Comparison of solo and ensemble performances with references to Pythagorean, just and equi-tempered intonations

MAS A. pore DIG Tet we AU MASON, JA . Ti COMPARISON OF SOLO AND ENSEMBLE PERFORMANCES _ ln = WITH REFERENCE TO PYTHAGOREAN, JUST, AND EQUI-TEMPERED INTONATIONS

MENC: The National Association for Music Education Comparison of Solo and Ensemble Performances with Reference to Pythagorean, Just, and Equi-Tempered Intonations Author(s): James A. Mason Source: Journal of Research in Music Education, Vol. 8, No. 1 (Spring, 1960), pp. 31-38 Published by: MENC: The National Association for Music Education Stable URL: http://www.jstor.org/stable/3344235 Accessed: 05/02/2009 06:15 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=menc. 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. MENC: The National Association for Music Education is collaborating with JSTOR to digitize, preserve and http://www.jstor.org

Comparisonof Solo and EnsemblePerformances with Referenceto Pythagorean,Just, and Equi-TemperedIntonations JAMES A. MASON AND PROBLEM I. INTRODUCTION ANY METHODS of intervallic division of the octave for purposes of melodic and harmonic treatments have been developed. From these methods have come three theoretical and practical standards of intonation for use in contemporaryWestern music, (1) Pythagorean, (2) just, and (3) equitempered. Pythagorean intonation.-This system of intonation derives all notes from the interval of the perfect fifth. For example, the major third is the fourth fifth above a predetermined tone reduced to the proper octave.1 Just intonation.-This system of tuning in effect undertakes to make use of all perfect intervals of the harmonic series. It is a system of tuning based on true ratios of intervals, as opposed to equi-tempered tunings. Unlike the Pythagoreantemperament,intervalsare derived not only from the perfect fifth, but also from the "pure"third. An occurrence of a new key requires the notes to be transformedto a new tonality. "This requires some fifty separate tones within a single octave for satisfactory accommodationsto all keys."2 1John Redfield, Music a Science and an Art (New York: Tudor,1937), p. 184. 2Donald W. Stauffer, Intonation Deficiencies of Wind Instruments in Ensemble (Washington D. C.: The CatholicUniversityof America Press,1954), p. 10. 31 Equi- tempered intonation. - The equi-temperedscale is a division of the octave interval into twelve equal semitones. In justification of the resulting distortion of every interval except that of the octave, the following arguments have been advanced: (1) Any group of human beings using imperfectmeans (instruments)for tone production must have a common point of understandingin the realmof scale pitches,so that artistic unity may be better achieved in an environmentof complexkey relationshipsand modulations. (2) The very act of building,tuning, and playing a musical instrument requires that there be one fixed pitch for every chromatic tone to avoid impossiblecomplexities. (3) In orderto bring togetherin ensemble the various unavoidableand at times opposing differencesof the intervaltuning of various instruments,a singlecommonstandardof pitch should be understoodby each player so that he may more intelligentlydirect his effort of humoringthe pitch, especiallywhen the ear is confused by other circumstances.3 Review of Pertinent Investigations In spite of the reasons cited and the extant cultural conditioning for equal temperament,there are musicians who feel it to be objectionable, and they 8Stauffer,

prefer using an unequal temperament harmonic series, few musicians have ever heard it and even fewerhave ever in their playing.4 of practiced it.9 Revesz has reportedthat players certain instruments,primarily those of Furthermore, Barbour points out the string choir and the human voice, that brass instrumentsmake use of exuse untemperedintonation when they tended portions of the harmonicseries. are not confined to performing with Therefore, performershave a natural inclinationto use just intonationin cerkeyboard instruments.5 The performanceof six professional tain keys.10 In reviewing the contemporarylitviolinists was investigated by Green. erature on tonality, Nickerson found Striking deviations from tempered inof the most informationhighly speculatervals were found, as well as considtive. The few pertinentexperimentsreerable agreementwith the intervals of not had in scale ported employed satisfactory the Pythagorean unaccompaanalytical methods.l1 Therefore, furnied performance.6 Nickerson conducted an experiment ther experimentationis needed to determine the extent to which Pythagousing twenty-four well-trained string rean, just, and equi-temperedsystems their He analyzed quartet players. solo and ensembleperformances,as re- are used in musical instruments' inlated to the three systems of intonation tonation anomalies. describedabove,and found the PythagStatement of Problem orean system in use typically for unThe purposeof this study was to deaccompanied melodies and ensemble termine: (1) if there is any consistent playing. of inHelmholtz, in conducting studies pattern differencesbetween the tonation of wind solo unaccompanied with choirs in England, found that those trained in solfeggio sang "pure" instrumentperformancesand wind enintervals (just intonation) when they semble performances; (2) if unaccomwere unaccompanied.8Williamson, on panied solo performancestend to prothe other hand, expressedthe idea that, duce Pythagorean, just, or equi-temwhile just intonationappeals to physi- pered intonation; (3) if ensemblepercists because of its relationshipto the formancestend to produce Pythagorean, just, or equi-temperedintonation. 4Stauffer, p. 7. 5Geza Revesz, The Psychology of Music, trans. G. De Courcy (Norman: University of Oklahoma Press, 1954), pp. 30-31. "Paul C. Green, "Violin Intonation," Journal of the AcousticalSociety of America,IX (1937), 43-44. 7James F. Nickerson, "Intonation of Solo and Ensemble Performance," Journal of the Acoustical Society of America,XXI (1949), 593. 'Herman L. Helmholtz, Sensations of Tone, trans. A. J. Ellis (London: Longman, Green and Co., 1912), p. 427. 9CharlesWilliamson, "Intonation in Musical Performance,"AmericanJournal of Physics, X (August, 942), 172. 'Oj.MurrayBarbour,Tuningand Temperament (East Lansing: Michigan State College Press, 1951), p. 200. njames F. Nickerson, "A Comparisonof Performancesof the Same Melody Played in Solo and in Ensemble with Reference to Equi-Tempered, Just, and PythagoreanIntonations" (unpublishedPh.D. dissertation,University of Minnesota, 1948), p. 49.

SOLO AND ENSEMBLE WOODWINDINTONATION EXPERIMENTAL DESIGN An experimentwas designed to seek further data concerning the nature of intonations used by performerson the instruments of the woodwind quintet. The investigation involved the members of two woodwindquintets. Recordings of their unaccompanied solo and ensemble performanceswere made. Description of Subjects Members of the woodwind quintets served as subjects. Each quintet was comprised of a flute, oboe, clarinet, horn, and bassoon. Both ensembles were associated with a university music department, one a faculty quintet and the other a student quintet. The faculty group consisted of well-trained performers, most of whom had had both professional and teaching experience on their respective instruments. The student group was comprised of schooled and experienced performers. However, the professional experience of the student group was limited. Selection of Music The music employed in this study was Ravel's "Pavane pour une infante defunte" transcribed for woodwind quintet by Lawrence Intravaia. This compositionwas selected because: (1) it presenteda typical playing situation; (2) it offereda satisfactory musical experience; (3) seven significantdiatonic pitches were presented in the melodic solo for each instrument; (4) the music was written in a harmonic rather than a polyphonic style; (5) it had a slow tempo (quarter note = 66); (6) modulationwas kept at a minimum.12 "Authorities maintain that a new tonality changes the dimension of the notes in unequal temperament.Stauffer,p. 10. Apparatus in this experiment utilized Apparatus included (1) a chromatic stroboscope (Stroboconn), an electronic device for rapid and accurate visual measurements of sound frequencies to within one hundredth part of one equi-tempered semitone; (2) a Strobotuner, a simple stroboscope for analyzing visually one tone at a time (calibrated to A-440 and used in this experiment for tuning the woodwind quintet instruments); (3) two Ampex tape recorders (Models 600 and 600Y), an Ampex amplifier and speaker (Model A692) and an Altec (No. 21 "Lip-stick") microphone for recording master tapes and for editing and preparing tape loops. Other miscellaneous equipment included a metronometo establish tempo, a thermometerto check recordingroom temperature,an A-440 tape loop13 for periodically checking accuracy of analyzing apparatus,and tape splicing supplies. Procedures Subjects were prepared for the experiment by playing a series of warmup experiencesand individuallypracticing the experimental music. Care was taken to tune each instrument (A-440) as determinedby the Strobotuner.The performers were instructed to play as accurately and musically as possible. Tempo was establishedby a metronome prior to each recording. Lighting, ventilation, temperature, and room acoustics were satisfactory. A standard woodwind quintet seating arrangementwas used. "STheA-440 tape loop was prepared from the U. S. Bureau of Standardssignal.

Individual recordings of unaccompanied solo performanceswere made previous to recordings of the complete ensembles.Each quintet rehearsed the music in ensemble and performed it five times. During each of the five ensembleperformancesthe microphone was placed immediately adjacent to a differentinstrumentso that each instrument could be easily distinguishedfrom the rest when stroboscopic analyses were made. Significantpitches were selected representing intervals of the G major scale. The same pitches were used for both solo and ensembleanalyses. These pitches were taken from melodic sections of the composition. Tape loops were preparedfrom master tapes. These loops representedsections of solo and ensemble performances chosen for analyses. Each loop was played until all selected pitches were analyzed in plus or minus cents.14 TABLE1 QUINTET X: Instrument INTERVALLICCOMPARISONSOF SOLO AND ENSEMBLE PERFORMANCES Root Maj. 2nd Maj. 3rd Per. 4th Aug. 4th Per. 5th Maj. 6th Maj. 7th 0 200 400 500 600 700 900 1100 Frequency cents from the tonic Flute Oboe Clarinet Horn Bassoon S -2 175 378 575 679 901 1096 E 10 202 404 605 707 920 1108 S 10 214 425 512 710 912 1115 E 6 202 399 506 705 904 1102 S 5 207 403 500 702 900 1100 E 9 207 405 502 705 903 1101 S 0 196 396 500 700 900 1100 E 9 192 405 501 706 900 1094 S 15 202 418 601 711 900 1107 E E 99 195 195 399 399 591 591 705 705 895 895 1107 1107 III. RESULTS AND INTERPRETATIONS The data concerning the obtained els, Table 3; and (3) ensemble versus frequenciesof the experimentalpitches Pythagorean, just, and equi-tempered for both solo and ensemble perform- pitch levels, Table 4. The two quintets are referred to as ances are presented in the tables and are expressedin cents, as follows: (1) is the intervalbetweentwo tones havsolo versus ensemble pitch levels, Ta- ing1Aascent a basic frequency ratio the twelve-hunbles 1 and 2; (2) solo versus Pythagor- dredth root of two. (One one-hundredthof an ean, just, and equi-temperedpitch lev- equi-temperedsemitone.)

SOLOAND ENSEMBLEWOODWIND INTONATION TABLE2 OF SOLOAND ENSEMBLE COMPARISONS QUINTETY: INTERVALLIC PERFORMANCES Root Maj. 2nd Maj. 3rd Per. 4th Aug. 4th Per. 5th Maj. 6th Maj. 7th 0 200 400 500 600 700 900 1100 S 15 204 417 620 719 918 1120 E 16 212 416 618 713 917 1120 S 5 205 410 505 707 913 1118 E 8 203 408 501 708 911 1106 S 12 203 397 495 699 899 1103 E 12 206 415 511 705 905 1104 S 0 202 400 500 712 903 1101 E 15 206 410 507 715 910 1104 S 25 222 418 615 719 905 1112 E 42 224 426 617 729 910 1118 Instrument Frequency cents from the tonic Flute Oboe Clarinet Horn Bassoon X and Y; quintet X representing the faculty ensemble and quintet Y the student ensemble. In Table 1 and 2, S and E are used to representsolo and ensemble performances respectively. struments constructed to conform with the international standard tuning frequency. However, these instrumentalists often tune to an A of significantly higher frequency to attain brilliancy. A few performershave been known to Solo Versus Ensemble Performances have had their instruments built to a Tables 1 and 2 present the frequency higher frequency than A-440.15 Such data obtained from stroboscopic anal- practices have possibly conditioned yses of certain pitches as produced in woodwind quintet instrumentalists to both the solo and ensemble perform- a higher pitch standard. Data in Tables 1 and 2 reveal that ances of quintets X and Y. In spite of the ample warm-up peri- there are few if any consistent patterns ods allowed and the care taken by the of differences between unaccompanied performers in tuning to A-440, there solo and ensemble performances.Howwasa generaltendency on the part of all ever, the finding that differences do performers to play sharper than the exist, even if random in nature, conestablished pitch. Particularly notice- tradicts what Nickerson found with reable deviations were evidenced in the "Robert W. Young, "Why an International solo performancesof flute X, and horns Standard Frequency?" Journal of the X and Y. As a general rule, contem- AcousticalTuning Society of America; XXVII (1955), porary wind instrumentalists use in- 380.

TABLE 3 SOLO VERSUS PYTHAGOREAN, JUST, AND EQui-TEMPERED INTONATIONS Intervals Root Maj. 2nd Maj. 3rd Per. 4th Aug. 4th X Y X Y Fl. -2 15 -2 15 -2 15 Ob. 10 5 10 5 10 5 Instruments Cl. 5 12 5 12 5 12 Hn. 0 0 0 0 0 0 Bsn. 15 25 15 25 15 25 Fl. -29 0 -29 0 -25 4 Ob. 10 1 10 1 3 - 1 14 7 3 -4 C.3 -1 -8 -2 -8 -2 Bsn. -2 18 -2 18 Fl. -30 9 -8 31 -22 17 Ob. Cl. 2 -5. -11 39 17 24 11 25 3 10 -3 Hn. -12 -8 10 14 -4 0 Bsn. 10 10 32 32 18 18 Ob. 14 7 12 2 14 2 7 Cl. -3 Hn. 2 2 2 2 0 0 Fl. Bsn. 37 -11 8 3 -15 11 30 25 -25 1 20 15 Fl. -23 -23 -17 -21 19 -3 10 2 -1 10 0 12 17 5 8 10 -2 9 17 11 19 34 1 18 7 28 29 15 12 13 16 0 -.1 -3 16 19 0 3 -1 16 21 0 -7 Hn. -6 Bsn. -6 6 -10 Bsn. -3 5 10 8 32 -4 20 8 -7 27 12 30 15 15 0 18 3 -9 12 13 0 1 19 24 7 12 5 C.-10 7 9 -6 Hn. 5 5 -5 17 Ob. Cl. -14 0 22 17 -5 Ob. -2 2 2 12 Fl. Fl. 8 0 -3 Bsn. Maj. 7th -3 -17 C.0 Hn. Maj. 6th 5 Hn. Oh. Per. 5th Equi-Tempered Just Pythagorean

TABLE 4 ENSEMBLE VERSUS PYTHAGOREAN, JUST, AND EQUi-TEMPERED INTONATIONS Just Pythagorean Intervals Instruments Y X y X y 10 16 10 16 10 16 Gb. 6 8 6 8 6 8 Cl. 9 12 9 12 9 12 Hn. 9 15 9 15 9 15 9 42 9 42 9 42 Fl. Root Bsn. Maj. 2nd Maj. 3rd Per. 4th Fl. -2 Ob. -2 Cl. Per. 5th Maj. 6th Maj. 7th 8 -1 3 -2 8 -2 -1 2 3 2 2 12 2 3 7 6 Rn. -12 2 -12 2 -8 6 Bsn. -9 20 -9 20 -5 24 Fl. -4 8 18 30 Ob. -9 0 13 22 Cl. -3 7 19 Rn. -3 2 19 Bsn. -9 18 13 40 4 -1 16 8 29 5 15 24 5 10 -1 26 Gb. 8 3 8 3 6 1 Ci. 4 13 4 13 2 11 Rn. 3 9 3 9 1 7 -7 6 15 28 5 18 1 27 Fl. Aug. 4th Equi-Tempered X Bsn. -21 5 Fl. 5 11 5 11 7 13 Ob. 3 6 3 6 5 8 -9 17 Cl. 3 3 3 3 5 5 Rn. 4 13 4 13 6 15 Bsn. 3 27 3 27 5 29 Fl. 14 11 36 33 20 17 Gb. -2 5 20 27 4 11 CL. -3 19 21 3 5 26 0 10 -1 Hn. -6 4 16 Bsn. -11 4 11 26 Fl. -2 10 20 32 8 20 Ob. -8 -4 14 18 2 6 Cl. -9 -6 13 16 1 4 Hn. -16 -6 6 16 Bsn. -3 19 30 8 10 -5 4

gard to string quartets. While results of the string quartet study evince no significantintonationalchanges to conform to harmonicdemands,l6this study seems to indicate that woodwindquintet performancesare significantly affected by the harmonic structure of music. Quintet X deviated least from equitempered intonation, while quintet Y deviated least from Pythagoreanintonation. In the solo performances,the greatest departure occurred from the just system of intonation. Ensemble PerformancesVersus Pythagorean,Just and Equi-Tempered Intonations Solo Versus Pythagorean, Just, and Equi-TemperedIntonations Table 4 presents the frequencydeviTable 3 presents the frequencydevi- ations of ensemble performancesfrom ations of solo performancesfrom PythPythagorean, just, and equi-tempered agorean, just, and equi-tempered in- intonations. tonations. The comparativedata were Data in Table 4, like those in Table obtained from stroboscopicanalyses of reveal a significantlack of conformi3, the intervals. These intervals are idenin woodwindensembleperformances ty tified in the column on the left side of either to Pythagorean, just, or equithe table. To the right of the interval column appear the instruments and tempered intonations. An averageof the deviationsfrom all their corresponding deviations from and Pythagorean, just, equi-tempered systems of intonation in ensembleperintonations. These comparativedevia- formancescomparesfavorablywith the tions are presented in plus and minus findingsfor solo performances.Quintet X deviated least from equi-tempered cents. Data in Table 3 reveal a significant intonation, while quintet Y deviated lack of conformity in woodwind solo least from Pythagorean intonation. In performances either to Pythagroean, the ensemble performances,the greatjust, or equi-tempered intonations. est departure occurred from the just system of intonation. "Intonationof Solo and Ensemble "6Nickerson, Performance,"p. 594. Brigham Young University