(Edited 1 Jun 2012 to add graphic of written ranges.)
Bohlen-Pierce clarinet ranges
Steven Fox has a web page about Bohlen-Pierce clarinets, and has made some of these instruments for sale. He describes three sizes: Soprano, about the size of a regular B♭ soprano clarinet; tenor, in between the sizes of the regular alto and bass clarinets; and contra, the size of a regular contra-alto clarinet. The first page linked above has seemingly not been edited in a long time; it says “work is under way” on the tenor, but in fact the tenor exists and can be heard on a few YouTube videos, e.g. this. A soprano can be heard here. As far as I know no contras have been made yet.
Standard clarinets tend to be mostly in the keys of B♭ and E♭, i.e. about a half octave apart in size. BP clarinets are further separated, about a half “tritave” (perfect twelfth in conventional tuning terms) apart. A standard clarinet choir might contain E♭, B♭, alto, bass, contra-alto, and/or contrabass clarinets, and might imaginably have even an A♭ sopranino clarinet — not that I’ve ever seen one used. A BP clarinet choir covering the same range would use fewer sizes.
Here’s a chart:
The horizontal axis is calibrated in MIDI note numbers; middle C is 60, and a step of 1 is a semitone. Red bars indicate low C extensions for the lowest clarinets. B♭ clarinet upper limit is from Wikipedia (the upper limit is ill defined, different authorities will give different values) and for other standard sizes I’ve just assumed — it’s not a very good assumption — the same upper limit aside from transposition for the other standard clarinets. It was tempting to add the octocontra-alto and octocontrabass clarinets to this chart, purely for entertainment value, but I know that upper limit assumption would be really unjustified for them and I’m not sure what their actual upper limit is.
BP clarinet ranges are from Fox’s page. To Fox’s three sizes I’ve added two hypothetical additional ones. The sopranino, a tritave higher than the tenor, would be nearly identical in range to the standard A♭ sopranino. The subcontra, a tritave lower than the tenor, would have about the same range as a standard contrabass with low C extension. The overall range of such a BP clarinet choir is approximately (in standard tuning and notation) from B♭0 to G7 — nearly 7 octaves, or 4 tritaves.
So why am I writing about instruments that don’t exist? Because they can be synthesized, of course. Which is what I’m planning to do: Write a piece for BP clarinet choir and do a synthesized rendering of it.
Standard clarinets are generally transposing instruments, mostly in B♭ or E♭. What about BP instruments? Well… that’s a little harder to pin down. There’s nothing inherently “transposing” about any instrument, it’s a matter of notational convention. And one problem is, BP notation isn’t very well standardized. I like the recommendation at the BP site, but Fox recommends writing for clarinets using standard notation such that each written note is fingered the same way as on a standard clarinet. That certainly makes sight reading far easier, but it obfuscates the music. And it would be silly to impose such notation on conductors and non-clarinet musicians in a piece for mixed instruments.
Of course, it’s all a non-issue for synthesized BP clarinets — no fingerings to worry about. I’ll probably work mostly in concert pitch. Still, it’s sort of fun to think about.
So let’s assume Bohlen’s notation. The premise with standard clarinets is that fingering should be the same for a given written note regardless of what size instrument you’re playing; in particular, the note in the clarion register with left thumb, three left fingers, and three right fingers down is notated as D regardless of actual pitch. On a C clarinet that would sound as concert D; on a B♭ clarinet it’s C; on an E♭ clarinet it’s F. This mean B♭ clarinets see a key signature with two more sharps or two fewer flats than concert pitch key, and E♭ clarinets, three more sharps or three fewer flats.
On the BP soprano, the note in the clarion register with left thumb, three left fingers, and three right fingers down is, if I’m reading Fox’s chart right, 15 cents below (standard) E♭ (617 Hz). Calling that (BP) D, then the lower notes in the clarion register would be D♭ (pad 4 closed), C (pad 3), B (pad 2), B♭ (pad 1, sounding at the bell). But that’s 440 Hz, or standard A, and in concert pitch it’d make sense to call it BP A too. If we were to notate that for soprano BP clarinet as B♭then music in concert C lambda (no flats or sharps) would be notated in D♭ lambda (4 flats). Which is silly. Given that the nomenclature is rather arbitrary anyway, why not notate the 440 Hz bell note as BP A, and make the soprano BP clarinet a concert pitch instrument?
Or in abc notation modified for BP, call it “A”, and the bottom note of the chalumeau register is a tritave lower, “A,”. The altissimo begins on “h”.
Then, to keep the fingerings the same across BP clarinets, the contra would also be written in concert pitch key, but a tritave higher than sounding (in BP treble clef). The sopranino plays seven BP steps higher than the soprano, so would be notated seven BP steps below concert pitch; written C would sound H. It would be in a key with two more sharps or two fewer flats than concert key. So would the tenor and the subcontra, but they’d be written one and two tritaves, respectively, above concert pitch. They all would go from written “A,” to “A” at the bottom of the clarion register to “h” at the bottom of the altissimo and up from there. But actual ranges would be: