Baroque D Trumpet Resonances

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Baroque D Trumpet Resonances

Dale Gedcke wrote (October 8, 2003):
The attached speadsheet summarizes the ideal frequencies and notes played by the Baroque D Trumpet (no valves) as used in Bach's compositions.

To hit these resonant frequencies (which are an integer number times the fundamental frequency) a bell has to be added to the tubing, and adjusted to lift the lower frequencies into agreement with the desired series. In addition, the mouthpiece, the taper of the mouthpiece backbore and the taper of the leadpipe (first section after the mouthpiece) all have to be adjusted to lower the higher resonant frequencies into agreement with the desired series. There is plenty of opportunity not to achieve the ideal frequencies due to design and fabrication limitations. Materials, design tools, acoustic modeling programs, and fabrication technology is much more advanced today than it was in the Baroque period.

Note that the frequency assignment to notes in the spreadsheet is based on today's North American standard of A4 = 440 Hz. Historically, the frequency assignment varied somewhat. But that is irrelevant to this discussion.

A modern D trumpet with valves, is designed for this same series of frequencies, except the series is shifted up by one octave. Valves are used to change the length of the modern trumpet to permit it to play all notes in the chromatic scale (written F#3 and higher) in addition to the basic notes in the valveless series. A modern Piccolo A Trumpet is pitched 7 half-tones above the modern D trumpet, and has a similar basic resonant series shifted 7 half-tones higher. The Piccolo Trumpet has a fourth valve to extend the lower limit by a fourth.

A few surprising limitations for the Baroque trumpet are apparent in this spreadsheet. The "Just" frequency is the target frequency for the basic resonant series. This can be matched up with the closest frequency in the "Even Temper" Scale to name the note in the concert pitch (third column). In the fifth column, the note has been named according to the transposition written for the D Trumpet score. The player reads this score as if he is playing in the key of C. But, he is actually playing in the concert key of D.

The sixth column lists the deviations of the "Just" frequencies (or natural resonant frequencies) from the frequencies assigned in the "Even Temper" Scale. The deviation is expressed in "cents". It is commonly agreed that the average listener can detect and out-of-tune deviation more than 10 cents. A number of the notes available to the Baroque trumpet player are out of tune with the Even Temper Scale by more than 10 cents. Today, a trumpet player would adjust the tension in his lips to bend those notes into conformity with the rest of the instruments in the orchestra.

Now examine the notes the Barque D trumpet could access. The base of the series, C2, is a pedal note which is normally not used because of bad tuning. From C3 through Bb4, the Baroque trumpet can only produce the bell tones generated by the 2, 3, 4, 5, 6, 7 series of resonances. From C5 on up, the trumpet can play the diatonic scale, with one exception: F natural is missing. Actually resonance 11 is about half way between F natural and F#. The player has to bend the note to either F natural or F# using lip tension.

Interestingly, Händel used both F natural and F# in "The Trumpet Shall Sound". The first 11 bars call for F natural. In bars 12 and 16 he specifies F#. That pattern is repeated throughout the piece. Furthermore, the player is required to lip-trill between E and F natural at several cadence points. Both requirements are difficult to accomplish on a Baroque trumpet, whereas it is easy and secure on a Piccolo A trumpet with valves.

How about tone quality? Baroque trumpet fabricators did not have the sophisticated materials and technology available today. Consequently, their tone and intonation likely varied substantially from instrument to instrument. Today the tone quality can be consistently tuned to the desired sound, and valves and valve slides work wonders for eliminating intonation problems.

There are trumpeters who enjoy playing Bach's and Händel's music on a Baroque trumpet. But, many of us are grateful that the Piccolo A Trumpet can make a quality performance easier, more secure, and more pleasing to the ear.

Baroque D Trumpet Resonances

	Just	Even	Temper	D Trumpet	Just / Even
D Trumpet	Frequency	Closest	Frequency	Written	Freq. Error
Resonance	(Hz)	Note	(Hz)	Note	in Cents
1	73.42	D2 Pedal Note	73.42	C2	0.0
2	146.83	D3	146.83	C3	0.0
3	220.25	A3	220.00	G3	2.0
4	293.66	D4	293.66	C4	0.0
5	367.08	F#4	369.99	E4	-13.7
6	440.50	A4	440.00	G4	2.0
7	513.91	C5	523.25	Bb4	-31.2
8	587.33	D5	587.33	C5	0.0
9	660.75	E5	659.26	D5	3.9
10	734.16	F#5	739.99	E5	-13.7
11	807.58	G#5	830.61	F#5	-48.7
12	880.99	A5	880.00	G5	2.0
13	954.41	B5	932.33	A5	40.5
14	1027.83	C6	1046.50	Bb6	-31.2
15	1101.24	C#6	1108.73	B6	-11.7
16	1174.66	D6	1174.66	C6	0.0
17	1248.08	D#6	1244.51	C#6	5.0
18	1321.49	E6	1318.51	D6	3.9
19	1394.91	F6	1396.91	Eb6	-2.5
20	1468.32	F#6	1479.98	E6	-13.7
21	1541.74	G6	1567.98	F6	-29.2
22	1615.16	G#6	1661.22	F#6	-48.7
23	1688.57	G#6	1661.22	F#6	28.3
24	1761.99	A6	1760.00	G6	2.0

Frequencies of Notes (Hz) [Even Temper; A4 = 440 Hz]

Octave	C	C#	D	D#	E	F	F#	G	G#	A	Bb	B
1	32.70	34.65	36.71	38.89	41.20	43.65	46.25	49.00	51.91	55.00	58.27	61.74
2	65.41	69.30	73.42	77.78	82.41	87.31	92.50	98.00	103.83	110.00	116.54	123.47
3	130.81	138.59	146.83	155.56	164.81	174.61	185.00	196.00	207.65	220.00	233.08	246.94
4	261.63	277.18	293.66	311.13	329.63	349.23	369.99	392.00	415.30	440.00	466.16	493.88
5	523.25	554.37	587.33	622.25	659.26	698.46	739.99	783.99	830.61	880.00	932.33	987.77
6	1046.50	1108.73	1174.66	1244.51	1318.51	1396.91	1479.98	1567.98	1661.22	1760.00	1864.66	1975.53
7	2093.00	2217.46	2349.32	2489.02	2637.02	2793.83	2959.96	3135.96	3322.44	3520.00	3729.31	3951.07
8	4186.01	4434.92	4698.64	4978.03	5274.04	5587.65	5919.91	6271.93	6644.88	7040.00	7458.62	7902.13

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Last update: Tuesday, June 13, 2017 05:18