Please note that all the material in this site is my copyright, but all the texts can be freely used for non-commercial purposes provided due acknowledgement is made quoting in full my name and this site's web URL. My authorisation is needed before using the material for commercial purposes. Enjoy!
Claudio Di Veroli. (pron. Cloudy-oh Deave-Erroly), Bray, Rep. Ireland, 2008                  E-mail:

The UNEQUAL TEMPERAMENTS free downloads and other goodies

The Unequal Temperaments ERRATA

This book was a major undertaking and inevitably a few significant errors were kindly spotted by informed readers: they were acknowledged in an Errata and fully corrected in the 2nd Edition, which was sent for free to all the buyers of the 1st Edition. Several months later, that initial Errata is no longer needed and has been deleted from this webpage.

No significant errors or omissions have been found since the present 2nd edition v.3 was published on 22 April 2009. Somebody in the HPSCHD-L online forum strenuously objected to section 16.9 of my Chapter 16 on Intonation for Violins and Voices. Purportedly my book would state that Variable Intonation was historically unsuccessful and not recommended nowadays: this is far from true and obvious to whoever read the book. For the benefit of those forum members that did not, I carefully clarified the matter in the forum. In section 16.9 of the book a page-long subsection explains in full detail how Variable Intonation was used—and is indeed recommended!—to improve the consonance of some crucial intervals when playing with fixed-note instruments tuned in Regular Temperaments. Another subsection deals with the historical alternatives for Circular Temperaments. What I did write in the first subsection of 16.9 is that Variable Intonation has been advocated in order to achieve Just Intonation throughout: failure here was and is inevitable, due to the internal inconsistencies of Just Intonation itself, as explained in section 4.5. To further clarify the matter I have now written a new subsection VARIABLE INTONATION IN HISTORY, where I show how easily early sources can be wrongly interpreted and how the assertions in the U.T. book are fully backed by a recent specialised publication by the main scholar in the history of Violin Intonation, Prof. Barbieri. Please find the new subsection and a few further minor errata and addenda in the updated Errata document, available here for download: ut_errata_23.doc.

The Unequal Temperaments web LINKS

The eBook includes many webpage addresses in blue colour. If you are viewing it in the commercial full Adobe Acrobat, and possibly in a few other "PDF viewers" as well, every webpage address is a link and clicking on it opens your browser in that page. In other viewers, e.g. Adobe Reader, you have to select the blue text with the mouse, copy (Control-C), go to your Internet Browser and paste it (Control-V) in the "Address" box.[Hint: in order to be able to select and copy text in Adobe Reader, you have to enable the Copy feature: click in the menu Edit, Preferences, General, and ensure that the first item "Enable text selection ..." is selected and click OK.]

The Unequal Temperaments SOUND EXAMPLES - free downloads

The examples below are in WMA compressed format, playable from Windows Media Player, yielding-—for the same file size—much better quality than MP3. You can hear them by clicking on them, or else you can download them to your PC's hard disk by right-clicking and selecting "Save As".

• Ex.1.02 for Section 1.2, Fig.1.2 - Beats between pure sounds of nearly identical frequency.

• Ex.1.04 for Sections 1.4 and 1.5 - Pure intervals with superparticular ratios.

• Ex.1.04V for Sections 1.4 and 1.5 - same, transposed a fifth upwards.

• Ex.1.06 for Section 1.6, after Law 3 - Tempering a fifth.

• Ex.1.07 for Section 1.7 - Pure intervals with non-superparticular ratios.

• Ex.1.07V for Section 1.7 - same, transposed a fifth upwards.

• Ex.1.08 for Section 1.8, Fig. 1.8 - Minor Third-Major Sixth octave test.

• Ex.1.09 for Section 1.9 - Minor and major pure triads played on an open diapason organ stop.

• Ex.1.09H for Section 1.9 - same on a lower 8' harpsichord stop.

• Ex.1.10 for Section 1.10 - Ornamental beats in a minor triad with pure fifth.

• Ex.2.02 for Section 2.2 - Fifth: pure and Pythagorean Wolf.

• Ex.3.04.1 for Sections 3.4 and 3.6 - Fifth: pure and Equal Temperament.

• Ex.3.04.2 for Sections 3.4 and 3.6 - Major Third: pure and Equal Temperament.

• Ex.3.04.3 for Sections 3.4 and 3.6 - Minor Third: pure and Equal Temperament.

• Ex.3.05.1 for Sections 3.5 and 3.6 - Major Triad: pure and Equal Temperament.

• Ex.3.05.2 for Sections 3.5 and 3.6 - Minor Triad: pure and Equal Temperament.

• Ex.3.08 for Section 3.8 - Major Third: pure and Pythagorean.

• Ex.5.31 for Section 5.3, Fig. 5.3.2 - The Bb major scale in thirds in Standard Meantone.

• Ex.5.40 for Section 5.4 - Enharmonic Flats and sharps in Standard Meantone.

• Ex.8.02 for Sections 8.2 and 21.2 - F.Couperin's Early French temperament: two examples from the Messe pour les Paroisses.

• Ex.9.03 for Section 9.3 - Fifths: pure, equally-tempered and Werckmeister III.

• Ex.9.11 for Section 9.11 - Sabbatini's octave-third split: Equal Temperament and Almost-Equal Temperament.

• Ex.11.03 for Section 11.3 - Gothic cadence from Adam de la Halle.

• Ex.11.05.1 for Section 11.3 - A fragment from Philip's Galiarda Dolorosa, in Pythagorean Intonation.

• Ex.11.05.2 for Section 11.3 - same in Standard 1/4 S.c. Meantone Temperament.

• Ex.12.03 for Section 12.3, Fig. 12.3.2 - Hearing the slowest beats.

• Ex.12.08 for Section 12.8, Fig 12.8 - Comparison of beat rates.

Of the unequally-tempered musical examples freely available from the Internet, the following are recommended:

• A piece in 13th-century style. This has been recorded by medieval music scholar Margo Schulter using standard Pythagorean intonation: note the "serene" pure fifths and the "tense" dissonant major thirds.

• Praetorious work played in a large organ tuned in Standard Meantone. Click on "Listen". Note the good but noticeable flat fifths and the beautiful pure major thirds. 3'25"

• Pachelbel Ciacona played on the Stertzing 1702 organ in Erfurt, tuned in Standard Meantone.

• Introduction to unequal temperaments in F Sharp. David Pitches introduces the various unequal temperaments playing on an electronic sampler organ. The piece is unplayable in Meantone. Here we hear temperaments in the following order: Meantone, d'Alembert, Vallotti, Kirnberger and Kellner.

• An organ masterclass with reeds and tierces in meantone.

• J.S. Bach's Dorian Fugue in meantone. This interesting performance by Mark Shepherd shows how some organ works by Bach are largely compatible with meantone temperament, still very common in church organs in Bach's time. Note however the awful discords in 4:07, 4:39 and later also: together with many other features of the score, they clearly show that this work was composed for a circular temperament.

• A few fragments recorded during recitals by the author, in different temperaments. Please note that the choice of temperament was dictated by the prevalent repertoire of the recital in which the piece was recorded: thus the temperament is sometimes not the ideal one for the piece (e.g. all the pieces by F.Couperin and Rameau should better be played in Rousseau's ordinaire).

Additional sound examples are planned to be produced and released by the author in the future, including:

• A passage played in Pythagorean Intonation, Pythagorean-Just, Equal Temperament and Standard Meantone
• A passage from Bach played in Barnes's Bach and Lehman's Bach temperaments
• Standard French ordinaire limits: Rameau's L'Enharmonique
• A passage from Bach played in Werckmeister III and Vallotti
• The 31-division chromatic scale for fretted and unfretted strings

The Unequal Temperaments SPREADSHEETS and ICONS

The Unequal Temperament spreadsheets, continuously evolving since their first version in 1991, have now been fully updated for the new eBook Unequal Temperaments: Theory, History and Practice. Every temperament has its own worksheet, showing the Circle of Fifths, the Circle of Major Thirds, the Offsets or deviations w.r.t. Equal Temperament, the Frequencies of notes in Hertz and a full Table of Beats. There is also a special sheet particularly useful for Advanced Electronic Tuning Devices – such as the Verituner, CyberTuner, Accu-Tuner III or TuneLab Pro – and also whenever the user has a description of a temperament in Offsets: entering them in the spreadsheet automatically provides a full description and analysis of the temperament. A short document on the spreadsheets and their contents, plus user instructions, can be downloaded here: UT_spreadsheet.doc. Last update: 06-Jan-2009.

You may download the spreadsheets here: UT_spreadsheets.zip. Last update: 22-Jan-2009.
Once you have downloaded the above zip file, just unzip it, using the Explorer in Windows XP or an utility like Winzip or else the excellent and reliable file manager Total Commander, downloadable from www.ghisler.com. The two spreadsheets UT-Regular.xls and UT-Irregular.xls are fully independent.

I have also designed special PC icons which you may find useful for your UT temperament documents, programs or other musical material in your PC: UT_icons.zip.

Other works of mine on Unequal Temperaments

My work on temperaments since 1978 has been summarised in the new Unequal Temperaments eBook and spreadsheets. Find below a list of my other published works on the subject.

1976-81. Audio-visual course on Musical Scales and Temperament. Held at the Goethe Institut in Buenos Aires. Most of the ideas of this successful course found their way into the Unequal Temperaments eBook.

1981. On Bach's Temperament in "Early Music". Letters and a mini-essay with a statistical analysis, plus basic considerations on musicological methodology. Published in Early Music vol 8 p 129 and vol 9 pp 219-222, Oxford University Press, London 1981. The final conclusions are now incorporated into the new Unequal Temperaments: Theory, History and Practice eBook.

1985. Early French Temperament. Investigating on the genesis of the French Baroque tempérament ordinaire, I found a hitherto neglected source of very valuable information in F.Couperin’s Organ "Messe pour les Paroisses". The work’s harmonic range made it ideal for the application of John Barnes’s statistical method, for which I developed some improvements. Sylvia Leidemann (then a harpsichord pupil of mine and today a most distinguished choir and orchestra conductor) gathered the data about every single Major 3^rd and 5^th in the work, for the statistical analysis. The research and final results were published in "A French temperament of 1690: a link between meantone and 18^th Century’s French circular temperaments" (in Spanish), read to the Second Argentine Musicology Symposium, Buenos Aires (Argentina) in 1985.  This is the temperament of organs in Paris at the time, different from Mersenne/Lambert Chaumont temperament. Both are included in the UT-Irregular spreadsheet. A translation of this paper, thoroughly updated, has been included in Unequal Temperaments: Theory, History and Practice.

1996. Temperament in Ancient Times and Today. A small didactical History of Temperament, originally commissioned in the late 80's by the late harpsichordist Igor Kipnis. I used it years later as a basis for a more elaborate work in Spanish, commissioned and published by the Bulletin of the "Departamento de Música Antigua", Collegium Musicum, Buenos Aires (Argentina) 1996, entitled "El Temperamento Musical Ayer y Hoy" ("Musical Temperament in Ancient Times and Today"). An easy-to-read 20-page work, it was in 1999 the material for a very successful half-day course held at the Conservatorio Giuseppe Verdi in Turin, Italy. A local lecturer later produced an Italian version which has been in use since in the Conservatorio. An English version has not been written yet.

2002. Tuning the tempérament ordinaire. Having perused recent research publications, during 2001 I performed a new comparative analysis of the main sources on the ordinaire and found hitherto unnoticed details impling a new definitive version, historically more accurate, better sounding and also easier to tune. An account of the research and its results was published in February 2003 by Harpsichord & fortepiano, Lincoln (UK), Volume 10, no. 1, "Autumn 2002". The temperament is included in the UT-Irregular spreadsheet. A thoroughly updated version has been included in Unequal Temperaments: Theory, History and Practice.

2003. A Concise Guide To The Most Useful 12-Note Unequal Temperaments. This is a comparative table with the main information a musician or tuner needs to know about 12 selected Unequal Temperaments plus Equal Temperament. Commissioned by Veritune Inc., it was written in March 2003, with helpful hints from David Bauguess. To read it, go to Veritune's page, click on DOCUMENTATION and download the User Guide PDF file: my Concise Guide is found in pages 93 to 107.

2010. Vallotti as the Ideal German Good Temperament. Recently some tuners and musicians have been using Neidhardt's temperaments describing them as better and more authentic than Vallotti, which they describe as a simplistic and unhistorical modern fad. On the contrary, the convenience and justification for using Vallotti in Baroque music making was fully explained in the two Unequal Temperament books. Further new arguments, showing Vallotti as the ideal average German "Good" temperament, are included in this new article published in November 2010 by Harpsichord & fortepiano, UK, Volume 15, no.1.

2011. Unequal Temperaments: Revisited, in The Viola da Gamba Society Journal (2010), Jan. 2011. This is a response of a review of the UT book previously published by Dr. Bradley Lehman: it includes, necessarily, a rebuttal to commonly-held and easy-to-disprove myths about scales and temperaments.

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