Selecting a Fifth Valve to use with a Standard 3rd Valve and a Long Fourth valve:

These are the systems advocated by Chester Roberts in the T.U.B.A. Journal, Vol. X, No. 1, Summer 1982. Roberts expressed strong opposition to using the 4th valve as a 1&3 substitute. Instead, he advised us to tune the 2&4, first as a substitute for 123, "as God, Reiner, and Szell obviously intended". Then 134 is useful, but 234 is too flat to use. The primary job of the 5th valve in this case is to provide good fingerings for the fifth and seventh semitones, replacing 13 and 14, respectively. The chart below is set up with that goal in mind.

Example 1: Long Whole-Step (Roberts Model)

Here the L5 value (fifth valve tubing length) is set at 0.148Lo as a compromise between optimizing the 5th and 7th semitones.
(If 125 is 4 cents sharp then 45 is only 6 cents flat.) The only note that may need slide pulling is the eighth semitone.

Interval.........Fingering...........Note Names

0 (open)..............open............Bb.....C.....Eb.....F

1 semitone..............2..............A.......B......D......E

2 semitones............1..............Ab.....Bb....Db.....Eb

3 (minor 3rd)..........12............G......A.....C......D.....(+)

4 (major 3rd)..........23...........Gb.....Ab....B......Db

5 (perfect 4th)........125...........F......G.....Bb.....C

6 (tritone)................24............E......Gb....A......B

7 (perfect 5th)..........45...........Eb.....F.....Ab.....Bb

8 (aug. 5th).............245...........D......E......G......A.....(++)

9 (sixth)............134/1245........Db.....Eb....Gb.....Ab

10 (seventh.............2345.........C......D......F.......G....(+)

11 (maj. seventh)....12345........B......Db....E......Gb

Example 2: Two Whole-Step 5th valve (Roberts Version)

Here the L5 value (fifth valve tubing length) is set at 0.237Lo and the fourth valve tubing is set to 0.354Lo as a compromise between optimizing the 6th and 8th semitones. The 24 fingering is just one cent sharp, 235 is two cents sharp, making 45 only 4 cents flat. A sharp 13 combination is the main disadvantage. The only alternate fingerings would be 4 or 15, both of which are very flat.

Interval...........Fingering...........Note Names

0 (open).............open...........Bb.....C.....Eb.....F

1 semitone..............2.............A......B.....D......E

2 semitones.............1...........Ab.....Bb....Db.....Eb

3 (minor 3rd)..........12..........G......A......C......D.....(+)

4 (major 3rd)..........23..........Gb.....Ab....B......Db.....(+)

5 (perfect 4th).........13...........F......G.....Bb.....C....(++)

6 (tritone)................24...........E......Gb....A.......B

7 (perfect 5th)........235..........Eb.....F.....Ab.....Bb

8 (aug. 5th).............45............D......E......G......A

9 (sixth).................134...........Db.....Eb....Gb.....Ab

10 (seventh............1245.........C......D......F......G

11 (maj. 7th)..........2345.........B......Db....E......Gb....(++)

Roberts advised against using a short third valve to be used alone for a minor third, saying that this "really fouls things up".
For completeness I have investigated that possibility anyway:
Systems with short 3rd valve and long 4th:

Back to "Choosing a 5th Valve"

Back to the main page of the Tuba Logic Website: