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 fully corrected in the 2nd Edition, which was sent for free to all the buyers of the 1st Edition.No important errors or omissions have been informed since the 2nd edition 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 members of HPSCHD-L that did not read it, 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 of the book 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.
Unequally Tempered musical recordings 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).
• Some of the pieces by François Couperin recorded (amateur video) in recital in 2011: La Manon (G major), Les Baricades Mistérieuses (B flat major), L'âme-en-peine (b minor), Les Fauvétes Plaintives (d minor) The temperament employed was Rousseau's ordinaire.
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.
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