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Page 00000001 WHY DOES THE ACOUSTIC SPACE OF CHURCHES EXALT GREGORIAN CHANT? A FIRST STEP TOWARDS ACOUSTIC CHARACTERIZATION BY MEANS OF THE MODULATION TRANSFER FUNCTION Renzo Vitale Department of Electrical Engineering University of L'Aquila - Italy Conservatorio "A. Casella" - L'Aquila firstname.lastname@example.org Raffaele Pisani, Paolo Onali Studio di Ingegneria Acustica Via Cavalieri di Vitt. Veneto Rivoli (TO) - Italy email@example.com Arianna Astolfi Department of Energy Technologies Politecnico di Torino Italy firstname.lastname@example.org ABSTRACT The positive success of a concert, of either classical or contemporary music, depends not only on the environment in which it takes place but also on the intrinsic structural characteristics of the performed musical piece (tempo, articulation, pitch, ensemble, etc.). All this suggests the need to tackle a scientific research in order to analyse the effects produced by interactions between acoustic space characteristics and the musical content there diffused, so that it is possible to predict the good success of a concert beforehand. It was decided to start with churches where, particularly in Italy, the performance of contemporary as well as classical music is becoming more frequent. Gregorian chant was choosen as the music genre, since it represents an exemplifying approach. Finding the reasons why Gregorian chant sounds properly in the acoustic spaces of churches, would help to develop an analysis methodology that could be extended to more complex musical phenomena. The results of an acoustics characterization of the chant and the environment are shown with particular reference to the reduction of the modulation index. It was observed that high reverberation times which exceed 5 seconds and especially at low frequencies, which is typical of Gothic cathedrals, act as a brake on the development of the chant, imposing a longer duration of the single notes and, consequently, a rhythmical expansion. As far as compatibility with the acoustic space is concerned, extracts from neumatic style pieces were used, whose characteristics have shown a reverberation influence both on the intensity variations and on the duration of the notes. The results reveal that reverberation acts as a low-pass filter on the intensity variations and as an element of disturbance for the correct intonation of the notes. 1. INTRODUCTION In a different way from verbal communication, whose main necessity lies in the correct comprehension of a transmitted message, there are two principal demands in Gregorian chant that need to be satisfied: performing, chant is a means of exalting words, therefore the acoustic space in which it takes place has to be comfortable; aesthetic-spiritual, in the sense that Gregorian chant is a prayer, and its aim is to raise the human soul towards God. These remarks clearly indicate how a large and reasonably reverberated environment (which is typical of a church) could favour ideas of mysticism, in function of the most intimate features of the chant itself. Furthermore, reverberation imposes a forced rest in correspondence to the end of each musical period thus contributing to allowing the singers to interiorize the profound meaning of the words they are pronouncing. It is important to underline that Gregorian chant consists of "words" that do not have the same value as verbal communication: it is not necessary that the words that are sung are clearly intelligible, as the main interlocutor is not a human being. Moreover, Gregorian chant does not have the particular characteristics of instrumental or virtuosistical vocal music, where a sequence of notes can be even faster. A sufficient intelligibility is only required among the choir singers, since when they are praying, there is no assembly: prayer is only for the monks. Having said this, the question arises whether it is the acoustics of the space where monks usually pray by singing that has determined the executive approach, or whether the aesthetics of Gregorian chant originated in other contests and was adapted to the acoustical characteristics of the space where it is expressed. A plausible answer to this question is suggested by the observation that the singers did not decide a priori how and where to sing, they sang in churches adjusting their performance and their mos canendi to the local acoustics. 2. THE STRUCTURE OF GREGORIAN CHANT Gregorian chant style can be divided into three main categories: syllabic (one note for each syllable), neumatic (several notes for each syllable), melismatic (up to 40 notes for one syllable) . The musical period of Gregorian chant is normally built like an arch: there is an elevation, a rest on the achieved pitch (phraseological accent) and a descent. The arched melodic line extends for an interval of an octave. This period can be varied in different ways; one of these suppresses the initial descending part, in order to adapt the melody to a short text. In another variation, the melody, coming from above, descends towards a rest point below the final
Page 00000002 point, and rises again to end on the final point. Another less common variation is called circular. Here the melody oscillates around a central note (generally the final note). Very often in a complete melody with rises, rests and descents, the rise is short and not very important, while the more extensive is gradual and calm. This probably happens as a consequence of the acoustics of churches. In the elevation stage, there is a frequency shift upwards and for singers, in the presence of reverberation, it is easier to achieve intonation since the sound, still present in the environment, presents a safe reference to ascend to. The same consideration can be made when the same note is repeated. Vice versa, in correspondence to a descent, the reverberation tail represents an obstacle for the correct intonation of the intervals; a tendency to sing descending intervals in an ascending manner has in fact been noted. In the descending stage the tonal base is unsteady since the reverberation extends to the just sung note, influencing the subsequent one. All this provokes an unconscious expansion of the temporal course that is useful to adjust the intonation. Ferretti defines the Gregorian period as a melodic unity of rather considerable proportions . He divides the period into phrases, and the phrases into half phrases or half members. The half phrases contain two or three "inciso". These observations lead to the definition of sufficiently long periods in which the phrasing is repeated. The afore-mentioned repetitions represent the longest periods or rather the lowest frequencies of a modulated signal both in amplitude and in frequency. 3. ANALYSIS PROCEDURE The first step for a compatibility analysis between Gregorian chant and the acoustics of the churches consists in determining the Modulation Transfer Function (MTF) in some points of a specifically selected church. The limited space where the monks sing, that is, the choir area of a cathedral, was in particular referred to. The Modulation Transfer Function, already used in other relevant music papers [3, 4], was found to provide the best framework to describe temporal intensity variations and the frequency variations, since phrasing melodic structure is demodulated by octave filter banks, covering the 125 to 8000 Hz range. The MTF represents the reduction factor of the modulation index of a signal as a function of the modulation frequency. It ranges from 0 to 1. A comparison of the envelope spectra, obtained directly from the source, with the corresponding spectra via a transmission path gives the reduction in fluctuations due to the path and leads to the MTF. Experiments were carried out in the Casamari Cathedral, which is part of a Cistercian Abbey situated in the heart of Italy. Beginning from the impulse response measurements the reverberation time and MTF were determined . The in situ investigation was preceded by a determination of the modulation indexes of both the anechoic singing and speaking voices. The speaking voices were analysed by checking with literature values . The MTF was determined for all cells of the matrix of seven octave bands and 27 modulation frequencies; in this way an acceptability frequency mask was obtained, that was compared with the modulation index values of the Gregorian chant and speaking voices. The modulation depth of the speaking voices was determined (from audio recordings of national television news speakers) in order to verify our analysis procedure, since spoken word has a faster rhythmical articulation that is less suitable for a highly reverberated environment, such as a cathedral. The Gregorian chant signal was acquired from some famous recordings. The phonic material that was used was extracted from CD's recorded in controlled acoustic conditions with microphones placed in the near field. 3.1. Intensity modulation The IEC 60268-16  and ANSI S3.5  standards use MTF for an objective estimation of speech intelligibility in a limited reverberant space. The procedures described in the standards require the determination of the reduction of the modulation index for some modulating frequencies that are typical of speech (from 0,63 Hz to 12,5 Hz for third-octave bands). In order to apply the same procedures to the present study, it was necessary to go beyond the analytical approaches used so far . A Matlab program was developed that, starting from the electroacoustic signal of the Gregorian chant filtered through octave bands, calculates the intensity of each band and executes the analysis of third octave bands, in the 0,08-31,5 Hz frequency range. Fig. 1 illustrates the modulation intensity level obtained from the analysis of the Gregorian chant filtered in the 250, 1000 and 4000 Hz octave bands. Fig. 2 shows, as a comparison, the average modulation level of television speakers' voices filtered in the same frequencies. 10,0250 Hz 1000 Hz - 4000 Hz - - -250 Hz - 1000 Hz - - 4000 Hz Figure 1. Average envelope spectra of the ChantModulation level versus 1/3 octave bands for the octave bands centered at 250Hz, 1000Hz and 4000 Hz. It is possible to observe that the speech syllabic rhythm, which is characterized by the occurrence of formants, has a maximum between 4 and 5 Hz (values that correspond to those in literature), while the Gregorian chant presents a maximum below 1,25 Hz (with the
Page 00000003 exception of the 250 Hz) which signifies the predominant presence of periodicity both in the musical phrase and in the "inciso". The contribution of the low frequencies of the chant, compared to the voice, can also be observed. 10,0 - - - 250 Hz -1000 Hz - 4000 Hz 5,0 So,o0 0 N 0 N X * ON, /st 1-11 d ONI ININ I MIRX 1* 1 X N X Vx -1,0", 11, M& * ~RX IN S -s,o 0'UN4 S-10,0o -15,0 -20,0 C CD 6D CD - C Frequency [Hz] Figure 2. Average envelope spectra of the speech - Modulation level versus 1/3 octave bands for the octave bands centered at 250Hz, 1000Hz and 4000Hz. In the chant intensity spectra, in addition to the musical periodicity that mostly corresponds to the movement of inspiration (1,25 Hz), there is another periodicity represented by words (6,3 Hz); this component becomes very evident in syllabic compositions and coincides with the articulation of the text. 3.2. Frequency modulation From a musical point a view, frequency modulation should be intended as a sequence of notes. Fig. 3 shows the tetragram notation with the neuma for a single period of an analyzed piece, and its relative transcription in frequency which was made possible thanks to a rigorous pitch detection study. Re 138C Do 120C f sol 70 I IIII Si 1110 Do10 La#1- -- Sib 96 8S --# 8 -C Sol 702 0 Fa# 1 Fa 61 -4 4- 4- 4 I I I I The duration of each note is expressed by the length of the segment and the ordinate position expresses the frequency value. The Pythagorean degrees are traced in the same graphic (in reference to the rules of the papal bull De vita et honestate clericorum, 1324). Music signal filtering by octave band filters can be interpreted as a transformation of the amplitude domain of a sound structure that contains information on the amplitude, frequency and time domain. Larger filters (octaves) mainly permit the voice formant structure to be more clearly distinguished, while narrower filters allow a better note separation. With reference to the analyzed signal, which is essentially a singing voice, it is sufficient to consider the harmonic (fundamental frequencies) and formant (syllable) structures. It is important to point out that the considered case is relative to a syllabic style Gregorian fragment, the most unfavourable regarding the duration of the notes: if a different style were to be considered (neumatic or melismatic) a longer average note duration would be observed and a consequent increase in the modulation depth level towards lower frequencies, a condition that further strengthens the results of Fig. 1. The importance of lower frequency bands in Gregorian chant, compared to speech can yet again be confirmed. 3.3. Calculation of the Modulation index The MTF was determined in the church together with the modulation index for the Gregorian chant and the speaking voice. In the first case, Schroeder's method was used , applying the following equation: m(e-2no. r(t)dt fo r(t)dt (1) where r(t) is the squared impulse response and F is the modulation frequency. In the second case, the block diagram shown in Fig. 4 was adopted. ma(F) - U 15 16 17 18 1 Figura 4. Block diagram to determine the Gregorian chant modulation index. The input signal x(t) consisted of an anechoic recording of Gregorian chant. After an octave-band filtering (1), there a squaring was carried out (2). In order to calibrate the signal, a spectrum analyser (LD 2900) through a 100 Hz sine wave was used (3 - 4), which becomes 1 kHz after block 5. The signal that comes from block 5 presents very low frequency components, therefore a frequency conversion was made by multiplying by a factor of 10. The spectrum analyser returns the envelope spectrum of x(t) (6). The modulation index was calculated as: Agnus red6mit ov-es: Christus innocens Pa- tri Figure 3. Pitch and duration of neumas in a fragment of Victimae Paschali Laudes.
Page 00000004 ma (F)= 10 20~ J (2) where a stands for the anechoic element and XfF for the generic element of the matrix represented in Figs. 5-6. Lref is the reference level that was used to calibrate the octave band level of the analyser. 4. RESULTS AND CONCLUSIONS Singing voices require different intelligibility requirements from speech. Gregorian chant is an example of vocal expression that originated in an environment acoustically adverse to speech comprehension. The compatibility between this singing expression and the acoustics of churches has been demonstrated, starting from an analysis of the MTF that was measured in a cathedral and adjusted to the frequency bands involved in Gregorian chant (range of modulation frequencies from 0,08 Hz to 31,5 Hz). Freq.[Hz] 125 250 500 1000 2000 4000 8000 0,10 0 I 0,13 >0.75 0,16 >0,7 0,20 30 0I l 8l 0,25 073 1,|| 0 0i84 0,32 0731 o8 ^ 0|81 0,40alues higher than 0,5 and 0,75, and Gregorian 0,50 06 01 080 0,63 0,72 0,91080 0,80 0,73 0,73 0,2571 2,50 1...........0....... 1,00 0;85 6,30 0980 31,5( Figure 6. Acceptability field for the choir area with MTF values higher than 0,5 and 0,75, and speech modulation index values. Fig. 5 sums up the most important results: it illustrates the MTF values that were measured in the choir area of the Casamari cathedral and its acceptability areas (reference values of 0,5 and 0,75) compared with the Gregorian chant modulation indexes, arbitrarily assuming a modulation index of 0.7, which corresponds to a modulation level of -3 dB, as a threshold level (Figs. 1 - 2). The modulation depths of the chant is high to the lowest modulation frequencies; these frequencies are less influenced by the acoustical characteristics of the church. Fig. 6 illustrates the MTF values compared with the modulation indexes of the speaking voice. The highest modulation depths of the voices were found to be almost in the same frequency bands as the chant, but at higher ranges of modulation frequencies. This frequency range results to be less compatible with the acoustical characteristics of the choir area of the church. 5. FURTHER APPLICATIONS The methodology developed to face the previously mentioned problems presents interesting investigation and application margins: in addition to the research in the musical choir field , it could be used to obtain an objective index or parameter that is able to define the compatibility of a musical event (polyphonic or instrumental) with the environment being used, thus obtaining a further aid for the evaluation and designing of places dedicated to music. 6. REFERENCES  Reese, G. La musica nel medioevo. Rusconi Ed., Milano, 1990.  Ferretti, P. Estetica gregoriana, o trattato delle forme musicali del canto gregoriano. 1934.  Naylor, G.M., Craik, R.J.M. "The effects of level difference and musical texture on ease of ensemble", Acustica 65, 1988.  Vitale, R. Analisi elettroacustica del canto gregoriano: problemi di intonazione e di stile. Master Thesis, University of L'Aquila, 2004.  Schroeder, M. R. "Modulation Transfer Function: definition and measurement". Acustica 49, 1981.  CEI IEC Nr. 60268-16. "Sound system equipment - Pt. 16: Objective rating of speech intelligibility by speech transm. index", 1998.  ANSI S3.5. "Method for calculation of the speech intelligibility index", 1997.  Steeneken, H., Houtgast, T. "The temporal envelope spectrum of speech and its significance in room acoustics", Proceedings of the 11 Int. Acoustic Conference, Paris, 1983.  Ternstr6m, S. "Physical and acoustic factors that interact with the singer to produce the choral sound", Journal of Voice, 5 (2), 1991.