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Musical Temperament References

This is a list of references related to Musical Temperaments cited throughout Flutopedia.

The references on this page are a sub-set of the complete list of Flutopedia references.

For information on the format and other details of these citations, see the main references page.

Musical Temperament References

[Asmussen 2001] Robert Asmussen. Periodicity of Sinusoidal Frequencies as a Basis for the Analysis of Baroque and Classical Harmony: A Computer Based Study, Doctoral dissertation – School of Music, The University of Leeds, England, September 2001. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: The thesis of this dissertation is that tonality is derived from very precise tonal relationships involving the first three primes. It is specifically asserted that within any piece of tonal music, with tonic being given as an octave equivalent of 1/1, the relative frequency for any note can be represented in the form (2/1)ˣ * (3/2)ʸ * (5/4)ᶻ, {x,y,z} ∈ Z. A database of chord progressions is electronically created and catalogued. Within this database, a higher rate of occurrence for the simplest chords of 5-limit just intonation is demonstrated. Listening experiments based upon the most commonly occurring chord progressions lend further support to the assertion that 5-limit just intonation is in fact the origin of Baroque tonality. Finally, a rule-based system that prioritises important tonal relationships is demonstrated by tuning several entire chorales according to the principles of 5-limit just intonation.

[Barbour 1951] James Murray Barbour. Tuning and Temperament: A Historical Survey, published by the Michigan State College Press, East Lansing, Michigan, 1951. Publication tuningtemperamen00barb on Archive.org (open access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

From the preface: This book is based upon my unpublished Cornell dissertation, Equal Temperament: Its History from Ramis (1482) to Rameau (1737), Ithaca, 1932. As the title indicates, the emphasis in the dissertation was upon individual writers. In the present work the emphasis is on the theories rather than on their promulgators. Since a great many tuning systems are discussed, a separate chapter is devoted to each of the principal varieties of tuning, with subsidiary divisions wherever necessary. Even so, the whole subject is so complex that it seemed best that these chapters be preceded by a running account (with a minimum of mathematics) of the entire history of tuning and temperament. Chapter I also contains the principal account of the Pythagorean tuning, for it is unnecessary to spend a chapter upon a tuning system that exists in one form only.

[Boswell 1970] George W. Boswell. “The Neutral Tone as a Function of Folk-Song Text”, Yearbook of the International Folk Music Council, Volume 2, published by the International Council for Traditional Music, 1970, pages 127–132. Publication 767430 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Braun-M 2002] Martin Braun. The Gamelan Pelog Scale of Central Java as an Example of a Non-harmonic Musical Scale, August 2002, retrieved January 20, 2015. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Bronk 2010] Beth Bronk. “It’s Just Intonation”, Bandmasters Review, published by the Texas Bandmasters Association, December 2010, pages 15–21. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Bucht 2004] Saku Bucht and Erkki Huovinen. “Perceived Consonance of Harmonic Intervals in 19-tone Equal Temperament”, Proceedings of the Conference on Interdisciplinary Musicology (CIM04), Graz, Austria, April 15–18, 2004, April 2004, pages 1–10. Perceived Consonance of Harmonic Intervals in 19-tone Equal Temperament Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Guided NAFlutomat - Step 4. Temperament, Glossary of Native American Flute Terms

Abstract:
Background in microtonal research: Regardless of the method of evaluation used, the 19-tone equal temperament (19-tet) has frequently emerged as one of the most plausible candidates for an alternative equally tempered tuning system (e.g. Krantz & Douthett, 1994). Speculations on consonance within the 19-tet have been presented by Yasser (1975/1932) and Mandelbaum (1961).
Background is psychoacoustics: According to Plomp and Levelt (1965), sensory consonance for harmonic complex tones reaches its local maxima at simple-integer frequency ratios (which represent the consonant intervals). These ratios are well approximated in e.g. 12-tet and 19-tet. Quite similar influence of coinciding and nearly coinciding partials can also be found for inharmonic tones (cf. e.g. Geary, 1980). Terhardt (1984/1976) suggested that sensory consonance is insufficient to describe the phenomenon of musical consonance, which also depends on culturally conditioned aspects of music.
Aims: The present study had two aims. First, we wanted to get a comprehensive overview of the relative amounts of consonance and dissonance perceived among the harmonic intervals of 19-tone equal temperament. Second, we aimed at producing general information about the strategies that are used for making judgments concerning musical consonance (e.g. the influence of fundamental frequency ratios vs. the matching of partials). This involved evaluating how well current models of sensory (or tonal) consonance would predict the experimentally obtained values of this study.
Method: Two experiments were conducted in order to study listeners’ tendencies to attribute patterns of relative consonance and dissonance to adjacent harmonic intervals of the 19-tet. The stimuli in Experiment 1 consisted of ordered pairs of harmonic intervals. The subjects indicated whether the perceived consonance increased or decreased from the first to the second interval. Experiment 2 was designed firstly to replicate the previous findings in an atemporal setting: now the subjects had to choose the most consonant interval from three alternatives that they were free to explore using three push-buttons. In half of the trials, Experiment 2 also incorporated inharmonic spectra, designed to yield maximum sensory consonance for intervals that would otherwise be heard as dissonant.
Results: The results suggest that (1) intervals, which approximate the familiar diatonic intervals, were perceived as most consonant. (2) The subjects used various strategies in their judgment on consonance of harmonic intervals: sensory consonance, fundamental-frequency relations and avoidance of slow beating were all significant factors. Sensory consonance seemed to be the dominating factor when subjects judged dyads incorporating an inharmonic spectrum. These findings do not support the previously proposed hypothetical consonance/dissonance rankings for 19-tet (by e.g. Yasser).
Conclusions: Although unsatisfactory in itself to describe musical consonance in 19-tet, the results obtained in this study will provide a psychoacoustic foundation for such a concept. As Huron (1994) has noted, there exists a connection between sensory aspects of consonance and most common musical scales and chords. Thus, our results will form a basis for practical suggestions concerning the use of the 19-tet.

[Carlos 1996] Wendy Carlos. “Three Asymmetric Divisions of the Octave”, 1996. Three Asymmetric Divisions of the Octave Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Cazden 1958] Norman Cazden. “Pythagoras and Aristoxenos Reconciled”, Journal of the American Musicological Society, Volume 11, Number 2/3, Summer–Autumn 1958, pages 97–105. Publication 829897 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Introduction: The Pythagorean and Aristoxenian viewpoints have represented poles of fundamental and irreconcilable conflict for some two thousand years. Pythagoras regards relationships among musical tones as manifestations of abstract number, signifying a pervasive cosmic principle. Aristoxenos ascribes the ordering of musical tones to the judgment of the ear, contingent therefore on mundane musical practice and its history.

[Cox 2013] Trevor Cox. Pitch Shifting to 432 Hz Doesn’t Improve Music, December 13, 2013, retrieved July 6, 2015. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Duffin 2008] Ross W. Duffin. How Equal Temperament Ruined Harmony (and Why You Should Care), published by W. W. Norton, 2008, 208 pages, ISBN 0-393-33420-1 (978-0-393-33420-3). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Favaro 2003] John Favaro. Slightly Out of Tune: The Story of Musical Temperament, April 12, 2003, 10 pages. See the John Favaro's web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Forinash 2015] K. Forinash. An Interactive eBook on the Physics of Sound, published by Indiana University Southeast, 2015, retrieved January 28, 2015. See the Physics of Sound Indiana University Southeast web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Gardner-Z 2013] Zen Gardner. 440Hz Music – Conspiracy to Detune Us from Natural 432Hz Harmonics?, August 6, 2013, retrieved July 6, 2015. See the Zen Gardner web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Geringer 1976] John M. Geringer. “Tuning Preferences in Recorded Orchestral Music”, Journal of Research in Music Education, Volume 24, Number 4, Winter 1976, pages 169–176, doi:10.2307/3345127. Publication 3345127 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: The purpose of this study was to investigate tuning preferences regarding recorded orchestral music. Specifically, the study was designed to test subjects' tuning preferences while investigating both the direction and magnitude of mistuning. Sixty randomly selected undergraduate and graduate music students modulated a variable speed tape recorder to preferred pitch levels. Stimuli were recorded excerpts of ten orchestral works, each representative of a different key. Subjects listened to the thirty-second excerpts and turned a linear continuous-speed control knob with a pitch range of approximately an augmented fourth. Data consisted of cent deviation scores relative to A = 440 Hz. Results indicated a marked propensity to tune these excerpts sharper than their recorded pitch level. Subjects' responses indicated the mean cent deviation for sharp tunings to be 149.29 cents (approximately 11/2 semi-tones); when tuning flat, the mean deviation was 88.43 cents.

[Hagerman 1980] B. Hagerman and J. Sundberg. “Fundamental Frequency Adjustment in Barbershop Singing”, Journal of Research in Singing, Volume 4, Number 1, 1980, pages 3–17. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Hahn-K 2002] Kathrin Hahn and Oliver Vitouch. “Preference for Musical Tuning Systems: How Cognitive Anatomy Interacts with Cultural Shaping”, Proceedings of the 7th International Conference on Music Perception and Cognition, Sydney, Australia, published by Causal Productions, Adelaide, Australia, 2002, pages 757–760, ISBN 1-876346-39-6 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Previous studies testing the production and evaluation of musical scales revealed a preference for Pythagorean intonation among violinists whereas pianists preferred equal temperament, with non-musicians showing no clear preferences. This study investigates preferences for four musical tuning systems using chord sequences and excerpts from musical compositions performed in different instrumental timbres. Forty participants (string players, pianists, non-musicians) made forced-choice preference judgments between pairs of tunings, as well as judgments of purity and sound brilliance. Results show that when using real music and instrumental sounds, the preferences for tuning systems vary not only between groups of participants but also between types of music and timbres. A general preference for a single tuning system therefore seems to be an over-simplified assumption.

[Hall 1984] Donald E. Hall and Joan Taylor Hess. “Perception of Musical Interval Tuning”, Music Perception: An Interdisciplinary Journal, Volume 2, Number 2, Winter 1984, pages 166–195, doi:10.2307/40285290. Publication 40285290 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: When musical intervals are altered from their usual frequency ratios, listeners may experience a sensation of mistuning. We report results of experiments in which subjects judged degrees of mistuning of all intervals from unison to octave, as well as major tenth and twelfth. Using two simultaneous tones with fundamental frequencies between 250 and 800 Hz and 5 to 10 strong harmonics in each, we find: (1) just intervals, rather than tempered, are considered best in tune; (2) the range of mistunings considered acceptable generally becomes narrower when expressed in cents but wider when described by beat rate as we go from unison to octave, fifth and fourth; (3) whether that trend continues to sixths and thirds depends on individual listening strategies; and (4) the difficulty of judgment generally increases in going from the consonant toward the dissonant intervals, with the latter often eliciting only crude discrimination. Ability to judge mistuning with dichotic stimuli was also tested. We conclude that the beat rates of nearly coinciding harmonics provide an important clue to mistuning, but that a more abstract ability to judge interval size is also used; relative importance of the two strategies differs among subjects.

[Heathwaite 2010] Andrew Heathwaite. Gallery of Just Intervals, Sepember 14, 2010, retrieved January 28, 2015. Gallery of Just Intervals Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Heathwaite 2011] Andrew Heathwaite. Overtone Scales, October 17, 2011, retrieved January 28, 2015. Overtone Scales Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Johnson-HB 1963] Hugh Bailey Johnson. An Investigation of the Tuning Preferences of a Selected Group of Singers with Reference to Just Intonation, Pythagorean Tuning, and Equal Temperament, Mus.Ed.D. dissertation – Indiana University, 1963, 116 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Jorgensen 1991] Owen H. {Henry} Jorgensen. Tuning — Containing The Perfection of Eighteenth-Century Temperament, The Lost Art of Nineteenth-Century Temperament, and The Science of Equal Temperament, Complete With Instructions for Aural and Electronic Tuning, published by, Michigan State University Press, East Lansing, Michigan, June 1991, 798 pages, ISBN 0-87013-290-3 (978-0-87013-290-2). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Jorgensen 2009] Owen H. {Henry} Jorgensen. About the Temperament Used by J. S. Bach and Others, published by, Frank French on Tuner's Art, 2009, 8 pages, retrieved November 24, 2011. See the Frank French's web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Jorgensen 2006] Owen Jorgensen and Jason Kanter. Temperaments Visualized, October 2, 2006, 130 pages. See the Jason Kanter web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Kanter 2006] Jason Kanter. Temperaments Visualized, September 29, 2006, retrieved December 6, 2011. See the Jason Kanter's web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Kappraff 2005] Jay Kappraff and Ernest G. McClain. “The System of Proportions of the Parthenon: A Work of Musically Inspired Architecture”, Music in Art, Volume 30, Number 1/2, Spring–Fall 2005, pages 5–16. Publication 41818772 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: The architecture historian Anne Bulckens has studied the proportions of the Parthenon based on the measurements of Francis Cranmer Penrose (the measurements referred to by most scholars). In her work she discovered the length of a module and measure of a Parthenon foot used throughout the structure conforming well to the architectural principals described by Vitruvius. The principal result of her studies is that all of the significant measurements can be reckoned as integers within the preset tolerance of 0.2% although the load bearing elements have deviations of far less. We have discovered that the integers can be correlated with the musical scale of Pythagoras. Most notably the length, width, and heights of the outer temple and the length and width of the celia form a pentatonic scale. Our contribution to Bulckens' work lies in trying to review it carefully within philosophical principles prevalent in the fifth century B.C. when it was under construction, for which we rely on Philolaus, the earliest Pythagorean author, writing in Tarentum while the Parthenon was under construction. This analysis may prove significant both for the study of other Greek temples and for a better understanding of Pythagorean influence on Greek ideals.

[Keenan 2003] David C. Keenan. Harmonic Errors in Equal Tempered Musical Scales, February 24, 2003. Originally published February 19, 1998. Harmonic Errors in Equal Tempered Musical Scales Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Keislar 1991] Douglas Keislar, Easley Blackwood, John Eaton, Lou Harrison, Ben Johnston, Joel Mandelbaum and William Schottstaedt. “Six American Composers on Nonstandard Tunings”, Perspectives of New Music, Volume 29, Number 1, Winter 1991, pages 176–211. Publication 833076 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Guided NAFlutomat - Step 4. Temperament, Glossary of Native American Flute Terms

[Kellner 1979] Herbert Anton Kellner. “A Mathematical Approach Reconstituting J. S. Bach's Keyboard-Temperament”, Bach, Volume 10, Number 4, October 1979, pages 2–8. Publication 41640089 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Kellner 1999] Herbert Anton Kellner. “A Mathematical Approach Reconstituting J. S. Bach's Keyboard-Temperament”, Bach, Volume 30, Number 1, Spring–Summer 1999, pages 1–9. Publication 41640471 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Kopiez 2003] Reinhard Kopiez. “Intonation of Harmonic Intervals: Adaptability of Expert Musicians to Equal Temperament and Just Intonation”, Music Perception: An Interdisciplinary Journal, Volume 20, Number 4, Summer 2003, pages 383–410, doi:10.1525/mp.2003.20.4.383. Publication 10.1525/mp.2003.20.4.383 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: This study examines the deviation in the intonation of simultaneously sounding tones under the condition of an embedded melody task. Two professional musicians (trumpet players) were chosen as subjects to play the missing upper voice of a four-part audio example, while listening via headphones to the remaining three parts in adaptive five-limit just intonation and equal temperament. The experimental paradigm was that of a controlled varied condition with a 2 (tuning systems) × 5 (interval categories) × 5 (renditions) × 2 (players) factorial design. An analysis of variance showed a nonsignificant difference between the average deviation of harmonic intonation in the two systems used. Mean deviations of 4.9 cents (SD = 6.5 cents) in the equal-temperament condition and of 6.7 cents (SD = 8.1 cents) in the just-intonation condition were found. Thus, we assume that the musicians employed the same intonation for equaltemperament and just-intonation versions (an unconscious "always the same" strategy) and could not successfully adapt their performances to the just-intonation tuning system. Fewer deviations could be observed in the equal-temperament condition. This overall tendency can be interpreted as a "burn in" effect and is probably the consequence of longterm intonation practice with equal-temperament. Finally, a theoretical model of intonation is developed by use of factor analysis. Four factors that determine intonation patterns were revealed: the "major third factor," the "minor third and partials factor," the "instrumental tuning factor," and the "octave-minor seventh factor." To summarize, even in expert musicians, intonation is not determined by abstract tuning systems but is the result of an interaction among compositional features, the acoustics of the particular musical instrument, and deviation patterns in specific intervals.

[Ladd 2008] D. Robert Ladd. Intonational Phonology, Cambridge Studies in Linguistics, published by Cambridge University Press, 2008, 349 pages, ISBN 0-521-67836-6 (978-0-521-67836-0). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Lee-KM 2015] Kyung Myun Lee, Erika Skoe, Nina Kraus, and Richard Ashley. “Neural Transformation of Dissonant Intervals in the Auditory Brainstem”, Music Perception: An Interdisciplinary Journal, Volume 32, Number 5, June 2015, pages 445–459, doi:10.1525/mp.2015.32.5.445. Publication 10.1525/mp.2015.32.5.445 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Acoustic periodicity is an important factor for discriminating consonant and dissonant intervals. While previous studies have found that the periodicity of musical intervals is temporally encoded by neural phase locking throughout the auditory system, how the nonlinearities of the auditory pathway influence the encoding of periodicity and how this effect is related to sensory consonance has been underexplored. By measuring human auditory brainstem responses (ABRs) to four diotically presented musical intervals with increasing degrees of dissonance, this study seeks to explicate how the subcortical auditory system transforms the neural representation of acoustic periodicity for consonant versus dissonant intervals. ABRs faithfully reflect neural activity in the brainstem synchronized to the stimulus while also capturing nonlinear aspects of auditory processing. Results show that for the most dissonant interval, which has a less periodic stimulus waveform than the most consonant interval, the aperiodicity of the stimulus is intensified in the subcortical response. The decreased periodicity of dissonant intervals is related to a larger number of nonlinearities (i.e., distortion products) in the response spectrum. Our findings suggest that the auditory system transforms the periodicity of dissonant intervals resulting in consonant and dissonant intervals becoming more distinct in the neural code than if they were to be processed by a linear auditory system.

[Lehman 1967] Paul R. Lehman. Review of An Investigation of the Tuning Preferences of a Selected Group of Singers with Reference to Just Intonation, Pythagorean Tuning, and Equal Temperament, Bulletin of the Council for Research in Music Education, Number 10, Summer 1967, pages 51–53. Publication 40316936 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Lewis-P 1998] Pierre Lewis. Understanding Temperaments, Version 1.2, 1998. Understanding Temperaments Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Long 2008] Derle Ray Long. Coincidence Theory: Seeking a Perceptual Preference for Just Intonation, Equal Temperament, and Pythagorean Intonation in Excerpts for Wind Instruments, Ph.D. dissertation – The University of Southern Mississippi, 2008. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Coincidence theory states that when the components of harmony are in enhanced alignment the sound will be more consonant to the human auditory system. An objective method of examining the components of harmony is by investigating alignment of the mathematics of a particular sound or harmony. The study examined preference responses to excerpts tuned in just intonation, Pythagorean intonation, and equal temperament. Musical excerpts were presented in pairs and study subjects simply picked one version from the pair that they perceived as the most consonant. Results of the study revealed an overall preference for equal temperament in contradiction to coincidence theory. Several additional areas for research are suggested to further investigate the results of this study.

[Loosen 1993] Franz Loosen. “Intonation of Solo Violin Performance with Reference to Equally Tempered, Pythagorean, and Just Intonations”, Journal of the Acoustical Society of America, Volume 93, Number 1, January 1993, pages 525–539, doi:10.1121/1.405632 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Determined which musical scale best modeled the solo performances of 8 25–33 yr old professional violinists, who played the diatonic scale of C major, very slowly, without vibrato, and as accurately as possible (i.e., the usual way of playing when a string teacher shows a pupil how a scale sounds). When individual scales were analyzed as a whole, violin performances fit Pythagorean and equally tempered intonations more precisely than the just intonation; performances fit the Pythagorean and the equally tempered model almost equally well. Interval size (analyzed not considering the context of the individual scales) was halfway between the interval sizes in Pythagorean and equally tempered intonations.

[Loosen 1995] Franz Loosen. “The Effect of Musical Experience on the Conception of Accurate Tuning”, Music Perception: An Interdisciplinary Journal, Volume 12, Number 3, published by the University of California Press, Spring 1995, pages 291–306. Publication 40286185 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: The present study investigates the relationship between musical experience and subjects' conception of accurate tuning. In a paired comparisons experiment, 7 violinists, 7 pianists, and 10 nonmusicians evaluated the tuning of computer-generated, ascending and descending eight-tone diatonic scales of C major. Subjects were required to indicate which member of the pair was "most accurately tuned." The subjects were unaware that all scales were perfectly tuned in the Pythagorean, just, or equal-tempered intonation, respectively. Results showed that (1) violinists, as a group, preferred Pythagorean to equal-tempered scales more frequently than vice versa (p< .01), (2) pianists preferred equaltempered to Pythagorean scales more frequently than vice versa (p < .01), (3) violinists and pianists judged just intoned scales to be less accurately tuned than either Pythagorean or equal-tempered scales (p < .01), and (4) nonmusicians did not show any preference for any of the three intonation models. These findings confirm the claim that subjects' conception of accurate tuning is determined by musical experience rather than by characteristics of the auditory system. Relevance of the results to assessment of tonal perception is discussed.

[Mandelbaum 1961] Mayer Joel Mandelbaum. Multuple Division of the Octave and the Tonal Resources of 19-Tone Temperament, Doctoral dissertation – Indiana University, June 1961, 461 pages. Multuple Division of the Octave and the Tonal Resources of 19-Tone Temperament Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Guided NAFlutomat - Step 4. Temperament, Glossary of Native American Flute Terms

[Marcus 1993] Scott Marcus. “The Interface between Theory and Practice: Intonation in Arab Music”, Asian Music, Volume 24, Number 2, published by the University of Texas Press, Spring–Summer 1993, pages 39–58. Publication 834466 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Glossary of Native American Flute Terms, Guided NAFlutomat - Step 4. Temperament

Introduction: Sometime probably in the eighteenth century, theorists in the Middle East developed a theoretical scale of 24 notes per octabe. The first detailed discussion of this scale, written by Syrian theorists in the early nineteenth century, show that many considered the new scale to be composed of equal-tembered quarter tones. In an equal-tempered quarter-tone system, the notes occur at 50 cent intervals, i.e. at 50, 100, 150, 200 cents, etc.

[Mason-JA 1960] James A. Mason. “Comparison of Solo and Ensemble Performances with Reference to Pythagorean, Just, and Equi-Tempered Intonations”, Journal of Research in Music Education, Volume 8, Number 1, published by Sage Publications, Inc. on behalf of MENC: The National Association for Music Education, Spring 1960, pages 31–38. Publication 3344235 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[McClain 1979] Ernest G. McClain; Ming Shui Hung (translations). “Chinese Cyclic Tunings in Late Antiquity”, Ethnomusicology, Volume 23, Number 2, May 1979, page 205–224. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Messiaen 1944] Olivier Messiaen; John Satterfield (translation). The Technique of My Musical Language — La technique de mon langage musical, published by Alfonse Leduc, Paris, France, 1944. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Missin 2004] Pat Missin. Audio Examples of Just Intonation and Equal Temperament Applied to the Harmonica, 2004, retrieved July 6, 2015. Audio Examples of Just Intonation and Equal Temperament Applied to the Harmonica Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Monzo 2004] Joseph L. Monzo. “The Measurement of Aristoxenus's Divisions of the Tetrachord”, 2004. The Measurement of Aristoxenus's Divisions of the Tetrachord Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Renold 2004] Maria Renold; Bevis Stevens (translation); Anna R. Meuss (editor). Intervals, Scales, Tones and the Concert Pitch C = 128 HZ, published by Temple Lodge Publishing, East Sussex, England, 2004, 198 pages, ISBN 1-902636-46-5 (978-1-902636-46-7). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Publisher's description: Why is it that certain intervals, scales and tones sound genuine and others false? Is the modern person able to experience a qualitative difference in a tone's pitch? If so, what are the implications for modern concert pitch and how instruments of fixed tuning are tuned? Maria Renold tackles these and many other questions, providing a wealth of scientific data. Her pioneering work is the result of a lifetime's research into Western music's Classical Greek origins, as well as a search for new developments in modern times. She strives to deepen musical understanding through Rudolf Steiner's spiritual-scientific research, and she also elucidates many of Steiner's often puzzling statements about music. The results of her work include the following discoveries: that the octave has two sizes (a 'genuine' sounding octave is bigger than the 'perfect' octave); that there are three sizes of 'perfect' fifths; that an underlying 'form principle' for all scales can be found; and, most importantly, the discovery of a method of tuning the piano which is more satisfactory than equal temperament. She also gives foundation to some of Rudolf Steiner's statements such as: 'c is always prime' and 'c = 128 Hz = Sun'.

[Rich-R 2010] Robert Rich. Tuning Presets in the MOTM 650, 2010, 3 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Russell-J 2013] Jim Russell. Towards a Difference Limen of Pitch Perception, published by 21harmony.com, August 13, 2013, 4 pages. Towards a Difference Limen of Pitch Perception Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Every twelve-tone musical tuning has a quantifiable deviation in its step sizes from those of Equal Temperament. While larger differences are easily detectable to the human ear, a smaller difference may be unnoticeable.

Previous research into the Just Noticeable Differences (JND) or Difference Limen between concurrent tones of different frequencies provides a good estimate of the thresholds of human pitch perception under strict (laboratory) conditions and using simple signals. In a practical context such as music listening, these data are made less useful by the introduction of many simultaneous signals presented together.

A pilot study is conducted in which listeners are presented with a musical piece, the tuning of which drifts over the course of 90 seconds to one of three extents – 4.76 cents RMS (Equal Temperament drifting to Meantone Temperament), 10.15 cents RMS (Equal Temperament drifting to Just Intonation) and 0 (no drift in tuning – Equal Temperament throughout).

Listeners are more likely to report a drift in the music’s tuning if one occurs, but are not seen to be statistically more likely to report one when presented with a stronger level of drift in tuning. Furthermore, the proportion of listeners reporting the two drifting tunings to have indeed ‘gone out of tune’ is approximately half. A better investigative model is suggested to inform further study.

[Schellenberg 1996] E. Glenn Schellenberg and Sandra E. Trehub. “Natural Musical Intervals: Evidence from Infant Listeners”, Psychological Science, Volume 7, Number 5, September 1996, pages 272–277. Publication 40062961 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Ancient and medieval scholars considered tones related by simple (small-integer) ratios to be naturally pleasing, but contemporary scholars attribute the special perceptual status of such sounds to exposure. We investigated the possihility of processing predispositions for some tone combinations by evaluating infants' ability to detect subtle changes to patterns of simultaneous and sequential tones. Infants detected such changes to pairs of pure tones (intervals) only when the tones were related by simple frequency ratios. This was the case for 9-month-old infants tested with harmonic (simultaneous) intervals and for 6-month-old infants tested with melodic (sequential) intervals. These results are consistent with a biological basis for the prevalence of particular intervals historically and cross-culturally.

[Schellenberg 2001] E. Glenn Schellenberg. “Asymmetries in the Discrimination of Musical Intervals: Going Out-of-Tune Is More Noticeable Than Going In-Tune”, Music Perception: An Interdisciplinary Journal, Volume 19, Number 2, Winter 2001, pages 223–248. Publication 10.1525/mp.2001.19.2.223 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Listeners were tested on their ability to discriminate "standard" and "comparison" pure-tone musical intervals that differed in size by 20 cents (1/ 5 of an equal-tempered semitone). Some of the intervals were prototypic, equal-tempered perfect fifths (exactly 7 semitones, or 700 cents). Others were mistuned to various degrees (660, 680, 720, or 740 cents). The intervals were melodic (sequential) in Experiments 1 and 2 and harmonic (simultaneous) in Experiment 3. Performance was neither enhanced nor impaired in comparisons that included the prototype. In other words, no "perceptual magnet" or "perceptual anchor" effects were observed. Nonetheless, performance was markedly asymmetric. Regardless of listeners' musical expertise, discrimination was superior when the standard interval was more accurately tuned than the comparison interval (e.g., 700- cent standard, 680-cent comparison), compared with when the comparison was more accurately tuned than the standard (e.g., 680-cent standard, 700-cent comparison).

[Surjodiningrat 1972] Wasisto Surjodiningrat, P. J. Sudarjana, and Adhi Susanto. Tone Measurements of Outstanding Javanese Gamelan in Jogjakarta and Surakata, Second Revised Edition, published by Gadjah Mada University Press, Jogjakarta, Indonesia, 1972, vi + 59 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Vurma 2006] Allan Vurma and Jaan Ross. “Production and Perception of Musical Intervals”, Music Perception: An Interdisciplinary Journal, Volume 23, Number 4, published by the University of California Press, April 2006, pages 331–344. Publication 10.1525/mp.2006.23.4.331 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: This Article Reports Two Experiments. In the first experiment, 13 professional singers performed a vocal exercise consisting of three ascending and descending melodic intervals: minor second, tritone, and perfect fifth. Seconds were sung more narrowly but fifths more widely in both directions, as compared to their equally tempered counterparts. In the second experiment, intonation accuracy in performances recorded from the first experiment was evaluated in a listening test. Tritones and fifths were more frequently classified as out of tune than seconds. Good correspondence was found between interval tuning and the listeners responses. The performers themselves evaluated their performance almost randomly in the immediate post-performance situation but acted comparably to the independent group after listening to their own recording. The data suggest that melodic intervals may be, on an average, 20 to 25 cents out of tune and still be estimated as correctly tuned by expert listeners.

[Zaw 1940] Khin Zaw. “Burmese Music — A Preliminary Enquiry”, Bulletin of the School of Oriental and African Studies, University of London, Volume 10, Number 3, published by Cambridge University Press, 1940, pages 717–754, doi:10.1017/S0041977X0008873X. Publication 608839 on JSTOR (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Introduction: Burmese music is a virgin field for research. Nobody can bewail this virginity more than myself. To help me there does not seem to exist a single western work on Burmese music though there are such classics as Fox Strangways' on Indian and J. H. Levis' on Chinese music. Many writers on Burma have passed remarks, kind or humorous, on Burmese music. But few have attempted a technical study of it. Nothing Burmese escaped the notice of Sir James George Scott, of course. But I know of only two who left some technical remarks on Burmese music: Paul Edmonds, the author of Peacocks and Pagodas; and P. A. Mariano, in an appendix on Burmese music to that most lovingly produced book Burma by Max and Bertha Ferrars.

[Zaw 1940a] Khin Zaw. “Burmese Music — A Preliminary Enquiry”, Journal of the Burma Research Society, Volume 30, Part 3, December 1940, pages 387–422. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

 
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