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Exercises for singing and playing in quarter-comma meantone temperament 
for singers non fixed-pitch instruments at A=440.

by Martin Perkins

Early Music Workout:

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  • Introduction
    This Workout is designed to help develop skills in playing and singing with historical tuning systems and temperaments. That is, playing and singing with a fixed-pitch instrument which is using non-equal temperament tuning systems that were used extensively before the 20th century. There is little theory here; just exercises in which you will play along to backing tracks. However, a few basic points of explanation are needed for those who are new to the concept of historical temperaments:
  • Pure Intervals
    By dividing up a note (let’s say, the top string of a violin) into basic ratios of a half, third, quarter, fifth, etc., we get the simple intervals of 8ve, 5th, 4th, major 3rd, minor 3rd, etc. These intervals are pure: there is none of the impurity, wavering or beating that you hear from a piano tuned in ‘equal temperament’. This is the way that modern string players tune their violins, violas and cellos, etc., with each of their fifths tuned pure. These pure intervals, however, are not compatible when playing with keyboard instruments using historical temperaments.
  • Fixed Pitch vs Flexible Pitch Instruments
    In the eighteenth century and before, instruments of fixed pitch (i.e., where it is not possible for the player to manipulate the tuning of each note – keyboard instruments) used tuning systems that utilized pure intervals. The drawback to this is that whilst most intervals sounded pure, a few sounded extremely out of tune. Equal temperament irons these discrepancies out whilst historical temperaments favour purer intervals, sacrificing others that may not be used often in the music (e.g., between two chromatic notes). Therefore, singers, wind, brass and string players not only need to use pure intervals according to the keys they are using, but also need to play with fixed pitch instruments (organs, harpsichords, etc.) that use some pure intervals but without the flexibility to adapt according to the keys.
  • The Evidence
    Pier Francesco Tosi (1653–1732), wrote about tuning in his influential Opinioni de' cantori antichi, e moderni published in 1723 and translated as Observations on the Florid Song in 1742/3. He regarded tuning to pure intervals as essential to all singers. However, given that singers needed to play with keyboard instruments, he advocated a flexible approach to tuning, stating that singing with a keyboard instrument would indermine a singer’s understanding of the different sizes of semitone. Every one knows not that there is a Semitone Major and Minor, because the Difference cannot be known by an Organ or Harpsichord, if the Keys of the Instruments are not split … this Knowledge … [in] Songs accompanied with bowed Instruments … becomes so necessary, that if a Soprano was to sing D sharp, like E flat, a nice Ear will find he is out of Tune. Francesco Geminiani (1687–1762) discussed tuning in his 1751 treatise, Art of Playing on the Violin. He gave exercises for violinists to practice playing pure intervals, making sure they noted the difference between greater and lesser semitones: … the Cromatic Scale must be composed only of the greater and lesser Semitone; and … the Octave also must be devided into 12 Semitones, that is, 7 of the greater and 5 of the lesser.
  • Quarter-comma Meantone Temperament
    In today’s historically informed performance of 16th and 17th music, keyboard instruments are generally tuned to meantone temperaments (where the tones are equally spaced) or some sort of Well temperament (which aims to make most keys usable). In quarter-comma meantone, the fifths are tuned narrow so that the major thirds are pure, and the tones between them are equally distanced (mean-tone). The result of this is very striking: the thirds often sound out of tune even though they are pure, because they are very narrow compared with equal temperament. As a general rule, sharps are lower than equal temperament, flats are higher.
  • Tuning Up
    Use the tuning tracks to make sure your instrument in completely in tune. String players need to ensure each string is in tune with the audio, not pure or ‘in tune’ with itself.

Exercise 1: Small steps, smaller steps…


In this exercise you will get used to singing and playing diatonic notes in quarter-comma meantone temperament.

Play or sing to the melody line making sure you match the tuning of the organ.

For each of the seven keys of this exercise, the try to be aware of the sizes of the tones and semitones: the semitones will be wider than with equal temperament and the first interval in each exercise will be larger (the second note lower).

Exercise 2: Scales, scales, scales… 


In this exercise you will play long notes of ascending and descending scales. Initially, these notes will be unaccompanied, but halfway through the bar the organ will play the note with appropriate chord. Use this opportunity to check if your own note is in tune with the meantone temperament. 
If the notes are out of range, transpose them up or down an octave. 
For each of the 7 scales, the tempo will increase, giving the following 7 speeds:

♩ = 30  |  ♩ = 45  |  ♩ = 60  |  ♩ = 75  |  ♩ = 90  |  ♩ = 105  |  ♩ = 120

Exercise 3. Chromatics


Now that you have had the opportunity to play and sing the different sizes of tones and semitones within specific keys, it is time to introduce chromaticism within one tonal centre. The arrows show how much each note is sharper or flatter than equal temperament. 
A small arrow indicates a slight difference; a large arrow indicates a large difference. Notice that flats are all higher than equal temperaments and the sharps are lower. This makes them unusable as their enharmonic spelling (e.g., E-flat cannot be used as a D-sharp).


Exercise 4: Meantone in context I (for instruments)


Girolamo Frescobaldi, Canzon Terza (Canzoni da sonare, 1634)
Play along to this short canzon by Frescobaldi. The accompaniment, played on organ, is played at a variety of tempi to aid progressive learning. 

Exercise 5: Meantone in context II (for voices or instruments)


Giovanni Paolo Cima ‘Adiuro vos, filiae Hierusalem’ (Concerti Ecclesiatici, 1634).
Play along to this short canzon by Cima. The accompaniment, played on organ, is played at a variety of tempi to aid progressive learning. 

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