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Why do we refer to Bb tubas as "BBb", C tubas as "CC" and Eb tubas as "Eb"?

I have parts of this answer, but not the full story. Looking to fill in some gaps.

Before we had the tuba, we had the valved ophicleide, or bombardon. These were first made in F (same as the original tuba) with the fundamental at F2 and the pedal at F1. But variations were soon made that had larger Eb and D variants, and smaller Bb and C variants. The Bb variants became today's baritone and euphonium.

As a need for a bigger tuba evolved, the names BBb and CC were used to differentiate the lower-octave versions from their little brothers. But why?

Helmholtz notation (which was formalized at least 17 years after these instruments were being produced) doesn't seem to work because you would use little c and big C for the fundamentals of the smaller and larger tubas. If we refer to their pedals instead of their fundamentals, then the octaves are C and C,.

The closest answer I can find is here and says that the organ's 8ft C (C2) was notated by the English as CC. Organ pipes are closed at one end, so they are effectively twice the length of a brass, so I think an 8ft organ pipe is equivalent to a 16ft tuba. Maybe I can see how the English used their organ notation to describe a C, tuba as CC.

But then why didn't the Bb,, tuba become BBBb? I seem to recall that the octave numbers wrapped around at A instead of C in Germany at some point, but I can't find any references to verify or check dates. The instruments started being produced in the 1830s and 1840s, but I don't know when the CC and BBb nomenclature came around.

Tuba Fundamental Pedal Length
C C3 or c C2 or C 8 ft
Bb (euphonium) Bb2 or Bb, Bb1 or Bb,, 9 ft
F F2 or F F1 or F, 12 ft
Eb Eb2 or Eb Eb1 or Eb, 13 ft
CC C2 or C C1 or C, 16 ft
BBb Bb1 or Bb, Bb0 or Bb,, 18 ft

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The predecessor to Helmholtz notation used doubled upper-case letters to refer to the lower octave. (Before that, medieval notation used doubled lower-case letters to refer to upper octaves.)

the organ's 8ft C (C2) was notated by the English as CC

Not only by the English.

Organ pipes are closed at one end, so they are effectively twice the length of a brass, so I think an 8ft organ pipe is equivalent to a 16ft tuba

Only some organ pipes are stopped. The length designation refers to an unstopped pipe, so stopped ranks sound in the same octave as unstopped ranks of the same designation. In other words, the low C of a stopped 16' rank is actually 8 feet long.

I seem to recall that the octave numbers wrapped around at A instead of C in Germany at some point

Not only in Germany, though of course the switch may have happened at different times in different places.

Around 1000 years ago, the gamut ran from Γ (gamma), modern G2, to ee, modern E5:

Γ, A ... G, a ... g, aa ... ee

With the advent of polyphony, the need arose to extend this upward and downward. People began to use one or two lines above the small letters instead of doubling and tripling them, and eventually the apostrophe-like marks that we still know from Helmholtz notation.

On the low end, Γ was problematic because it is the third letter of the Greek alphabet, not the seventh. People started using doubled upper case letters, GG, FF, EE, etc.

At some point, no doubt different points in different places, the octave boundaries came to be between B and C instead of between G and A.

Your question, it seems, is why, for tubas, does the boundary lie somewhere between C and E♭? I can only conclude that the answer is tradition, and presumably a lack of concern for consistency with organ notation. If you already have C, B♭, F, and E♭ instruments with fundamentals ranging from C3 down to E♭2, then you already have an implicit octave boundary somewhere between C and E♭. If you add lower instruments to your set, you either have to modify the names of the existing instruments or to accept that they're not consistent with other systems of octave designation and use an idiosyncratic one.

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  • Reed pipes are generally open, but depending upon the construction of the reed housing they may either sound at the same pitch as an open or closed flue pipe (so a reed pipe that plays at 8' pitch might be 4' or 8' long). Additionally, some pipes, with or without reeds, may be a multiple of the open-pipe length for that pitch, but constructed in such a manner as to suppress the fundamental. This may improve the clarity of sound of short high-pitched pipes.
    – supercat
    Jan 26 at 22:23
  • @supercat but the point remains that the length designation of a stop (4', 8', 16', etc.) identifies the sounding pitch, not the actual length of the pipe, regardless of the reasons. That is, the low C of an 8' stop sounds at (roughly) 65 Hz even though it might be (roughly) 4 feet long or any other length.
    – phoog
    Jan 27 at 8:32
  • True, but I think it worth noting that while a 16' tuba stop that uses pipes that are 8' long might seem like a straight version of an actual tuba, the reaction of the reed to reflected sound waves would be the opposite of a tuba player's lips. I'm curious whether it would be possible to make a subcontrabass clarinet, whose sounding pitch would be an octave below that of a tuba having the same length.
    – supercat
    Jan 27 at 17:18

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