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Do people with perfect pitch distinguish between equal temperament and just temperament?

Suppose someone with perfect pitch is singing a duet and wants to harmonise in thirds above the main melody. Will they harmonise in equal temperament or just temperament, or will they have a choice?

To hear the difference between these intervals, here is an excerpt from a video Why I use autotune

I personally do not have perfect pitch but I can clearly hear the difference and can reproduce the sounds.

Question

How do people with perfect pitch experience different tuning systems?

piiperi Reinstate Monica
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chasly - supports Monica
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    There is not such thing as _just temperament_. There's just intonation, and there's equal temperament. (To be more precise, there are actually many different kinds of both just intonation and equal temperament, but by itself the former is usually taken to mean [Ptolemaic tuning](https://en.wikipedia.org/wiki/Ptolemy%27s_intense_diatonic_scale), the latter [12-edo](https://en.wikipedia.org/wiki/12_equal_temperament).) – leftaroundabout Nov 08 '20 at 20:44
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    I can _definitely_ hear the difference between an equal-tempered major chord and a just major chord. And I definitely don't have perfect (meaning absolute?) pitch. – cyco130 Nov 09 '20 at 07:14
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    In my experience, in ensembles where all instruments have continuously varying pitches (string quartets and a cappella groups, for example), skilled musicians always go to just intonation—regardless of whether they have perfect pitch. When an instrument is limited to a particular tuning, so is the ensemble. – Greg Martin Nov 09 '20 at 07:14
  • @leftaroundabout there's only one equal temperament that can be used to tune a modern 12-tone keyboard, however. The only other kinds of equal temperament cannot be used to tune a standard 12-tone keyboard because they have a different number of pitches. And I would argue that there's only one kind of just intonation because it's a process rather than a set of pitches. – phoog Nov 10 '20 at 05:50
  • I had a physics professor in college who's wife was a cellist for Chicago symphony. He had perfect pitch and had all kinds of stories about being able to hear changed in intonation with temperature, etc. He claimed to not be able to listen to the piano due to the extreme dissonance of ET. He once was in a cathedral in Germany and based on the out of tune pipe organ determined the temperature. He considered it a curse, not something to envy. –  Nov 10 '20 at 11:06
  • @phoog well, by that logic you certainly can't tune a 12-tone keyboard to a meantone temperament either, because these have in general an _infinite_ number of pitches! In practice, it's quite possible though to map a 12-tone subset of just-intonation scales, of meantone, or of 19- or 31-edo onto the keyboard, it just won't be symmetric then. – leftaroundabout Nov 10 '20 at 11:14
  • @leftaroundabout you are confusing "temperament" and "tuning system." A meantone tuning system may have an infinite number of pitches, but a meantone temperament is what you get when you choose some finite subset of those pitches for the keys on a keyboard. (And this is why the first sentence of your first comment is correct: just intonation is a tuning system, not a temperament.) – phoog Nov 11 '20 at 16:48
  • @phoog whose definition is that? To me, “temperament” only means that some kind of compromise is being made between some nearly-equal ideal intervals. It does not say anything about finite selection of pitches. “Meantone” specifies that the intervals which are being approximated by the same are the Pythagorean ditone and the 5:4 just third, so meantone is always a temperament even if you use the term “meantone tuning”. Still no mention of finite number of pitches, for sure not necessarily 12. It can make sense to map e.g. ¼-comma MT to a 17-key keyboard (with different black keys for ♭ and ♯). – leftaroundabout Nov 11 '20 at 20:46
  • Related question: [Absolute pitch - has it varied through the centuries?](https://music.stackexchange.com/questions/37951/absolute-pitch-has-it-varied-through-the-centuries) – Aaron Nov 16 '20 at 07:21

4 Answers4

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My experience about this: even people without perfect pitch can distinguish between temperaments.

As an example, when I play a pipe organ with unequal temperament, some chords sound very pure, without any "beating" effect (mathematically, the ratio between the frequency of the notes are close to the integer fraction defining the intervals, such as 3/2, 5/4, etc.), and playing such a chord gives a very "satisfying" feeling.

TL;DR: You can clearly identifiy non-equal temperaments, even without perfect pitch.

Basj
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    While this is true, it does not answer the question "How do people with perfect pitch experience different tuning systems?" – phoog Nov 10 '20 at 05:43
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    @phoog I wanted to emphasize that being able to distinguish temperaments is something that is not really 'correlated' to perfect pitch. These variables are somehow independent. Temperament is about *relative* pitch between notes and how close the ratio between frequencies of an interval are from the fractions 3/2, 5/4, etc. Being able to detect this is not really linked to the ability of having an ear that has an *absolute* reference. – Basj Nov 10 '20 at 07:46
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    Thank you. Exactly what I'm trying to say (in a different way) with my answer too. – Nobody Nov 10 '20 at 09:41
  • @Basj that's true when more than one note is sounded. I had assumed that the question is trying to decide whether someone with perfect pitch, on hearing 352 Hz _in isolation,_ recognizes the pitch as "just-intonation F" or as "slightly-sharp F" or as something else; or whether that person when hearing 352 Hz and 440 Hz together would be more likely than someone without perfect pitch to experience the interval as _less well tuned_ than 349.228 Hz and 440 Hz sounded together rather than _better tuned._ I know one singer whom I suspect to be in the second category. – phoog Nov 11 '20 at 17:11
  • And I guess some chords sound terribly off, giving a very "displeasing" feeling? – Luiz Cordeiro Sep 11 '21 at 15:12
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    Indeed @LuizCordeiro, the art of temperament is essentially how you distribute a certain total amount of "detuning" amond the 12 notes: either each chord is *a little bit* detuned (with respect to pure frequency ratio intervals), like in the equal temperament. Or you have some chords which sound really *perfect*, and others which sound in a very unpleasant way! – Basj Sep 11 '21 at 15:56
  • @Basj Awesome. Your mention on "distributing the detuning" actually sums up the problem of temperament really well, at least for someone who is just getting into it (such as myself). – Luiz Cordeiro Sep 11 '21 at 19:28
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My experience with musicians with perfect pitch (I don't have it myself), is that their pitch sense is 12TET (twelve-tone equal temperament) and in other tuning systems pitches would be identifiable, but "out of tune".

Basj
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Aaron
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  • Yup, that's my experience listening to music in just intonation (which typically tries to use every note in a major scale). – Dekkadeci Nov 08 '20 at 13:36
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    @Dekkadeci - with no instruments to reference, acapella singers tend to move slightly away from 12tet, as the blends are more harmonious. – Tim Nov 08 '20 at 15:13
  • @Tim - I suspect I wouldn't be able to tank barbershop 7ths for very long regardless of how harmonious they sound. – Dekkadeci Nov 09 '20 at 08:28
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    @Dekkadeci - I think it's a natural occurrence when people sing unaccompanied - they revert to what sounds best. Don't think anyone tries to sing in 12tet unless there are instruments that dictate that's what will have to happen.Not sure which way pitch correction stuff pushes vocals. Could be an interesting insight. – Tim Nov 09 '20 at 08:33
  • My experience has been the opposite. People I know with perfect pitch hear Just and can't ET sounds horrible. –  Nov 10 '20 at 11:07
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This doesn't really have anything to do with perfect pitch. Equal vs just temperament is about relative pitch, not absolute.

Only in equal temperament does a certain frequency have a unique matching note. If given a frequency you are supposed to tell the note in just temperament, then you would also need the context - and the context is inherently about relative frequencies, i.e. how is this note supposed to harmonize with other notes. Of course you can fix the frequency/note assignment, but then you can just play certain harmonies, and others might be horribly out of tune - the whole point of equal temperament is that this is a very good approximation of just temperament if you don't want to restrict yourself to certain keys.

The "perfect pitch" ability can take on many forms.

  1. Some people might have "equal temperament standard modern tuning" perfect pitch, and will just tell you that everything else is out of tune.
  2. Some people might have "equal temperament" perfect pitch, but one week it might be standard modern tuning, and if the following week they spend 50 hours playing in a historical tuning of A=415Hz they will subconsiously switch to that tuning during the week, and will have equal temperament A=415Hz perfect pitch the week following that.
  3. Some people can actually tell you the numerical measurement in Hertz, i.e. they hear "300Hz" for example, and not some musical note.

Each of those persons respectively, with purely academic learning (no inherent ability required), can learn to tell you that

  1. If a frequency sounds too low/high for a certain pitch, then it might be correct in just temperament in some context - for example an F that sounds too high to them could be a just major below A.
  2. They know their tuning switches back and forth and can always relativize the note they hear to "probably a modern A=440Hz" or "I have played so much in A=415Hz recently that I'm sure this is an A in that tuning".
  3. etc.
Nobody
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    It has to do with perfect pitch in that (given A=440 Hz) F might be 352 Hz (a just major third below A) or 349.228 Hz (an equal-tempered major third below A). Can people with perfect pitch perceive that difference, and, if so, what do they make of it? – phoog Nov 08 '20 at 20:35
  • _“subconsciously switch their reference note to a=415Hz or a=440Hz”_ AFAIK this is called [_relative_ pitch](https://en.wikipedia.org/wiki/Relative_pitch), not [absolute (or perfect) pitch](https://en.wikipedia.org/wiki/Absolute_pitch). – Melebius Nov 09 '20 at 08:40
  • @Melebius What I meant is that person can, if they hear a frequency, tell you a corresponding note - that's perfect pitch. But depending on the tuning system (standard modern, or a variety of historical and others) the same frequency can be a different note and some people who have perfect pitch in principle get confused by this. So they can tell you a corresponding note, but might not be sure if the note is in standard modern tuning, or for example baroque tuning. – Nobody Nov 09 '20 at 10:20
  • @phoog Of course they can hear the difference. But depending on the context, they might just hear the numerical value (with some accuracy, I've only met one person who could do this and don't know their exact accuracy), or they might hear "ok, this could be an F in this context, but it would be too low/high for an F in other contexts". And if they actually *have* the context then of course they can tell if it fits the context because that just needs the usual relative pitch ability which people with perfect pitch *also* have, obviously. – Nobody Nov 09 '20 at 10:24
  • @Nobody what do you mean "of course"? If it is self evident that they can tell the difference between 352 Hz and 349.228 Hz, is it also self evident that they can they tell the difference between 330 Hz and 329.628 Hz (just E and equal-tempered E)? Where is the threshold for perceiving pitch differences? How do you explain subjective disagreements among people with perfect pitch (which are far from uncommon in my experience)? – phoog Nov 10 '20 at 05:23
  • "Only in equal temperament does a certain frequency have a unique matching note": are you saying that it's not possible to calculate the pitch of E4 on a keyboard tuned to Werckmeister IV at A=415 Hz? If so, that's incorrect: every temperament fixes the frequencies of all of its notes. – phoog Nov 10 '20 at 05:42
  • @phoog You had to give more information than "just temperament" to make the mapping fixed. That's what I meant. Just temperament only has fixed frequency/note assignments given a certain key, and if the piece you want to play switches keys it's possible that it's impossible to play this piece on a just temperament tuned keyboard (without retuning during the piece, which I'm sure happens for some niche modern music, but isn't practical). Of course there are compromises (like the one you quoted), but those aren't really the essence of just temperament, they are imperfect approximations. – Nobody Nov 10 '20 at 09:28
  • @phoog By of course I mean given their ability to tell nearby notes apart, something in my opinion clearly not related to tuning systems. – Nobody Nov 10 '20 at 09:39
  • @Melebius - relative pitch isn't what you think. It's the ability to name other notes once a particuar note is named. – Tim Nov 10 '20 at 16:33
  • @Nobody there's no such thing as just temperament. A temperament is what you get when you pick a finite set of pitches for the keys of a keyboard (or the logical equivalent). You can't do that and have all the intervals be just. Any keyboard temperament is therefore something other than just. You run into problems before you try switching keys. For example, the ratio between 5:3 and 9:8 is 40:27, not 3:2. The "compromises" of which you speak are the very nature of temperament, from which the word derives. – phoog Nov 11 '20 at 16:55
  • @phoog I'm pretty sure it must be obvious I'm not familiar with the subject specific words. Please suggest better wordings. Other than that: Yeah duh. – Nobody Nov 11 '20 at 19:06
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    @Nobody sorry, it wasn't obvious. If you were unfamiliar with the terminology then it makes sense that you would use "just temperament" because that term is used in the question. People often confuse "tuning" and "temperament," and I am just trying to make the distinction clear (a point that I make frequently on this site). There's also a widely held misconception that "just intonation" is the tuning system that sounds best in a single key, but anyone who has tried to tune a keyboard in "just intonation" quickly discovers that it isn't true (unless they accept Pythagorean major 3rds). – phoog Nov 11 '20 at 20:27
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It's going to depend on what else is happening. When there are instruments which can only play in 12tet accompanying the vox, they will sing in 12tet. I reckon they have to!

Acapella it's different. The restrictions in the above scenario are lifted, and often singers will revert to just temperament, which will sound more natural and 'in tune'.

Tim
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  • If acapella groups revert to just temperament, do they experience pitch drift as they go along a song? – orlp Nov 08 '20 at 14:21
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    @orlp - I think a lot of the time, acapella groups drift, albeit slightly, anyway. Whether that's due to any temperament or not, not at all sure. But I think it happens regardless. – Tim Nov 08 '20 at 15:10
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    What about instruments that can only play in some 12-tone unequal temperament such as quarter-comma meantone? How precise is perfect pitch? Can people with perfect pitch differentiate between 330 Hz and 329.628 Hz? I'm skeptical. What about between 329.628 Hz and 328.977 Hz? – phoog Nov 08 '20 at 20:30
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    @phoog - I'm not completely sure about a <1 Hz difference, but from my experience, I can detect when someone is using A432 instead of A440. – Dekkadeci Nov 09 '20 at 08:26
  • @Dekkadeci the subtractive difference in Hz isn't particularly significant. I reckon almost anyone can hear a difference of 1 Hz at A1 (where a reduction of 1 Hz corresponds to A4=432 Hz) and probably nobody can hear it at F6. Regardless, this doesn't answer the question "How do people with perfect pitch experience different tuning systems?" – phoog Nov 10 '20 at 05:39