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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
  • I realize I'm commenting on a 6-mo-old post, but for others dropping by: I highly recommend A History of Performing Pitch: The Story of "A" by Bruce Haynes. The idea of one answer for "The Past" is, unfortunately, just the tip of one crazy iceberg. Jun 24 at 19:54
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As phoog's answer notes, most (all?) tuning instructions you find in 17th and 18th century sources tend to be given in terms of actual pitch names, where specific intervals between specific pitches were tuned precisely. So, it's not so much, "Start on your tonic note and tune these intervals around it," and more like, "temper the fifth from E-B like this, and the one from A-E like that," etc.

However, the effective "key center" of most of these historical temperament instructions tends to be around keys with few sharps or flats. So, if the question of the "base note" here means something like "What key/keys were most in-tune for historical temperaments?" then keys like C major, G major, A minor, etc. were generally least likely to have intervals that sounded awful. The more black keys that appeared in a particular piece, generally the more likely you'll start to veer into intervals that sounded less in-tune. (This is a broad and very general statement, as temperament systems varied a lot in how they were designed.)

I suspect this question is generated by the feature that appears on many modern electronic keyboards where one can choose a "center note" for the particular tuning, like selecting an A♭ center pitch for a piece written in A♭ major. What this effectively does on most keyboards is to transpose the tuning system so that A♭ and neighboring keys tend to be most "in-tune," rather than C or whatever. This process is very ahistorical, though it can be fun to play around with on keyboards that have such a function.

I do seem to remember reading somewhere about composers or performers making adjustments to tuning to accommodate different keys. So, one might choose to temper a different set of fifths according to the instructions instead of the standard one. Or perhaps just use a different tuning system altogether to accommodate playing in more sharp keys or more flat keys or something. I can't recall where I read this off-hand, but it certainly wasn't commonly practiced in performance or anything. Maybe a performer who knew the pieces on a program had a wider selection of keys or something might choose a more "forgiving" temperament when tuning the harpsichord in preparation for a performance, but I don't know off-hand if we have any accounts of this.

The other thing to remember before going too far down the temperament obsession rabbit hole (something many people have done, myself included) is to recognize that these complicated sets of tuning instructions were generally only applicable to keyboard instruments like harpsichords and organs. When you start involving varieties of other instruments in ensembles and singers, suddenly there's often going to be a much greater variety of tuning issues. And you'll effectively have several different simultaneous "base notes" for tuning. The trumpet or horn (using natural harmonics) pitched in whatever key combined with a flute or oboe pitched in another key combined with the strings (with their Pythagorean tuning tendencies) will suddenly make a lot of those "a few cents here or there" tuning issues for the keyboardist less relevant. Particularly once you get to the 18th century and had circulating temperaments that sounded "passable" in all keys.

In general, I think what the question is getting at is whether and how performers adjusted instruments to make the keys of their programs sound "more in-tune" by changing the temperament. And the general answer is that once a large variety of standard keys became common (with several sharps and flats), the notion of the "characters of the keys" started to emerge, probably at least partly due to the differences in which keys sounded more or less in-tune with common temperament procedures. (And this could be exploited in composition: I remember encountering a passage in a Handel recitative that rapidly modulated through some unusual keys, stopping for a while in A♭ minor on the words "horrible, horrible." Yes, the accompanying harpsichord probably did sound a bit "horrible" during that passage, which likely was the point.) Reorienting your tuning system to accommodate music of different keys would likely undermine these tendencies.

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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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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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If you were to retune for every piece, that would mean that all keys had the same intervals and sounded identical... there would be no point in playing pieces in different keys.

Composers used different chords, different chord voicings, different chord progressions and different modulations in different keys precisely to exploit the different characters of those keys.

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