[Pt. III Proj.1] – Handel’s Dixit Dominus and Figured Bass ~Research point 3.0: Renaissance and Baroque tuning systems.

[Pt. III Proj.1] – Handel’s Dixit Dominus and Figured Bass ~Research point 3.0: Renaissance and Baroque tuning systems. Instrumental tunings around the world and throughout history. How instruments are tuned around the world and throughout history is a fascinating field to discover. Make some initial investigations of your own, initially focusing on the tuning systems of the renaissance and baroque periods and innovations of the early 20th century by the likes of Alois Hába. This may prove an ear-opening experience. Write around 400 words to summarise your findings.

500 words on Renaissance and Baroque tuning systems:

Twelve-tone equal temperament (12-TET) is the tuning system we use in the West today and has been the most frequently used tuning system since the 18th century. It is a system which divides the octave into 12 equal parts with a ratio of 12√2 ≈ 1.05946. These intervals are called a semitone and are all equal in size (112 the width of an octave). These days they are tuned to 440 Hz representing the pitch A (concert pitch). Concert pitch has not always been the same and did in fact used to be lower than it is today. There are other equal temperaments which divide the octave in greater numbers, such as 19-TET and 31-TET or the Arabic scales which use 24-TET (quarter tone scales). Equal temperament was not always the standard tuning in Western music.

In nature, the purest intervals, the most consonant intervals are created using just intonation. Just intervals (and chords created by combining them) are made from a single harmonic series with one fixed low fundamental and intervals 2:1 octave, 3:2 perfect fifth, 4:3 perfect fourth and 5:4 major third like in the natural overtone series. The difference between a just interval and an equal-tempered interval (and sometimes between just intervals created using different overtone series is called a comma. For example, equal temperament narrows the fifths by circa 2 cents (1/12 of a Pythagorean comma) whereas the major thirds fare much worse and are more dissonant in equal temperament. The Hilliard Ensemble still use Just Intonation for it’s purity. Some modern composer such as Lou Harrison also favour Just Intonation because of it’s richness of time and the nuances afforded.

Hillard Ensemble – Renaissance Madrigals
Lou Harrison – Suite for Violin and American Gamelan.

The most common tuning system used during the Renaissance and Baroque period was called the Meantone Tuning.

Meantone Tuning dates from the late 15th century and was in use until the early 18th century (and in English organs throughout the 19th century). The Meantone Tuning favoured the consonance of the major thirds (C to E, F to A, G to B) over the perfect fifths (C to G, F to C, G to D). Acoustically the notes of an ‘out-of-tune’ third are closer together than in a fifth, creating faster beats (and therefore more dissonance). Hence the purity of the thirds was prioritised to create a ‘sweeter’ sound. Open fifths without thirds were avoided for tuning reasons. Major thirds of around 386 cents sound the most in pitch and are present in on C, D, Eb, E, F, G, A, and Bb, but not Db, F#, Ab, and B. Hence the tendency to stick to the keys grouped together around C (in the circle of fifths) in Renaissance and early Baroque music.  Bach used ‘Werckmeister III’. Other systems included ‘Temperament ordinaire’, ‘Kirnbeger temperament’, ‘septimal meantone’.

Orlando Gibbons’s Lord Salisbury Pavane played in 1/4-comma meantone temperament (copied from https://www.kylegann.com/histune.html)
Orlando Gibbons’s Lord Salisbury Pavane played in 12-tone equal temperament. (copied from https://www.kylegann.com/histune.html)
Equal Temperament versus Bach-Lehman and Werckmeister – J.S. Bach: Prelude in C major.
This is a comparison of three different tunings:
The Bach-Lehman temperament,
The equal temperament (2:08),
Werckmeister III (4:16).
The demonstration is done by playing the same midi file through Hauptwerk virtual pipe organ software with the Mietke Harpsichord sample set by Sonus Paradisi. Thanks to Brad Lehman for all the research and to Martin Martin Dümig for the temperament file.

When listening to some of these pieces performed using one of the Meantone Tuning systems it is striking how much warmer and colourful they sound. Every key has a distinctly different flavour and mood rather than just sounding like a transposition to a different key. I can’t help but feel that we are really missing the point of this music, not hearing it the way the composer would have heard it.

Mozart Fantasie KV397 in Three Different Temperaments. The performer is Enid Katahn.

A video uploaded to demonstrate the differences in three historical tunings/temperaments on the same piece and instrument. Temperaments used are as follows:
00:0005:36 Equal temperament
05:4011:33 Prelleur temperament
11:4017:50 1/4 Comma Meantone tuning.

Innovations of the early 20th century by the likes of Alois Hába.

Alois Hába – Sonata for Quarter-tone Piano. 1 – Allegro agitato

Alois Hába (1893 –1973) the Czech composer was a major exponent of microtonal compositions in modern classical music. He used a quarter- tone scale (and occasionally sixth, fifth and twelfth- tone scales). He wrote several theoretical works on the subject nd had specially designed quarter tone instruments (keyboards and woodwind). Alois Hába harked from the Moravian Wallachia. Moravian folk music uses intervals other than the ones included in equal temperament. Hába decided to revive the use of older European folk scales and incorporate them into his contemporary classical music. There were several of his friends and colleagues who were undertaking similar experiments, such as Busoni who had developed a harmonium for sixth-tone music. His theories and teachings laid the foundation for a movement towards microtonal music in contemporary classical music. Others have since carried on in this tradition and there’s a body of microtonal compositions by the likes of Harry Partch, Ben Johnston, La Monte Young, Lou Harrison, Tony Conrad and Terry Riley. I am a fan of both Partch, La Monte Young and Terry Riley have had the pleasure of working with Tony Conrad. The possibilities of these micro tuning systems are very rewarding. Having grown up with Serbian folk music which frequently uses neutral seconds, I find equal temperament extremely limiting.

The Well-Tuned Piano (Excerpt) – La Monte Young. Experimental pioneer La Monte Young spent decades designing and refining his own tuning system, and building a piano that could realise it – including by adding most of an extra octave to the bottom end. The tuning incorporates elements of Gregorian Chant, Hindustani music, Indonesian Gamelan, Pythagoras-derived harmony, and more. His work seems to occupy a separate listening space to anything else, perhaps because he is improvising indirectly with emergent frequency interactions rather than with notes in the usual sense. It is as if he is devising a pattern for throwing stones into water, with the aim of creating the most interesting ripple patterns as the waves cross paths.
Terry Riley – The Harp of New Albion – 1. The New Albion Chorale / The Discovery.