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--- FROM THE PROLOGUE AND INTRODUCTION
The [1978] book received a detailed favourable review by Prof. Rudolf Rasch in Stimulus (Utrecht) … [and] positive comments by … well-known musicians … such as Igor Kipnis … Hubert Bédard … and John Barnes …. Bédard wrote: 'The most useful text on the subject I have seen yet. … This book … seems to settle the matter at last.'. ... This is [however] … a new work written from scratch, including … a significant amount of new ideas arising from latest discussions with specialists… The figures … have been produced and/or processed with the latest computer tools.
PART ONE of this book begins with a substantial introduction to the acoustics and simple modern mathematics of temperament. The most important historical temperaments are then covered, with a systematic analysis of their acoustical and musical features. This part ends with a detailed HISTORICAL SURVEY intended to guide the performer in the selection of the temperament(s) to be utilised for his/her repertoire.
PART TWO consists of keyboard tuning and fretting instructions for several temperaments, plus unequal temperament directions for unfretted strings, voices, woodwinds and brass wind instruments, including variable intonation techniques.
PART THREE covers multiple divisions of the octave and the analysis of historical sources, including some hitherto-unpublished research results.
--- FROM PART ONE
With our relatively simple yet powerful "dissection tools" we are now ready to enter, in the following Chapters, the fascinating world of early temperaments in Renaissance, Baroque and Classical times.
In both old and recent times, Just Intonation has been advocated for … violins and voices. The system is deceptively simple … In practice however ...
In meantone temperament … Contrary to an often repeated but wrong belief, the main restriction to modulations is not caused by the wolf fifth but instead by the 4 wolf major thirds, or rather ...
The fascinating properties and proportions of the Standard meantone diatonic and chromatic scales are treated in the following ...
Let us now see how ancient musicians fared in practice when asked to produce a Spiral of Fifths with up to … 5 pairs of flats and sharps ... :
Voices, unfretted strings, trombones and trombe da tirarsi ... Other brass wind instruments ... Fretted strings ...Woodwinds ... Keyboards ...
Standard 1/4 S.c. has always been the most popular 'flavour' of meantone. Baroque and Classical theoreticians did not always agree on this point: lengthy polemics were held ...
A dictum, often found in 17th and 18th century sources, states that 'there are nine commas in a tone, with one comma separating the sharp from the flat' ... it can be shown that the dictum is not true for any conceivable meantone temperament ... A thorough discussion of the dictum is included ...
Semi-meantone ... is a hopeless system, with only one good tonality: C major. ... A few early organs and fretted clavichords have been reported as originally tuned in semi-meantone. In most cases this is likely to be an error ... as shown in Appendix 4.
In spite of assertions often found in ancient and modern writings, accurate meantone temperament … was and is perfectly viable in fretted string instruments. ...
Good temperaments ... Some modern writers have imposed the custom of calling them 'Well temperaments'. This is almost a malapropism and unnecessarily violates basic language rules….
Clearly therefore Chaumont and F.Couperin were using different variants of the temperament ... The reconstructed Couperin organ temperament is shown below ...
A disproportionate amount of effort and ink has been dedicated [by modern writers] to the analysis of the multiple variants of circular temperaments proposed by German Baroque theoreticians. ... We will eventually find out that only a handful is really worth studying and tuning to ...
If the reader still finds it difficult to grasp which flavour of 'Good' temperament J.S.Bach advocated or preferred, he/she is in good company ...
Neidhardt's temperaments ... full analysis … Most of Neidhardt's temperaments are more mathematical amusements than useful musical proposals: ... Out of the scores of Neidhardt's proposals, there is only one that seems to fit the requirements for Bach ...
Everything seems to show that Bach did not write the WTC in order to advocate a peculiar tuning to be discovered by archaeologists of the future trying to decipher 'Rosetta stones' ...
A full classification of the time (Artusi 1603) had the instruments divided into three families according to their temperament … However … as we come into Baroque times, fretted instruments are found increasingly playing together with keyboards…
The Baroque is the only period in Western musical history in which the different amount of temperament of the intervals around the Circle of Fifths eventually becomes a component of musical expression. …
Unequal temperaments were still feasible and practised. But Equal Temperament … was now gaining considerable momentum. What was the most common situation in so called Classical times? What were most musicians doing after 1750?...
--- FROM PARTS TWO AND THREE
THIRTY(30) HINTS AND TRICKS FOR HARPSICHORD TUNING. [For] early stringed keyboards …the following guidelines are an integrated set of suggestions and instructions … in a working-practice sequence. ...
'J.S. Bach never needed more than 15 minutes to tune his harpsichord'. This often-quoted statement is a myth … Most people will need between 30 and 50 minutes—novice tuners possibly more—…
Theoretical/geometrical [fretting] values are most useful in order to get an initial idea about the place and shape of the frets and related consistency issues … The charts … help the player to keep in mind the few notes that need a bit of 'tweaking' while playing. However, the final position of the frets for accurate tuning has to be found…
Meantone Fretting … Unlike the pure intonations where some considerable mistuning was expected by early audiences and anyway unavoidable … in meantone … a precise tuning is both feasible and expected. A simple [fretting] procedure follows …
A very tempting alternative … enharmonic sharp-and-flat frets. … the practice … is historical and well documented … Historically however double enharmonic frets were never commonplace …
Standard French ordinaire being the most unequal circular temperament, the conclusion back in 1978 was that a most accurate fretting was possible for all the remaining circular temperaments as well. This has now been confirmed …
This Chapter is intended to show how to play— easily and accurately—unfretted instruments in unequal temperaments. This is achieved by using specific fingering charts and techniques. ... The text has been written so as to be most useful to singers as well. …
“The road to intonation hell is paved with just-intonation intentions”. ...
Were Bach's horn and trumpet players (e.g. the famous Reiche) better than Handel's (e.g. the famous Snow)? ... were perhaps Bach's players using narrow-bore instruments that would play more softly but with increased flexibility and ease in the upper parts of the register? Were they perhaps using node-holes ... ?
Some musicians tried to find … a 'violin-friendly' temperament, one that would agree with the few pure fifths of violins, violas and cellos … tempering the other fifths so as to avoid a frankly Pythagorean intonation with its awful major thirds …
Logarithmic Units ... the Cent has three strong points in its favour that ... far outweigh any adverse theoretical/acoustical/practical argument ...
--- ABOUT ANCIENT AND MODERN WRITERS
For a modern abridged version of Helmholtz's detailed treatment of beat frequencies, the reader is referred to Rasch (Rasch, Berkeley 1984).
1/6 S.c. meantone... has been said to be precisely the temperament advocated by the elderly Telemann in his writings (Telemann c1742 rev.1767). This cannot be proved and may well not be the case.…
In spite of its thirds, triads and tritones being so much better than in Equal Temperament, most modern listeners do not find meantone so attractive at first. The ancients were in a better position, because 'their ears had not been dulled as ours have been' (Hubbard 1965, p.32).
Semi-Meantone ... Barbour (1951) attributed the earliest source of this system to Artusi's lengthy and sometimes confused description (Artusi 1603). A more recent analysis (Lindley 1984, pp.84 ff.) shows however that Artusi was not actually advocating this temperament at all. ... An unmistakable description of semi-meantone has been found in ... an autograph note by Vincenzo Galilei (Barbieri 1994, p.213) ...
In the 18th century three famous men published their accounts on this temperament …. They were Rameau (1726), d'Alembert (1752) and Rousseau (1765). For decades French sources referred to this widely-used system as "tempérament ordinaire" ... or "tempérament établi". ... a recent full reappraisal of the above writings ... (Di Veroli 2002).
Kellner's Bach temperament is a ... modern hypothetical reconstruction... (Kellner 1978), based on a drawing of Bach's own seal ring, as well as numerological methods which were the target of sharp criticism. However … Kellner's temperament is a subtle but interesting ...
By then most musicians would be following strict Equal Temperament, even in England ... As late as the 1880's … Ellis (1885) noticed how some tuners ... tended to err [their Equal Temperament tuning] on the side of Good temperaments ... Jorgensen (1991) ... "Victorian temperaments". ...
[In German countries] many organs were not retuned for decades and remained in use tuned to strict meantone until mid-18th century (Ortgies 2004, Abstract) …. however … an important change was taking place …
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