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I’m trying to understand how the different tuning systems and temperaments were used from the past.

Would people tune their instruments based on the key of the piece they were going to play? Is there a more common/standard base note that most people use when tuning?

For example, if using pure major temperament, the same chord of different keys can sound very different, based on the base note they tuned to. If I’m playing a piece in D major, but the instrument is tuned on the base note of C, the dominant chord would sound pretty bad. But if it’s tuned on the base note of D, it would sound pretty good.

So I’m wondering how would this be done in the past. Tuning between each piece that’s in a different key doesn’t sound very practical. Or maybe they always group them base on keys? If I find a random harpsichord in the early baroque period, what would be the most likely base note they used to tune it?

I hope I’ve made the question clear. Any sources to look to would be appreciated too. Thanks in advance for answering.

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    "If I’m playing a piece in D major, but the instrument is tuned on the base note of C, the dominant chord would sound pretty bad": actually, if you use the usual ratios given for just intonation, the dominant chord would be just fine, but the tonic chord would sound pretty bad. But the D and Dm chords also appear frequently in pieces in C major, which means that tuning in C major doesn't even work for C major. For that reason, these ratios generally were not used to tune keyboards for the purpose of playing harmonic music. You need to temper the tuning even to play in one key. – phoog Jan 13 at 17:15
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    Does this answer your question? How did people tune their instruments in the past? – Aaron Jan 14 at 1:20
  • @Aaron Thank you for the link. It doesn't really answer my question (since it's mostly meant for keyboard instruments) but it's interesting to know about the lute! – octacube Jan 14 at 16:52
  • @phoog Thank you. It's just an example I gave using pure major tunings, so that the major thirds are pure. In this case the C# in the dominant of D would sound flat in a tuning based on C. And yes the tonic of D would sound bad too since the D-A fifth is not pure. My question is that let's say using just intonation, you have to tune everything based on a fundamental, or the harmonic series of a fundamental to start with (before tempering with any specific intervals), and I wonder which fundamentals they would choose to use in the past. Because that's not practical to change on stage. – octacube Jan 14 at 17:02
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Partial answer.

I'm not sure if we know how exactly it was done in the past. Various systems were used. One concept is that in non-equal temperaments various keys sounded differently, and sometimes some keys or chords were avoided because of worse sound.

On the other hand I once saw a harpsichordist re-tuning the instrument on the stage; it took her just several minutes to change the temperament in a short break in the concert.

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  • Thank you, that’s very good to know. I wish there are some writings from the past about this somewhere... I’ve read about avoiding some keys/chords as well, that’s why I’m thinking they must be writing for some already tuned instruments, and those instruments must be tuned on some base notes that caused the avoidance. – octacube Jan 13 at 4:12
  • Maybe it’s just a mess and it’s different everywhere...? – octacube Jan 13 at 4:19
  • If I remember correctly, there is a wide range between the single base used for tuning (which of course has to sound perfect) and intolerably out of tune. The closer you remain to the base (in circle of fifths view), the more acceptable the result will sound. So any tuning does not imply restriction to a single key. – guidot Jan 13 at 12:02
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    @octacube keep in mind, however, that although a harpsichord can be retempered during a break in a concert, the same is not true of a large pipe organ. This perhaps explains why the individuals who have given their names to temperaments (for example Werckmeister, Kirnberger, Vallotti) are all organists. Also, user1079505, there is quite a lot of detail about these temperaments available in historical texts. – phoog Jan 13 at 17:23
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    @octacube "those instruments must be tuned on some base notes that caused the avoidance": the base note of the temperament is not as important as the nature of the temperament itself. Whether you start at A or C or some other note, the temperament will specify that the fifth between (for example) G and D should be (for example) 1/5 of a comma smaller than pure. – phoog Jan 13 at 17:27
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As the other answer suggests, this is a huge topic, not really answerable in a few sentences. There's lots of information online. The Wiki article is a good place to start: https://en.wikipedia.org/wiki/Musical_temperament

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The base note of the temperament isn't necessarily important. What matters is the degree to which any given fifth is tempered. Instructions for the temperament might say to start with A, then tune D to a perfect fifth below A and then raise it by some specific amount. You would then proceed to G and C, each time with a specific instruction about how much sharper each of those notes should be compared to a pure fifth. You can of course give instructions that lead to the equivalent temperament starting from C, going up by fifths, and each time lowering the upper note by the same ratio.

As an example, look at Werckmeister's Musicalische (sic) Temperatur (published in 1691). The tables, for example on page 78, do not talk about intervals between various degrees of whatever key you happen to be tuning to, but rather to intervals between specific pitches such as G and C.

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  • Thank you for the link. Unfortunately my German is not good enough to read it. :( I wonder if there's an English version of it somewhere. I think I understand what you said about tempering with specific intervals to make them sound how you want, especially for well temperament. But they must all start somewhere, right? What does the text say about the starting pitch? In most cases I've seen talking about these things they seem to start with C, but I don't know if that's common practice. Is it always the same, or there are some common starting pitches, or they are just different every time? – octacube Jan 14 at 17:13

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