We talk of equal temperament but just intonation.

From wikipedia, tempering is described as

"the process of altering the size of an interval by making it narrower or wider than pure."

where intonation is

"a musician's realization of pitch accuracy, or the pitch accuracy of a musical instrument. Intonation may be flat, sharp, or both, successively or simultaneously"

Mmmmm... They sound rather similar, don't they?

For a moment entirely divorcing temperament and intonation from the notions of "equal" or "just", can someone clarify the difference -if any- between the two?

Test case: are (or would) we in fact be free to use the terms interchangably?

To be clear, I am specifically not interested in narrower definitions, as in the context of equal temperament and just intonation.

  • 3
    The premise of your question is a little off, as the meaning of temperament specifically relates to just intonation (or the lack of it). Tempering is "the process of altering the size of an interval by making it narrower or wider than pure [usually for the purpose of transposition]", pure here meaning the same as "just". Intonation relates simply to pitch accuracy in general.
    – Some_Guy
    Jul 30, 2015 at 16:21

3 Answers 3


A pithy way of saying it is that intonation is the process by which a temperament is achieved.

Intonation is what is done in order that the sound is produced at the desired/intended pitch. This can be done as part of instrument setup, e.g. "setting the guitar intonation", or as an integral part of performing the music, e.g. as in expressive intonation.

Temperament is an adjustment of intervals away from their pure (just) ratios in order to set up scales with desirable properties, mostly so that music sounds good in multiple keys.

A singer has good intonation when he/she is able to achieve the pitches in the desired scale, whatever the temperament of that desired scale is; maybe just intonation in pure vocal music, maybe 12TET if the singer is performing along with a fixed pitched instrument. A guitar has "good intonation" if all of notes across the fretboard are in tune, where "in tune" is (essentially always) in reference to 12TET.

But then why is "just intonation" an intonation rather than a temperament? This has to do with historical precedent. At least in theory, in early Western music the idea was to always use a "just intonation" -- so the terminology makes sense when you sing "justly" you are creating the proper "tones" -- i.e. you are "intoning justly" (I tend to begin the discussion with 5 limit, though Pythagorean tuning was the theoretical ideal earlier) scale. The word temperament came about because just intonation is well suited only for polyphonic music in a single key, and if you try to modulate you end up with intervals that sound bad. In order to alleviate this constraint for fixed pitched instruments, these intervals were "tempered" to make them sound less harsh so as to allow music to be played in more keys (see def. 3 here, which evolved into the music usage). So (another connotation of) a temperament is a way of adjusting the pitches of a just intonated scale to construct another scale. This brings us back to the beginning: temperament involves the construction/definition of scale of notes used by the music; intonation is the execution of realizing those notes, whether that is setting up an instrument to produce those pitches or the execution of the same during performance.

  • 2
    Tempering definition (in a general sense): 'act as a neutralizing or counterbalancing force to (something)'. If I understand you correctly, intonation implies a striving for pure (harmonic) tone, whereas musical temperament implies de-tuning from this to foster musical compatibility in any key. In this sense, the claim that 'intonation is the process by which a temperament is achieved' seems a little dubious. Jul 30, 2015 at 12:07
  • 3
    @user1019696 No, intonation implies striving for the desired tone, which is not always a pure harmonic tone.
    – Dave
    Jul 30, 2015 at 12:22
  • 2
    Just to emphasize what's already been said: intonation is the description of how close one is to desired pitch. For example, when playing something like a violin or singing, one must have "good intonation" to be able to successfully hit a desired pitch accurately. Similarly, when building an instrument, one must build it with "good intonation" if it is to sound as intended (e.g. fret placement on a guitar). Temperament refers to the process of tuning notes in an octave to "compromise" pitches. If you wanted to play music in a given temperament, you would have to have good intonation to do so.
    – Some_Guy
    Jul 30, 2015 at 16:03
  • 2
    Temperaments, are an example of a type of tuning system based on compromise. Intonation refers to the process of accurately playing notes at a chosen pitch (most often the pitch of a given tuning system). Essentially, intonation is the ability to "tune" something. In this context intonate and tune are rough synonyms. The confusion with the naming of the untempered tuning system just intonation comes about because it has the word "intonation" in it.But this is explainable by the fact that just intonation means that one should intonate "justly" i.e. to the "just" tuning system.
    – Some_Guy
    Jul 30, 2015 at 16:13
  • 1
    @user1019696 there are at least two shades of meaning for intonation; the more basic one would be 1:1 -- ie the performer produces the notes of the desired scale. For some instruments (notably voice and unfretted strings) and some styles of musical performance, there is an additional layer of intonation which involves shading notes away from what they'd naively be in a manner that depends on the musical context and the interpretation of the player; this would be 1:many. The link to "expressive intonation" and the final paragraph of @aparente001's answer get at this additional layer.
    – Dave
    Jul 30, 2015 at 19:11

Well, before the keyboard instruments were well tempered [think of the Well-Tempered Klavier], it was impossible to play in tune (i.e. with good intonation) in certain keys. And by the old system it would be impossible to do the annual (or semi-annual) tuning in such a way as to be able to play all keys in tune.

Modern string players still have this problem, albeit to a much lesser extent. When I'm tuning my cello, say I start by choosing an appropriate A, and then tune the first fifth (A and D) to a very exact fifth. So far so good. If I then forget all about the A and tune the next fifth (D and G) in an isolated way, to be a very exact fifth, and then do the same thing with the last fifth (G and C), ignoring the other strings, I will have a problem when I try to get certain chords and intervals in tune. [Each individual fifth was very pleasing, but over the whole range of the instrument, one quickly discovers that this untempered way of tuning the instrument results in unresolvable contradictions.]

My solution is to tune the instrument as follows:

  • Match my A to whatever has been given
  • Tune the D to the standard exact fifth below the A
  • Make the next fifth a hair on the small side
  • Make the last fifth a little smaller still

Now I have a structure I can work with pretty well.

I have read descriptions in a viola forum that were rather similar in procedure, with much the same final result. [The result is slightly skimpy fifths. Taken out of context, each of these fifths is a little smaller than it should be, strictly speaking. However, this is what prevents me from getting some unavoidably ugly results.]

[Through this tuning procedure, I am trying to achieve consistency. I can adjust all the stopped notes (i.e. the fingered notes), but I can't adjust the open strings. So, this tuning procedure results in a set of compromises that creates many tiny intonation problems, for the sake of avoiding a small number of large intonation problems. Just as tempering the keyboard instruments did.]

Intonation is a subjective thing. I am a string player. However, I took a couple of semesters of voice lessons. My [voice] teacher sometimes remarked that my "string player style intonation" would not fly in the vocal world -- as an example, my leading tones were too high for vocalists' taste -- but she recognized that I was not alone; the whole breed of string players play their leading tones higher than many other musicians.

[As a string player, for a leading tone to sound pleasing to my ear, and "in tune," I need to bend it quite close to the tonic, i.e. I need to get it very, very close to the tonic. I feel that I am milking that leading tone for all it's worth. I feel that if I did not do that, it would be like when someone is telling a joke and just as he's about to pronounce the punchline, someone comes in and distracts the listener with some unimportant but very distracting interruption. When the joke teller tries to pick up where he left off, it's not the same -- and the punch line doesn't satisfy.]

*[What I'm talking about in this section is the effort, and the satisfaction, of getting a series of individual notes to be in tune with each other, within a particular tonality (=key). (This is possible because of the tempered way I tuned the instrument.)

Edit, responding to your comment checking your understanding:

So (testing my understanding) given a desirable (pure) musical pitch, tempering represents a divergence from it in the name of compromise.

Yes, I think we are on the same page here, except that intonation, for me, is always relative to something. Having played the first note, I now will listen very carefully and adjust as needed so that the second note will be in tune with respect to the first. (I'm not sure a person with perfect pitch would feel the same as I do about this....)

Intonation is the striving towards realisation of pitch regardless whether pure or compromised.

Not sure what you're saying here, so I'll skip this sentence.

As we tend for historical reasons to associate intonation with purity -rather than simple realisation- of tone, it has become more or less synonymous with just tunings, which can be misleading.

I don't think I agree with this sentence.

In particular, the terms temperament and intonation cannot be interchanged.

I think I agree. Having a well-tempered instrument makes it feasible for us to play in tune in any arbitrary key.


Temperament refers to consistent establishment of the relationship among the notes of an instrument, to adhere to a particular theory of pitch. Why the word "temper" is used is because the idea is that any means of choosing pitches for an instrument (particularly an instrument which supports modulation) is a compromise away from the pure intervals: the pure intervals are tempered (i.e. altered, like metal being hammered by a blacksmith) to create a good sounding compromise, according to some consciously chosen system. An example of a temperament is the "equal temperament", which divides the octave into 12 semitones, which are all equal: each step from one semitone to the next one changes the frequency by the same percentage.

Intonation is the degree to which an instrument conforms to its temperament. Deviation from intonation is an unwanted detuning which is not consistent across the instrument. It could be due to the reality of how the instrument is constructed, or due to the musician also.

On a guitar, bad intonation causes notes higher on the neck to have different relationships than the corresponding notes twelve frets (one octave) down. The same chord shape or melody which sounds as it should in the low position is out of tune in the high position.

A singer or violinist also exhibits "good intonation". This just means singing or playing in tune. The violinist is placing fingers in the right spots on the neck to produce the right pitch. When a singer has "bad intonation", that's basically a fancy way of saying that the singing is "off key".

Essentially, "intonation" just means "correct tuning", but with a special emphasis on the relative tuning, on instruments where that applies. Randomly tweaking the tuning pegs on a guitar results in a detuned situation which is simply called "out of tune", rather than "bad intonation". Bad intonation cannot be cured with any adjustment of the tuning pegs; at best, the tuning pegs can decide where that bad intonation is exhibited. (The guitar can be tuned so that scales and chords sound good at the 12th fret position, but then the open chords are not tuned.) It's like fitting an 11 foot carpet into a 10 foot room by moving around where the bump is, rather than trimming it away.

There is a term called "just intonation" which somewhat confuses the two. Just intonation is in fact a choice of temperament: a temperament whose goal is to have perfect ratios between the frequencies of notes in the scale to the root note. Though in one sense the notes aren't "tempered" under just intonation, the pure relationships among the notes are only accurate for playing in one key: there is a compromise in that modulation is sacrificed for purity.

So, in summary, temperament is a choice of tuning for the notes of a scale whose name refers to a compromise from some ideal tuning which is not practically achievable (pure intervals in any key whatsoever), and intonation is the adherence to the temperament: how well is the chosen tuning actually achieved by the instrument or the musician.

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