages on hearing.
On-line Text: Why You Hear What You Hear is an on-line textbook, with lots of software and sound examples, and links to software and examples. It is based on an undergraduate non-science-major's course at Harvard taught by physicist Eric Heller.
F. Mammano and R. Nobili's The Cochlea HomePage contains good detail, with many illustrations and animations, of both the basic mechanical, and the more advanced electromechanical structures, of the ear and cochlea.
Here is Some Other Nice Software with Some Overlap in Function to Mine:
Sonic Visualizer Geared towards exploring music spectrograms, just like mine. From the Centre for Digital Music, Queen Mary, University of London. It's free, is available for PC, Linux, or Mac, and has a nicer interface than my program. If you download it, you should also download the plugins, available separately, which can extend its non-constant-Q spectrograms to constant Q ones, and can also let you mess around with some key and chord identification algorithms from the academic world.
Comparison: It does certain things that my software does not do. I think it's fair to say that my software is a bit better (at the moment) for looking at recorded music in the context of the key of the music (i.e. spectral components can be shown at position of the notes with respect to the tonic). My software has more aural feedback (MIDI notes playable by clicking on the the spectrogram, and also sing-along overlay on the spectrogram: of course you will not need these if you have perfect pitch!) Sonic Visualizer also doesn't have any analysis of live sound, as far as I can tell. But Sonic Visualizer is a pretty big project, reliable, widely used, with a bunch of demo videos on YouTube, and an excellent choice for many, many needs. And it's constantly being expanded, and there are new plugins for it coming out frequently, giving it new functionality.
SPEAR (Sinusoidal Partial Editing Analysis and Resynthesis) from Professor Michael Klingbeil is mainly geared towards sound editing by moving fundamentals or harmonics, pitch shifting, etc. You can also identify many of the harmonics and notes. It's free, is available for PC, Linux, or Mac, and also has a much nicer interface than my program.
Stuff at Princeton Sound Lab, especially a package called sndtools. There are 3 different programs in sndtools, which do in real time stuff geared both towards speech recognition and music analysis. (Note that, though I can't find frequency labels, everything appears to be scaled according to frequency, rather than the musical-note-spaced log frequency which my programs use.) If you are interested in looking at how linear predictive coding works on your own sounds and voice (linear predictive coding is a standard technique used in speech recognition and instrument analysis to separate the excitation signal, e.g. the vocal cord, mouth-noise, reed, or string sound, from the resonance of the mouth and nose or instrument body), sndtools component rt_lpc will do that. There is also a real time phase vocoder (pitch-shifter) in the package. All 3 programs have versions for Windows, linux, and Mac, though for the vocoder I can find a ready-to-run version only for Mac. All 3 programs are open source, so if you want to make sure you understand the underlying algorithms that you read about in a paper or book, you can use the source code available on the site.
Overtone Analyzer This purchasable software will let you look at tones and overtones of live sound or recordings through spectrograms, and has MIDI feedback of notes against the spectrograms. It has a polished, musician-friendly interface. There are several versions with 30-day trials, and a free version.
Rapid Evolution (Automatic Key Detection) This free java-based software is designed as a kind of database and control panel for song-mixing DJ's, but my purpose in listing it here is that it has an automatic key detection for songs in .wav files that people who visit my page may wish to experiment with. (Given the complexity of the key-detection task, my guess is that it may occasionally give a wrong key, and that it may be thrown by classical music with a lot of key changes, but it should be fun to try out and compare against my spectrograms.)
Intonation training software: These modestly priced programs work on live music, showing single pitch and/or spectrograms at each instant, like my Spectratune software in live-mode, but also show progression over time, and remember and can play back both the analysis and the input live sounds. They are designed to help instrument/voice students work on intonation and/or other aspects of their sound. Intonia, Sing and See.
There is also other software out there geared at either transcibing music from a recording, helping you transcribe music from a recording, or creating a MIDI score. The ones listed below are not free, but most have trial versions that let you test them out. I suspect that anything that claims to transcribe fully automatically can only work perfectly in certain cases, but I may be wrong.
Here is one, Transcribe! that makes a modest claim, of helping you manually transcribe a recording. (A free trial is available.) That site also has a list of other sites that have software that are supposed to transcribe or help you transcribe music , (here).
This one, Neuratron Audioscore attempts a transcription. (A free trial is available, so you can test it out and see how well it works even if you don't want to buy it.)
This one, Twelve Keys also attempts a transcription. (A free trial is available, so you can test it out and see how well it works even if you don't want to buy it.)
Finally is another one which attempts a transcription, Intelliscore. (A free trial is available, so you can test it out and see how well it works even if you don't want to buy it.)
Related to Speech Analysis and Speech Synthesis (of interest in its own right and also relevant to music because it shows up in singing):
This one, Prof. Peter Birkholz's Vocal Tract Lab does "articulatory voice synthesis", meaning synthesis based on modeling of the the vocal chords and the vocal tract components (tongue, etc.) in motion. It's very cool, giving you a 3D picture of the vocal tract in motion, along with all kinds of supplementary plots of vocal tract formants, and the ability to adjust and make your own vocal tracts. It also can do spectral analyses of sound, geared towards speech.(A particularly fun and instructive thing that I noticed on Prof. Birkholz's site, for people interested in music, is a video of two synthetic vocal tracts singing together a piece called "Dona Nobis Pacem", available if you scroll down on this page of his.)
Praat does nice-for-speech spectrograms that automatically finds formants. It also has several kinds of speech synthesis.
Spectral Cues for Phonemes Page is a basic "reference chart" on the various phonemes, and how the spectrograms look for each of them. [With this and the speech-oriented software listed just above, you should note that the SpectratunePlus frequency is on a "logarithmic" scale (which puts the same distance between musical half-steps and is best for understanding musical relations), while speech spectrograms have a "linear" scale (which puts the same distance between each cycle per second). Thus, you will have to do a little mental translation between the two spectrogram types if you look at a voice within music with my software, and want to correspond sung word with the formants as shown with the linear software and charts.]
What are formants?: In speech (including singing), you have an initial vibration from the vocal chords (or, for non-voiced sounds, just a noise made by air in the throat), which goes through the rest of the vocal tract. The rest of the vocal tract, because of its shape when enunciating a particular sound, passes different frequencies at varying proportions. That is, for a particular person's vocal tract enunciating long "e", it may pass 12.1 times as much 2000 hz as it does 1000 hz. The full function that indicates the proportion of power that passes at each frequency (say 20-20,000hz) is called the transfer function, and it tends to have a few peaks at resonances, maybe 10db or more higher, which characterize the sound, and which are called formants. (For voiced sounds, the vocal chords emit a fundamental frequency and then a certain slightly smaller amount of twice the fundamental, a certain other slightly smaller amount of 3 X the frequency, etc., and nothing else, and the output after the vocal tract still contains just these frequencies from the vocal chords. However, generally the formants are frequencies a good bit higher than the vocal tract frequencies, and are wide enough so that they contain several multiples of the vocal chord fundamental (maybe the 12, 13, 14, 15 -th multiple), and so all formants tend to define the sound no matter what the fundamental of the vocal chord frequency. The formants are responsible for how one speech sound ("phoneme", i.e. "t", "short e", etc.) is different from another, and also how voices vary between people.
Automatic Transcription / Automatic Recognition at MIREX:. A good number of sound engineering academics and some others compete every year on software for music transcription and chord recognition from recordings, etc., at a MIREX (=Music Information Retrieval Evaluation eXchange) gathering. They come up with % accuracy numbers for each algorithm, typically around 80% (computers at this point are no match for skilled human musicians, who hit 100%). You can keep an eye on how they are doing at MIREX by checking here. (The results for each year are accessible from the left of the page.)
(As you might guess, transcription and chord recognition algorithms typically start by generating something like the constant-Q spectrogram that you see in my SpectratunePlus, and then do computerized figuring out from that thing. For chord recognition, they also frequently use something like the SpectratunePlus octave-overlaid display, which in the musical signal processing literature is called a "chromogram". However, SpectratunePlus stops short of giving you any final guesses on transcription and chords -- it leaves you to figure them out yourself, giving at most some suggestions on possible chords via visual cues.)
If you are interested in writing programs yourself to do this kind of stuff, you need to know how to program a computer (just some personal-sized computer in say the C++ language), and need to know some math with a little physics to a decent engineering level. Search terms to find out about this are "Computer Music Transcription", "Signal Processing", and also "Speech Recognition". Here is a nice link to some free references on the math:
Free Tracts from Julius Orion Smith III at the CCRMA at Stanford U.
Papers from prof. Anssi Klapuri's site at Tampere University of Technology in Finland. (One topic on the site is automatic music transciption) (here).
Papers from prof. Richard Parncutt's site (on many music perceptual concepts, including tonality and the perception of chords as they relate to the spectrum of music) (here).
Papers from prof. Norman Cook's site including papers giving a theory on the cause of why major chords sound happy, and minor sad, with also some open-source software for testing this out yourself. (here).
Numerous free papers and reports that you can get by searching Google SCHOLAR.
Numerous IEEE papers, accessible from a good university library, or with membership and optional IEEE library subscriptions plans, or perhaps instead of a subscription plan, signal processing society membership with the optional expanded access that costs $15. more (The relevant items seem to be proceedings and conference records on "acoustics, speech, and signal processing". Unfortunately, even if you shell out around $230 for an IEEE membership with the Signal Processing Society membership and expanded signal processing library access, much of what you may want to look at will be in conference proceedings, or other publications that you don't get with the IEEE signal processing society expanded membership. Your alternatives will be to pay $180 a year additional for 3 of these items a month, or $420 additional for 25 a month. However, note that many of these conference proceedings, etc., can be found on the web, if you use Google and Google Scholar, though the trick is that often you need to start with an exact paper title taken from a reference.)
Papers in the Journal of the Acoustial Society of America, all prior and current of which are accessible from a good university library, or with membership in the Acoustical Society of America, which runs just about $100 a year. Some autho names of interest relating to music theory and a psychoacoustical concept of "virtual pitch" are Terhardt and Parncutt. (Fortunately, unlike with IEEE, membership gives you access to everything you will want from the Acoustical Society of America.)
Free Individual Instrument Samples for many instruments are available from Philharmonia Orchestra Sounds and Sonatina Symphonic Orchestra Sounds. The Philharmonia sounds are supplied as .mp3. You can convert them to the .wav that my SpectratunePlus program needs by using the free Audacity program. The Sonatina samples are in some .sfz format that I don't know much about, but if you download them, and then drill down to their "Samples" directory, you get to .wav file samples.