To celebrate what in the US we call 3.14 or PI day, today I’m offering stories that deal with mathematics and circles. First up, an app named for the great philosopher who is credited – even if perhaps ahistorically so – with finding that ratio and ratios in harmonies.

Technology has long introduced innovations that make playing easier for specialists and non-specialists alike. Just ask anyone who plays an instrument like the guitar – frets, and the simplified notation that went with it, go back centuries as a means of allowing more people to make music.

Developer Rob Fielding wants to rethink frets, to bring their disposition and playability closer to the way harmonics work in sound. The creator of the microtonal iPad app Mugician, his next app in development, Pythagoras, offers some fascinating ideas. Forgive me getting a bit theoretical in the prose for those who do speak that language; the videos are always the best way of understanding what’s going on. (The vast majority of even untrained ears have the ability to perceive pitch with astounding accuracy, so you don’t have to be an expert. Usually when people claim to be tone deaf, the problem is that they can’t sing, not that they can’t hear, in my experience.)

I’ll let Rob explain:

Pitch

Pythagoras’ fretless mode uses geometry to mark the harmonically relevant points, not fixed frets. Where the lines intersect with strings, the notes are perfect ratios to each other. This helps you to locate and get to know the useful pitches that are used in world music. [See image, top for a beautiful visualization of how this works. -Ed.] That is explained here:
The Spectrum – Pythagoras’s interface

When you play a chord like a major third, you line up the blue notes to overlap perfectly, and you get shiningly perfect major thirds that way. Same for harmonically correct fifths and fourths. These are the pitches that you hear as overtones when you listen carefully to instruments with lots of sympathetics, etc.

I do want to respond to this one lamentation in Rob’s post: he frets (ahem) that MIDI doesn’t use frequency, and that OSC isn’t well-supported. I actually think MIDI isn’t far off – it just lacks precision. Perception of pitch is complex, but a logarithmic scale (in which 440 sounds one octave higher than 220) is reasonably close to how we hear. And that’s precisely what MIDI gives you; if you just wanted to number the piano, its solution of using a number like 60 for middle C makes perfect sense. (We can overlook for a moment that the definition of MIDI fumbled the octave. The basic idea was still right.)

Even outside MIDI, a numbering system like that in MIDI – mapping pitch space to a logarithmic scale to make them match intuitively what we hear – is not uncommon. The problem is that MIDI doesn’t have a rational way of dealing with what happens in between the notes, as it used integers for efficiency. Take MIDI’s logarithmic scale and set floating-point numbers (numbers with a decimal place, like 60.5 instead of 60), and you have a pretty decent solution. You could still, if you didn’t want integers to represent 12-tone equal-tempered pitch, apply different scales and modes. But I think if you wanted a decent way of communicating note values, unless I’m really missing something, sending floating point numbers that default to a 12-TET logarithmic scale can’t be too bad. I understand that most instruments don’t yet respond in any standardized way, but I refuse to believe this is an intractable problem. I’m happy to discuss in comments. Heck, if we just got Max and Pd patchers to agree on something, I’d be pleased.

On to another very cool idea:

Octave Rounding

Pythagoras is using octave rounding in its latest incarnation when you press the “Auto” button for the octave switch. What this means is simply that it doesn’t care about what octave a note is in, it will pick the closest octave to the last played note. This allows for astounding feats of arpeggiation and pentatonic scales – even when playing fretless. Here is the more popular video:

And here is the improvement upon it the next day (much less viewed video) where you can slide up or down a fourth:

This octave rounding is an idea I implemented a few years ago in my Samchillian derivative called Xstrument. (Both Xstrument and Mugician are open source projects on github). This idea is very applicable to 2 octave keyboards as well.

Here is the idea with a trivial Pd program:

It’s really great stuff. As it happens, I’ve been exploring new geometries for music making myself, interested along similar lines. And musical inventor Roger Linn has had a lot of things to say about it lately, too, including his respect for Rob’s work.

So, I’d love to have a discussion. What interesting interfaces have you seen for music? Are there any you find playable in practical circumstances? And why can’t we just solve this issue of how to transmit pitch information between software and hardware once and for all? (I don’t yet know how HD-MIDI will address the issue; that’ll be interesting to see.)

And don’t miss Rob’s blog:
http://rrr00bb.blogspot.com/

Finally, here’s Jordan Rudess rocking out with Mugician, Rob’s (currently-available) app.

There was a time when Tascam was associated with cheap, solid mobile gear for recording, like the Portastudio. The handheld DR-03 could be a landmark for a more digital age. It’s just US$99 for a microSD recorder with built-in stereo mic in a package Tascam describes as “smaller than an energy bar.” It’s designed to be operated handheld without a lot of noise (we’ll have to test that), and – in what I think may be the killer feature – it includes looping and Variable Speed Audition, so you can use it easily as a practice, music transcription, or interview transcription tool. Just slow down the audio, without impacting the pitch.

Feature set from Tascam:

• Stereo condenser microphone design
• Up to 48kHz/24-bit WAV recording or MP3 recording modes
• Records to microSD media
• Auto-recording function starts when input exceeds a reference level
• Limiter, low cut filter and auto gain control for input
• Variable Speed Audition changes the playback speed without changing the pitch
• Loop playback mode
• USB 2.0 connection for file transfer
• 1/8″ stereo microphone/line input
• 1/8″ stereo headphone output
• 96×96 backlit LCD display
• Powered by two AAA batteries or USB bus power
• Built-in speaker
• Built-in desktop stand
• Includes 2GB microSD card and AAA batteries

Available now.
http://tascam.com/product/dr-03/

And yes, there are higher-end options from Tascam if you so choose, though that gets them into competition with Sony, Roland/Edirol, M-Audio, Korg, and Zoom, all of whom make some nice options. I’m guessing the $100 price point and pitch control option could be the winner for a lot of customers. (There are some reasons to look at the full line; the DR-03 has fixed stereo mics; on the DR-08, the stereo mic flips out like cute Mickey Mouse ears for better spatialization. I’d probably chose the -03 as a practice recorder.)

See also the awesome and likewise adorable Zoom H1:
Zoom H1 @ Samson

Big minus for the H1: no pitch control. Big plus for the H1: a shoe mount for attaching to a camera. The H1 is a little larger, so a tripod mount becomes possible. That’s probably your deciding point right there. The Tascam only works as a handheld, as it’s smaller, so you’ll have to prop it up against something or use its desktop kickstand. If transcription is your main application, the Tascam wins. If you want to be able to shoot with a camera or put it somewhere other than your hand or balanced on a ledge, the Zoom is a better choice.

World Science Festival 2009: Bobby McFerrin Demonstrates the Power of the Pentatonic Scale from World Science Festival on Vimeo.

At the World Science Festival in June here in New York, specialists – including musical specialist Bobby McFerrin – gathered to ask what in music we humans hear universally, versus what is culturally specific.

Is our response to music hard-wired or culturally determined? Is the reaction to rhythm and melody universal or influenced by environment? Join host John Schaefer, Jamshed Barucha, scientist Daniel Levitin, Professor Lawrence Parsons and musical artist Bobby McFerrin for live performances and cross cultural demonstrations to illustrate music’s note-worthy interaction with the brain and our emotions.

You can watch a series of five video highlights, but the one above is perhaps the most striking. (I believe it’s already more than made the rounds around the Interwebs, but, well, we can say we were all busy creating digital music.)

Notes and Neurons videos

It’s funny just how low the average person’s opinion of their musical ability can be. Ask an average “non-musician,” and they’ll often claim to be deaf to rhythm and pitch. Push the issue, though, and typically you’ll discover quite the opposite. Listen as the crowd laughs at discovering they all share some basic intuition about how pitch works. These are, after all, science and neurology types, not musicians.

Ah, you say, but this is just a crowd in New York. And most of us interact only with people in our own cultural circles. For me, that means people surrounded by pop music, Western harmony and counterpoint, chord changes derived from Protestant hymns — the lot.

What’s wonderful is that certain basic rhythmic and pitch elements – belying rich complexities of psychoacoustic phenomena underneath – do indeed seem to be universal. To me, that profound universality says something about what we share as human beings. At the same time, it makes me even more interested in all of the local details. When playing Balinese gamelan, some Western-trained musicians literally turned up their noses because they said the results sounded “out of tune.” Like a pungent flavoring in a foreign food, they discovered something unfamiliar. (I wonder if they would have the same reaction to sambal.) Of course, the underlying pitch systems are related to pentatonic (and heptatonic) pitch collections. And the same thing that disturbed one person has excited other musicians – not simply because it’s exotic, but because it can speak to something deeper in our hearing that we don’t get from other music.

Anyway, thanks to (noou) for this story, via IRCAM’s Eric Boyer; it really made my day. And it should certainly spark (ahem) some interest in neurology and the brain. Or, as I’m going to start saying whenever coming across something like this,

“Larry, what the hell just happened here?”

The wait is over – and rumors that Melodyne’s bleeding-edge technologies to allow direct access to notes in polyphonic audio had failed to come to fruition turn out to be false. (I was skeptical about those rumors in April.) Melodyne DNA did take longer than expected to ship, but then, that isn’t exactly news in the software business. And now you can try this “note access” concept for yourself and see what you think (well, provided you’re an existing customer). Coupled with time-based manipulation of audio in the form of updated tools in Ableton Live 8, Cakewalk SONAR 8.5, Propellerhead Record, Logic Studio 9, and others, with Melodyne handling the pitch, audio today could be more fluid than ever.

Celemony Melodyne
(Note, since you are a bleeding-edge type — the software is also considered compatible with Snow Leopard, though host-by-host certification is still forthcoming.)

What Melodyne’s editor enables:

• Harmonies are accessible, note by note.
• Pitch, position, duration, and loudness and softness can be modified.
• Formant spectra, vibrato, and pitch drift are accessible.
• Pitch, amplitude, and formant transitions between notes can be edited.

Now, all of this is in a plug-in, but that plug-in is more capable than previous versions, with better multi-threading, an adjustable window size (sigh of relief), and the ability to audition and scrub as you edit. That’s not quite as good as having this functionality in your host, but it’s more than good enough to make this usable.

I’m especially interested in what unusual sound design possibilities can be harnessed using this technology – abusing it rather than using it as intended.

Here’s how to get it:
Registered Melodyne customers are able to participate in the beta.
Launch is planned for early November at US$349 / EUR349.

I’m testing a copy now, so if you’re not a Melodyne user, I will get to report back.

More videos:

(Part 3 of 3 appears to be temporarily missing; I’ll add it once it is re-posted!)