The Technique of the Monochord

Author(s): Cecil Adkins Source: Acta Musicologica, Vol. 39, Fasc. 1/2, (Tan. - Tun., 1967), pp. 34-43 Published by: International Musicological Society Stable URL: http://www jstor.org/stable/932465 Accessed: 16/07/2008 11:49 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=inmuso. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. http://www. jstor.org

Author(s): Cecil Adkins Source: Acta Musicologica, Vol. 39, Fasc. 1/2 (Jan. - Jun., 1967), pp. 34-43 Published by: International Musicological Society Stable URL: http://www.jstor.org/stable/932465 . Accessed: 18/09/2013 10:06 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . International Musicological Society is collaborating with JSTOR to digitize, preserve and extend access to Acta Musicologica. http://www.jstor.org

E. F. Flindell:SyllabicNotation and Changeof Mode Explanation of Symbols = r -= jr ligatura binaria -= notae currentes -I I nota plicata = designates motives. = maxima = notae simplices or together double writing = breath pause occasionally Silbenstrich r• = indicates J J The Techniqueof the Monochord CECIL ADKINS (DENTON/TEXAS) The relation of the monochord to musical theory and practice is often referred to by writers on music but seldom explained. There is almost no detailed information concerning the monochord and its techniques available outside the original sources. As a result, the interested reader is often confused or misled by the multiplicity of terms applied to the instrument, as well as the many methods used in dividing the string. The following remarks on the construction and techniques of the monochord are offered as a means of clarifying and standardizing some of the more obscure aspects of its theory and practice. The monochord in its early form, and in the form utilized throughout the Middle Ages (Diagram 1), was a table or plank (AC) upon which were erected two fixed bridges (EB and FD). The string was stretched across the bridges (EF) and securely fastened at the ends (AC). A movable bridge (K) was then placed underneath the string, dividing it into two sections (EK and KF). The marks indicating the placement of the movable bridge were then inscribed on the table underneath the string, between the two end bridges (B and D). The resonating box, generally considered an integral part of the instrument, is not mentioned in the treatises of the Middle Ages, but is depicted in miniatures after the twelfth century. It was probably a late medieval addition directed at increasing the portability of the instrument as well as enhancing its tone.

Diagram1. Medievaldiagramof the monochord.1 SKI F B D The only major change in the instrument was made after 1500 when one of the end bridges was replaced by a nut, and the movable bridge was removed. When the remaining bridge was lowered the string came close enough to the table so that the pitches could be produced by pressing the string against the table or top of the resonator (Plate 1). This procedure, however, must have greatly reduced the accuracy of the pitches by further stretching the string, and by rendering the pitches capable of instantaneous slight alteration-governed perhaps by ear rather than calculation-such as one produces on a violin. Andreas Ornitoparchus (Ornithoparcus2), in 1517, gave an account of the manner of constructing an instrument like the one shown in Plate 1. In his directions he suggested that the size of the monochord be "about a yard long, or what length you please." Glareanus also specifies three feet as the length of his instrument. These dimensions give little indication of what the standard of pitch may have been at this time since the pitch of a three-foot instrument would also be influenced by the diameter and tension of the string as well as the resonating frequency of the body Plate 1. A Renaissance monochord.3 -IDI~a~ ' ..? ? /,:." •.F~r ,. ..........o / //-.-" f-9ap•... ..... • "1"??? ......."'' ..... .. "". " "•: ". ~- "..•.. ~Oft Q:.-'P, II\ of the instrument.4 The medieval theorists say nothing about the size of the monochord, although medieval iconography enables one to deduce that the monochord of the late Middle Ages must also have been between three and four feet in length. 1 BOETHIUS,De musica, ed. G. Friedlein, Lipsiae, Teubneri, 1867, Bk. IV, Cap. XVIII, p. 349. This diagram illustrates what appears to have been a misconception of the medieval writers. Ptolemey's directions for the monochord (I. DtiRING, Ptolemaios und Porphyrios iiber die Musik, G6teborg, Elanders, 1934, pp. 35-6) indicates that only the edge of the bridge is to be rounded, but many later writers have taken this to mean that the bridge is to be constructed in the form of a semicircle. Cf. GLAREANUS'SDodecachordon (1547) and ZARLINO'S Dimostrationi harmoniche (1571); these writers frequently refer to this kind of bridge as a hemisphere or semisphere. 2 A. ORNITHOPARCUS, Micrologus, tr. by John Dowland, London, T. Adams, 1609, p. 22. 3 A. KIRCHER,Musurgia universalis, Roma, 1650, Bk. III, p. 187. (Arithmetica applicirt oder gezogen 4 Similar directions were also provided by HENRICUSGRAMMATEUS auff die edel kunst musica, in: Ayn new kunstlich Buech, Niirnberg, 1518, p. 25) who specified a length of six spannen (48-54 inches), and later by HENRI CHOQUEL(La musique rendue sensible par la mechanique, new ed., Paris, 1762, appendix) who provided a diagram 317/8 inches long for his monochord.

These factors seem to suggest that the basic pitch varied considerablybetween instrumentsandwas influencedmoreby the physicalcharacteristicsof the individual instrumentsand the vocal rangeof the userthan by a given standardof pitch. Laterwritersdescribethe constructionof monochordsof a variety of sizes and shapes,many of which are equippedwith morethan one string.Technically,these multi-stringedinstrumentshouldnot be called monochords,but the consensuswas that, if the stringswere tuned in unison, the designationwas to be retained.In the instancesof multi-stringedmonochordstuned in octaves or other intervalsthe use of the instrumentlike an ordinarymonochordaccountedfor the retentionof the name.5 The primarypurposeor use of the monochordwas to sound intervalsor scales whose pitch relationshipshad been predeterminedby means of mathematical calculation.Traditionally,any kind of determinationof the notes of a scale, whether a mathematicalor an aural determination,has been called a monochorddivision. This custom is neverthelessmisleadingbecause, although the mathematicaldeterminationof the pitch relationshipsis necessaryfor the correctproductionof the desiredsounds,these determinationsare not usable for practicalmusicalpurposes unless they can be applieddirectly to a monochordwithout furthercalculation.It is perhapspreferableto use the term manual division to designate any set of calculationsthat may be applied directly to a string under tension, that is, the mathematicalformulaswhichwill producethe desiredsoundswhen applieddirectly to the monochord.The manual division of the monochordis the only kind of divisionto attain any practicalsignificancebeforethe earlytwentiethcentury.6 ACOUSTICALSYSTEMSAPPLIED TO THE MONOCHORD The divisionsof the monochordare usually presentedin musical literaturein termsof proportions,stringlengths,or cents. The firsttwo methodshave a tradition almost as old as the monochorditself and are both directly applicableto the instrument.The third is greatly favored by most contemporarywriters on tem5 In all of the Greek and in many of the Latin sourcesdealing with the monochordone encounters the word canon. In many of these sourcesit is used synonymouslywith the word monochord.In its strictestsense, however,it seems reservedfor instructionson dividingthe string, or for the diagram that is to be placedunderthe stringto facilitate the exact placementof the bridge,just as the word monochord,in its strictest sense, is reservedfor referenceto the instrument. and temperamentsin the eighteenthand nineteenthcenturies 6 The appearanceof so many tunings that are not physicallyapplicableto the monochordbringsup a point that is of great importancein the study of the scale variationsof this period:that tuningsbeforethe early twentiethcenturywhich did not employ the monochordwere virtually worthlessfrom a practical musical standpoint.The applicationof such impracticaltunings,producedmainly by mathematicianswhose interest in scale divisionwas intellectualand as much a matterof scientificas of musicalinterest,had to be done by ear accordingto a set of verbaldirections. The practicingmusicians,on the other hand, who were interestedin actual tunings,used the monochord in order to give their theories some practical realization.Because of the limitations of the instrumentand of the ear, however, tuning by means of a monochordmay be presumedto be as difficultand inaccurateas a tuning determinedby ear, but at least a tuning that was applicableto the monochordwas heard by its inventorin the most accurateway available and was not just a series of numbers.

peramentsand tunings, but because of its nonproportionalnature it needs to be reducedeither to stringlengths or to proportions,beforeit can be used to produce pitches aurally.7 Proportions Proportions The Pythagoreanconceptof monochorddivisionby proportionsis basedon two means:the arithmeticmean and the harmonicmean.The four main intervalsof the systemare derivedby relating,in pairs,the smallestwholeintegersthat can be used to showthe relationshipsof thesetwo means.Thesenumbersare 6, 8, 9, and 12. The ratio 12:6 produces the diapason (octave); 9:6 and 12:8, the diapente (fifth); 8:6 and 12:9, the diatessaron (fourth); and 9:8, the tone (major second). Fromright to left in Diagram2 these numbersproducemultiplexand superparticular proportions (2:1,dupla; 3:2, sesquialtera; 4:3, sesquitertia; 9:8, sesquioctava). Fromleft to right these numbersare transposedinto submultiplexand subsuperparticular proportions (1:2, subdupla; 2:3, subsesquialtera; 3:4, subsesquitertia; 8:9, Other multiplexand submultiplexproportionsused on the monosubsesquioctava). chord are tripla (3:1), subtripla (1:3), quadrupla (4:1), and subquadrupla (1:4). Whetheran octave, for example,is expressedas dupla(i. e., by doublinga given length of string) or as subdupla(i. e., by halving a given length of string) and whetherthe other proportionsare expressedwith their larger terms first or last (e. g., 3:2 or 2:3 or 3/2 or 2/3), may seem of small import at this time; but a clear Diagram2. The basic Pythagoreanintervals. diapason diapente diatessaron 6 8 9 12 diatessaron diapente diapason of the relationshipsof both kindsof proportionsto intervalproduction understanding is necessaryfor understandingall kinds of monochorddivisionsand their influence on medievalpedagogy.8 A fourth method, that of expressing string lengths by means of logarithms, appears not infrequently in the literature olf the eighteenth century. This system, from which the cents were later derived, is also not directly applicable to the monochord. 8 This aspect of the division of the monochord is apparent in all of the medieval treatises that discuss the elements of music. As such it plays a vital part in the medieval retention of the Pythagorean tuning and the Greek genera as well as in the expansion of the scale system, the use of letter notation and the development of didactic techniques. Cf. C. ADKINS, The Theory and Practice of the Monochord, unpublished dissertation, State University of Iowa, 1963, pp. 68-190. The reader is also referred to the monochord studies of SIGFRIDWANTZLOEBEN (Das Monochord als Instrument und als System, Halle, Karras, 1911), K. W. GUiMPEL (Das Tasten-Monochord Conrads von Zabern, in: Archiv fiir Musikwissenschaft, XII, 1955, pp. 143-66), and the brief but excellent article Monochord by HANS HEINZ DRXGER, in: Die Musik in Geschichte und Gegenwart (IX, 1957, col. 474-75).

of theMonochord Systemof StringLengths The cumbersomeness of the proportionalsystemand the difficultyencounteredin a monochord by meansof a compasscausedsomeinvestigatorsto manuallydividing adopt the systemof stringlengths. If, for example,a string is assigneda length of 10,000 units of measurement,its upperoctavewouldbe regardedas havinga length of 5,000 units.This systemis an accurateand simplemethodof abstractpitch representation,but it is difficultto reproduceaurallyon a monochordbecauseof the size of the numbersinvolved.A case in point is the set of stringlengths for equaltemperamentdevisedby JohannNeidhardtin 1706.9 The stringlength specifiedfor the secondscale step of this systemwas 1781.82 units. Therewere manylike Marpurg, however, who believed that a temperamentcould be more easily reproducedby reducingthe numberof digitsrepresentingthe total length of the stringto as few as three-a compromiserarely confessedto by the users of string lengths in an era when the systemwas at its height of popularity.10 Systemof Cents The systemof cents,introducedby AlexanderEllis in the late nineteenthcentury, has been widely adoptedas a uniformbasis for the comparisonof intervals.The applicationof this kind of abstractrepresentationto an intervallicseries originally determinedby othermeans(i. e., proportionsor stringlengths)is of doubtfulvalue natureof the centsrendersthemincapable for two reasons.First,the nonproportional and second, the end result of a monochord of direct mechanicalreproduction;11 divisionis often not so importantor interestingfrom the historicalpoint of view as the meansby whichit is attained. With regardto the methodof dividingthe monochord,one shouldbe awarethat the techniqueused in workingout a specficmonochorddivisionwas often selected with a view to its intendedusage.For example,in the MiddleAges the monochord divisionsall achievethe same end result and all utilize the same four proportions (dupla,sesquialtera,sesquitertia,sesquioctava),yet the techniquesof divisionvary accordingto whetherthe division was made for use in a speculativeor practical musical treatise. There are also significanttrends toward simplificationof the division of the instrumentthat appearto have directly influencednot only the expansionof the whole medievalmusical concept but also the eventual discontinuanceof the Pythagoreantuningsystemin the earlyRenaissance.12 7. Sectio canonis harmonici, K6nigsberg, Eckart, 1724, p. 9 J. G. NEIDHARDT, 1757, o10F. W. MARPURG,Anfangsgrniide der theoretischen Musik, Leipzig, J. G. I. Breitkopf, pp. 172-75. 11 See Ellis's own description of this attempt in his annotations to the English translation of HERMANN On the Sensationsof Tone as a PhysiologicalBasisfor the Theoryof Music, 5th ed., VONHELMHOLTZ, London, Longmans, Green, and Co., 1930, p. 523. 12 See ADKINS,op. cit., pp. 29-30, 68-284.

THEMANUAL OFTHEMONOCHORD TECHNIQUE The techniqueof the manual division of the monochordis divided into three categories:the firstcontainsdiatonicdivisionsbasedon superparticular proportions; the secondincludesthe variousmethodsof addingchromaticsemitonesto a diatonic division;the third comprisesdivisionswhose notes are determinedmathematically in terms of string lengths. Of these classifications,the first representspractically all of the monochorddivisionsof the Greek,medievalandearlyRenaissanceperiods. The secondwas usedmainlyin the Renaissanceera and the thirdis the mainmethod of the post-Renaissance period(after1600). Sincethe mannerof dividingthe monochordby meansof the systemof stringlengthsand a ruleris self-explanatoryit will not be dealt with further.The techniquesof the other categoriesare presented,not as specificdivisionsof a particulartuning,but as generalconceptsnecessaryto an of the instrument. understanding The ManualDivision of Diatonic Superparticular Tunings The manualdivisionsof the monochordin the Greekand medievalerasarebased upon an extensionof the relationshipsof the superparticular proportions.A given divisionis usuallybased on a preponderanceof either superparticular or subsuperparticularproportions.The initial note of a divisionbased on a pluralityof superparticularproportionsis found as a part of the total length of the string, and the remainingnotes aredetermined,not in relationto the length of the entirestring,but in relation to the string length of the initial note. Divisions using mainly subsuperparticular proportions usually have the total length of the string as the initial note and the succeeding notes are related to this length. For example, if a given portion of a length of stringis dividedinto eight parts,a tone may be producedby adding the length of one of these parts to the originalportion,makingnine. Conversely, if the stringlength is dividedinto nine parts,one part must be subtractedin order to producethe tone. The first of these divisions,using a superparticular proportion (sesquioctava),proceedsfrom a higher to a lower pitch; the second using a subsuperparticulardivision (subsesquioctava), proceeds from a lower pitch to a higher. A division containing predominantly superparticularproportions progresses in a descending manner, that is, from the higher sounding pitches to the lower through the use of longer and longer portions of the string, and many be called a descending division. The use of subsuperparticularproportions produces an ascending division that utilizes shorter and shorter portions of the string. A division using both kinds of proportions may be said to be an alternating division, and, -dependingon the primary sesquioctaval division of the string, it may be classed as an alternatingdescending or an alternating-ascending division. As a means of clarification, the two following divisions for determining the notes of a tetrachord are offered. It will be noticed that the semitone of the descending division is between the lower two pitches, whereas that of the ascending division

appears between the upper two pitches. This arrangement of the tetrachord is a result of the simplest mechanical method of finding the Pythagorean semitone, which is to subtracttwo whole tonesfromthe diatessaron.13 The descending division for determining the tetrachord. (For this demonstration a point 25 cm. from the end of a one meter string has been selected.) The first note will have a sounding length of 25 cm. The second pitch, a whole tone lower, is determined by taking a sesquioctava proportion to the first pitch. The string length of the second pitch will be 28.125 cm. The logical completion of these divisions results in a tetrachord that may be summarized as follows: Pitch 4 3 2 1 String 33.333 cm. 31.641 cm. 28.125 cm. 25.00 cm. 256 243 9 89-- 9 8 semitone tone tone String length Proportion Interval A visual representation of this division is shown in Diagram 3. 14 Diagram 3. A sample descending monochord division. +321 H1II 392 8 7 6 54 3 211 :1 4 I I 3 I 2 I 3 '3 The ratio of the Pythagoreansemitone(256:243) is not directlyapplicableto the manualdivision, since any mechanicaldivisionof the string into 243 and 256 units wouldbe grosslyimpractical.This ratio is found as a sort of by-productby subtractingthe sum of the two whole tones (x 9 = ) from the fourth . Proceduresuch as this illustratea cardinalprincipleof monochord 243 (4.-6= ratios are determinedby calculationwith simpleratios. The corollaryto this prindivision:complex ciple is that in most theoreticalwritingsall ratios, both simpleand complex,are basicallyassociated with mathematicalcalculationratherthan measurement. 14 By using a series of parallel lines to representsuccessivemeasurements,one can show the reladivision tion of these measurementsto the whole string. The measurementsof the superparticular divisionsare are numberedfrom right to left (see steps 1 and 2 of Diagram3); subsuperparticular numberedfromleft to right (steps 1 and 2 of Diagram4). The linear representationof the complete divisionis presentedon the top line of the diagram.The particularmeasurementof each step is listed under"proportions"at the right end of each line.

The ascending division for determining the tetrachord. For this division the entire sounding length of the monochord's string (one meter) may be used for the first pitch. The second pitch, found by means of a subsesquioctava proportion has a length of 88.889 cm. The completion of the division results in the following tetrachord. Pitch String String length 1 2 3 4 100.00 cm. 88.889 cm. 79.023 cm. 75.00 cm. 88 88 9 9 256 tone tone semitone Proportion Interval 243 243 Diagram 4 visually represents the above procedure. Diagram 4. A sample ascending monochord division. 1 2 stSI 2 1t 21 1 2 S1 31 1 39 11 2 3 3 2 1 6 4 I 4 3 2 7 6 ~5 3 SI 81 7 8 proplrtions 9 9 4 The completion of either of the above divisions in the manner of the Middle Ages would result in a two-octave scale in the Pythagorean tuning whose lowest note would be obtained from the entire length of the string. These two kinds of division, ascending and descending, exerted great influence upon the development of Western music. In general it may be said that the Greek writers up to A. D. 500 utilized the descending division; medieval scholars used both ascending and descending divisions; and later writers (Renaissance and post-Renaissance) preferred the ascending division. 15 The Manual Division of the Chromatic Scale There are three methods of determining semitones by means of the manual division of the monochord: an extension of the superparticularratios, an arithmetical division of the tone, and a mean-proportional division of the tone. In superparticulartunings one has the option of dividing to produce either of two complete and different (different even for notes which are "enharmonic equivalents") sets of chromatic notes. These may be obtained by the successive application of the sesquialtera proportion (beginning with B-natural) or of the subsesquialtera 15 The specificreasonsfortheseusagesarediscussed in detailin ADKINS, op. cit., pp. 35-337.

proportion (beginning with the note F). The resultant intervals will be a series of perfect fifths in descending order (sesquialtera) or ascending order (subsesquialtera).16The descending semitones may be called sharp semitones and the ascending semitones, flat semitones. Arithmetic semitones are determined by an equal division of the difference between the string lengths of two notes a step apart.Even though the resulting semitones are of unequal size, this method was frequently used in the post-medieval period. Equal semitones are determined from mean proportional string lengths and are usually found by means of the Euclidean construction. This geometric construction is effective for finding one mean proportional, but in order to determine more than one proportional string length, one needs to resort to more complicated mechanical devices such as the mesolabium17or to the kind of geometric figures used by Lemme Rossi in his Sistema musico of 1666.18 While the mesolabium and other geometrical methods of determining mean proportionals are not frequently encountered in connection with the monochord, they are often used in placing the frets on stringed instruments.19 THEMONOCHORD CONCERNING SOMEOBSERVATIONS Information about the construction and technique of dividing the monochord as discussed in the preceding pages is readily obtainable from the original sources. Once a working knowledge of the instrument has been acquired, however, other less easily understood, but more intriguing aspects present themselves. Some of these facets of the monochord and its relation to musical practice are: the efficiency and accuracy of the division; the kind of scale tuning or temperament produced; and the uses of the completed monochord division. Because the monochord of the Greek and medieval periods was almost always employed as a didactic device, its users attempted to make the division as efficient and as accurate possible. The efficiency of a monochord division depends on the relation between the number of separate measurements made and the number of notes produced. For example, a division that will produce fifteen pitches in seven measurements is much more efficient than a division that needs seventeen measurements to produce the same number of pitches. The results of these efforts are particularly noticeable after 1450, since, after this date, each new division often produced a new variation of a given tuning. Often the 16 This phenomenonis due to the idiosyncraciesof the superparticulartunings. For a detailed explanation,see Ibid., ChaptersIII and IV. 17 Clearlydescribedin J. Gow, A Short History of Greek Mathematics, London,Cambridge University Press, 1884, pp. 245-6. KIRCHER (Op. cit., I, p. 207) is Besides RossI (Sistema musico, Perugia, Laurenzi, 1666, pp. 62, 82), was apparentlythe only other author to use anything other than the mesolabiumin connection with the monochord. 19 See J. M. BARBOUR,Tuning and Temperament, East Lansing,MichiganState College Press, 1951, pp. 51ff.

musician wished to change the tuning but not infrequently he was only seeking a simpler method of division. It would seem that the appearance of an altered tuning bothered the Renaissance musician little, for in view of the inaccuracy of the monochord, a variation of a few cents (in some cases as much as 22 cents) was a small sacrifice to pay for a more efficient division. A case in point is the division of Ramos de Pareia whose monochord tuning varied widely from the accepted Pythagorean standard. Ramos, however, was apparently not bothered by the pitch deviation as long as he was able to simplify the division of the instrument. To this end he stated: "So therefore we have made all of our division very easy, because the fractions are common and not difficult."20 In many cases this desire is not stated expressly, as it was by Ramos, but it may be suspected that it served as the underlying cause of many of the new tunings of the Renaissance and succeeding periods. Therefore, in addition to the efficiency of a division (the relationship of the number of measurements to the number of pitches produced), a second criterion of a good division is how closely it approximates the musical or acoustical result desired by its inventor. In other words, does a given division achieve accuracy as well as efficiency, or is one sacrificed for the other? Although the origins of the instrument are shrouded in the haze of antiquity, its usage can be definitely traced to about 300 B. C., when, according to Greek writings, the monochord seems to have been most often a tool of the mathematician. In the hands of the mathematicians the monochord was used as a device to provide both visual and aural representation of the mathematical ratios of the intervals. There is also evidence that the monochord may have found, among the Greeks, some small favor as a performing instrument.21 In the Middle Ages the monochord not only fulfilled the basic functions allotted to it by the Greeks, but it also served as the principal method of expounding details of music theory-that is, it was employed frequently in explanation of the mathematical manner of determining intervals and scales, and also as a pitch-producing device for the teaching of singing. The Renaissance and later periods utilized the instrument to a great extent as a practical means of experimenting with scalar variants, and to a lesser extent as a pitch-producing medium for the tuning of keyboard instruments. A system of acoustical representation expressed in the form of string lengths, which was derived from the monochord, also found great favor with theorists, composers, and mathematicians in this latter era. Symbolic use was made of the monochord in the Renaissance to illustrate the unity that existed between man and his environment-both physical and spiritual. As more accurate devices for pitch experimentation became available, the monochord fell into disuse, surviving in the twentieth century only as a laboratory instrument. 20 BARTOLOME Musica Practica (1482), ed. J. Wolf, Leipzig, Breitkopf und RAMOS DE PAREIA, Hirtel, 1901, p. 60. 21 ADKINS, 361-5. cit., op.