Posted by Dr. Frederick J. Young on February 01, 2001 at 18:51:57:
In Reply to: Re: Re: C scale posted by Matt G on February 01, 2001 at 08:45:31:
Two tubas playing in 5ths is frequently used to produce the difference tone which is much stronger a bass than the same note on the tuba. For example the tubas play a first space A and and a third space E. The frequency of A is 110 Hertz and the equal tempered E is
110x(2)^(7/12) = 164.81 Hertz. The difference frequency is 54.81 Hertz which is flat of AA which should be 55 Hertz. If the player of the E lips it up to 165 Hertz the difference tone is at 55 Hertz and there is a summation tone at 275 Hertz. This is a C# on the natural scale. When the E is tuned up to the A by lipping it up about 2 cents from the equal tempered note the sum and difference tone materialize!. I was amazed when I talked to a couple of clinicians from one of the US military bands. They said they never heard of such and that they thought tuba fifths were muddy. I had them tune one up and they were astonished at the low octave. It is very impressive when done an octave lower. I picked the particular example just to make the arithmetic easy.