CHALLENGING EQUAL TEMPERAMENT: PERCEIVED DIFFERENCES BETWEEN TWELVE-TONE EQUAL TEMPERAMENT AND TWELVE FIFTH-TONES TUNING Mikko Leimu Master’s Thesis Music, Mind & Technology Department of Music 5 January 2017 University of Jyväskylä JYVÄSKYLÄN YLIOPISTO Tiedekunta – Faculty Laitos – Department Faculty of Humanities Department of Music Tekijä – Author Mikko Leimu Työn nimi – Title Challenging equal temperament: Perceived differences between twelve-tone equal temperament and twelve fifth-tones tuning. Oppiaine – Subject Työn laji – Level Music, Mind & Technology Master’s Thesis Aika – Month and year Sivumäärä – Number of pages December 2016 90+7 Tiivistelmä – Abstract A listening experiment was arranged to evaluate perceptual preferences between two musical tuning systems: twelve-tone equal temperament (i.e. the current international standard) and twelve fifth-tones tuning. The latter being a system that, according to its author Maria Renold, provides a more accurate and aurally genuine reproduction of musical harmonics. Hence, it is considered a superior tuning method compared to the equal temperament tuning. 34 participants (mainly experienced musicians) evaluated realistic musical stimuli consisting of intervals, chords and simple musical sequences using a grand piano timbre. Results showed that the standard twelve-tone equal temperament system was found overall more in-tune, with ca. 68% of the participants preferred it over the twelve fifth-tones tuning. This is considered to be most likely due to enculturation affects, i.e. people have preferred the tonality that is more familiar to them. No evidence for the supposed aural genuineness of the Renold’s tuning systems was found. Instead, it may be concluded that intonation preferences in perceptual context are subject to high amounts of individual variation and clear definition of tonality preferences is often a difficult task. Asiasanat – Keywords Tuning, intonation, temperament, equal temperament, scale of twelve fifths, twelve fifth-tones tuning, harmonics Department of Music, University of Säilytyspaikka – Depository Jyväskylä Muita tietoja – Additional information CONTENTS 1 INTRODUCTION .............................................................................................................. 5 2 THEORETICAL BACKGROUND ................................................................................... 8 2.1 Sound, frequency & pitch ...................................................................................................................... 8 2.2 Harmonic series ................................................................................................................................... 10 2.3 Intervals ............................................................................................................................................... 12 2.4 Perception of frequency and pitch ....................................................................................................... 14 2.5 Consonance and dissonance ................................................................................................................ 17 2.6 Perception of intervals ......................................................................................................................... 20 2.7 Tuning and temperament ..................................................................................................................... 23 2.8 Natural tunings .................................................................................................................................... 25 2.8.1 Pythagorean tuning .................................................................................................................... 25 2.8.2 Just intonation ............................................................................................................................ 28 2.9 Temperament systems ......................................................................................................................... 29 2.9.1 Meantone temperament ............................................................................................................. 30 2.9.2 Equal temperament .................................................................................................................... 31 2.9.3 Origins of the equal temperament.............................................................................................. 33 2.9.4 Equal temperament criticism ..................................................................................................... 35 2.10 The scale of twelve true fifths ............................................................................................................. 39 2.10.1 Aural genuineness ...................................................................................................................... 40 2.10.2 Mathematics of the scale of twelve true fifths ........................................................................... 43 2.10.3 Comparison with other tuning systems...................................................................................... 47 2.10.4 Auditory roughness comparison ................................................................................................ 49 3 RESEARCH TOPIC ........................................................................................................ 51 3.1.1 Previous research ....................................................................................................................... 51 3.1.2 Current study ............................................................................................................................. 53 3.1.3 About comparative research ...................................................................................................... 54 3.1.4 Hypothesis ................................................................................................................................. 55 4 METHOD ......................................................................................................................... 56 4.1 Participants .......................................................................................................................................... 57 4.2 Stimuli ................................................................................................................................................. 57 4.3 Design .................................................................................................................................................. 60 4.4 Pilot ..................................................................................................................................................... 62 5 RESULTS......................................................................................................................... 63 5.1 Experiment part 1 ................................................................................................................................ 63 5.2 Experiment part 2 ................................................................................................................................ 65 5.3 Experiment part 3 ................................................................................................................................ 69 5.4 Discussion ........................................................................................................................................... 73 5.4.1 Tonality preferences .................................................................................................................. 73 5.4.2 Evaluation consistency .............................................................................................................. 75 5.4.3 Aural genuineness ...................................................................................................................... 77 5.4.4 Just noticeable frequency differences ........................................................................................ 78 5.4.5 Enculturation affects .................................................................................................................. 79 5.4.6 Methodology and design............................................................................................................ 80 5.5 Conclusions ......................................................................................................................................... 81 REFERENCES ......................................................................................................................... 82 APPENDICES .......................................................................................................................... 91 Appendix A ........................................................................................................................................................ 91 Appendix B ........................................................................................................................................................ 92 Appendix C ........................................................................................................................................................ 93 Appendix D ........................................................................................................................................................ 95 5 1 INTRODUCTION In music, a system of tuning is a specification that defines the