Acoustic simulation of Elizabeth I at Tilbury
Braxton Boren(1)(1) Audio Technology Program, American University, Washington, DC, USA, boren@american.edu

Abstract
The largest gatherings in human history prior to the advent of electronic amplification were all effectively limitedby the loudness and intelligibility of the human voice. Various accounts throughout history depict single orators
addressing crowds or armies of many tens of thousands, though some historians have cast doubts onto theveracity of these claims. Prior acoustic simulation has shown that reasonable intelligibility might be achievedfor over 20,000 listeners for very loud orators and very quiet crowds with high density. Nearly all such accounts,
however, depict a man addressing the crowd, with one notable exception: in 1588 Elizabeth I of Englandaddressed a large army of between 5,000-23,000 troops gathered to repel the impending invasion by the Spanish
Armada. The acoustic plausibility of this account is tested via STI simulations, focusing primarily on the density,
noise, and environmental conditions at the time of the speech, as well as the frequency-dependent differences
between female and male orators’ vocal spectra and a sound radiation patterns.
Keywords: Acoustics, Intelligibility, Elizabeth I, Spanish Armada, Oratory

1

INTRODUCTION

Before the advent of electronic amplification, the largest gatherings in history were effectively limited by the
maximum intelligible range of a single human voice. Many accounts throughout history depict a single commander addressing their troops, and modern plays and films often show an army drawn up for battle receiving
inspiration from a charismatic general with a voice loud enough to reach every soldier.
Until the 1990s, modern historiography largely accepted these accounts throughout history, primarily on accountof the many references by different ancient writers. However, in 1993 Mogens Herman Hansen questioned thevery existence of the general’s speech to the army, arguing that the inclusion in ancient histories was largely
rhetorical, meant to advance the argument of the speech attributed to the general [20]. The next year W.
Kendrick Pritchett responded with the traditionalist position, showing many other accounts throughout ancientand modern history, including many where speeches were reported though no words were recorded [31]. Interestingly, both the skeptic (Hansen) and the traditionalist (Pritchett) both made allusions to acoustics in theiressays, although neither made any detailed quantitative or perceptual argument.
Acoustical analysis, however, was attempted centuries earlier by Benjamin Franklin as he attempted to verify
the very large crowd sizes reported in England listening to the Reverend George Whitefield in 1739. Franklin
used Whitefield’s on-axis intelligible distance to estimate the area of a semicircle and the number of listeners
that could fit inside this space [17]. Analysis [8] and computer simulation [6] of Franklin’s experiment showthat Whitefield must have had a very loud voice, with an on-axis A-weighted time-averaged SPL of around
90 dB; this is similar to the largest dB values recorded for trained vocalists in laboratory conditions in theexisting literature [9]. This in turn is roughly 12-16 dB over the relevant standards for loud speech in thegeneral population [1]. Previous simulations have predicted that Whitefield (assuming overall vocal level ofabout 90 dBA) could be heard intelligibly by over 20,000 listeners even assuming moderate noise and density
conditions [6].
However, for different historical situations the maximum crowd size may vary drastically due to other factors.
Computer simulations of Julius Caesar’s post-battle speech after his loss at Dyrrachium have shown that thehistorical account is acoustically plausible even under pessimistic conditions. But for Caesar’s pre-battle speech
at Pharsalus, due to the noise of soldiers on the march and the low density of his army in formation, evenunder optimistic noise conditions it does not seem acoustically plausible that Caesar could have addressed his311

entire army as described [7].
Other such famous speeches throughout history are much treasured by their respective cultural descendants
though often called into question by historians. Because nearly all participants in ancient warfare were men, so
too nearly all speeches to large audiences are recorded with male generals or kings addressing the troops. One
significant outlier to this pattern is England’s Queen Elizabeth I (1533-1603, r. 1558-1603) who gave many
public speeches after gaining the crown. The largest crowd attributed to Elizabeth (and perhaps the largest
crowd addressed by a woman in pre-amplified history) was the army she had gathered at Tilbury to prepare forthe invasion by the Spanish Armada in 1588.
This paper will first give some background on Elizabeth’s rhetorical training and physical stature, as well as
the historical estimates for the size of her army at the time she visited Tilbury. Next, the speech’s intelligible
range is investigated via geometrical acoustic simulation. Finally, some conclusions are drawn about Elizabeth’s
maximum intelligible crowd size as well as the effects of the female spectrum when addressing large outdoor
crowds.

2

BACKGROUND

2.1 Education and Experience
The daughter of Henry VIII and Anne Boleyn, Elizabeth’s mother was charged with treason and beheaded in
1536 when the child was only three years of age. The marriage was annulled, making Elizabeth an illegitimate
heir of the king. However, Henry did ensure that his daughter would receive the education of “a Renaissance
Prince” [35]. Her main tutor, the Cambridge scholar Roger Ascham, claimed that “no six of the best gentlemen of this court” could equal his student in diligence or learning [33]. The humanist education she received
privileged the classical Greek and Roman models of language and rhetoric, and Elizabeth learned to read andconverse in six languages besides English [35]. In particular Elizabeth studied the oratory of both Demosthenes [33] and Cicero [4], perhaps with some forethought given to her possible future on the throne, giventhat her father restored her to the line of succession before his death in 1546 [35]. As Mary Thomas Crane putit, “Elizabeth was trained, as other women were not, in the use of rhetoric to assert authority.” [12]Indeed, Elizabeth frequently used her reputation for scholarly and rhetorical excellence to justify the thencontroversial idea of an unmarried female monarch in England [33]. Before her coronation, Elizabeth gavea speech to a large outdoor crowd in London in 1559, and later gave pre-written speeches to Parliament establishing her own authority to choose when and whether to marry [4]. In addition, she gave addresses in Latin
in 1564 at Cambridge University to a crowd estimated at 1,800, and another in 1566 at Oxford University, toa crowd estimated at 1,700 [32]. But her most famous speech, for various reasons, is undoubtably her Tilbury
address of August 19th (August 9th Old Style), 1588, to her army awaiting the invasion of the Spanish Armada.
Given her exceptional rhetorical training and experience in public speaking, Elizabeth’s effective vocal level(including benefits from superior elocution, which are not included directly in an STI simulation but will affectintelligibility and so can be included by increasing the vocal SPL instead) was probably higher than for the
average speaker. However, the second variable correlated with very high vocal levels is youth [24], and since
Elizabeth was in her mid-fifties at the time of the Tilbury speech, she probably could not attain the exceptionallyhigh vocal levels (around 90 dBA) associated with the loudest human speech [9]. Because of this, Elizabeth’s
overall vocal level at 1 m is assumed here to be 80 dBA, applying the IEC standard female spectrum [2].
2.2 Occasion and Audience
The fortress at Tilbury, first built under Henry VIII, was located at the mouth of the Thames River and provided
a defense against an invading force headed for London. As it became clear that the Spanish intended to invade,Elizabeth charged the Earl of Leicester with heading the Royal Camp at Tilbury and ordered her troops togather there to prepare for an attack on London. By the time Elizabeth decided to visit her troops at Tilbury
on August 18, the English fleet had already defeated the Armada at sea. On land the extent of the damage to312the Armada was still largely unknown, and an invasion by the Spanish army, led by the Duke of Parma, wasstill expected [28].
At Leicester’s invitation, Elizabeth and her guard took barges from London to Tilbury and inspected the troops
on August 18th, carrying a truncheon but wearing no helmet. She stayed nearby that evening, and returned tothe camp the next day, where she gave her famous speech:
I know I have the body of a weak and feeble woman, but I have the heart and stomach of a king,and of a king of England too, and think it foul scorn that Parma or Spain, or any prince of Europe,
should dare invade the borders of my realm; to which, rather than any dishonour shall grow by me,
I myself will take up arms, I myself will be your general, judge, and rewarder of every one of yourvirtues. [35]Due to the haphazard nature of the English response to the Armada, precise numbers are lacking for the English
forces. Elizabeth planned to assemble over 100,000 men to repel the invasion [10], and early Elizabethan
chronicler William Camden reported the forces at Tilbury at 23,000 [28].
Some historians have expressed skepticism toward this value: Parker [30] gives the lowest estimate of only
5,000 based on pay records for the Kentish forces, while Frye [18] guesses 8,000 based on Leicester’s personalcorrespondence. However, even these low estimates need to add Elizabeth’s own guards and retinue, which
filled several barges and must have numbered at least in the hundreds [10]. Hutchinson [22] puts the number at
16,000 infantry and 2,000 horsemen, while Christy [10], relying on the chronicle of Elizabeth’s Privy Council,
puts the number at 18,000 footmen and 2,000 horsemen, plus additional troops south of the river at Gravesend.
Mattingly [28] argues for a value in between the high and low estimates, without giving a specific guess.
As important as the size of the army is the layout and density of the troops hearing the speech. Previous
work has shown that the largest intelligible area is present for informal speeches where the crowd encloses the
speaker densely on all sides [6, 7]. Though we do not have perfect documentary evidence for the layout of
Elizabeth’s army, the descriptions of the event suggest a more formal affair. It is true that the occasion of the
Queen’s visit provoked ecstatic and even worshipful bows from her troops when she arrived on the 18th, which
had to be stopped at the Queen’s request [22]. However, the primary source descriptions of the event focus on
her inspecting the army in formation, riding around the entire army on horseback with the rest of the mounted
cavalry [10]. Thomas Deloney’s 1588 account describes the atmosphere before her speech as follows (emphasis
added):The valiant Captaines of the field,
meane space them selues in order set:
And each of them with speare and shéelde,
to ioyne in battaile did not let.
...
Such a battaile pitcht in England,
many a day hath not béene séene:Thus they stood in order waiting,for the presence of our Quéene.
At length her grace most royally,receiued was and brought againe:
Where she might sé most loyally,
this noble hoast and warlike traine.
How they cam martching all together,like a wood in winters weather.
With the strokes of drummers sounding,
and with trampling horses than:The earth and aire did sound like thunder,
to the eares of euerie man.
The warlike Armie then stood still,and drummers left their dubbing sound:
Because it was our Princes will,
to ride about the Armie round.
Her Ladies she did leaue behind her,and her Guarde which still did minde her.
...
And then bespake our noble Queene. [15]2.3 Setting
Though earlier historians had located the camp farther to the west at Purfleet, Christy’s survey of the land,
primary sources, and local tradition led him to the now-accepted conclusion that the camp was located on the313

hill at what is today the village of West Tilbury [10]. This hill is more like a plateau, with a large flat plain
to the north on which the army was encamped, with a steep drop-off to the south allowing a good view of themarshlands and the river. The queen and her guard rode up the hill to meet the army, and the speech was givenon the plateau, so the overall geometry of the speech site was completely flat.
Hutchinson [22] estimates the size of the tented encampment at 5 acres (about 20,000 m2 ), but the plateau itself
is much larger, containing over 2 square kilometers of flat ground to the north of the steep hills at the southernedge of the camp. The army seems to have had plenty of open space for the proceedings once Elizabeth
arrived, as the entire force paraded past her and staged a mock engagement for her viewing. This suggests thatthe entire force was gathered together in one open area of the plateau, except perhaps the forces stationed at
Gravesend south of the river.
Most historians have accepted Elizabeth’s Tilbury address as authentic. The overall speech as recorded by Lionel
Sharpe, one of Leicester’s chaplains, is brief, about 250 words overall and has many rhetorical similarities toothers of Elizabeth’s published speeches [19]. One version of Sharpe’s written account is subtitled “Gatheredby on who heard it, and was commanded to utter it to the whole army the next day,” [19], leading some toquestion how many soldiers could have heard Elizabeth’s oration [35, 29].
2.4 Environment
Since any acoustical simulation must also account for the environmental background to properly simulate air
absorption. Unfortunately, the well-known HadCET database of surface temperatures in Central England does
not have data prior to 1659 [26]. Previous climate work has analyzed the famous “Protestant Wind” that stymied
the Spanish fleet, including the relevant high and low pressure systems, but this did not include estimates oftemperatures [16]. Period accounts suggest that the year 1588 was unusually rainy [3], although none of theaccounts of Elizabeth’s speech at Tilbury mention rain. Because of the "Little Ice Age” that was present inEurope during this period, the temperature might be expected to be slightly lower than modern averages, butsince the accounts do not describe the weather as particularly hot or cold, it did not likely stray from normal
values for early August. As a result, a value of 16.0◦ C, similar to long-term averages for Tilbury during
August in recent years, was adopted for the acoustic models described.
Similarly, no historical data for percent humidity is available for the site of the speech, so an average value of
65% was adopted based on averages from recent years. Since August is a relatively humid time of the year,
even the large uncertainty around this value may be of negligible significance in the final simulation, as soundabsorption from air peaks below 20% humidity and is relatively small for all values above 50% humidity [21].
The final important acoustical question is the level of background noise in the army. Elizabeth’s visit seems
to have encouraged frequent outcries among the soldiers, as well as drums that were used while she paradedaround the forces and significant noise from horses’ hooves on the march [15] However, Deloney’s accountseems to emphasize the contrast of this noisy scene with the troops’ awe and respect for their monarch whenat last she spoke. At this point the cavalry was still and the drums were silenced, which may have given an
implicit signal to the infantry in formation to be silent as well. While no doubt some foot soldier or horse may
have made some small noise, overall the army seems to have been fairly quiet during the speech itself. As
such, the army here is modeled with background noise values from 45 dBA (very quiet) to 50 dBA (quiet).

3

SIMULATION

3.1 CATT Model
Based on the historical data described above, Elizabeth’s speech at Tilbury was simulated in CATT Acoustic
v9.1 [14, 13], a popular cone-tracing acoustic simulation engine. The infantry was modeled as a flat squareaudience plane measuring 130x130m with a height of 1.5 m, corresponding to the largest estimation of about
20,000 troops at a density of 1.17 persons per m2 . In front of this was a 130x4 m empty grass space, corresponding to an assumed distance of 4 m between the infantry and cavalry. The cavalry was modeled as a314

130x30 m plane with a height of 2.5 m (Figure 1). Elizabeth was modeled as a point source with human voice
directivity in the center of the grass area and height 2.5 m, facing the infantry. Again, the exact height of Elizabeth’s horse is not known, but previous analysis has shown that small changes in height do not significantly
affect intelligible area, once a direct line of sight is established to every part of the crowd [5]. Elizabeth’s voice
was modeled with a standard IEC female spectrum with overall sound pressure of 80 dBA [2].
Absorption coefficients for the army and grass area are given in Table 1. Due to the nature of Sabine absorption
coefficients, some high-frequency values were initially measured as greater than 1 but were truncated to 99%
absorptive as that is the highest absorption value CATT allows [13]. Scattering coefficients were estimated using
CATT’s Lambert estimation function for an average surface roughness of 0.1 m for the army and 0.03 m forthe grass.
Table 1. Absorption coefficients by octave band center frequency (Hz) for soldiers and grass in Tilbury model.
Surface

125

250

500

1000

2000

4000

Audience (1.17 persons per m2 ) [27]

0.20
0.40

0.35
0.51

0.70
0.63

0.99
0.74

0.99
0.90

0.99
0.95

1.2” Dry Grass [25]The army’s background noise was modeled for a “very quiet” and “quiet” condition, corresponding to 45 dBA
and 50 dBA respectively. The noise levels by octave band are given in Table 2.
Table 2. Background noise levels by octave band for different noise conditions modeled.
Surface

125

250

500

1000

2000

4000

45 dBA (very quiet)
50 dBA (quiet)

55
60

48
53

41
46

36
41

33
38

31
36

STI was simulated for the scene under both background noise conditions using the IEC STI (female) protocol [2]. The STI maps, with 2x2 m grid spacing, for both models are shown in Figure 1. It can be seen that
the STI rating drops significantly over the 5 dB increase in noise conditions.

(a) 45 dBA background noise(b) 50 dBA background noise

Figure 1. STI (0-1) at Tilbury Based on Crowd Background Noise315

3.2 Crowd Estimation
To estimate the size of the crowd that could have heard Elizabeth, the STI maps for both the infantry andcavalry were exported as text files representing a series of 2x2 m squares. These were read into a script inMatlab that summed the area for each group that was greater than a minimum STI threshold. In this study,
as with previous work [6, 7], a threshold value of 0.3 for the STI was used, as this is usually seen as thevalue below which STI is “Bad” and also because perceptual phoneme-group scores drop significantly below
this level [34].
The infantry’s density was assumed to be 1.17 persons per m2 , similar to that of other infantries in formation [23]. The cavalry was assumed to have a much lower density of 0.5 persons per m2 , though the exact sizeof horses in Elizabeth’s cavalry is not known to the author. Based on this data, estimations of the number of
infantry and cavalry members who could have heard the speech were summed and shown in Table 3.
Table 3. Intelligible Crowd Sizes at Tilbury for Different Noise Conditions.

4

Noise Level

Infantry

Cavalry

Total

45 dBA
50 dBA

588
172

4975
1732

5563
1904

CONCLUSIONS

Based on the simulations shown here, it does not seem plausible for Elizabeth to have spoken intelligibly
to an army of 20,000 at once, even assuming relatively optimistic conditions for the density of an army information, the distance between the infantry and cavalry, and the background noise of the assembly. While
there is not sufficient historical evidence to prove the army did not crowd together into a denser configuration,
all the subjective descriptions of the event seem to argue against it and for a more standard, spaced-out infantry
formation. This computer model predicts that Elizabeth might have been able to be heard by 5,000 to 6,000
troops when they were extremely silent, which is in keeping with the smallest estimates for her force at Tilbury.
If however, the larger force estimates are correct, it seems likely that a large portion (perhaps the majority) of
her troops could not have made out the words of her speech, which supports the hypothesis that Sharpe wrote
it down to deliver to the “whole army” the next day because many of them could not hear it the first time.
In the view of many of her royal councilors, Elizabeth was a woman in a man’s job, a job that included
speeches to armies and parliaments. She often made reference to this fact and did so in the text of the Tilbury
speech, claiming that she had “body of a weak and feeble woman, but ... the heart and stomach of a king.” [35].
In this case however, having the vocal tract of a woman may have helped her: although there is not significant difference in vocal radiation patterns between men and women [11], women’s smaller vocal tracts tend toincrease the resonance at the higher frequency bands which are most important for speech intelligibility andare thus weighted most in the STI calculation [34]. While these frequencies are also more prone to air absorption, this effect is still relatively small over the distances in question. Because of this, in laboratory tests,
trained women vocalists can often produce the greatest A-weighted speech levels even when male vocalists (whohave larger vocal tracts and can produce greater subglottal pressure) produced greater flat-spectrum (Z-weighted)
SPLs [9].
This suggests that, given equal oratorical training and opportunity, women would have been a better conduit forspeeches to large audiences than men in terms of intelligible range. Unfortunately, in the historical record suchoccasions are hard to find: the author has searched extensively for large addresses by other female leaders like
Joan of Arc or Cleopatra, but so far has not found evidence of anything on the scale of the Tilbury oration (tipsfrom interested historians are always welcomed, of course). In this sense the Tilbury speech must be seen as
one of those rarest occurrences in history: thousands and thousands of men – all intently listening to a woman.

316

REFERENCES[1] American National Standard – Methods for Calculation of the Speech Intelligibility Index. In ANSI 3.51997, 1997.
[2] IEC 60268-16: Objective rating of speech intelligibility by speech transmission index. Technical report,
International Electrotechnical Commission, Geneva, Switzerland, 2003.
[3] W. Behringer. Climatic Change and Witch-hunting: The Impact of the Little Ice Age on Mentalities.
Climatic Change, 43:335–351, 1999.
[4] I. Bell. Elizabeth I: The Voice of a Monarch. Palgrave Macmillan, New York, NY, 2010.
[5] B. B. Boren. The Maximum Intelligible Range of the Human Voice. PhD thesis, New York University, 2014.
[6] B. B. Boren. George Whitefield’s Voice. In D. C. Jones and G. Hammond, editors, George Whitefield:
Life, Context and Legacy. Oxford University Press, Oxford, UK, 2015.
[7] B. B. Boren. Acoustic Simulation of Julius Caesar’s Battlefield Speeches. Acoustics, 1(1):3–13, 2018.
[8] B. B. Boren and A. Roginska. Analysis of noise sources in colonial Philadelphia. In Internoise 2012, New
York, NY, 2012.
[9] B. B. Boren and A. Roginska. Maximum Averaged and Peak Levels of Vocal Sound Pressure. In {Proceedings of the 135th Audio Engineering Society Convention}, New York, NY, 2013.
[10] M. Christy. Queen Elizabeth’s Visit to Tilbury in 1588. The English Heritage Review, 34(133):43–61, 1919.
[11] W. T. Chu and A. C. C. Warnock. Detailed Directivity of Sound Fields Around Human Talkers. Technicalreport, National Research Council Canada, 2002.
[12] M. T. Crane. "Video et Taceo": Elizabeth I and the Rhetoric of Counsel. Studies in English Literature,
1500-1900, 28(1):1–15, 1988.
[13] B. Dalenback. CATT-Acoustic v9. CATT, Gothenburg, Sweden, 2011.
[14] B.-I. Dalenback. Room acoustic prediction based on a unified treatment of diffuse and specular reflection.
Journal of the Acoustical Society of America, 100(2), 1996.
[15] T. Deloney. The Queenes visiting of the Campe at Tilsburie with her entertainment there, To the Tune of Wilsons
wilde. John Wolfe, London, 1588.
[16] K. S. Douglas and H. H. Lamb. Weather Observations and a Tentative Meteorological Analysis of the
Period May to July 1588. Technical report, University of East Anglia, Norwich, UK, 1979.
[17] B. Franklin. The Autobiography of Benjamin Franklin. Yale University Press, New Haven and London, 2ndedition, 1964.
[18] S. Frye. The Myth of Elizabeth at Tilbury. The Sixteenth Century Journal, 23(1):95–114, 1992.
[19] J. M. Green. "I My Self": Queen Elizabeth I’s Oration at Tilbury Camp. The Sixteenth Century Journal,
28(2):421–445, 1997.
[20] M. H. Hansen. The battle exhortation in ancient historiography: fact or fiction ? Historia, 42(2):161–180,
1993.

317

[21] C. Harris. Absorption of Sound in Air versus Humidity and Temperature. Journal of the Acoustical Societyof America, 40(1):141–159, 1966.
[22] R. Hutchinson. The Spanish Armada. St. Martin’s Press, New York, NY, 2013.
[23] S. James. 48 BC: The Battle of Pharsalus. In Rome’s Legions: Decoding their Pythagorean Organization
753 BC to 410 AD. Academia.edu, 2010.
[24] R. Kent, J. Kent, and J. Rosenbek. Maximum Performance Tests of Speech Production. Journal of Speechand Hearing Disorders, 52:367–87, 1987.
[25] N. Londhe, M. D. Rao, and J. R. Blough. Application of the ISO 13472-1 in situ technique for measuring
the acoustic absorption coefficient of grass and artificial turf surfaces. Applied Acoustics, 70(1):129–141,
2009.
[26] G. Manley. The mean temperature of Central England, 1698 to 1952. Quarterly Journal of the Royal
Meteorological Society, 100:389–405, 1953.
[27] F. Martellotta, M. D’Alba, and S. D. Crociata. Laboratory measurement of sound absorption of occupied
pews and standing audiences. Applied Acoustics, 72(6):341–349, 2011.
[28] G. Mattingly. The Defeat of the Spanish Armada. The Folio Society, London, UK, 2002.
[29] S. W. May. Queen Elizabeth to her Subjects: The Tilbury and Golden Speeches. Explorations in Renaissance Culture, 30(1):23–40, 2004.
[30] G. Parker. If the Armada Had Landed. History, 61(203):358–368, 1976.
[31] W. K. Pritchett. The General’s Exhorations in Greek Warfare. In Essays in Greek History, pages 27–109.
J. C. Gieben, Amsterdam, 1994.
[32] G. P. Rice. The Public Speaking of Queen Elizabeth. Columbia University Press, New York, NY, 1951.
[33] L. Shenk. Learned Queen: The Image of Elizabeth I in Politics and Poetry. Palgrave Macmillan, New York,NY, 2010.
[34] H. J. M. Steeneken and T. Houtgast. Basics of the STI measuring method. In S. J. van Wijngaarden, editor,
Past, present and future of the Speech Transmission Index, pages 13–43. TNO Human Factors, Soesterberg,
Netherlands, 2002.
[35] A. Weir. The Life of Elizabeth I. Random House Ballantine Publishing Group, New York, NY, 1998.

318