This article focuses on a question that several saxophone players ask when they come to Syos studio or when they order a custom mouthpiece so they can compare different versions of a mouthpiece with slight changes:
Why do the saxophone mouthpieces have different lengths?
To be clear, we are talking about mouthpieces for the same saxophone: two alto mouthpieces for example.
Some acoustic basics
To have a better understanding, we must talk a bit about acoustics. I promise it will be quick and simple. In acoustics, there is a direct relationship between the lenght of the vibrating part and the pitch of the sound. What you have to remember is
The shorter, the higher.
It's a kind of generic rule: a soprano saxophone is small so it's high-pitched, a baritone is big so it's low-pitched. It's the same for string instruments: small strings are high register and long strings are low register. It's basically EVERYWHERE!
The saxophone is a metal cone
Now let's have a look at the saxophone. It's a cone made of metal that is cut in the upper part. The soprano stays like that, and the other saxophones are a bit hammered everywhere to bend the cone. Otherwise the whole saxophone would be too big and it would be hard to play it.
Look on that picture:
Yes, we did visit the Selmer Factory some months ago! In real life this is a bit more complicated (don't try that at home!) but I bet you got the idea : the saxophone is a bent cone.
Blow in a pipe
Let's get back to acoustics: the pitch changes when the length changes. So if you blow in a pipe, the laws of physics say: the frequency is inversely proportionnal to the length of the pipe.
The law gives the fundamental frequency of the pipe according to its length L and its diameter d, and the velocity of sound in the air V (which is approximately 334 m/s). For the cone, it's nearly the same as the cylinder so we can use the same law.
Let's check that with an alto and tenor saxophone :
alto : Length = 1.20 m, Diameter = 0,1 m (around 10 cm). With the formula we find f = 134 Hz, which is (not exactly but very close) a D flat 3. If you close all the keys on the alto, which note it is ? A D flat! (don't forget that the saxophone is a transposing instrument in Eb, so a B flat for the alto sax is a D flat for a pianist)
tenor : Lenght = 1.40 m, Diameter = 0,1 m (around 10 cm). With the formula we find f = 116 Hz, which gives exactly a A flat 2. If you close all the keys on the tenor, which note it is ? An A flat !
The complementary volume
The point of the article was to talk about saxophone mouthpieces so let's get back to that. When you fix the mouthpiece on the cork, it will add some length to the pipe. When your intonation is too high or too low, you can push or pull the mouthpiece to change the pipe's length so the intonation changes accordingly.
What is important is the air volume that is added to the saxophone when the mouthpiece is put on the cork : this volume is indicated in red in the above figure (V1 or V2). For an optimal fit between the mouthpiece and the saxophone, this volume must have a very precise value V* (that corresponds to the missing part of the cone we cut with our scissors sooner in the article).
This value V* depends on the volume of the saxophone body, so it's about the same for all mouthpieces of a given saxophone kind (alto, tenor...). But of course, different models have different geometries. That's why, for example, "modern" mouthpieces don't work well on Old Conn Baritone, because it's missing volume V* is bigger than "modern" baritones.
Changing the complementary volume
Okay, we saw it's important to keep the complementary volume identical to have a good fit between the mouthpiece and the instrument. But let's take a mouthpiece and slightly change something inside, like the baffle or the chamber: what happens?
The volume is smaller if the baffle is high or if the chamber is small (look on my figure above which is kind of extreme). To keep the volume in order to respect the sacred rule of the complementary volume, we have only one solution: add some length to the mouthpiece shank!
Indeed, if the length of the cylinder is increased (while keeping the diameter) there will be more air volume in the mouthpiece so we can correct the decrease of the volume we lost while changing the baffle and chamber, and bring back the volume to the holy value V*.
Quizz to see if you got it
I'm sure you understood all the matter about air volume and saxophone mouthpieces length. So it's the time to prove it, by answering the 3 following questions in the article comments:
Question 1 : I play on an old Conn baritone from the 30's that is two high in the intonation, help me! What can I do?
A) Add some length to the mouthpiece
B) Shorten the mouthpiece
C) Change your saxophone, man
Question 2 : My Syos custom mouthpiece is amazing, but I would love to have a bit less brightness. The Syos soundshaper told me he would lower the baffle and enlarge the chamber:
A) The second version of my mouthpiece will have a longer shank
B) The second version of my mouthpiece will have a shorter shank
C) The second version of my mouthpiece will have the same length
Question 3 : I have in my hand two alto Syos mouthpieces that have exactly the same length. My deduction is :
A) That they have the same chamber size
B) That they have the same chamber size and the same baffle
C) Nothing. There I nothing to deduce.
So, what are your answers?