Scarlatti composed when ¼ and 1/5 comma mean tone were the accepted standard, although modified mean tone and well tempered tunings were gradually being adopted. Scarlatti wrote some of his "essercisi" in the keys of B, Eb and E major. B major is one of the very poorly intonated keys in 1/4 comma mean tone; E and Eb contain large single interval errors. This means that at some point he adopted a modified mean tone tuning. John Sankey has recorded all 555 sonatas as midi files, using D'Alembert's modified mean tone temperament. This tuning was published in 1752, so this cannot be the tuning that Scarlatti used. The most likely tuning was 18th century italian (or similar) temperament. Sankey however, found that the sonata's sounded better using D'Alembert's tuning. This is one of the modified mean tone temperaments in which it is possible (at a pinch) to play in all 24 keys. Scarlatti's music sounds rather plain and gutless when played on an equally tempered piano, and the piano swamps the delicate trills and chords, simply by being too powerful an instrument for such music. It was (and to a lesser extent still is) fashionable to play Scarlatti on a modern piano, but the result is not a happy one. Some of the sonatas are ideal for learning playing techniques on the piano, butit is wrong to consider playing the sonatas on a piano in the concert hall or recording them, because the quality of the music is impaired. Harpsichord recitalists play his music, using a well-tempered tuning, but even this has resulted in some criticism. One of the objections often raised when music by Scarlatti and other contemporary composers is performed at recitals today, is that even the selected well-tempered tuning (frequently Young or Vallotti) is in itself inauthentic, and recitalists should take care to use either the known or likely tuning used by the composer. The same argument applies to those that persist in playing Bach’s Well Tempered Clavier in equal temperament, when the tuning should be Werckmeister III or Bach's tuning. There is increasingly a demand for authenticity. Purists object to Bach, Scarlatti, Rameau etc. being played on a piano, and performers appear puzzled by the increasing objections, but naively it seems, go blithely on. I think that a sensible compromise can be reached. If works intended for harpsichords and clavichords are played on a piano, which as the performer must be aware of, is inauthentic, then the obvious and sensible solution is to tune the piano more appropriately. Admittedly, tuning to some of the mean tone temperaments simply is not practical, but using a mean tone based tuning such as Kirnberger III would be a fair compromise. Pianists cannot justify the claim that it is historically incorrect to use well tempered tunings on modern concert grands, and then play music on them which was intended for earlier types of keyboard instruments and in different temperaments; this is far more contrary to historical authenticity! As an example, Jean Phillippe Rameau wrote his keyboard works for a modified mean tone temperament, with six 1/4 comma tempered 5ths and two small "wolves". Rameau wrote some of his "suites" for both major and minor modes, and used the keys in his tuning which were good in both modes, such as D,E,G, and A. C, Bb, and F major are good keys but the minor modes have rather flat 3rds, although C minor is not excessively so. Rameau therefore avoided these keys when writing works for major/minor modes. As Rameau's tuning was specific, harpsichord performers of his music should use his tuning and not Young, Vallotti, or Kirnberger. Equal temperament would be wholly inappropriate for his music. It lacks the expression of Rameau's tuning and gives his music a rather sterile quality; especially on a piano with some of the trills and ornaments edited out. If Rameau's music is played upon a piano, Kirnberger III would not be ideal but would suffice. Interestingly, the keyboard works of both Haydn and Mozart can be played using a modified mean tone temperament, such as Rameau's or D'Alembert's.

Thomas Young's Idealised Well Temperament Of 1799

In order to play in the likely temperament preferred by the composer, the period in which a given piece of music was written must be considered. The following list gives a number of composers, covering successive periods, together with an appropriate temperament.

• 1/4 Comma Mean Tone
• Frescobaldi
• Purcell
• Vivaldi
• Scarlatti (earlier compositions)?
• Werckmeister III; Bach’s (Rediscovered by Kellner); Handel’s; Neidhardt
• J.S. Bach
• C.P.E. Bach
• Handel
• Modified Mean Tone
• Soler
• Rameau
• Scarlatti (later compositions)
• Froberger
• Buxtehude
• Kirnberger III; Vallotti; Prelleur; YoungI; YoungII;
• Haydn (modified mean tone)
• Mozart (modified mean tone)
• Beethoven
• Schubert
• Chopin
• Weber
• Brahms
• Equal Temperament
• Debussy
• Schoenberg
• Webern
• Stravinsky
• Martin
• Cage
• Stockhausen
• Sessions

The above list gives an indication of the appropriate temperament for the appropriate composer or era. Although the list applies generally to keyboard instruments, equal temperament is such an unsatisfactory organ tuning that it is better to disregard it, even if modern music is to be played on the organ.

There are an increasing number of recordings, featuring unequally tuned organs, harpsichords and whole orchestras, as well as recordings of works for chamber instruments and voices, which sounds fascinating; especially works by composers such as Purcell performed in ¼ comma mean tone (which is the temperament he would have written for). Occasionally, the temperament used for the recording is given within the sleeve notes. Also, a number of recordings have been made of Bach’s “Well Tempered Clavier”, on harpsichords tuned unequally: exploding the myth, once and for all that it is not possible to use all 24 keys in unequal temperament. The two versions in my possesion use Werckmeister III and Bach's tuning. It now remains for an artist to record the W.T.C. on a well tempered piano

Whilst it is true to say, that most people cannot identify what temperament an instrument has been tuned to, many would recognise the undoubtedly better, overall perceived sound of a well tempered instrument; particularly when given the opportunity to compare a well tempered instrument, with an equally tuned example.

I have so far mentioned the various advantages of unequal temperament; so what of the disadvantages? This to some extent depends on the choice of temperament; some are undoubtedly better balanced than others. The more fifths that the comma is distributed upon, the milder the key character; but if the comma is absorbed by only two or three fifths as in Kirnberger II and Stanhope, the key character is quite pronounced. There are a few very good keys, whilst the remainder are acceptable. The restricted temperaments, give generally good results in the popular keys: in churches, for example, generally only the popular keys are used during worship, so one of the mean tone temperaments would be ideal. In a concert hall, a closed circle temperament, with all 24 keys usable is more desirable and practical. In the modified mean tone temperaments, most keys are usable, and some (like 18thc. English) access all 24 keys at a pinch. Although in the poorest keys the major 3rds are very sharp and therefore harsh, and consequently can only be used as "passing" chords. The modified mean tone temperaments provide an even greater variety of key character than the well-tempered tunings. However, with the well tempered tunings, all 24 keys can be used without incurring any particularly harsh or dissonant intervals. To assess whether the intonation is likely to be good or not in a given key, the number of errors in cents for a diatonic octave can be added together (the errors being compared with just value’s); if the number of errors is less than 49, the intonation is better than equal temperament which contains this number of errors in every key. If the number of errors is higher, the intonation may still be perfectly acceptable, up to around 70 cents. The more 5ths that the comma is distributed around the circle, the milder the key character will be. For instance, there is a marked difference between Kirnberger II, where most of the tempering is on only two 5ths, and temperaments where the comma is distributed absorbed amongst six, seven, or eight 5ths. Ultimately, the best way to find out what different tunings sound like is to try them!

Kirnberger II

However, it is also important to check how the scale relates, note to note, and to see if the errors are composed of one or two intervals being badly out of tune, whilst the remainder are generally good. If the errors are well distributed, the intonation is likely to be satisfactory, and of course, there is the fact that this results in individual “key character”. Some temperaments, such as ¼ comma mean tone give very good intonation in some keys, but appalling intonation in others. The best keys in ¼ comma mean tone have 32 cents of errors in a diatonic octave, but F# major and Eb minor have 145, C# major 164, and Ab major 195!! It has to be heard to be believed!

Some might argue that unequal temperament is fine for baroque music, and perhaps tonal music of the 19th and early 20^th century; but what of music written by composers such as Schoenberg, Webern and Bartok? Particularly piano works composed using the 12-tone system? Surely such music must demand equal temperament. This is where equal temperament comes into its own as the ideal tuning. The grey, bland colouring is not the ideal for tonal (key centred) music, but it is excellent for atonal works, basically because it is a non-tonal system. Equal temperament does not favour any key or combination of chords, as music composed in the note-row technique, does not favour any key. This said, it would be interesting to hear a non-tonal work composed for mean tone tuning. The discords could be used to good effect! A number of contemporary composers have abandoned equal temperament in favour of mean tone or just intonation. Modern electronic instruments be programmed to play just intervals, or close equivalents by using more than twelve notes to the octave. 31 note equal temperament gives many 1/4 comma mean tone intervals, and by using 53 or more notes to the octave, just or almost pure intervals can be used in music with unlimited modulation and non tonal forms. Some modern composers hav adopted well-tempered tunings for their works. Lou Harrison's concerto for well tempered piano and orchestra (1985) was written specifically for Kirnberger II, the composers favourite keyboard tuning. This tuning has more just intervals than any other circulating temperament.

I have prepared a number of temperament charts, splitting the various tunings into four categories: Mean Tone; Modified Mean Tone; Well Tempered and miscellaneous. The mean tone tunings all have eleven 5ths flattened by equal amounts, with the twelth 5th taking up the excess flattening (the wolf). The modified mean tone tunings spread the wolf over two or more 5ths, and contain tempered 5ths of different sizes. The well tempered tunings are circulating (no wolf) temperaments, some of the modified mean tone temperaments such as 18th century English, contain very small "wolves" where the comma has been slightly exceeded, and some 5ths have been widened by 1/12th or 1/6th of a comma. The miscellaneous tables, contain tunings which do not belong to any of the main categories. Placing equal temperament in the miscellaneous section may seem strange, as it is a circulating temperament with no wolf, and permits unlimited modulation. However, it is not a "well-tempered" tuning in the true sense. When this term came into use at the beginning of the 18th century, its definition was for a temperament that was circulating; contained no wolf; allowed unlimited modulation and accessed all 24 keys, but that every key was different in character. One of the main purposes of "The Well Tempered Clavier" was to demonstrate the differing key characters of a well tempered tuning.

The temperament errors table give examples of accumulated errors in different keys, of some well known temperaments. I have included 1/3^rd comma mean tone for interest, although it was never widely used. It is rather an extreme example, as the errors in some keys indicate; however, the best keys are no worse than equal temperament: the difference is that the errors are as a result of intervals being flat, whereas, in equal temperament, the errors are mainly the consequence of sharp intervals. Its advantage is that it produces pure minor 3rds in nine keys, and there are nine major keys with pure 6ths. This is achieved, at the expense of eight slightly flat major 3rds, very flat leading notes (7ths) and of course, eleven flattened 5ths and sharp 4ths. The “wolf” 5^th is 2 3/8 commas wide: 55.5 cents!

The Purest 3rd
(0b/#)
C388E
F(1b)A-393-G(1#)B
Bb(2b)D-396-D(2#)F#
Eb(3b)G-401-A(3#)C#
G#(4b)C-406-E(4#)G#
Db(5b)F-406-B(5#)D#
F#408A#
(6#)
The Widest 3rd

It is said that we live in an equal tempered world and that the human ear has accepted equal temperament. However, equal temperament is only used on certain fixed pitch instruments. Stringed instruments such as string quartets, the human voice and trombones do not play in any particular temperament. A skilful player will vary the pitches to emphasise expression, as will a singer. I have already mentioned that orchestras do not produce an equal tempered sound, because of the variation in fixed pitch and non-fixed pich instruments, as well as the variations in blown instruments with and without valves. brass bands do not play in equal temperament for the same reason, and blown instruments vary in pich according to how they are blown and the extent to which the notes "waver". Equal temperament is the standard piano tuning in the western world and is likely to remain so. However, unequal temperament has now returned to stay, and equal temperament is no longer the standard tuning for harpsichords and other kindred instruments, and it is being superseded by unequal tunings for organs. Harps also benefit considerably from being tuned to one of the well tempered tuning systems, as they sound quite "rough" when tuned equally. As knowlege of the advantages of well-tempered tunings amongst musicians continues to expand, it will inevitably become more widely used. Typically, Britain lags behind the rest of Europe with respect to the use of unequal temperament. Far more organs are unequally tempered in countries such as Germany and Holland. In Britain, the catholic church and non-conformist churches have more unequally tempered organs than the church of England, and seem therefore to be better informed, although why this should be so is something of a mystery. Demands for authenticity in performances, and more interesting and expressive alternatives to the bland uniformity of equal temperament will guarantee the continued expansion of well-tempered tuning. Of the numerous well-tempered systems, Young I or II are effective for any music, covering the period from Bach to Brahms. Bach's tuning is also becoming increasingly popular, and like Young, is suitable for all keyboard instruments. My own well-tempered tuning is balanced in the same manner as Thomas Young's No. I: sharing the same number of accidentals have the same major 3rd values. For instance, D and Bb (two accidentals) both have major 3rds of 396 cents. It is similar in some respects to Young, but has more pronounced "key character", rather like Kirnberger III, although modulation is a little smoother. This tuning is also suitable for all types of keyboard instrument.