The Art of Tuning - Claude Montal
The Art of Tuning - Claude Montal
cover

The Piano Technicians Guild Foundation (PTGF) is pleased to announce the publication of The Art of Tuning, Fred Sturm’s English translation of Claude Montal’s book l’Art d’accorder soi-même son piano, the first comprehensive text on piano tuning and repair. Published in France in 1836 and revised in 1865, it spans three decades of the development of the piano, during the period when Chopin and Liszt were at the height of their careers.

Piano technician and pianist Fred Sturm has translated Montal’s book, in both its original 1836 version and that of the revised edition Montal published in 1865. He has combined these translations for publication by presenting the 1865 version as the main text, and including material from the original 1836 edition in footnotes and appendices, allowing the reader to compare the two versions so as to see how the piano had evolved during those three decades. This publication of The Art of Tuning includes all the illustrations from the original plates, explanatory material in footnotes, a translator’s introduction providing both historical context and biographical details concerning Montal, and a preface by tuning scholar and fortepiano builder Paul Poletti.

The Art of Tuning contains materials of interest to a broad variety of readers. As would be expected from the title, Montal provides a comprehensive account of his tuning method, which he developed himself and honed while teaching it to others before setting it down on paper. His is a very pragmatic approach, training the ear to hear how intervals and chords should sound in equal temperament, then presenting a procedure for creating those intervals.

But Montal went far beyond creating a tuning manual. He wanted to introduce the piano to his readers in all its details. In the course of the book, pianos of a wide variety of styles and designs, many of them unique to the mid 19th century, are vividly described. Criteria are given for judging how well a piano is built, the quality of its tone and the responsiveness of its action. He provided advice for how to care for the instrument, and step-by-step instructions for packing a piano in a crate for moving.

The most extensive section of the book is devoted to a wide range of repairs, for the square pianos of the late 18th and early 19th century as well as the more modern uprights and grands. Techniques for such procedures as re-covering hammers, replacing strings and parchment hinges, and fashioning replacements for broken springs are described in basic, step-by-step detail. Regulation and troubleshooting are covered separately for square, upright and grand pianos, including malfunctions, squeaks and clicks.

In the 1836 edition, Montal included a lengthy appendix on the history of the piano, with special emphasis on the first decades of the 19th century, a seminal period of piano history. In 1865 he added a chapter on education for blind people, giving insight into early development of educational programs created specifically for blind people, offering them training in a lucrative and honorable profession. A chapter on acoustics demonstrates the accuracy with which Montal approached the mathematics of temperament.

In his appendix to the 1865 edition, Montal included various reports and reviews of his own work, both as piano manufacturer and as author, providing considerable biographical material. He also quoted lengthy passages from two biographies written about him during his lifetime, in his chapter about teaching blind people the profession of piano technician.

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About the Author

Montal was a major figure in the musical world of mid 19th century Paris. Blind from the age of five, Montal taught himself to tune and repair pianos, began teaching his tuning method, and then created his book, aimed at amateurs and pianists as well as those who made a living working on pianos. Montal’s writing style is vivid and minutely descriptive, giving a detailed look into the pianos of his time from the point of view of the piano technician. The tuning portion of the book was soon translated into several other languages, but never into English.

Montal later became a major, respected piano manufacturer, who received many medals including the Legion of Honor, and patented several important inventions. He was also responsible for the creation of a training program in piano technology at the National Institute for Blind Youth of Paris (Institut National des Jeunes Aveugles), a program that was imitated in many other countries.

About the Translator

Fred Sturm, RPT, is a professional piano technician with a deep interest in the history of the piano and of the skills and crafts involved in the profession of piano technician. He has researched the history of tuning and temperament in detail, focusing on the practical activity of tuning by reading instructions and first-hand accounts from throughout Europe over the past four centuries, always relying on original sources. This resulted in a series of nine articles entitled “A Clear and Practical Introduction to the History of Temperament,” published in the Piano Technicians Journal in 2009-10, for which Sturm received the coveted Jack Greenfield Award from the Piano Technicians Guild

During his research for that project, Sturm came upon the work of Claude Montal, which he thought should be available to non-French readers. In the course of translation, he investigated Montal’s life, scouring the 19th-century Parisian musical press for articles, obtaining copies of all of Montal’s patents, and collecting other biographical and background material. 

Sturm is also a performing and recording classical pianist, with a specialty in Latin American music, with a particular specialty in Brazilian composer Heitor Villa-Lobos. He has recorded six CDs to date, the latest of which is devoted to the works of contemporary Mexican composer Federico Ibarra. He makes his home in Albuquerque, New Mexico, where he has been employed as piano technician for the University of New Mexico for over 25 years. For further information, see http://fredsturm.net.

Advance Praise for The Art of Tuning

 

“A very important work . . . It proves that in the first half of the 19th century, even without tuning by beats, a good piano tuner could achieve Equal Temperament with an accuracy rivaling modern-day tuners with their methods and devices.

“Montal . . . provide[s] a unique view into the world of piano tuners and technicians in mid-19th century Europe [with] useful hints for repairing the action of square pianos.

“I strongly recommend this book to anybody involved in either piano servicing or studying piano history and tuning.”

—Claudio Di Veroli
Author of Unequal Temperaments

 

 “A fascinating and valuable contribution to the technical literature [that] offers intriguing biographical and social insights to Montal and his profession. Congratulations to . . . PTGF for taking on this useful project.”

—Laurence Libin
Editor-in-Chief, Grove Dictionary of Musical Instruments

 

“An essential library addition for anybody hungry to know more about early to mid-19th century European pianos and tuning. An enjoyable glimpse into the world . . . not so unlike that of the modern piano technician.”

—Anne Acker
Senior Editor, Grove Dictionary of Musical Instruments, 2nd ed.

 

Fred Sturm’s brilliant translation of The Art of Tuning brings the world of a piano technician in nineteenth-century Paris vividly to life. Reading Montal, you feel as though the instruments of his day are under your fingers, and you are holding his tools and materials in your hands.

—Daniel Levitan

Author, The Craft of Piano Tuning

 

Many years ago I had the random good fortune to inherit from an older colleague a copy of the original 1836 edition of Claude Montal's great work of piano technology. Clearly a work of genius, this is not just a book of instructions on how pianos were tuned and repaired in nineteenth-century France: it should be regarded as a fundamental resource for the history of an instrument of vital importance to the history of music itself. One can only applaud the publication of this superb translation, which deserves a place in every serious music library.

—John Koster

Professor of Music & Curator of Keyboard Instruments,

National Music Museum, University of South Dakota  

Translator's Preface

A few years ago, when I first read Montal's l'Art d'accorder soi-même son piano, I was particularly struck by the immediacy of his writing style. Here was someone speaking to me across a span of over 150 years, yet the experiences he was describing were precisely the same as my own, as a working piano tuner and technician. The differences lay mostly in the fact that, where I might face a spinet upright piano of the 20th century, the sort of inexpensive instrument Montal would usually have serviced was a small square piano without escapement. Piano designs had changed, but the procedures and experiences remain very familiar. (For the full Preface, download the pdf below)

Translator's Preface, complete.
TranslatorsPreface.pdf
Adobe Acrobat document [113.0 KB]

Montal's original table of contents

Like most books of the 19th century, Montal's Art of Tuning had a very lengthy table of contents, covering the contents of each chapter in detail. This was replaced in the translated version by an index. 

Table of Contents from Montal's 1865 edition of The Art of Tuning
A very detailed account of the contents of each chapter of the book, seven pages in length.
zTable of Contents65.pdf
Adobe Acrobat document [104.9 KB]

Table of Contents

 

Introduction

The need and possibility of taking care of your own piano yourself. – Usefulness of this work for amateurs, tuners, craftsman makers, and blind tuners. – Additions to this work. – New tables and plates in this third edition. – Examination of works written about piano tuning. – Instruments or mechanical means invented to facilitate the tuning of the piano. –  Sonometer of F. Loulié. – Diapasorama of Matrot. – Chromameter of Roller and Blanchet. – Tuning Guide of Delsarte. – History of temperament. – Necessity of equal temperament. – Table of chapters and appendix of this work. – Conclusion.

 

Chapter 1. – Summary of the elementary principles of music needed in order to understand this book      

Tones of the scale. – Steps and half steps of the natural scale. – Comma. – Sharps, flats, naturals, double sharps, double flats; chromatic semitone, diatonic semitone; chromatic scale; enharmonic notes; diatonic genre, chromatic genre, harmonic genre; intervals; natural intervals, inversions; consonant and dissonant intervals; major mode, minor mode; accidental signs and key signs; harmonic circle.

 

Chapter 2. – A succinct account of harmony                                                                       

Chords. – The perfect major chord. – The perfect minor chord. – Their inversions. – Modulation. – The harmonic circle in four part perfect chords.

 

Chapter 3. – Pianos of diverse forms; their principal internal parts                                    

Square pianos. – Grand pianos. – Upright pianos of various forms. – False soundboard. – Tuning pins. – Pin block. – Hitch pin rail. – Hitch pin nut – Tuning pin nut – Bridge. – Speaking length of strings. – Dampers. – Damper lifting wires. – Action proper. –Principle parts of the action. – Action systems. – Fixed jack action. – Double fixed jack action. – Escapement and double escapement action. – Petzold escapement. – English escapement for grand pianos. – Érard double escapement action for grand pianos. – Various double escapement and repetition actions of Montal for grand and square pianos. – Upright action, the ones most generally used. – English action. – Érard action. – Various Montal actions. – Roller action. – Pianos with double strings. – Pianos with triple strings. – Range of pianos. – Various Pedals, forte, celeste, sourdine, bassoon, shift, expression, jalousie, prolonged tone.

 

Chapter 4. – Layout and labeling of tuning pins; their relationship with the keys of the keyboard 

Tuning pins placed two by two or three by three. – Relationship of groups to the keys indicated by the letters of the alphabet. – Disposition of these groups in different pianos. – Pianos with quadruple strings.

 

Chapter 5. – Tuning wrench. – Mute. – Tuning fork, how to use it.

Tuning wrench. – Ordinary wrench. – Curved wrench. – Wrench with exchangeable shafts. – Mute for square pianos. – Mute for grand pianos and mute for upright pianos. – Tuning fork [diapason]. – Other meanings of the word diapason. – Old Pitch of the Opera. – Of the Comic Opera. – Of the Italian Opera. – Their number of vibrations. – Advantage of a standard pitch. – History of pitch. – Origin of the diapason normal [standard pitch]. – Adoption of standard pitch by ministerial decree. – Its form and number of vibrations.

 

Chapter 6. – Piano to use for the study of tuning                                                                

 

Chapter 7. – Exercise to learn to use the wrench and to perfect the organ of hearing, by tuning consonances and the perfect major chord rigorously justly                                                                                                                                              

Exercise to learn to use the wrench. – Precautions to take so that the string will stay in tune. – Beats. – Exercise to perfect the organ of hearing. – Tuning the unison, the octave, the fifth. – Means to habituate the ear to find the fifth when setting pitch on new pianos. – Tuning the major third and the perfect major chord.

 

Chapter 8. – Temperament and the perfect major chord suitably tempered                       

Thirty-five tones of the physical scale reduced to twelve. – Major semitone. – Equal [mean] temperament. – Wide interval. – Narrow interval. – Alteration of the major third, the minor third, the fifth and their inversions. – Alteration of consonances. – Excess of the octave over three just major thirds. – Excess of four just minor thirds over the octave. – Ascending fifth. – Descending fifth. – Excess of four just fifths over the just major third. – Excess of twelve just fifths over the octave. – The perfect major chord suitably tempered.

 

Chapter 9. – Partition and Counter–Partition in A                                                              

Partition. – Example and Advantage of that of the author. – Remark concerning the stability of tuning. – Table A of the partition in A with proofs, in musical notation. – Explanation of the table. – Procedure to execute the partition. – Counter-Partition in A. – Table B of that counter-partition. – Procedure to execute the counter-partition.

 

Chapter 10. – Tuning the treble, the bass, and general verification of the tuning                

Pianos with double strings. – Precaution to take so as not to break wound strings. – General verification of the tuning. – Pianos with triple strings. – Quicker method for tuning the treble and bass of pianos with double strings.

 

Chapter 11. – Partition and counter-partition in C                                                              

Usage of this partition in certain countries. – Example and advantage of that of the author. –Table C of the partition in C with proofs in musical notation. – Explanation of the table. – Procedure to execute the partition. – Counter-Partition in C. – Table D of that counter-partition. – Procedure to execute the counter–partition. – Tuning the treble and the bass to complete the tuning of the piano.

 

Chapter 12. – Piano Strings. – How to replace them and the tools necessary for this operation     

Steel, iron and brass strings. – English strings. – Superior strings. – Viennese strings. – Strings from other areas. – Old Berlin strings. – Brass strings from Nuremberg. – Different systems of numbering. – Series of numbers and half numbers of English and Viennese (called German) strings by order of thickness. – Same for Berlin strings. – Relationship of English strings with Berlin strings. – Approximate relationship of commonly used Nuremberg strings with Berlin strings. – Tool to determine the exact thickness of strings. – Wrapped strings. – Solder and wrapping ends of these strings. – Tools necessary to replace strings. – Procedure for replacing strings. – General explanations. – Indication of string size numbers on the pin block. – Tails. – Different methods for making them. – How to proceed to replace strings. – Means for finding the thickness of strings when the numbers are not marked on the pin block. – Counter-point of the pin block. – Method of hooking the strings, stretching them, rolling them on the tuning pin, bringing them to pitch, and marking them.

 

Chapter 13 How to touch up a piano without tuning it completely                                   

 

Chapter 14 The influence of temperature on piano strings, and precautions to take when raising or lowering pitch by one or many semitones   

 

Chapter 15 Tuning many pianos together. – Tuning a piano to other instruments             

Tuning many pianos together. – Tuning the piano to the oboe and the flute, – to the Bassoon, – to the valved cornet. – Tuning to the clarinet, – to the flageolet, – to the horn. – Tuning the piano to stringed instruments, Violin, viola, bass, guitar, harp, etc., etc.

 

Chapter 16 Pianos of different forms and particular dispositions; how to tune them and replace their strings       

Transposing pianos. – Roller system. – Montal system. – Grand pianos. – Upright pianos. – Pianino. – Pianos with vertical strings and pianos with semi-oblique strings. – Vertical piano, called cabinet piano. – Piano with action on top. – Pianos with screw tuners. – Pianos with reversed soundboard. – Square Pianos with extended hitchpin rail, in which the groups of tuning pins are two by two in the same oblique line. – Square Pianos with extended hitchpin rail in which the groups of tuning pins follow an irregular pattern. – Pianos with quadruple strings.

 

Chapter 17 Qualities of a good piano                                                                                   

Qualities of tone. – What is understood by a large tone and a nervous tone. – Influence on the size of the soundboard on the strength of tone. – Evenness of tone in the different parts of the keyboard. – Character of the treble. – Defects often found in the mid range and treble. – Perfection of the keyboard. – Rapid repetition of the same note. – Actions with single and double escapement. – Precision of the keyboard. – Clarity of tone. – Precision of the dampers. – Pedal function, – Advantage of the expression pedal over the other pedals, – Resume of the qualities of a good piano. – Character of German, English and French pianos.– Qualities of the exterior of pianos.

 

Chapter 18 Solidity of a piano and duration of its tuning                                                    

Solidity. – Difficulty an amateur experiences in judging the solidity of a piano. – Explanation of solidity characteristics of the case. – Square pianos. – How to recognize if the case is too weak and yields to the tension of the strings. – What is understood by racking. – Means employed sometimes to contribute to the solidity of the case – Upright pianos with vertical, oblique and semi–oblique strings. – Solidity of their frame. – Advantages of flanges, bars and iron hitch pin rails for stability of tuning and conserving the soundboard. – Counter–tension framing. – Advantages of this construction. – Grand pianos. – Advantages of bars and iron hitch pin rails in the construction of grand pianos as well as brass nuts and agraffes on the pin block. – Causes of solidity of the soundboard. – Principal places where strings break, and causes of breakage. – Means to avoid this. – Length of the speaking length of strings. – Blow of the hammers. – Its influence on the good quality of tone. – Their proportions. – Advantages of extended hitch pin rails. – Use of the Petzold escapement. – Its superiority and problems. – English action in upright pianos. – It origin. – Its improvements. – Individual brass flanges, with pressure screws, etc. – Disadvantage of hammers strung on the same pin. – English action in grand and square pianos. – Double escapement action. – Solidity of the keyboard. – Its good construction. – Hammer covering. – Its influence on the quality of tone. – Preference for the use of felt– Use of felt instead of cloth for dampers. – Reflections concerning pedals and other parts of the piano. – Conditions for the Duration of tuning.

 

Chapter 19 Precautions to take to preserve a piano, and method to pack it                       

Precautions to take to preserve a piano. – Type of material to cover it. – Precautions against humidity; – against cold and heat; – against air currents; – against the rays of the sun. – Choosing where to place it. – Damage caused by humidity. –  Pitch at which to keep the piano. – Times when one should have a piano tuned. – Repose of the instrument after tuning. – Replacement of strings. – How to preserve the evenness of the keyboard. – Keeping it clean. – How to move a piano. – How to pack a square, grand and upright piano. – Special packing for across the sea.

 

Chapter  20 How to repair the principal problems that may arise in the piano action when deprived of a maker technician         

Difficulty of finding a maker technician in the country for urgent repairs. – Means of escaping this inconvenience. – Old pianos with fixed jacks. – How to remove the keyboard. – Indications and repairs of problems that keep a note from speaking in a fixed jack piano. – Repair of a hammer and a false hammer. – Repair of problems that keep the key from rising. – How to regulate the attack of the piano. – Damper repairs. – Repair of Pedals. – Square pianos with escapement. – How to remove the keyboard. – Causes that keep a note from speaking in square pianos with escapement. – How to repair them. – Problems that keep a Petzold escapement from functioning. – How to repair them. English semi–escapement. – How to regulate it. – English action in square pianos. – Problems that keep an English escapement from functioning. – How to remedy them. –Repair of a hammer in an escapement action. – How to repair a misstrike. – How to correct the rubbing of a hammer against the pin block. – How to make a hammer function when it stays up in the air. – Repair of problems that keep the key from rising in an escapement square piano. – Damper repairs. – Clicks in square pianos with fixed jacks and escapement and how to remedy them. – Clicks of the key. – Clicks of the hammer. – Clicks of the damper. – Whistles. – A few miscellaneous repairs. – How to make them go away. – How to make pedals function is square pianos with escapement, and how to make noises disappear. – Grand pianos. – How to remove the keyboard. – Precautions to take when replacing it, and to make the shift pedal function. – Various grand actions. – English action generally used with modifications. – Problems that keep a note from speaking in the English grand action and how to repair them. – Repair of problems that keep a key from functioning. – Repair of problems that keep an English escapement from functioning. – Repairs of a hammer in grand pianos. – Clicks in grand pianos. – Reflections of certain repairs of grand pianos. – Repairs of pedals of these same pianos. – Upright pianos. – Different types of upright pianos. – Their actions. – Causes that keep a note from speaking in upright pianos. – Problems that keep a key from rising. – How to repair them. – Problems that keep an English action in upright pianos from functioning, and how to repair them. – Observations on the different types of English actions in upright pianos. – Repair of a hammer in upright pianos. – How to remedy a misstrike in upright pianos with oblique strings. – Repair of dampers in upright pianos. – Repair of pedals. – Reflections on the expression pedal. – Proof that it is less subject than others to problems. – How to regulate the keyboard and action of upright pianos. – Leveling the keyboard. – Means of increasing or decreasing key dip. – How to remedy the settling that occurs at the contact of the keys with the action. – How to align the hammers to the strings. – Same, so as to give them play when they do not return freely to their place. – How to regulate the action in general. – Bridles. – Checks. – Set escapement. – Regulate the dampers, etc. – Clicks in upright pianos. – How to remedy them. – Clicks of the key. – Clicks of the hammer. – Clicks of the escapement and the damper. – Whistles [squeaks] and how to remedy them. – A few miscellaneous repairs. – How to proceed to replace the strings. – Replacement of loose tuning pins in the pin block. – How to remove and replace a tuning pin broken in the pin block. – How to re–cover the hammers. – Deerskin. – Felt. – Advantages of felt over deerskin. – Mold or press to cover hammers. – How to needle hammers, that is to say to make them softer. – Repair of a soundboard crack. – How to replace a pin in the hitch pin rail. – The same in the bridge and in the nut. – How to repair bridges and nuts when they are split. – Conclusions concerning repairs.

 

Chapter 21. – Blind tuners, teaching them their profession                                                 

Division of the chapter. – General considerations concerning blindness. – Education of blind people created by Valentin Haüy, their benefactor. – Schools for blind people. – Imperial Institution for Blind Youth of Paris. – Usefulness of the profession of tuning for blind people. – Aptitude and superiority of blind tuners. – Obstacles in the way of blind tuners. – Success of blind tuners. – Establishments that first hired blind people as tuners. – Blind piano makers. – Extract of a short work On the tuning of pianos by blind people by M. Gaudet, head of teaching at the Imperial Institution for blind people in Paris. – This extract contains the definitive account of the beginning of the profession of tuning for blind people. – New partition by Montal. – Montal tuner for professors of the Conservatory, after a difficult experience he was subjected to. – Public course of tuning according to the new method. – Exposition of the products of industry of 1834. – Brief version of The Art of tuning one’s piano oneself by Montal. – Creation of the piano factory of Montal. – Publication of the complete work on the tuning of the piano. – Extract of a biography of Montal and his works, by M. Dufau, former director of the Institution for blind people. – Process for teaching tuning to blind people. – Practical part of this teaching. – Teaching blind people all the exterior parts of the piano. – How to have them disassemble these instruments. – Teaching blind people all the interior parts of the piano. – Explanation of the function of each of these parts. – Knowledge for blind people to acquire concerning the letters labeling the tuning pins. – Their relationship with the keys of the keyboard. – Difficulties presented by this. – Diverse groupings of tuning pins. – Differences of disposition. – Manner of marking tuning pins for blind people. – Manner for having them know all the tuning pins by means of the marks. – Particular manner for marking pins of square pianos. – Observations on the way to hold the fingers to find pins. – Use by blind people of the tuning wrench, wedge mute, and tuning fork. – Way to hold the wrench and place it. – Particular way for blind people to place the mute. – Piano to use for studying tuning. – Exercises to learn to use the wrench and perfect the organ of hearing. – Temperament and tuning the tempered perfect chord. – Study of the partition in A and the counter-partition. – Tuning the treble, the bass, and general verification of the tuning. – Partition in C and counter-partition. – Tables of partitions and counter-partitions. – Strings of the piano. – Their thicknesses. – Their numbering. – Means for blind people to know them. – Gauge. – Particular observations for blind people. – How to make tails. – How to replace strings. – Knowledge of the tools needed for this operation. – How to touch up a piano. – Influence of temperature on the tuning of a piano. – Tuning many pianos together and with other instruments. – Tuning pianos of different forms and constructions. – Particular advice for blind people. – Knowledge of the qualities of a good piano. – Solidity of a piano and duration of its tuning. – Conservation of a piano. – Advice to blind people for packing a piano for moving. – Repairs that are possible for blind people to make. – Difficulties that can arise. – Use of a young sighted person as a helper. – Knowledge of tools used to work wood and metal. – Precautions to use for glue. – Small woodworking projects executed by blind people. – Types of repair that blind people can make on pianos. – Precautions for blind people to take when removing the keyboard and action from the instrument. – Advice to blind people about repairs. – General conclusions about the profession of tuning for blind people. – Conclusions.

 

Chapter 22 Acoustics                                                                                                           

Production and propagation of sound. – Vibration. – Tones. – Noise. – Means to prove the existence of vibrations. – Transmission of sound. – Speed of sound. – Means to determine the speed of sound. – Comparison and numerical expression of tones. – Principles of low and high pitch of a tone. – Development of these principles. – Consequences one can draw for the piano and the harp. – Influence of temperature on instruments. – Causes of the variation of gut strings and drum skins. – Monochord or sonometer. – Description of that instrument. – Divisions of the string into aliquot parts. – Notes that result. – Number of their vibrations. – Table of the number of vibrations of the notes of the scale, with the length of the strings. – Comparison of the tones of this table. Major step and the minor step that results. – Their number of vibrations. – Diatonic scale, – Position of the minor steps. – Practical application of the monochord. – Determination of the tones of the scale in different octaves, – Determination of any tone of which you know the numerical value. – Sharps, flat, semi–tone, comma, limma, and apotome. – Their numerical value. – Table of these intervals. – Difference that exists between theory and practice concerning semitones. – Mathematical demonstration of temperament. – Proof that three ascending major thirds make less than an octave. – Proof that four ascending minor thirds make more than an octave. – Proof that twelve ascending just fifths produce a B sharp higher than the octave. – Evaluation of the alteration of consonant intervals. – Difference between the just third and the third produced by four fifths. – Demonstration of these same principles of alteration for descending intervals. – Alteration of dissonances. – Manner to calculate in decimal fractions the numerical expression of the twelve mean semitones with the length of strings these semitones produce. – Manner to calculate the length of strings of this table. – Comparison of true and mean chromatic scales with the length of strings. – Evaluation of true intervals and mean semitones. – Harmonic tones. – Nodes of vibrations. – Means to recognize them. – Vibrations of surfaces. – Nodal lines. – Influence of surrounding bodies on the sonority of instruments. – Usefulness that can be drawn from consideration of nodal lines in the soundboard.

 

Appendix                                                                                                                              

Reviews of the first editions of this work. – Reports of various juries and appreciations of artists concerning the manufacture and improvements of the pianos of M. Montal. – Report by M. Francoeur to the Society for the Encouragement on The Art of Tuning . . .. – Report by M. Bienaimé to the Free Society of the Fine Arts on The Art of Tuning . . .. – Report by M. Dufau to the international jury of the Universal Exposition of London in 1862 on The Art of Tuning . . .. – Extract from a report by M. La Hausse to the Academy of Industry on the manufacture of pianos by M. Montal. – Extract of a report by M. Kerris to the Society for the Encouragement on the upright pianos of M. Montal. – Extract from a report by M. Delaire to the Free Society of the Fine Arts on the upright pianos of M. Montal. – Extract of a report by M. Kerris to the Society for the Encouragement on a system of rectilinear counter–tension and other improvements in the upright pianos of M. Montal. – Extract of a report by Taskin to the Atheneum of the Arts on the pianos manufactured by M. Montal. – Extract of a report by Sainte–Fare–Bontemps to the Academy of Industry on the works of M. Montal. – Extract of an article by Henri Blanchard from the Musical Gazette on the pianos of M. Montal. – Extract of an article by M. Fétis from the Musical Gazette on the pianos of M. Montal. – Extract of an article by Adrien de la Fage from the Musical Gazette on the pianos of M. Montal. – Appreciations of artists extracted from the autograph album of M. Montal. – M. F. Baudillon. – Mm. A. Baudillon. – MM. F. Masini. – E. Lubeck. – A. Giacomelli. – L. Hall. – C. Wehle. – Goblin. – F. Brisson. – Ponchard. – H. Duvernoy. – Th. Ritter. – O. Comettant. – J. Lissajou. – L. Lacombe. – W. Kruger. – E. Bienaimé. – A. Goria. – J. Ascher. – T. Walsh. – J. B. Wekerlin. – A. Sowinski. – E. Batiste. – P. Dorval–Valentino. – J. Barbier. – Ermel. – Rheim. – Courtat. – Extract of the report on the exposition of Bordeaux by M. Elwart on the pianos of M. Montal. – Extract of the report of the French section of the Universal Exposition of London in 1862, by M. Lissajou, on the pianos of M. Montal. Extract of the report by M. William Pole to the international jury of the Universal Exposition of London in 1862, in English (translated into French) on the pianos of M. Montal. – Note extracted from the French catalogue of the Universal Exposition of London in 1862 on the manufacture of pianos of M. Montal.

 

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