CHARACTERIZATION OF INTONATION IN CARNATIC MUSIC BY PARAMETRIZING PITCH HISTOGRAMS Gopala K. Koduri1, Joan Serra`2, and Xavier Serra1 1 Music Technology Group, Universitat Pompeu Fabra, Barcelona, Spain. 2 Artificial Intelligence Research Institute (IIIA-CSIC), Bellaterra, Barcelona, Spain. [email protected], [email protected], [email protected] ABSTRACT on the artist and the raaga [8, 15]. The study of intona- tion differs from that of tuning in its fundamental empha- Intonation is an important concept in Carnatic music that sis. When we talk about tuning we refer to the discrete is characteristic of a raaga, and intrinsic to the musical ex- frequencies with which we tune an instrument, thus it is pression of a performer. In this paper we approach the de- more of a theoretical concept than the one of intonation, scription of intonation from a computational perspective, with which we focus in the pitches used during a perfor- obtaining a compact representation of the pitch track of a mance. The two concepts are basically the same when we recording. First, we extract pitch contours from automat- study instruments that can only produce a fixed set of dis- ically selected voice segments. Then, we obtain a a pitch crete frequencies, like the piano. histogram of its full pitch-range, normalized by the tonic Given than in Indian music there is basically no instru- frequency, from which each prominent peak is automati- ment with fixed frequencies (the harmonium is an impor- cally labelled and parametrized. We validate such parame- tant exception), in practice tuning and intonation can be trization by considering an explorative classification task: considered the same. Here we will maintain the terms, tun- three raagas are disambiguated using the characterization ing or intonation, used by the different studies. of a single peak (a task that would seriously challenge a Krishnaswamy [7] discusses various tuning studies in more na¨ıve parametrization). Results show consistent im- the context of Carnatic music, proposing a hybrid tuning provements for this particular task. Furthermore, we per- scheme based simple frequency ratios plus various tun- form a qualitative assessment on a larger collection of raa- ing systems, specially equal temperament. His work also gas, showing the discriminative power of the entire repre- points out the lack of empirical evidence thus far. Recently, sentation. The proposed generic parametrization of the in- Serra` et al. [12] have shown important quantitative differ- tonation histogram should be useful for musically relevant ences between the tuning systems in modern Carnatic and tasks such as performer and instrument characterization. Hindustani 2 musics. In particular, they show that Carnatic music follows a tuning system which is very close to just- intonation, whereas Hindustani music follows a tuning sys- 1. INTRODUCTION tem which tends to be more equi-tempered. Although there Carnatic music is the south Indian art music tradition and are several studies on intonation and tuning in Indian mu- Raaga is the melodic framework on which Indian art mu- sic, the emphasis so far has been in the interpretation of sic thrives. The intonation of a single swara 1 can be dif- ancient texts rather than on analysing real musical prac- ferent due to the melodic context established by different tise(see [7, 8, 12] and references therein). raagas. Therefore, to understand and model Carnatic music In a study that was conducted with Hindustani music computationally, intonation analysis becomes a fundamen- performances [8], pitch consistency is shown to be highly tal step. dependent on the nature of gamaka 3 usage. The swaras We define intonation as the pitches used by a performer sung with gamakas were often found to have a greater vari- in a given musical piece. From this definition our approach ance within and across the performances, and across dif- will consider a performance of a piece as our intonation ferent performers. Furthermore, the less dissonant swaras unit. In Carnatic music practice, it is known that the in- were also found to have greater variance. However, it was tonation of a given swara can vary significantly depending noted that across the performances of the same raaga by a given performer, this variance in intonation was minor. 1 A swara-sthana is a frequency region which indicates the note and its The same work concludes that the swaras used in the an- allowed intonation in different melodic contexts. alyzed performances do not strictly adhere to either just- intonation or equal-tempered tuning systems. Belle et al [1] Permission to make digital or hard copies of all or part of this work for use the intonation information of swaras to classify Hin- personal or classroom use is granted without fee provided that copies are dustani raagas. Another recent experiment conducted with not made or distributed for profit or commercial advantage and that copies 2 The north Indian art music tradition. bear this notice and the full citation on the first page. 3 Gamakas are a class of short melodic movements sung around and c 2012 International Society for Music Information Retrieval. between swaras. Carnatic music performances draws similar conclusions 2.1 Segmentation about the variance in intonation [15]. However, the method- Cleaning the data is a crucial pre-processing step for our ology employed in these experiments cannot easily be scaled experiments. All the Carnatic vocal performances are ac- to a larger set of recordings due to the human involvement companied by a violin and one or more percussion instru- at several phases of the study, primarily in cleaning the data ments. We just use the sections in which the voice is alone and the pitch tracks, and also in interpreting of the obser- or very prominent. In order to do this automatically, we vations made. train an SVM model [5] on 300 minutes of audio data, Approaches to tuning analysis of real musical practise equally split between vocal, violin and percussion sections usually follow a so-called ‘stable region’ approach, in which of 10 seconds each. The features extracted from the audio only stable frequency regions are considered for the anal- and used in the classification task are [4]: Mel-frequency ysis (cf. [12]). However, it is known [14] that the most cepstral coefficients, pitch confidence, spectral flatness, portion of the performance in Carnatic music is gamaka- spectral flux, spectral rms, spectral rolloff, spectral strong- embellished. Since gamakas are characteristic to a given peak, zero crossing rate and tristimulus. This method scores raaga, such an approach is not suitable to understand the an accuracy of 96% in a 10-fold cross validation test. crucial information provided by them. So far, the tuning analysis was approached to explain the interval positions 2.2 F0 Analysis of Carnatic music with one of the known tuning methods like just-intonation or equal-temperament. But consider- With the segmentation module in place, we minimize to ing that these intervals are prone to be influenced by factors a large extent pitch errors due to the interfering accompa- like raaga, performer [8] and instrument [7], computational nying instruments. However, there is a significant number analysis of swara intonation for different raagas, artists and of the obtained voice segments in which the violinist fills instruments has much more relevance to the Carnatic mu- short pauses or in which the violin is present in the back- sic tradition. ground, mimicing the vocalist very closely with a small time lag. This is one of the main problems we encountered when using pitch tracking algorithms like YIN [3], since the violin was also being tracked in quite a number of por- 2. HISTOGRAM PEAK PARAMETRIZATION tions. The solution has been to extract the predominant melody [10] using a multi-pitch analysis approach. Then, In this contribution we propose a methodology based on given that the pitch accuracy of YIN is better, we com- histogram peak parametrization that helps to describe the pare the pitch obtained from the multi-pitch analysis with intonation of a given recording by characterizing the distri- YIN at each time frame, and we only keep the pitch from bution of pitch values around each swara. From the obser- those frames where both methods agree within a threshold. vations made by Krishnaswamy [7] and Subramanian [14], Though it is a computationally intensive step, this helps in it is apparent that steady swaras only tell us part of the obtaining clean pitch tracks, free of f0-estimation and oc- story that goes with a given Carnatic music performance. tave errors. The frequencies are then converted to cents and The gamaka-embellished swaras pose a difficult challenge normalized with the tonic frequency obtained using [11]. for automatic swara identification. Therefore, alternative The octave information is retained. means of deriving meaningful information about the into- nation of swaras becomes important. The gamakas and the 2.3 Histogram Computation role of a swara are prone to influence the aggregate dis- As Bozkurt et al. [2] point out, there is a trade-off in choos- tribution of a swara. We believe that this information can ing the bin resolution of a pitch histogram. A good bin res- be derived by parametrizing the distribution around each olution keeps the precision high, but significantly affects swara. the peak detection accuracy. However, unlike Turkish- Our intonation description method can be broadly di- maqam music where the octave is divided into 53 Holdrian vided into six steps. In the first step, the prominently vocal commas, Carnatic music uses roughly 12 swaras [13]. segments of each performance are extracted using a trained Hence, in this context, choosing a finer bin width is not support vector machine (SVM) model. In the second step, as much a problem as it is in Turkish-maqam music.