Tuning History

Over 300 years ago, Giuseppe Tartini recognised that intervals could be measured by means of a combination tone which he called terzo suono (third tone). When two tones are played in their exact vibration ratio, a third tone (or even more additional tones) appears at a mathematically predictable position. This acoustic phenomenon is the basis for manifold applications which awaken the ear, increase its sensitivity, and generally expand the notion of sound. On the violin, for example, syntonic scales (diatonic or chromatic) can be created without external technical aids—only using the ear. Of special interest is the lowest combination tone, which forms a real- sounding bass accompaniment. Musical examples show how this demands from the performer clear decisions about intonation and the size of specific intervals. An awareness of the phenome- non of combination tones adds a new dimension to the interpretation of works such as J. S. Bach’s Sonatas and Partitas for solo violin, and helps to navigate intonation in ensemble playing.

The Collatz conjecture suggests that for any integer, n ∈ ℤ + , iterating the function: 𝐧/𝟐 if n is even F(n) = 3n +1 if n is odd eventually leads to 1. This paper presents a complete proof by demonstrating the impossibility of the two potential counterexamples: non-trivial integer cycles and divergent trajectories. First, the non-existence of non-trivial cycles is proven using an algebraic framework that analyzes perturbations of division exponents from a foundational Diophantine equation. A general proof demonstrates that the algebraic structure required for an integer cycle is impossible. This theoretical result is further supported by a separate brute force proof for a cycle model derived from modulo 16 and modulo 32 analyses, which is shown to be impossible due to conflicting structural constraints. Second, the non-existence of divergent trajectories is proven by modeling the system as a finite-state machine over modular classes. Using 2-adic analysis, it is shown that any growth-inducing modular loop is inherently unstable, a conclusion verified by the exhaustive solution of all 911 corresponding Diophantine equations for the modulo 16 system. Since both counterexamples are proven impossible, the conjecture is affirmed.
I found some errors in the previous version. This is a rectified version of the previous one.

This paper contains a full algebraic proof with empirical demonstration and exhaustive validation of the theoretical using Python scripts.
Briefing:
Step I: First the paper establishes a foundational lemma (lemma 0) that creates a deterministic frame of finite exponents with predictable values.
Step II: Then the paper establishes the fundamental Diophantine equation (which is well known in this parlance) that represents a loop structure of path sequence.
Step III: Then the paper proves algebraically that if all exponents are equal and equal to 2, then only an integer cycle is possible which is the trivial 4 - 2 -1 cycle (lemma 1A).
Step III: Next the paper introduces a new tool 'perturbation model' that analyze two possible outcomes of all permutations of the exponents => a net decrease or a net increase.
Step III: By lemma 1B the paper proves that none of the two outcomes can yield a non-trivial cycle. The lemma uses Euclidean division algorithm and exponent comparison strategy.
Step IV: The paper uses lemma 1C that separately deals with the last exponent perturbation and closes the door for non-trivial loop conclusively.
Step V: The paper then introduces another new tool: modular loop which analyzes the reappearance of same modular class in Collatz sequence. This tool shows how a Collatz sequence may grow or shrink in deterministic and predictable way. By lemma 2A, and 2B the paper disproves wondering path or indefinite growth for any integer.
Step VI: The theoretical section of this paper concludes invoking pigeonhole principle showing 4 -2 -1 is the only orbit any integer can end up with.
Step VII: Each theoretical claim is supported by empirical demonstration of another dedicated section.

This article examines, from certain perspectives and by way of comparison, the mean-tone temperaments of 1/5 syntonic comma (SC), 1/6 SC, and 2/7 SC, in the context of Renaissance and Baroque music, presenting some historical testimonies, a hypothesis on the approach to monochord division, and having in mind the classical interval ratios rein-troduced by Gioseffo Zarlino. The analysis compares the major third, minor third, regular fifth, and wolf fifth intervals, highlighting the mathematical advantages of the 2/7 SC in terms of symmetrical balance between the thirds, and a potentially more functional wolf fifth. It is argued that, on one hand, historical evidence such as brisés harpsichords and the testimony of Joseph Sauveur favors the 1/5 SC; on the other, the 1/6 SC has docu-mented advocates; while the 2/7 SC, in turn, besides also being the preference of some historical testimonies — beginning with Zarlino himself — would offer, as the conclusion of a mathematical analysis of its intervals, some interesting advantages.

Keywords: temperament, mesotonic, tuning, monochord, keyboard

Encyclopedie de la Musique et Dictionnaire du Conservatoire isimli ansiklo-
pedinin 1922 basımlı birinci kısmı, 25 ülkenin musikisi hakkında geniş bilgi
vermektedir. Türk Musikisi konulu makaleyi Rauf Yekta Bey 1913 yılında
Fransızca olarak yazmıştır.
Makalede Türk musikisinin dizisi yanında Türk çalgılar arasında tambur an-
latılmaktadır, bu sırasında tambur telin bölünmesiyle oluşan ve 49 perde ismi
içeren ses sistemi mevcuttur. Bu ses sistemi bugün de güncelliği yitirmediğin-
den Kantemiroğlu Edvarındaki ses sistemine kıyas için temel oluşturmaktadır.
Anahtar Kelimeler: Türk Musikisi Ses Sistemi, Perde, Rauf Yekta Bey, Di-
mitri Kantemiroğlu.

Matematik ile sanatın ilişkili olduğu alanlardan biri de müziktir. İnsanlık tarihi boyunca pek çok matematikçi müzik ile ilgilenmiştir. Bu çalışmamızda matematik ve müzik arasındaki ilişkiler incelenmiş ve bu ikilinin aslında biri diğerinin ayrılmaz bir parçası olduğu çeşitli örneklerle anlatılmaya çalışılmış ve matematiğin müzik ile iç içe var olduğu vurgulanmaya çalışılmıştır.

We, the editors, thought it would be interesting for readers to hear from the dedicatee of this volume himself. We posed several questions to Kevin Korsyn and asked him to respond. Our correspondence unfolded as follows. In Decentering Music, you offered a sobering critique of the discipline of musicology and of the relations among, and the schisms separating, its three primary subdisciplines-music theory, historical musicology, and ethnomusicology. At the time, you heard them speaking different dialects, as it were, and often working at cross purposes. That was almost two decades ago (2003). Do you feel that the dynamic among these fields has changed in the interim? How has your critical stance evolved over the years? My book Decentering Music is a critique of musicology as an institutional discourse, analyzing the struggle for the cultural authority to write about music under the regime of late capitalism, in which the postmodern fracturing of our individual and collective identities exists alongside an opposite impulse toward conformity and a counterfeit consensus in a commodified world. You refer to academic factions "speaking different dialects" and "working at cross purposes," but this captures only one pole of the dialectic I envisioned; the lack of a common language or value system through which to represent musical experience, which I called the Tower of Babel, is shadowed by a drive toward abstract uniformity that I called the Ministry of Truth, in which cultural differences become marketable commodities, and knowledge is reduced to its exchange value in the managed university. The increasing fragmentation of language in the Tower of Babel reflects the divided nature of identity today. As Ernesto Laclau and Chantal Mouffe have shown, society is no longer structured around a central struggle such as that of the people versus the ancien régime; we now encounter

fits into a narrow conception of what a Work should and must be; her call for less reliance on nationalistic language also fits into this larger discussion, but is no less compelling or important. In the Epilogue, she mentions that, for each identification of a methodology that has historically been problematic or ineffective, she hopes 'to have identified ways forward' (p.151). In this respect, she has most certainly succeeded: Angel song is as much a book about the practice of musicology as it is about one specific musicological topic, and will prove to be an invaluable learning text for young scholars working on medieval sources, no matter what their provenance may be.

Semitone sizes Vicentino described for his Archicembalo (ratios 21:20 and 14:13) together exceed a major whole tone, which Maniates called a "glaring discrepancy". Vicentino gives an illustration of the frets for an enharmonic lute, previously adjudged as flawed. The fourth is not badly divided, but has correct major and minor tones in Roman inches to which a flawed semitone was added. The whole tone of 2½" implies that the Roman Archicembalo's c¹ string length is 22½" and the 21:20 ratio is an intended part of the scheme, expressed as 21" and 20". The enharmonic tetrachord is skillfully constructed as three overlapping series of superparticular ratios, creating arithmetical series, but not with equal diesis sizes. The Archicembalo's physical string lengths (in its higher-pitched version) and the interval ratios are in agreement, documenting in hidden fashion the practice and describing the theory, which is a numerological feat of great elegance. Vicentino's enharmonic is different from Zarlino's, but Vicentino's three genera do not provide mutually compatible parts of an octave division. The arithmetical division is incompatible with a practical harpsichord temperament, but the 21:20 ratio is not a "glaring discrepancy". It represents the difference between musica speculativa and Vicentino's compositions which were musica prattica.

The monochord made in Vito Trasuntino's workshop for his 1606 "Clavemusicum Omnitonum" with 31 keys per octave was designed with Zarlino's 2/7 comma tuning. Zarlino's diagram (Le Istitutioni Harmoniche, 1558) was the basis, but the whole tones were reproduced without tempering. Zarlino's 24-note/octave harpsichord (built in 1548) had a harmonic range G♭-A♯♯, although Zarlino's design required a further eight notes. This range avoided 30 cent mistunings of tetrachords resulting from Zarlino's 2/7 comma tuning. Trasuntino's 1601 enharmonic harpsichord exceeded the G♭-A♯♯ range, but the monochord reveals that Trasuntino changed the tuning system to avoid Zarlino's problem. The discrepant ♭♭ notes in the monochord were constructed with a 16:15 interval from the ♯♯ ones, leading to ♭♭ notes which were too flat in 2/7 comma. They would have been nearly correct for Trasuntino's new tuning: 31-note equal temperament [ETS 31], which was required for correctly-tuned tetrachords, and is close to 1/4 comma meantone. The Clavemusicum Omnitonum's monochord could not set the tuning because of the conflict of two tuning systems, but also from inaccurate manufacture. Nevertheless, the monochord documents Trasuntino's enharmonic instruments, which initially followed Zarlino's tradition, and differed from Vicentino's enharmonic system and his Archicembalo.

Christoph Meinel once compared a list, describing the content of Joachim Jungius’ (1587– 1657) scholarly library, with a Swiftian «Battle of Books» (Meinel 1993). Unfortunately, many of such battles, as well as earlier scholarly libraries from seventeenth-century Hamburg, are difficult to reconstruct after the devastation of the Second World War. This also applies to a specific issue in the frame of the turn from traditional Humanism to the modern sciences: that is, a redefinition of the traditional discipline of Harmonics in the strict relationship of music theory and new methods of calculation. The present discussion will focus on the circles around Jungius and Johann Adam Reincken.
The Collegium Apodicticum et exemplare (D-Hs NJJ Wo.29) belongs to the Jungius Archive, including parts of a lecture on musical intervals (Section [3]) and ‘Definitiones musicae’ (Section [3a]) in the handwriting of Christian Buncke (??–1659), as well as anonymous lecture notes on Harmonics (Section [6]). These writings precede the edition of the ‘Harmonica’ (Hamburg 1679) by Johann Vaget (1633—1691), a former student of Jungius. Previous research has shown how Jungius introduced a specific terminology for tempered intervals, beginning with the quarter of the syntonic comma: the «quartula» (Barbieri 1987). Furthermore, Jungius’ lectures can be related to library holdings (Meinel 1992, Vidic 2022), such as Kepler’s Harmonices mundi libri v (Linz 1619).
Besides a persisting reception of Kepler’s book, a comparison with Reincken’s Aritmethicae Harmonicae (D-Hs ND VI 5002) also allows a broader contextualization. As we know, the logarithmic transformation of linear pitch values was originally proposed to avoid the overcomplicated root calculations necessary for the different temperaments (Lindley 1987, Barbieri 1996). Early research including logarithms was, however, scarcely publicized (Rasch 2002). After describing the genre and structure of different writings, it is important to examine the specific notation and purpose of a certain ‘comma calculation’. Concluding, it can never be emphasized enough how these sources witness a special educational commitment.

This brochure discusses NOTUS’s place in the music landscape:
- interpretation of the specific target groups;
- description of the threshold-reducing aspects;
- didactic advantages by simplification: only 7 basic notes, two new noteheads for the alterations, new tonic key signature, new tie mark, new indication for tuplets, international terminology;
- music theory and which instruments in NOTUS Music Notation;
- music pedagogical and didactic properties that attract students;
- integration possibilities in education and in social music projects.

This article examines early modern interactions between music-theoretical writings on tuning and consonance, natural philosophy (systematic, scientific understanding of the natural world), and the colonization of the American tropics. Part I argues that early modern music theorists leveraged justificatory frameworks inherited from contemporaneous natural philosophy to conceptualize utilizing tonal spaces and subduing dissonances (like keyboard temperaments' "wolf fifths"). Early modern natural philosophy heavily emphasized ideas of "improving nature," and maximally utilizing natural resources-key rationalities buttressing the colonial project. Part II examines how concepts of tuning and consonance served early modern colonizers' descriptions of exploiting and "improving" the tropical Americas. Europeans commonly described non-Europeans' musics in the American tropics as discordant and mistuned, supposedly demonstrating how nature and its "uncivilized" peoples needed to be maximally utilized, managed, and "improved." But other descriptions treated Indigenous and enslaved African peoples' musics as well tuned and consonant-metaphors for non-Europeans' being harmoniously integrated into colonization's project of dominating Earthly nature. This study addresses the natural philosophy of empire both to better articulate the political-economic dimensions surrounding music theory's adjacency to natural philosophy (and history of science), and to better situate music theory's relation to the colonial past alongside early modern epistemological trends.

Einige Texte E.T.A. Hoffmanns werden vor dem Hintergrund des Problems der musikalischen Stimmung gelesen. Die Prominenz der weiblichen Stimme und die Verstimmtheit der männlichen Charaktere erweisen sich dabei als Transponierungen eines musikologischen Sachverhaltes, der für das Diskurssystem des beginnenden 19. Jahrhunderts emblematischen Charakter hat. Selected texts of E. T.A. Hoffmann are interpreted against a backdrop of problems of musical tuning. The prominence of the female voice and the irritation of the male characters prove to be transpositions of musicological facts that have emblematic value for the discourse system of the early 19th century.

The article discusses the relationship between sound frequencies, music, and human perception, focusing on the debate surrounding the tuning standard used in music. The paper begins by questioning the metaphysical and religious implications of sound as a creative force. It then delves into the physics of music and human hearing and continues emphasizing the role of frequencies in shaping tonality and timbre. The significance and effects of different tuning standards, particularly comparing 432Hz tuning to the more commonly used 440Hz standard, have also been reviewed. Additionally, the historical context and potential motives behind the adoption of the 440Hz tuning standard, suggesting military and commercial interests, have been investigated. By examining these aspects, the article aims to deepen our understanding of the effects of different musical tunings on human well-being and perception, calling for further research. Ultimately, the article serves as a call to action for further research in the field.

Much as it might appear so to the doctoral student, an exegesis is not created in isolation. Many factors and individuals affect the process, for good and ill. It is traditional to mention at least some of these in preamble, and in this case I will bow to tradition. Any acknowledgements must begin with my wife, for reasons of which she is well aware and which could not be listed in anything approaching proper detail here. I would also like to explicitly thank my fellow musicians and friends, David Manning and Terry Buckridge, the latter also a fellow performer in the Spectral Om Ensemble. Without their constant help and encouragement, these words would likely not have been written at all. I must also particularly thank Korowal School in Hazelbrook in the Blue Mountains for its diligent and nurturing care of my children while this project was being undertaken-a care that in many ways went well beyond the call of mere duty. My adored children themselves had to deal all-too-often with a father discernibly short of time, temper and sleep. Kimberley Bianca of the University of New South Wales took an open-platform approach to her custody of the Electrofringe Festival of electronic music in Sydney; I thank her for this philosophy, which resulted in the Ensemble performing twice at Electrofringe, and I wish her all the very best with her current doctoral studies in Colorado. I thank my friends who bravely read drafts of the work in progress. Associate Professor Clare Maclean and Dr Andrew Milne of the University of Western Sydney were unfailingly helpful and encouraging, and this process, which has often proven trying beyond the normal experience of such things, very nearly wound up being finished under their aegis. The intrepid sponsors of my initial application for doctoral study also have my deep and abiding gratitude. I hope this document is sufficient reward for their faith. I would also like to thank and acknowledge the MARCS Institute for Brain, Behaviour and Development, also of the University of Western Sydney, for its offer of a fully funded scholarship to convert my studies into a more conventional PhD in music perception and cognition. I have often since regretted the nevertheless pressing personal reasons that led me to reluctantly refuse the offer. I am also deeply grateful to the academics and journals who published and otherwise supported my research in Australian history-a process that is now outside the ambit of this document, although it was an outgrowth of early research into possible final creative products. These specifically include

The Japanese music theorist Tanaka Shōhei captivated turn-of-the-century German audiences with three musical keyboards—the enharmonium, the syntonia, and the Demonstration Harmonium—that could perform tonal music in just intonation, a tuning system in which every interval is tuned to a whole number ratio. Such instruments, he proposed, would “return music to Nature’s eternal laws” by averting musicians from using equal temperament, which “artificially” exploited irrational numbers while dividing the octave into twelve equal steps. This article analyzes Tanaka’s theories and instruments alongside their reception history in Europe, based on archival research conducted by the author with Tanaka Tasuku, the theorist’s grandson. The analysis is contextualized within a broader discussion of the historical development of just intonation theory in Germany and Japan, and Tanaka’s efforts to use his instruments to cultivate transnational dialogue between the two countries. The article advances two claims: first, that only through close study of the technical specifications of Tanaka’s instruments can we grasp the co-productive relation between his theories, the sensations he sought to elicit, and material constraints; and second, that musical instruments can double as “instruments of the global history of theory,” by revealing how musical theories and practices have shaped global encounters.

Basierend auf den Forschungen des Sophie Drinker Instituts für das Online-Lexikon "Europäische Instrumentalistinnen des 18. und 19. Jahrhunderts" (seit 2006) und mit Hilfe vorliegender regionaler Untersuchungen wird ein erster Überblick über die Kultur-und Professionalisierungsgeschichte der Organistin gegeben: deutschsprachiger Raum, französische Schweiz, Frankreich und England. Kriterien der Professionalisierung waren der Zugang zum Instrument (Frage der ‚Schicklichkeit'), private und institutionelle Ausbildung, Probespiele, Anstellungen, Bezahlung, Umfang der Dienstverpflichtungen und die Verbindung mit Dirigententätigkeit. Baugeschichtliche Besonderheiten (zeitweiliges Fehlen von Pedalregistern) und das Spannungsverhältnis zwischen künstlerischer Tätigkeit und "anspruchslosem" Gemeindedienst haben dazu beigetragen, Frauen den Weg an die Orgel zu erleichtern oder auch zu erschweren.

The Harmonic Walk is an interactive physical environment designed for learning and practicing the accompaniment of a tonal melody. Employing a highly innovative multimedia system, the application offers to the user the possibility of getting in touch with some fundamental tonal music features in a very simple and readily available way. Notwithstanding tonal music is very common in our lives, unskilled people as well as music students and even professionals are scarcely conscious of what these features actually are. The Harmonic Walk, through the body movement in space, can provide all these users a live experience of tonal melody structure, chords progressions, melody accompaniment, and improvisation. Enactive knowledge and embodied cognition allow the user to build an inner map of these musical features, which can be acted by moving on the active surface with a simple step. Thorough assessment tests with musicians and nonmusicians high school students could prove the high communicative power and efficiency of the Harmonic Walk application both in improving musical knowledge and in accomplishing complex musical tasks.

Die norddeutsche freie pedaliter-Literatur wurde in letzten Jahren wiederholt und mehr als irgendein anderes barockes Tastenrepertoire im Hinblick auf ihre Funktionalität sowie instrumentale Zugehörigkeit diskutiert, ihre aufführungspraktischen Prämissen oft neu hinterfragt und kontradiktorisch beantwortet. Neue musikwissenschaftliche Erkenntnisse, einschließlich der Dokumentation und Restaurierungen norddeutscher Orgeln, kongruierten oft nicht mit der bisherigen Sicht dieses Repertoires, deren Wur-UDK 780.8:780.616.3/.4(430)»16/17«

Ergebnisse 2.1 Ergebnisse der Laborversuche 2.1.1 Versuche zur bioziden Ausstattung von Oberflächen 2.1.2 Auswirkungen von Beschichtungen 2.1.3 Versuche zum Einsatz von UV-C-Bestrahlung zur Hemmung von mikrobiologischer Aktivität 2.1.4 Versuche zum Einsatz von Ozon zur Hemmung von mikrobiologischer Aktivität 2.1.5 Anzuchtversuche weiterer Mikroorganismen in Abhängigkeit von raumklimatischen Umgebungsbedingungen 2.1.6 Simulationsberechnungen zu den Ursachen und Behandlungsmöglichkeiten von Schimmel in Orgeln 2.1.7 Ergebnisse der mikrobiologischen und raumklimatischen Untersuchungen an Referenzobjekten in Verbindung mit einer Bewertung der mikrobiologischen Wachstumsbedingungen: Interpretation der Klimawerte und simulierten Wachstumsbedingungen 2.1.8 Untersuchung des Einflusses von Luftbewegungen auf das Schimmelwachstum 2.1.9 Untersuchung der Einsatzmöglichkeit von Heizteppichen und Infrarot-Heizfolien als Flächenheizungen 2.2 Praxisversuche zur Erprobung von Technologien zur Hemmung mikrobiologischer Aktivität 2.2.1 Versuche mit einer luftfeuchtegesteuerten Raumlufttemperierung zur Konditionierung der Raumluft im Gehäuse der Kapellenorgel im Kloster Michaelstein 2.2.2 Anwendungsbeispiel für Heizteppiche: die Orgel in Geseke 2.2.3 Temperierung der Wand hinter der Orgel: die Orgel in der Christuskirche Karlsruhe 2.2.4 Auswirkung einer Raumlufttemperierung auf die Stimmung einer Orgel am Praxisbeispiel der Orgel im Kloster Michaelstein 2.2.5 Erprobung einer technischen Luftentfeuchtung zur Hemmung des mikrobiologischen Wachstums am Praxisbeispiel Hünhan und Wöllnitz 2.2.6 Bewertung des Energieverbrauchs: Entfeuchter versus Temperierung versus Erhöhung der Grundtemperatur 2.2.7 Erprobung der Auswirkung einer Dämmplatte auf die Raumklimasituation in der Orgel in Freiberg 2.2.8 Reinigungsmethoden 2.2.9 Ergebnisse der Entfernung/Ausdünnung von das Schimmelwachstum begünstigenden Beschichtungen 2.2.10 Praxisversuche zum Einsatz von Ozon zur Schimmelbehandlung in Orgeln 2.2.11 Bewertung der Praxis der Schwefelbegasung von Orgelgehäusen am Beispiel von Schwarzenberg 2.

Scholars of American music have long and painstakingly contemplated how most effectively to express the dynamics, distinctions, and nuances of such a vast repertoire. In his foreword to Gilbert Chase's 1987 edition of America's Music, Richard Crawford cites Chase's earlier commentary on the writing of music history. Chase, Crawford states, "[O]bserved that historians of music have generally taken a 'diachronic' view of time, which considers phenomena sequentially, in the order in which events in their development have occurred." This approach, according to Chase, was effective in tracing the history of a single idiom. However, "where two or more equally important kinds of music do coexist, time is better thought of spatially or 'synchronically,' ... juxtaposing accounts of many different musics, just as they live side by side in real life." 1 Embracing the challenge of writing a "highly variegated" account of American music, Richard Crawford and Larry Hamberlin give us a second, reconfigured edition of Crawford's textbook, An Introduction to America's Music. Departing from the chronological narrative employed in the first edition, the second edition, although roughly sequential, adopts a more holistic approach. Categories such as classical, popular, and folk/traditional are treated less rigidly. Crawford and Hamberlin expand on Crawford's well-known interest in the broader, dynamic context of music-making that encompasses performers, teachers, audiences, and the music business. Giving inclusive consideration to the interaction of these elements tests the bounds of a century-by-century template. Thus, the larger sections of the current edition are envisioned and titled according to acts of human engagement, specifically employing war as a benchmark of social and cultural change. In this malleable framework the authors "probe the boundaries drawn to separate different types of music and, by implication, different groups of listeners from each other" and argue convincingly for the interconnectedness of "music and the life that surrounds it" (xvii). Part 1, America's Music from Colonization through the Civil War, encompasses a period often defined by its disparity. Yet, out of the conflict and tumult that emanated in waves across this era, Crawford and Hamberlin depict continuity and community through musical expression. Drawing upon the writings of European

Iconography, literature, theological essays and music treatises make it clear that fiddles had a very high profile during the Middle Ages. They were involved in dances, banquets, sacred music, journeys, and private entertainment. One theorist describes the fiddle as the most versatile of all instruments, capable of performing every kind of composition. 1 From what is known about the fiddles' tunings and physical setups, however, there are serious questions about the actual technique employed in performance. This essay looks at the characteristics of one type of fiddle, attempts to show how it might have served in various kinds of compositions and situations, and suggests that notions of historical fiddle performance may need to expand to accommodate the aesthetics and techniques implied by the off-board fiddle.

Raga collections are mostly used in the music information systems. Melakartha ragas are the most important concept in the music theory. All the existing ragas in music theory are derived from mela kartha ragas. The main objective of this paper is to generate all 72 ragas automatically. This paper identifies an application of graph theory in music information technology. An undirected graph is constructed using the melakartha algorithm with seven swaras and its variations as its vertices. By applying the Breadth First Search algorithm, to the constructed graph, we generated all possible paths that represent the 72 Melakartha ragas.

Raga collections are mostly used in the music information systems. Melakartha ragas are the most important concept in the music theory. All the existing ragas in music theory are derived from mela kartha ragas. The main objective of this paper is to generate all 72 ragas automatically. This paper identifies an application of graph theory in music information technology. An undirected graph is constructed using the melakartha algorithm with seven swaras and its variations as its vertices. By applying the Breadth First Search algorithm, to the constructed graph, we generated all possible paths that represent the 72 Melakartha ragas.

Die Musik als Bildspenderin der für die Literatur zentralen Begriffe wie Harmonie, Ton und Stimmung zu eruieren, liegt auf der Hand. Dennoch ist für ihre diskursive Anschlussstelle historisch auf die Epoche der Aufklärung zurückzugreifen, da später nur noch implizit auf die Musik Bezug genommen wird. Folgt man zunächst der lexikalischen Inventur des 19. Jahrhunderts, so erfahren die drei Begriffe im Laufe des 18. Jahrhunderts eine Übertragung aus dem akustischmusikalischen Bereich in andere Disziplinen. So "erscheint" das Wort "harmonie" "recht eingebürgert seit der zweiten hälfte" des 18. Jahrhunderts; belegt wird Harmonie als "verbindung von einzelnen gleichzeitig angeschlagenen tönen zu einem wolklingenden ganzen" bei Klopstock und Schiller (Grimm DWB 10, Sp. 484), in Rekurrenz auf die Sphärenharmonie bereits bei Hagedorn (Grimm DWB 10, Sp. 485). Auch wenn der Begriff partiell metaphorisiert wird "in ästhetischem, philosophischem, mathematischem Sinne" (Grimm DWB 10, Sp. 485), steht der musikalische Kontext meist im Vordergrund. Komplexer gestaltet sich das Bedeutungsfeld von Ton: Zwar nimmt der Ton als Konzept in der Malerei, als "stimmung der farbe" (Grimm DWB 21, Sp. 749) bzw. als physiologischer Fachbegriff des tónos (Grimm DWB 21, Sp. 751) deutlich weniger Raum ein. Doch selbst als akustischer Begriff bleibt er ambivalent zwischen "unmusikalische[m] ‚geräusch'" und "kunstmäsziger ‚melodie', als ‚musikstück' und ‚lied' überhaupt" (Grimm DWB 21, Sp. 681). Spätestens in der Literatursprache des 18. Jahrhunderts tritt er "als der bestimmte ton in der musik, als musikalischer ‚sonus'" markant hervor (Grimm DWB 21, Sp. 687). Die größte Metaphorisierung durchläuft im 18. Jahrhundert jedoch der Stimmungsbegriff, der als explizit musikalischer Terminus bereits im 16. Jahrhundert bezeugt ist (Becker 2012, 261). So sehr er sich im 19. und 20. Jahrhundert vom musikalischen Bildspender löst, so sehr ist er im ausgehenden 18. Jahrhundert mit der Musik verknüpft, in deren Bereich er drei semantische Felder bespielt und entsprechend metaphorisiert wird: 1. Stimmung als Prozess, als "ausführung des stimmens" an Musikinstrumenten (Stimmen der Saiten etc.), dessen Grundbedeutung in Musiktraktaten von

In this study, I propose a theory of voice leading for use with the tonal space of the just-intonation Tonnetz. The theory is based largely upon established theories of diatonic voice leading and chromatic harmony, and also draws upon the principles of just ...

Das konsonanteste Tonintervall ist die Oktave. Wenn ein Ton eine Oktave höher ist als der Grundton, so stehen die Frequenzen dieser Töne im Verhältnis $2:1$. Es besteht also zwischen Tonhöhe und Frequenz ein exponentieller Zusammenhang. Ebenfalls sehr konsonant ist das Tonintervall Quinte mit dem Frequenzverhältnis $3:2$. Möchte man eine Tonskala mit Oktaven, Quinten und gleichen Abständen zwischen benachbarten Tönen erstellen, so ist dies nicht möglich, da $\log_{2}{(\frac{3}{2})}$ irrational ist.

Durch das Berechnen der Näherungs- und Zwischenbrüche der Kettenbruchdarstellung von reellen Zahlen lassen sich beste Approximationen erster und zweiter Art finden. Jede beste Approximation zweiter Art ist auch eine beste Approximation erster Art. Wenn $\frac{a}{b}$ eine beste Approximation erster Art an $\log_{2}{(\frac{3}{2})}$ ist, so gibt es keine andere rationale Zahl mit gleichem oder kleinerem Nenner, die $\log_{2}{(\frac{3}{2})}$ noch besser annähern würde. Teilt man die Oktave in $b$ Töne auf, so ist der $a$-te davon eine gute Näherung an die Quinte.

In der pythagoräischen Stimmung werden durch das sukzessive Erhöhen des Grundtones um eine Quinte und das gleichzeitige Erniedrigen um eine Oktave, wann immer die Verhältnisse größer als $2:1$ werden würden, weitere Töne erzeugt. Nach zwölf Quinten und sieben Oktaven erreicht man beinahe wieder den Grundton. Den tatsächlichen Tonunterschied bezeichnet man als pythagoräisches Komma. Der Näherungsbruch $\frac{7}{12}$ ist eine beste Approximation zweiter Art an $\log_{2}{(\frac{3}{2})}$, und nähert als solche nicht nur $\log_{2}{(\frac{3}{2})}$ sondern die gesamte pythagoräische 12-Ton-Skala gut an. Eine bessere Näherung gäbe es erst wieder mit 41 Tönen pro Oktave. Dies ist der Grund, warum fast die gesamte westliche Musik die gleichstufige 12-Ton-Skala verwendet.

Es gibt allerdings auch Beispiele für andere sinnvolle gleichstufige Skalen. Etwa die 53-Ton-Skala ($\frac{31}{53}$ ist ein Näherungsbruch von $\log_{2}{(\frac{3}{2})}$) oder die 31-Ton Skala ($\frac{18}{31}$ ist ein Näherungsbruch von $\log_{2}{(\sqrt[4]{5})}$), welche statt der reinen die mitteltönige Quinte annähert.

1. Zunehmende Digitalisierung
Es gibt teils exzellente regionale Datenbanken wie die Orgeldatenbank Bayern mit 10.000 Dispositionen, das Institut für Orgelforschung Brandenburg oder die Orgeldatenbank der Ev.-luth. Landeskirche Sachsens. Hervorzuheben an überregionalen, frei zugänglichen Datenbanken sind die niederländische Orgeldatabase (http://www.orgbase.nl/) von Piet Bron mit 48.500 internationalen Dispositionen und Organ index (https://organindex.de/) mit 12.000 Dispositionen, das auf Wiki-Basis als Mitmachprojekt konzipiert ist. Die GdO bietet auf ihrer Homepage eine entsprechende Linkliste.

2. Belege erforderlich
Da Wikipedia im strengen Sinne Tertiärliteratur ist, ist die Suche und Verarbeitung von Sekundärliteratur grundlegend. Während Artikel aus den Anfangsjahren der Enzyklopädie noch ohne Referenzen auskamen, wird heute auf Belege großen Wert gelegt.

3. Mitarbeit erwünscht?!
Zwischen dem Anspruch, dass jeder in Wikipedia mitarbeiten kann, und den Erfahrungen in der Praxis besteht eine Spannung. Empfehlenswert ist, nicht gleich neue Artikel zu schreiben oder bestehende umzuschreiben, sondern im Kleinen anzufangen, um sich mit der Syntax vertraut zu machen.

4. Relevanz und Relevanzkriterien
Über alles, was enzyklopädisch relevant ist, kann man einen Artikel schreiben. Hierzu hat die Wiki-Gemeinschaft im Einzelnen Relevanzkriterien festgelegt.

5. Probleme mit den Bildern
Alle Bilder sind im Schwesterprojekt Commons hochgeladen, auf das alle internationalen Wikipedias Zugriff haben. Eine Beschränkung der Bildrechte „nur für Wikipedia“ oder „zu nicht-kommerziellen Zwecken“ ist auf Commons nicht möglich.

5. Ausblick und Plädoyer
- Wartung, Aktualisierung, Korrektur, Verbesserung und Ausbau bestehender Artikel
- Anlegen von weiteren Orgellisten, beispielsweise Inventare ganzer Landkreise
- Ausbau bestehender und Anlegen neuer Artikel im Bereich Orgelbau und Orgelmusik
- Innerhalb der deutschen Orgellandschaften fehlen noch Artikel über Berlin und Brandenburg, Nordrhein-Westfalen, Rheinland-Pfalz, Baden-Württemberg, Sachsen-Anhalt und Mecklenburg-Vorpommern.
- Hochladen von qualitativ guten Orgelbildern und Bebilderung der Artikel
- Wünschenswert wären weitere Audioaufnahmen von bedeutenden Orgeln.

Bu çalışmada, Türk Mûsikîsi'nde perde düzeninin Türk Mûsikîsi ses sitemine uygunluğu ve bu sisteme bağlı olarak Türk Mûsikisi perdelerini ve Türk Mûsikîsi incelenmiştir. Öncelikle farklı yapımcıların yerleşim aralıkları bakımından incelener düzeneği örneklenmiştir. Bu mandal düzeneğinden elde edileb Türk Mûsikîsi perdelerinin ve Türk Mûsikîsi dörtlü ve dizi beşlilerin aralık değerleri ahenklerde yapılarak, kanunda göçürme konusunda belirlenmesi amaçlanmıştır. Sonuçta çözümlenebilmesi için çeşitli önerilerde bulunulmuştur. Anahtar Kelimeler: Türk Mûsikîsi ses sistemi, ka kanunda göçürme. A STUDY IN TUNING SYSTEM PROBLEMS OF KANUN ABSTRACT In this study, the ability of the kânun instruments in Turkish music in playing the sounds of Turkish microtonal system and Turkish music maqams, is analyzed. Before analyzing various kânuns different manufacturers, luthiers were examined to determine a mechanism. This mechanism's pitch values were used to compare intervals and microtones in Turkish microtonal system with intervals and pitches played by the kânun. These comparisons were made for all Turkish Music tones in order to analyze the transposition ability of kânun. Consequently some suggestions have been made that offer solutions to problems observed during the evaluation process.

Séminaire IRCAM MaMUX 2015Dans un tempérament inégal défini, certaines tonalités sont plus ou moins dissonantes ou mal adaptées. Les différences étant parfois peu perceptibles, même pour un musicien entrainé, nous avons cherché une méthode graphique afin de voir ce que l’oreille perçoit peu, ou ne perçoit pas. Pour cette première tentative de visualisation, nous caractérisons une tonalité par son accord tonal principal. Un accord parfait étant constitué de m3, M3 et P5 nous utilisons ces trois paramètres comme trois dimensions. Nous avons enregistré la même pièce contenant les 24 tonalités et laissé PianoTeq™ produire le son désiré avec des tempéraments inégaux choisis. L’impression de consonance varie le long du parcours harmonique. Cette approche ne reflète bien sûr pas exactement la réalité de ce qui ce passe dans une oreille avertie, mais permet de se lancer dans un domaine à découvrir en y apportant une dimension visuelle, pédagogique et dynamique

We present a computational model of tonality cognition derived from physical and cognitive principles on the frequency ratios of consonant intervals. The proposed model, which we call the Prime Factor-based Generalized Tonnetz (PFG Tonnetz), is based on the Prime Factor Representation of frequency ratios and can be regarded as a generalization of the Tonnetz. Our assumed application of the PFG Tonnetz is a system for supporting spontaneous and improvisational participation of inexpert citizens in music performance for regional promotion. For this application, the system needs to determine the pitch satisfying constraints on tonality against surrounding polyphonic music because inexpert users frequently lack music skills related to tonality. We also explore a working hypothesis on the robustness of the PFG Tonnetz against recognition errors on harmonic overtones in polyphonic audio signals. On the basis of this hypothesis, the PFG Tonnetz has a good potential as a representation of the tonality constraints of surrounding polyphonic music. Copyright: c ⃝2015 Shun Shiramatsu et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 Unported License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

The Understanding Library Impacts (ULI) protocol is a suite of instruments designed to demonstrate connections between undergraduate student use of the academic library and faculty-defined expectations for student learning. The ULI protocol features a Critical Incident Technique (CIT) survey for exploring student use of the library during `high-impact' academic experiences such as capstone courses. A `Learning Activities Crosswalk' links student use of the library to faculty-defined, discipline-specific and general education expectations for student learning. This methodological study evaluated the protocol with a population of undergraduate students enrolled in upper-level and capstone history courses at six colleges and universities. The protocol focuses on students' use of traditional and electronic information resources, library services, and library facilities during learning activities associated with `high-impact' experiences in the academic major. Learning ac...

Ausgangspunkt der Dissertation sind zwei süddeutsche Orgeln des frühen 17. Jahrhunderts, die in Forschungsprojekten mit unterschiedlichen Zielsetzungen dokumentiert wurden, bevor sie einer Konservierung bzw. einem Rückbau unterzogen werden sollten. Die Arbeit fasst im ersten Band alte und neue Erkenntnisse zur jeweiligen Geschichte der beiden Instrumente zusammen, die bei Archivrecherchen und durch Abgleich der Befunds-Analysen am Instrument mit den gefundenen Archivalien gewonnen wurden. Diese Erkenntnisse stellt sie durch vergleichende Studien mit zeitgenössischen erhaltenen Orgeln in einen größeren orgelbaugeschichtlichen Zusammenhang, der wiederum durch Fragen an den musikgeschichtlichen und gesellschaftlichen Kontext mit Schwerpunkt auf der Reformation und ihrer Folgen für Orgelgebrauch und –bau erweitert wird. Die Marx Günzer-Orgel in Gabelbach bei Augsburg und die Thalkirchner Orgel im Deutschen Museum in München gehören zu den wenigen noch erhaltenen Orgeln des frühen 17. Ja...

It is an honor and a little terrifying to be invited to give the first Seeger-Seeger lecture since the series was started in 1976, when Charles Seeger delivered a plenary address on "The Musicological Juncture: 1976." The challenges for a Seeger to deliver a lecture named after Charles are legion. Being born a Seeger in the mid 20th Century itself brought with it a certain amount of baggage. There were my father's stories from his youth about traveling with his brothers in a C. Seeger lecture for publication draft 12/27/05, p 2 trailer and playing while his parents delivered concerts on the violin and keyboard to sparse audiences. Growing up in New York City I met Lead Belly, Woody Guthrie, and many other artists. I attended many free concerts and made many backstage visits-like the one at Carnegie Hall in December 1963 (figure 1). An advantage of being a Seeger in those days was that people usually remembered my last name, On the other hand, many acquaintances to this day occasionally call me "Pete" or "Charles" or "Mike." I have frequently been either praised and blamed for the actions of other members of my family for which I had no responsibility. Alan Lomax, for example, once complained to me on the telephone "You and three generations of Seegers have ruined American folk music." ii My parents sang, as did most of their acquaintances, and so did I, starting very early. I learned to play the banjo at age ten at my parents' summer camp, had a fan club of screaming fourth grade girls when I was in 8 th grade, and with friend Rusty Simonds won the Town of Putney Vermont's talent show with friend when I was sixteen that had a prize of $25.00 and a television appearance. The promised television appearance never materialized-even teenage Seegers were apparently blacklisted in those days. I kept on playing anyway, until I decided there were far too many Seegers in the performance arena and that I would rather become an anthropologist who studied music than make a place for myself among the other performers.

BY TIM CARTER An American in Paris (1951) was one of a number of Hollywood films of its period that served t fix America's new postwar relationship with a Europe that had now been left far behind. The tropes are well known. A supremely confident if somewhat naive American-able to get by with a smile, reasonably good looks, and some nifty footwork-galumphs through the streets of Paris, tasting the food, sampling the wine, flirting with the natives, trying out the language (bu it is important, not too fluently) yet in the end remaining, well, unremittingly American. The

Objectives – The purpose of this collaborative qualitative research project, initiated by the Greater Western Library Alliance (GWLA), was to explore how librarians were involved in the designing, implementing, assessing, and disseminating student learning outcomes (SLOs) in GWLA member academic libraries. The original objective of the research was to identify library evaluation/assessment practices at the different libraries to share and discuss by consortia members at a GWLA-sponsored Student Learning Assessment Symposium in 2013. However, findings raised new questions and areas to explore beyond student learning assessment, and additional research was continued by two of the GWLA collaborators after the Symposium. The purpose of this second phase of research was to explore the intersection of library and institutional contexts and academic library assessment practices. Methods – This qualitative research study involved a survey of librarians at 23 GWLA member libraries, about stu...