## Tuning and Temperament: A Historical SurveyThe demands of tuning (attaining the perfect scale) and temperament (the compromises necessary for composing in every key) have challenged musicians from the earliest civilizations onward. This guide surveys these longstanding problems, devoting a chapter to each principal theory and offering a running account of the complete history of tuning and temperament. Organized chronologically, the book features a helpful glossary and numerous illustrative tables, and it requires minimal background in music theory. This new reissue is currently the only edition in print of a much-quoted classic. 9 figures. 180 tables. |

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### Contents

History of Tuning and Temperament Ii Greek Tunings | 1 |

Meantone Temperament | 6 |

Other Varieties of Meantone Temperament | 31 |

Equal Temperament | 32 |

Fig A Schneegass Division of the Monochord | 38 |

Geometrical and Mechanical Approximations | 49 |

metric Mean Proportionals | 52 |

Numerical Approximations | 55 |

Modifications of Regular Temperaments | 139 |

Temperaments Largely Pythagorean | 151 |

Bermudos Method for Placing Frets | 165 |

Divisions of Ditonic Comma Metius System | 177 |

Good Temperaments | 178 |

From Theory to Practice | 185 |

Tuning of Keyboard Instruments | 188 |

Just Intonation in Choral Music | 196 |

E Strahles Geometrical Approximation | 66 |

Just Intonation | 71 |

Theory of Just Intonation | 102 |

Multiple Division | 107 |

Notes inthe Octave | 109 |

Equal Divisions | 113 |

Theory of Multiple Division | 128 |

VI1 Irregular Systems | 133 |

Present Practice | 199 |

Literature Cited | 203 |

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226 | |

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### Common terms and phrases

31-division approximation Aristoxenus arithmetical division B C Cents bonded clavichord Cents Lengths Names cents sharp Chapter chromatic semitone circle of fifths clavichords clavier comma flat comma sharp Comma Temperament compass construction correct diatonic semitone ditonic comma divided E F x Cents E F x G Ellis enharmonic equal semitones equal temperament error fifths tempered flat by 1/4 fretted instruments Galilei’s Ganassi’s geometrical Grammateus intervals intonation irregular systems Johann keyboard instruments keys Leipzig logarithms lute major third mean deviation mean proportionals meantone temperament Mersenne Mersenne’s mesolabium method minor monochord multiple division musique Names Cents Names G Neidhardt’s Fifth-Circle notes numbers octave organ perament perfect fifth pitches practice pure fifths pure thirds Pythagorean tuning Ramis ratio regular temperament Salinas Sauveur scale Schlick shown in Table string string-lengths superparticular symmetric syntonic comma temperament Table tempered fifths theorists Third-Circle tone triads tuning system Werckmeister wolf fifth Zarlino