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I found the link in Random Monday this week to a recent (2009) study very interesting, on the topic of hand position.
The title of the project is “Spectral Analysis of the French Horn and the Hand-in-Bell Effect” and author Adam Watts wrote the paper as a Senior Thesis in the Department of Physics, University of Illinois at Urbana-Champaign. In the introduction he sets out that
The placement of the player’s hand serves two functions, both vital to the playability of the horn. First, the hand causes upper resonances to decrease in pitch, effectively bringing the usually sharp higher notes more in line with standard tuning. This intonation effect is due to the added acoustical mass the hand creates at the end of the air column as it is pushed farther into the bell, lowering the frequencies of the system, which can be thought of as an approximate Helmholtz resonator …. The second effect of the hand placement inside the bell is the increase in playability of the upper resonances of the instrument; this is where the problem of accuracy in the upper range is addressed.
The second point is a very important one; when the hand is in the correct position it will give the most stability in the upper range, and improve accuracy, and help avoid tendencies toward being sharp in the high range. In the conclusions he notes also that
The normal playing hand technique of the French Horn player, wherein the hand is cupped inside the bell end of the instrument, serves to help the player access the high frequency resonant modes, or partials, of the horn. The hand helps reflect higher frequency waves back up to the player’s mouth, reinforcing the buzzing of the lips and increasing the stability of the note. This effect is supported by the data presented in this paper, as well as Backus’ data with the hand simulation, in that impedance peaks became more pronounced and defined in the upper range when the hand was added. The cupped hand also lowers the pitch of the higher notes, bringing them more into line with the harmonic series, and thus more in tune. The data in this paper supports this by showing that the peaks of the impedance curve, which correspond to playable notes, shifted downward in pitch in the upper range once the hand was added
The other major area studied in this paper has to do with hand stopping the bell. Traditionally we are taught in general these three points:
- Close the bell tightly with the hand
- Finger the note pitch a half step below the pitch you want to play
- Use the F side of the horn only for better intonation.
My old standard article on the topic, which sticks to the traditional understanding, is here; the traditional understanding is also the basis of why a stopping valve also works on horns so equipped. It is a practical way that works well with a standard stop mute and speaking generally used to work for most horn players. I say “used to” as if you look back a hundred years most horn players were men which implies big hands. Today horn players are much closer to 50/50 male/female and the result is that the traditional approach does not work well for probably half of horn players out there and even back in the day did not work for everyone. The problem being that the traditional method will generally result in sharp stopped notes for players with small hands.
As a stop gap I have over the years developed a way of devising flatter fingerings based on the standard approach (see this article) that I often use with my students, and certainly I tell people often to use different fingerings than the standard way, experimenting until we finally get the problem pitches in tune. If it is in the staff or above it is possible to get any stopped note in tune with experimentation.
But the underlying problem is that the traditional understanding of stopped horn really it is not what is actually going on acoustically. That is pretty widely known but reading this new study out to the conclusion has given me even more to ponder. In the conclusion he notes that
Hand-stopping the horn inexorably changes the frequencies of the partials, but the exact nature of this change has been steeped in controversy. The apparent controversy between the nature of partial-shifting due to handstopping centers around the question of the direction of the shift; players disagree as to whether partials are shifting up or down, because there is reportedly mixed success with transposing in either direction to compensate for the shift. However, Backus’ data using a rubber stopped in the bell, further supported by the data in this thesis using a real hand, suggests that the partials are indeed lowered by the addition of a stopping mechanism. The confusion arises because apparently many players are inadvertently playing the next partial up from the note they want while stopping, and transposing downward to compensate. This situation explains why most horn teachers instruct to transpose down a semitone while playing stopped horn; they are encouraging their students to play the next partial up and to compensate downward with the instrument’s valves.
However, the data in this paper (to wit, Figure 15) shows that the partials do not drop a consistent amount due to stopping throughout the horn’s range. Rather, it appears that hand stopping drops the pitch of the horn’s partials substantially more than a semitone (100 cents) in the lower range, but hardly drops the pitch at all in the upper range. This could be a problem for horn students that are taught to transpose down a semitone all the time; if they are trying to play in the upper range, they will end up over-compensating. Apparently the rule to transpose down a semitone while stopping is only valid in the middle range of the instrument. This could have wide-ranging implications on how this particular technique is taught; armed with the data in this paper, horn teachers could begin showing that an all-encompassing transposition rule is oversimplifying the hand-stopping phenomenon.
In a comment on this paper where it was originally linked on Horn Matters on Monday this week Fred Richardson wrote the question to answer:
The handstop pitch change measurements in the article imply a new basis for stopped horn fingerings. It should be possible to take the findings (stopping changes pitch different amounts for different partials) and estimates of the deviation of different partials from even temperment to work out a more in tune fingerings than the standard ones. Any takers?
That would be a project that would take a little time but for sure it would be possible to work out a set of custom fingerings that took into account the variation of pitch change when stopping with the hand based on the statistics in the paper.
But then I back up and think well, but what about with a stop mute? There have been some recent innovations in these and the traditional approach does seem to work for most players with a standard stop mute, which again points to hand (and bell) size variations as the problem with the traditional approach.
I don’t have the answers but there are certainly things to reevaluate in terms of standard horn pedagogy and stopped horn. This study is an interesting one in relation to that topic and certainly worth a look.
