modulant 
Modius. Head of St 
or Proserpine, found at Cnidus. 
That which modulates or varies. See modulo te, 
r. t., 2. 
In modern English verse alliteration only plays the 
subordinate part of a modulant, not to be unduly decried 
where not overdone. 
E. Wadham, Eng. Versification, p. 119. 
modular (mod'u-lar), (i. [= F. modulaire; as 
module + -ar 3 .} "Pertaining to modulation; 
pertaining to or regulated by a module or a 
modulus Modular equation. See equation. Mod- 
ular focus, a focus of a conicoid or quadric surface. "The 
distance of any point on the quadric from such a focus is 
in a constant ratio to its distance from the corresponding 
directrix, the latter distance being measured parallel to 
either of the planes of circular section. " (Salman.) Mod- 
ular function, a higher periodic function connected 
with a group of periods 
3816 
modulation (mod-u-la'shon), H. [< F. modula- 
tion = Sp. modulation = Pg. ModulaqSo = It. 
modulations, <. L. modulatio(n-) ,<, modulari, regu- 
late, modulate: see modulate.] 1. The act of 
modulating, (a) The act of modifying, adjusting, or 
adapting. 
The cmperours . . . delited in daunsyng, perceyuing 
therein to be a perfecte measure, whiche maye be called 
Modulation. Sir T. Elyot, The Governour, i. 20. 
When we fix ourselves upon the meditation and modu- 
lation of the mercy of God, even his judgments cannot put 
us out of tune, but we shall sing and be cheerful even in 
them. Donne, Sermons, ii. 
(6) The act of inflecting the voice or any instrument in a 
musical manner. 
The rings of the wind-pipe are fitted for the modulation 
of the voice. N. Grew, Cosmologia Sacra, I. v. 10. 
(e) The modification of the voice or of utterance, to express 
various shades of meaning or emotion. 
The poets of Elizabeth had attained an art of modulation 
which was afterwards neglected and forgotten. 
Johnson, Waller. 
2. A state or condition reached by a process of 
modulating, modifying, or varying. 
That delicate modulation of surface treatment which 
gives high value to the best Florentine metal work. 
C. C. Perkins, Italian Sculpture, p. 124. 
3. (a) In Gregorian music, one of the tones in 
where ad be = i.- Modular method of generation 
Of quadrics, amethod based on the fundamental property 
of the modular foci. Modular numbers, in Landen's 
transformation, numbers approximating to the value of 
the new modulus. They are the successive approxima- 
tions in the process of finding the arithmetico-geometrical 
mean of the old complementary modulus and unity. 
Modular ratio, the modulus of a system of logarithms. 
See logarithm. Modular transformation of an ellip- 
tic Integral, a transformation of the elliptic integral into 
another with a different modulus. 
modulate (mod'u-lat), r. ; pret. and pp. modu- 
lated, ppr. modulating. [< L. modulalus, pp. of 
modulari, measure, regulate, modulate/ modu- 
lus, measure : see modulus. Cf. module, v.~] I. 
trans. 1. To modify; adjust; adapt; regulate. 
With the gift of song, Carlyle would have been the 
greatest of epic poets since Homer. Without it, to modu- 
late and harmonize and bring parts into their proper rela- 
tion, he is the most amorphous of humorists, the most 
shining avatar of whim the world has ever seen. 
Lowell, Study Windows, p. 148. 
2. To vary or inflect the sound or utterance 
of, especially so as to give expressiveness to 
what is uttered ; vary or adapt in tone. 
In all vocal musick it [the tongue] helpeth the wind- 
pipe to modulate the sounds. 
N. Grew, Cosmologia Sacra, I. v. 16. 
He listened to the voice of nature, and modulated his 
own unto it. Sterne, Tristram Shandy, v. 8. 
Caius Gracchus, it is said, when he harangued the Roman 
populace, modulated his tone by an oratorical flute or 
pitch-pipe. Irving, Knickerbocker, p. -213. 
We are conscious of a murmuring humble voice : it is a 
beggar, who is modulating a prayer for alms and bowing 
assiduously. Harper's Mag., LXXIX. 680. 
3. To vary the pitch of; inflect; melodize. 
The master's hand, in modulated air, 
Bids the loud organ breathe. 
SomervUle, The Chase, iii. 
He [Gliick] Is to play on a set of drinking-glasses, which 
he modulates with water. Walpole, Letters, II. 14. 
4. In music, to change from one key (tonality) 
to another, by utilizing one or more of the tones 
common to both. 
II. intrans. 1. Inwi usic, to pass from one key 
(tonality) into another, or from the major into 
the minor mode, or vice versa. See modula- 
tion, 3 (6). Hence 2. To vary, oscillate, or 
fluctuate. [Rare.] 
It is written from no well-defined standpoint, but modu- 
lates from illustrations of the Kochefort experimenters to 
the telepathic drawings of the English society for psychic 
research, and thence to the localization diagrams of Fer- 
rier, with no clear method. Amer. Jour. Psychol., I. 516. 
8 
DOHi 
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Modulator. 
f 
e: see mode 1 . Cf. 
a mode with which every phrase of a melody in 
that mode must begin and end. The regular mod- 
ulations of each mode Include the final, the dominant, 
the mediant, and the participant, eacli of which has its 
own peculiar functions. (See these words, and also model.) 
To these are added two other tones in each mode, called 
conceded modulations, which are of minor importance. 
(6) In mod. music, the act, process, or result of 
changing, in the course of a piece, from one key 
(tonality) to another, so that a new tone be- 
comes the key-note and the relative significance 
of all the tones common to both tonalities is 
altered. When a tone foreign to the original tonality of 
a piece is used, a modulatory effect is nearly always pro- 
duced. If this effect is carried out into a cadence in the 
new key, the modulation is called final ; otherwise it is 
passing or transient. All modulations, however, require 
a return to the original key before the end of the piece. 
The tone by which the transition is introduced or effected 
is called the note of modulation ; this tone in the simpler 
forms of modulation is usually the fourth or the seventh 
tone of the new key. The simplicity of a modulation de- 
pends upon the closeness of relationship between the 
keys involved. The simplest modulations are into the 
keys either of the dominant or of the subdominant, and are 
effected by sharping the fourth tone or flatting the seventh 
tone respectively of the original key. Modulations into 
the relative minor or into the minor keys of the supertonic 
or of the mediant are effected by sharping the fifth, the 
first, or the second tone of the original key respectively. 
Numerous other more intricate modulations are possible, 
especially in instrumental music. A modulation is abrupt, 
distant, or extraneous, when it leads into a key not closely 
related with the original one. It is deceptive when it uti- 
lizes a series of chords in an unusual and startling way. It 
is melodic when produced by the introduction of a tone for- 
eign to the original tonality, and harmonic when produced 
by the use of a chord common to both tonalities first in its 
relation to one and then in that to the other. It is enhar- 
monic when it is effected on an instrument of fixed intona- 
tion, like the pianoforte, by calling a key (digital) first by 
one name and then by another, as when E|) in the key of B> 
is called DJ in the key of BJ. Modulation is one of the 
most Important resources of modern music. It introduces 
endless variety of both melodic and harmonic effect, with 
great possibilities in the way of sequences and imitations. 
It increases the unity of a composition and the importance 
of the original tonality by introducing a temporary disturb- 
ance of original tonal relations, with a subsequent complete 
and emphatic resumption of them. It affords means for 
the expression of very complex emotional conditions, par- 
ticularly those of unrest, contrast, etc. In the style of 
Wagner it has often been pushed to the limit of toleration, 
so as almost to destroy that sense of fixed tonality which 
is the basis of musical certitude. The most remarkable 
harmonic convenience for modulation, at least in instru- 
mental music, is a chord of four tones consisting of three 
minor thirds successively superposed, which is called the 
chord of the diminished seventh. This chord may be re- 
garded as based upon any one of Its four tones, which is 
then the seventh tone of either a major or a minor scale. 
Its harmonic nature is therefore peculiarly ambiguous and 
unstable. ( t ) A musical composition exemplify- 
ing modulation. 4. Sound modulated; mel- 
ody. 
Immmerous songsters, in the freshening shade 
Of new-spring leaves, their modulations mix 
Mellifluous. Thomson, Spring, 1. 009. 
5. In arcli., the proportion of the different pai-1 n 
of an order according to a module, = Syn. 1 (&). 
Accent, etc. See inflection. 
modulator (mod'u-la-tor), . [= F. modula- 
tcur = Sp. Pg. modulador = It. modulatore, < 
L. modulator, a regulator, director, < modulari, 
regulate: see modulate.'] 1. One who or that 
which modulates. 
What a variety of uses hath nature laid upon that one 
member, the tongue, the grand instrument of taste, the 
faithful judge, the centinel, the watchman of all our 
nourishment, the artful modulator of our voice ! 
Derham, Physico-Theology, v. 5. 
modulus 
2. A chart of the musical scale, indicating the 
relations of its essential tones to each other 
and of the whole scale to its 
related scales. The form of 
modulator generally used in the 
tonic sol-fa system of teaching 
music is shown in the accompany- 
ing chart. 
modulatory (mod'u-la-to- 
ri), o. [< modulate + -era.] 
Of or pertaining to modu- 
lation. 
Modulations are really govern- 
ed by the same laws which apply 
to any succession of harmonies 
whatsoever, and the possibilities 
of modulatory device are in the 
end chiefly dependant upon in- 
telligible order in the progres- 
sion of the parts. 
Grove's Diet. Music, II. 345. 
module (mod'ul), . [< F. 
module = Sp. modulo = Pg. 
It. modulo, a measure, mod- 
ule, < L. modulus, a small 
measure, a measure, mode, 
meter, dim. of modus, measu 
modulus, model, mold*.} It. A little measure; 
hence, a small quantity. 2. In arch., a stan- 
dard of measure often taken, particularly in 
antiquity and the middle ages, to regulate the 
proportions of an order or the disposition of an 
entire building. In the classical styles the diameter 
or semidiamete'r of the column at the base of the shaft is 
usually selected as the module, and this is subdivided into 
parts or minutes, the diameter generally into sixty or 
the semidiameter into thirty. Some architects employ 
no fixed number of divisions of the module, but divide 
it into as many parts as they deem serviceable for the 
work in hand. 
3f. A model or representation ; a mold ; a pat- 
tern. 
Among so many Modules admirable, 
Th' admired beauties of the King of Creatures, 
Com, com, and see the Womans rapting features. 
Sylvester, tr. of Du Bartas's Weeks, i. 6. 
4. In nmnis., the size of a coin or medal, mea- 
sured by the diameter. [Rare.] 
modulet (mod'ul), r. t. [< F. modeller = Sp. Pg. 
modular = It. modularc, modolare, modulate, 
< L. modulari, regulate, modulate: see modu- 
late.} 1. To model; shape. 
0, would I could my father's cunning use, 
And souls into well moduled clay infuse. 
Sandye, Ovid (1688), p. 10. (Latham.) 
2. To modulate. 
That Charmer of the Night, . . . 
That moduleth her tunes so admirably rare, 
As man to set in parts at first had leam'd of her. 
Drayton, Polyolbion, xtii. 70. 
modulett (mod'u-let), . [< module + -et.~\ A 
small model; a microcosm. 
But soft, my Muse : what ? wilt thou re-repeat 
The Little-Worlds admired Modulelf 
Sylvester, tr. of Du Bartas's Weeks, i. 7. 
Modulidse (mo-du'li-de), n. pi. [NL., < Modulus 
+ -idee.'] Afamilyofttenioglossaterostriferous 
gastropods represented by the genus Modulus. 
The animal has a radula like that of the Cerithiida, but 
has no siphon, and the shell is holostomatous and trochi- 
form, but with a columellar tooth. The species are inhabi- 
tants of tropical seas, and one, Modulus tectum, is abun- 
dant in the West Indies. 
modulizet (mod'u-liz), r. t. [< module + -ize.~] 
To model. 
While with the Duke, th' Eternall did deuise, 
And to his inward sight did modulize 
His Tabernacle's admirable Form. 
Sylvester, tr. of Du Bartas's Weeks, ii., The Lawe. 
modulus (mod'u-lus), n. [< L. modulus, a mea- 
sure, dim. of modus, measure: see module, 
mode 1 .] 1. In math., a real positive number 
that serves as measure or parameter of a func- 
tion or effect. Represented by M. or ft. 2. 
In physics, the measure of an effect under con- 
ditions whose measure is unity. Thus, a physi- 
cal modulus is not a number, but a physical 
quantity. 3. {cap.'] In conch., a genus of gas- 
tropods, referred to the Littorinidic or periwin- 
kles, or made type of the family Modulida 1 . The 
shell is depressed and trochif orm, with a deeply 
cut columellar tooth and many-whorled oper- 
culum Absolute modulus of gravitation, the ac- 
celeration due to the gravitation of a body toward a mass 
of one gram at a distance of one centimeter. It amounts 
to 648 x 10 10 centimeters per second. Angle of the 
modulus, in math., the angle of which the modulus is 
the sine. Complementary modulus, in math., the co- 
sine of the angle of the modulus. Gravity-modulus 
in plti/.-.-ici*. a modulus of elasticity in which the weight of 
a unit mass is taken as the unit of force. Length Of 
modulus, in jihyvics, a modulus of elasticity expressed as 
a length by taking the weight of the unit volume of the 
material referred to as the unit of force. Modulus of a 
congruence, in math., that measure or divisor which gives 
