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From Western Sheet Music to Harmonygrams

The traditional notation of Georgian vocal music in Western 5-line staff notation, which is still the standard practice in ethnomusicology,  presents various challenges, some of which have been the subject of scholarly discussion for quite some time. First, it is well known that the 12-tone equal temperament (12-TET) tuning system, on which the western 5-line staff notation is based, is inappropriate for capturing the traditional tuning of Georgian music (Tsereteli and Veshapidze, 2014, 2015; Scherbaum et al., 2020, 2022,2023). It can, for example, introduce artificial semi-tones into the transcribed music. Western notation also fails to do justice to the importance of the harmonic aspects of traditional Georgian vocal music, which are for example expressed in the way how singers interact harmonically. Traditional Georgian singers are well known for their remarkable ability to rapidly adjust their intonation, often to achieve pure harmonic intervals at particular locations in a song. This phenomenon has already been described qualitatively by Siegfried Nadel nearly a hundred years ago (Nadel, 1933). Recently it was also investigated in detail quantitatively in an acoustic analysis by Scherbaum and Müller (2023).

For traditional Georgian singers, the perception of the harmonic content of a song, sometimes referred to as ‘vertical thinking’, is an intuitive and natural process which is favored through the mechanism of oral transmission, through many years of practice and continuous exposure to the music. For singers who are used to learning songs from Western 5-line staff notation, rapidly recognizing chords is often a major challenge. Part of the problem is related to what we actually see when we look at a score. Independent of our score reading skills, I  conjecture that melodic information is the first thing we all perceive. Even if we can’t read scores at all, we can recognize the rough melody contours from the ups and downs of the notes in the individual staffs. The determination of the exact pitches takes already some efforts, because we first have to identify the kind of clef of each system and the number and type of accidentals.  But when it comes to deciphering the harmonies we have to think even harder, because we have to scan the score sequentially and determine the harmony for each harmonic state one by one. 

So in terms of Daniel Kahnemann’s model of human rationality (Kahnemann, 2012), the recognition of melodies from a score would, at least for experienced score readers, belong to the fast category while the perception of harmonies belongs to the slow category of thinking. That’s a pity, because for singing practice and music analysis, it would be very convenient to access the harmonic information about a piece of music at the same speed and ease as the melodic information. And that’s exactly what the Hartmonygram concept  tries to solve.

The Harmonygram Concept

The proposed solution, Harmonygrams (Scherbaum and Mzhavanadze, 2024; video (20 min) of the presentation in Bologna: https://youtu.be/8pWI9z_SSUM), addresses this by integrating melodic and harmonic aspects of a song into a single, intuitive graph. Individual voices are represented as note sequences in  “Global Notation” (Killick, 2020). Subsequently, the vertical spaces between the individual voices are color-coded to indicate the corresponding harmonic intervals. The interval between the bass voice (which is always the lowest voice in the investigated corpus) and the highest voice is portrayed as a vertical mirror image, with the note trajectory of the bass voice serving as the reference curve. A 1-min video illustrates the individual conceptual processing steps.

Harmonygram of the Gurian song Batonebo Sabodisho. Click on image to enlarge it.

Harmonygrams  allow users with minimal training to grasp both individual melodies and harmonies more or less effortlessly. Most importantly, Harmonygrams contain essentially the same information as the corresponding musical scores, but offer several additional noteworthy features:

  • Harmonygrams can be generated computationally from traditional musical scores. 
  • Harmonygrams (as well as Melodygrams)  allow for algorithmic correction of some of the tuning system distortions happening during the transcription into Western notation. For details and examples see document A below and Scherbaum et al. (2024). 
  • The perception of the whole chord progression structure of a song becomes easily possible with Harmonygrams, even for lay people, since it all boils down to recognizing simple visual patterns. 
  • The simplicity of Harmonygrams eliminates the need to read complex Western scores, making them an accessible yet information-rich tool for singing practice, providing a bridge for both novices and experts.
  • Harmonygrams are not restricted to musical scores, but can also be calculated directly from the pitch trajectories of audio signals and used in the analysis of ethnomusicological field recordings (Mzhavanadze und Scherbaum, 2020; Scherbaum and Mzhavanadze, 2020).

The following two documents contain further information on the concept of Harmonygrams and on the use of Harmonygrams in singing practice .  

Harmonygrams: A Graphical Notation System for Three-Voiced Music Facilitating the Perception of Harmonies. 
This document describes the theoretical basis for the presentation of Harmonygrams at the Eighth International Conference on Analytical Approaches to World Musics (AAWM 2024) June 10-14, 2024, in Bologna (Scherbaum and Mzhavavandze, 2024). It explains in technical terms what Harmonygrams are, how they are generated, and how they can be adapted to different tuning systems. 

Harmonygrams in practical exercises. 
This document is intended as a "starting aid" for the practical use of Harmonygrams in singing practice, e.g. with the song collection below. It contains my personal notes and exercises on selected songs in the form of a logbook. These give examples of what I have seen from the 'Harmonygram perspective' in individual songs, or what I have used them for. These can be quite trivial things, but they seemed interesting to me, at least at a certain point in time.  I would like to emphasize that this part does neither claim to be scientific nor complete. Rather, it is intended as stimulation for the use of Harmonygrams in your own work.

Yet another Georgian song collection

Below you will find a collection of 44 selected Georgian songs  in various Harmonygram representations, all of which are explained in the two documents  above. This material is aimed at anyone who is interested in traditional Georgian vocal music and would like to learn more about the harmonic structure of these songs and/or learn these songs without the use of sheet music.

Despite all my personal reservations about using Western notation to represent traditional Georgian vocal music, I have decided to add a scan of the respective scores to the material collection.  Since digital sheet music is the starting point for the creation of all visualizations, this is done for the sake of completeness, but can also be useful for comparison with existing song collections and for identifying the version of a song used.  With regard to the layout of the scores, which  I created in Musescore, it should be noted that for technical reasons, namely to make the calculation of the Melodygrams and Harmonygrams as simple and error-free as possible, each voice was written on a separate system and the corresponding text was entered for each note. In other words, the automatic completion of song texts with hyphens (especially for ornaments), which many notation programs allow, was deliberately omitted in order to increase the legibility of the song texts in the Melodygram and Harmonygram representation. In addition, to standardize the Latin spelling of the Georgian texts, all accent marks were omitted, as these were treated very differently in the freely available transcriptions and the effort involved in standardizing them would have been too great. In addition, punctuation marks were omitted and all texts were written in lower case.

Regarding the display of Melodygrams and Harmonygrams, I have generated two display modes. First a single-line display and second  a display in which the song is divided into shorter phrases that are arranged vertically one below the other. Both forms of presentation have advantages and disadvantages.  For short songs, I prefer the horizontal, single-line display, as it allows one to see the entire song "in one piece", but for longer songs this display reaches its limits. 

List of songs:  Alilo (2),  Aragvis Piruli, Batonebis Nanina, Batonebis Simghera, Batonebo (2) Deda Mogikvdesa, Deli deli, Dghres Saghvtoman Madlman, Didavoi Nana, Dideba, Erekles Mravalzhamier, Es Akvani Kharatuli, Gighini, Ghmerti Upali, Heyamoli, Ia Patonepi, Iavnana, Ima Mtaze, Jvaris Tsinasa, Jvarsa Shensa, Kriste Aghdga, Lale, Lazare, Lazhgvash, Lile, Maspindzelsa, Misdevs Mela Lomsa, Mze Shina, Nana (2), Nanina, Naninada Batonebo, Ortameluri, Samshoblo, Sedeko, Shen Khar Venakhi, Sisatura, Thebrone, Tsmindao Ghmerto, Va Giorko, Varado, Zruni Glola.

The number of songs provided is limited by the maximum size of the PDF files that can be uploaded on this website.  Please feel free tocontact me in case you have questions or  comments or are interested in particular songs which are not provided here (but may be in my archive).

Finally, I want to emphasize that  I do not guarantee the accuracy of the scores (some of which were rewritten from scores freely available in the internet) and/or  lyrics!  All material to which I hold the copyright is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. This means that you may use it for pretty much anything, except  for making money .  Enjoy!

Scores

Melodygrams in 12-TET representation  (single-line display)

Melodygrams in 12-TET representation

Harmonygrams in 12-TET representation (single-line display)

Harmonygrams in 12-TET representation

Harmonygrams for pure intervals only in 12-TET representation (single-line display)

Harmonygrams for pure intervals only in 12-TET representation 

Melodygrams in Scale-Degree-Index (SDI) representation (single-line display)

Melodygrams in Scale-Degree-Index (SDI) representation

Harmonygrams in Scale-Degree-Index (SDI) representation (single-line display)

Harmonygrams in Scale-Degree-Index (SDI) representation

Harmonygrams for pure intervals only in Scale-Degree-Index (SDI) representation (single-line display)

Harmonygrams for pure intervals only in Scale-Degree-Index (SDI) representation

References

Kahnemann, Daniel. (2012). Thinking, fast and slow. Farrar, Straus and Giroux. 512 pp., ISBN 9780141033570.

Killick, Andrew. (2020). “Global Notation as a Tool for Cross-Cultural and Comparative Music Analysis.” Analytical Approaches to World Music 8(2): 235-279. Retrieved from: https://journal.iftawm.org/wp-content/uploads/2022/02/Killick_AAWM_Vol_8_2.pdf

Mzhavanadze, Nana and Scherbaum, Frank. (2020). Svan Funeral Dirges (Zär): Musicological Analysis, Musicologist, 4, 2, 168-197, DOI: 10.33906/musicologist.782185.  Retrieved from: https://dergipark.org.tr/en/download/article-file/1246319

Nadel, Siegfrid F. (1933). Georgische Gesänge (Georgian Songs). Lautabt., Leipzig: Harrassowitz in Komm.

Scherbaum, Frank and Mzhavanadze, Nana. (2020). "Svan Funeral Dirges (Zär): Musical Acoustical Analysis of a New Collection of Field Recordings". Musicologist, 4(2): 138–167. Retrieved from https://dergipark.org.tr/en/download/article-file/1246012

Scherbaum, Frank; Mzhavanadze; Nana, Arom; Simha; Rosenzweig, Sebastian and Müller, Meinard. (2020). "Tonal Organization of the Erkomaishvili Dataset: Pitches, Scales, Melodies and Harmonies" Scherbaum, Frank (Ed.), Computational Analysis of Traditional Georgian Vocal Music (Issue 1). Potsdam: Universitätsverlag Potsdam. Retrieved from: https://doi.org/10.25932/publishup-47614.

Scherbaum, Frank; Mzhavanadze, Nana; Rosenzweig, Sebastian and Müller, Meinard. (2022). "Tuning Systems of Traditional Georgian Singing Determined From a New Corpus of Field Recordings". Musicologist, 6(2): 142-168. Retrieved from https://dergipark.org.tr/en/download/article-file/2235567

Scherbaum, Frank and Müller, Meinard.  (2023). "From Intonation Adjustments to Synchronisation of Heart Beat Variability: Singer Interaction in Traditional Georgian Vocal Music". Musicologist,  7 (2): 155-177. Retrieved from https://dergipark.org.tr/tr/download/article-file/2542106

Scherbaum, Frank;  Müller, Meinard;  Nana Mzhavanadze and Sebastian Rosenzweig (2023). Scales beyond major and minor, in DFG-Journal  german research  2/2023, p. 25-29. (PDF

Scherbaum, Frank and Nana Mzhavanadze (2024). Harmonygrams: A Graphical Notation System for Three-Voiced Music Facilitating  the Perception of Harmonies, presentation at the Eighth International Conference on Analytical Approaches to World Musics (AAWM 2024) on June 12, 2024. Video (20 min) of the presentation in Bologna: https://youtu.be/8pWI9z_SSUM

Scherbaum,  F., Arom,  S. ,  Caron-Darras,  F., Lolashvili,  A., and Frank Kane (2024).  On the Classification of Traditional Georgian Vocal Music by Computer-Assisted Score Analysis, in production for  Musicologist June 2024.

Tsereteli, Zaal, and Levan Veshapidze. 2014. “On the Georgian Traditional Scale.”,  p. 288–95 in The Seventh International Symposium on Traditional Polyphony: 22-26 September, 2014, Tbilisi, Georgia. Retrieved from: https://www.academia.edu/36531585/On_the_Georgian_Traditional_Scale

Tsereteli, Zaal, and Levan Veshapidze. 2015. “Video of the Presentation ‘The Empirical Research of a Georgian Sound Scale.’” in 2015 IAML/IMS Congress. New York City, USA. Retrieved from: https://www.youtube.com/watch?v=TFncneafovI