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Equal Temperament vs. Well Temperament (Read 19597 times)

Offline lovetheboywiththebread

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Equal Temperament vs. Well Temperament
« on: July 28, 2012, 05:54:52 PM »
Hi, I'm new here :D (although I posted music here before through my sister's account)
I'm studying music history (RCM History 1) by myself and I'm confused about the definition of equal temperament and how it differs from well temperament in the baroque era.
The definition in my book, Bach to Bernstein by Lynn Harting-Ware says that equal temperament "was developed as a tuning adjustment to the keyboard that enabled it to play in all keys. It was discovered by slightly cheating the distance between pitches that the keyboard could be adjusted to be in tune for all keys. It became extremely important with the major-minor tonality system... Bach demonstrated that he could compose in all 12 major and minor keys in the Well Tempered Clavier".
However, from my research online I've read that equal temperament is a system of tuning where the distance between the pitches is equal, and that well temperament is "means that the twelve notes per octave of the standard keyboard are tuned in such a way that it is possible to play music in most major or minor keys and it will not sound perceptibly out of tune." Isn't this the same as the definition for equal temperament in my textbook?

I'm kinda confused, could someone please explain this? And how do both temperaments relate to the baroque era. Any help would be appreciated.

Offline withindale

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Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #2 on: July 29, 2012, 06:24:58 AM »
I kind of geek out on tuning stuff, so I love it when anyone gets curious or asks questions about stuff like this!

I think your confusion is understandable - both equal temperament and well temperaments (there are many, many so-called "well" temperaments) have one similar goal - which is, as you have stated, to be able to play in all keys without anyone cringing. However, they accomplish this in DIFFERENT ways.   

Equal temperament divides the octave into equally spaced parts - each being a semitone that we're accustomed to seeing on a keyboard. This means that no matter what pitch LEVEL you play at, the music will sound the same in terms of how the pitches are related to each other melodically and harmonically.  Equal temperament homogenizes the keyboard, and, essentially, makes all keys equally out of tune in exactly the same ways.  Our modern ears have gotten used to this "out of tune-ness" so much that it sounds in tune to us.  The major thirds, in particular, in equal temperament are really much wider than pure thirds - so much so that pure thirds now sound out of tune to most of us at first, I think.  But I digress...

Well temperaments, on the other hand, do NOT divide the octave equally. They prioritize certain keys and harmonies to be more pure and some to be less so, as had been done for a long time (this is why, btw, much of earlier keyboard music is written in keys that do not have many sharps or flats - they wrote for keys were the ones that were tuned more "pure" or "just", which was very beautiful and the preferred aesthetic for a long time but made the remaining keys that much more discordant.  When early keyboard composers "strayed" into keys like, say, F# or something, it was (I believe) with the INTENT to exploit the very uncomfortable sound of F, thus creating a different kind of musical tension than that which we are used to today.  This sort of tension was very effective, and made coming back to the home key that much more beautiful and restful). Unlike previous temperament practices, though, which deliberately favored the purity and beauty of some keys while rendering other keys basically unplayable, well-temperaments made more keys palatable for composers and keyboard players to actually use.  Some "well temperaments" do this more gently than others, but none do it with exactly equal spacing among all the notes on the keyboard. 

With well-temperaments the pitches are related to one another in more unique ways for every key, thereby giving each key a particular sound or "character."  This subtle difference in the sound of a particular key might not be so noticeable in a quickly-moving piece, and certainly less noticeable on the modern piano than on instruments more appropriate to the day - like the harpsichord, but the difference is there.

In terms of keyboard music, equal temperament was nothing more than a theory in the baroque era, and arguably would have been rejected as a musical reality to ears of that day (in my opinion) even if someone did manage to tune a keyboard with equal temperament.  Why?  Because in those days, people were used to different tuning schemes, as I mentioned above- ones that did NOT divide the octave equally, but that "favored" certain keys.  When you get all the way to Bach, tuning is evolving, but the compromise is uneven, unequal well-temperament.

Some argue that Bach wrote WTC with equal in mind, but I (and many others) would adamantly disagree.  What would be the point of writing something in every key if every key in fact sounds the same?  I'd argue that such pieces showcase the beauties of unequal WELL temperaments, and the character and dimension that the tuning alone can give a piece - ESPECIALLY on the harpsichord (or organ, as the case may be) (reasons for this, but that's another discussion).

So, how'd I do?  Clear as mud?  As I said, I kinda geek out on this stuff, so please ask any questions you have, and I'll do my best to answer them.

One final fun fact... I never understood this as a kid, and no one could explain it to me, because the equal temperament that we are used to makes C# and Db, say, the same exact note.  But.  In reality C# and Db are VERY different notes, when tuned "pure", as, say, thirds in relation to other notes.    Db is actually HIGHER than C# - but our keyboards don't have the capability of offering us both notes.

Some early keyboard builders made keyboards with split keys so that both C# and Db could be available, and the player could choose whichever was appropriate for the key and piece they were playing.  I have to say, I do understand this - there is nothing quite like the beauty of a major chord tuned perfectly just and pure... you can't do much with it, but my, what a beautiful sound.  I can understand why historically people were not quite ready to compromise a lot on this for a long while....

It can be kinda mind-blowing stuff when you dive in...  but in good and eye-opening in lots of ways.  In my humble (?) opinion.

:)

JH.


Offline lovetheboywiththebread

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Re: Equal Temperament vs. Well Temperament
«Reply #3 on: July 31, 2012, 12:01:39 AM »
@Withindale  Thanks! The chart was really helpful and interesting. ;D

@justharmony  Wow! Thanks for the long and detailed response, and was really interesting! :D That cleared up a lot of things for me and made perfect sense. (:

The reason I was confused was that my book, "Bach to Bernstein," by Lynn Harting-ware, does not even mention well temperament, and neither did the RCM syllabus. The book implied that Bach used equal temperament, as seen in the quotation in my first post.
(By the way, does anyone know if this book is a credible source? I have found many errors and typos in it  :/)
 

Offline davidjosepha

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Re: Equal Temperament vs. Well Temperament
«Reply #4 on: July 31, 2012, 01:30:26 PM »
...

Holy cow, that was interesting. I have a couple questions for you.

1) Have you personally heard a harpsichord tuned in different ways, so you can compare? If so, what does the difference in key sound like, as you mentioned, on a tuning where each key isn't the same as other keys, just shifted in pitch by x number of steps? What you're mentioning sounds really cool in theory, but I'm wondering if it might sound less fun in practice.

Also, do you know of a YouTube video or something where I could hear this?

2) Have you heard both a D-flat and a C-sharp personally, or are you speaking from what you've read? How much of a difference is there? Is it very subtle, like, they both sound like the same note, basically, but one sounds much fuller in a certain chord, or are they distinctly different pitches?

When I was younger, I never questioned the flat/sharp thing because my teacher explained that it was all theory based on which note should be which (in B-flat major, it's E-flat instead of D-sharp because the E-flat takes the place of E in the scale). That's interesting to hear what you say though.

3) How do string and wind instruments compare on this? You say that in well-temperament, certain keys sound different because they spacing is different, but how would that work with an instrument that can theoretically play any pitch between their highest and lowest note? Does a violin play a C-sharp different from a D-flat depending on context in order to stay in tune with the orchestra? Is it something so subtle its done unconsciously by the violinist with a good ear because he can hear the intervals?

4) I've heard that equal temperament's chromatic scale through an octave can be written as A(2)^(1/12), A(2)^(2/12), A(2)^(3/12), ..., A(2)^(11/12), A(2)^(12/12) = A(2), where A is the pitch of the first note. Is this accurate? It seems like it would work for every key because (A(2)^(1/12))*2^(1/12) = A(2)^(2/12) - the "A(2)^(1/12)" representing B-flat (so one chromatic step up from B-flat is the same as two from A, according to this formula, which is accurate)

If this is true, what decides that a 3rd (from A to A(2)^(4/12)) isn't a "pure" 3rd? What exactly defines a pure third?

Thanks for the interesting post!

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #5 on: July 31, 2012, 09:06:03 PM »
I'd like to reply to all your questions, so this may come in installments... :)

"1) Have you personally heard a harpsichord tuned in different ways, so you can compare? If so, what does the difference in key sound like, as you mentioned, on a tuning where each key isn't the same as other keys, just shifted in pitch by x number of steps? What you're mentioning sounds really cool in theory, but I'm wondering if it might sound less fun in practice.

Also, do you know of a YouTube video or something where I could hear this?"

Most definitely, in response to the first q.  I’ve heard, tuned, used different temperaments on various instruments – harpsichord, historic pianos, and modern piano (I have and tune my own harpsichord, but do not attempt to tune my own piano or any others). 

The difference between playing in different keys varies a lot depending on temperament.  Some well temperaments are “gentle”, and the effect is subtle and might not even be noticeable consciously to one not listening for it, though we often “hear” such things and respond to them without even realizing we are doing so or to what, exactly, we are responding. 

As any piano technician can tell you (I am NOT one, btw), we use lots of different language to describe what we hear or experience that does not tell him or her what exactly it is we are hearing, just how we experience it, subjectively.  The art of being a technician is being able to hear whatever it is we say (i.e. “This sounds sharp/bright/muffled/dark/tinny ETC.”) to a particular physical thing going on with the piano that they can manipulate in a way so as to please our ears.  Point is, we often can identify something we hear or experience without being able to say what it is we are hearing, exactly, or why we hear or experience that.  I believe temperament can be among those things that we hear and experience without being able to pin down exactly what it is.  Of course, it can be very obvious, too, if a temperament is not so gradual or gentle.   A meantone temperament, for example, will sound heavenly in certain keys, and absolutely unusable in others.
 
As far as youtube is concerned, I'm sure there are good videos out there - lots of stuff comes up in a quick search, but I did not find anything quickly that I would recommend for a temperament "newbie" to got to first, which surprises me.  I will keep looking (or make my own), but in the meantime, what I would look for is a demonstration on a real harpsichord (no electronic reproduction of anything, least of all piano) of just intervals, chords - comparison of just intervals vs. equal temperament or some such.  Thirds, in particular.  Or the difference between Db and C# you talk about below, for example.  Will look further when have more time...   (Keep in mind, too, that much depends on the quality of recording and quality of playback equipment).

"2) Have you heard both a D-flat and a C-sharp personally, or are you speaking from what you've read? How much of a difference is there? Is it very subtle, like, they both sound like the same note, basically, but one sounds much fuller in a certain chord, or are they distinctly different pitches?

When I was younger, I never questioned the flat/sharp thing because my teacher explained that it was all theory based on which note should be which (in B-flat major, it's E-flat instead of D-sharp because the E-flat takes the place of E in the scale). That's interesting to hear what you say though."

Absolutely - I hear, choose between them, every time I tune say, a meantone temperament on my harpsichord. There is a BIG difference - enough so that they CANNOT be interchanged - which is why you choose.  If you know you're going to be playing in E major, for example, you choose G# because Ab would render E major unplayable, basically. 

In Equal temperament, though, each note has been compromised enough such that they become the same pitch, and whether you call that one note Eb or D# becomes simply a matter of semantics, as you suggested (and this was how it was basically explained to me once upon a time, too - valid for equal temperament, but not quite the whole truth).

Again, I'd love to demonstrate this for you... when I have a bit of time I'll give it a try...

And with that I"ll have to conclude for now.   Would love to address your other questions too - no time right now.  But stay tuned (yar yar yar)! :)

JH

Offline davidjosepha

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Re: Equal Temperament vs. Well Temperament
«Reply #6 on: July 31, 2012, 09:25:20 PM »
...

Oh my God, this thread is awesome. It's honestly everything I've wanted to know about pianos and keyboards but have never had anyone knowledgeable enough to ask, and have always been too daunted by encyclopedic articles that are so specific I can't understand what they're saying.

I really look forward to your other responses, and thank you very much for taking the time to explain all this!

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #7 on: August 01, 2012, 12:33:15 AM »
Wow.  That's a big compliment - thank you!  As I've mentioned before, I kinda geek out on this stuff, and love talking about it with anyone who's interested. 

It was truly a revelation to me when I first began learning about all this stuff, and music came to life in new, vivid, wonderful ways that I never knew I was missing out on previously.  If I can share even just a tiny tidbit of something that will pique someone else's curiosity, or open them to exploring the sorts of things that became such revelations to me, then I will very happily and gladly do so!  So I welcome your curiosity and interest, and hope that I can continue to offer something of value in response!

To return to your questions...

"3) How do string and wind instruments compare on this? You say that in well-temperament, certain keys sound different because they spacing is different, but how would that work with an instrument that can theoretically play any pitch between their highest and lowest note? Does a violin play a C-sharp different from a D-flat depending on context in order to stay in tune with the orchestra? Is it something so subtle its done unconsciously by the violinist with a good ear because he can hear the intervals?"

Excellent question.  I've had the same one.  I know there have been schools of thought at various times that try to teach tempering of certain notes to string players, for example, etc.  The only notes that are “fixed” on a stringed instrument are the open strings (though this is maybe misleading as they can also play these notes on other strings where the pitch would be variable).   If you have ever tried to play chamber music with a string player where neither of you understands that the fifths on a piano are tempered and not pure, you may find yourself with a very confused and frustrated string player trying to tune to match the piano.  They are used to tuning pure fifths that simply don’t match the piano, so generally they end up tuning note by note to the piano – out of tune, and frustrated by the fact that suddenly they cannot seem to tune their instrument!  It’s not them, it’s the keyboard!
 
Where pitch is variable, though, it’s my understanding that other instrumentalists tend toward constant “pure” tuning – ever shifting as they are able to do.  Same with voices.   It is only where tuning is “fixed” – like on fretted instruments, or those like harp or piano that require a fixed tuning for every note - where temperament becomes relevant.
 
Interestingly, the lute was, I believe, the FIRST instrument to be built using equal temperament as a model.  Flies in the face of what was happening with other instruments and music at the time, and I’ve never investigated the implications or effects of this, though that would be most interesting.   I guess I don’t even remember my source for this information so it may not be correct.  But if it is, that would be most interesting that they’d go to equal vs. the keyboard tempering to favor certain keys…  Perhaps it has to do more with the fact that frets are less easy to adjust than tuning pegs and that these frets affect all strings rather than just one? I don't know enough about that to say, but it would be interesting to investigate.  To return to the original question, though, "temperaments" really only apply to those instruments with truly fixed tuning systems, like the keyboard.  A temperament is a compromise, really, and if you don't have to compromise, why would you?  :)

OK, your last question is a very juicy one - one that essentially asks how we arrive at what is "in tune" and what is not?  It's NOT arbitrary, but based in the natural series of overtones (harmonics) that is present in any pitch made by any instrument (though sometimes electronic sounds can be manipulated in terms of structure of the tone).  I don't know how much you know about the overtone series, so forgive me if I say something you already know.  Many know of the existence of the overtone series and what notes they are, but not, perhaps, the implications of them.  Each pitch contains within it each of these overtones, sounding at varying strengths - the combination of which helps us determine that we are hearing an A on a trumpet vs. an A on a piano, say.  The overtones determine the tone, the color, the character of the pitch. 

They also have EVERYTHING to do with tuning and what is in tune and not.  I will break here - have to run out for something, but will be back.  In the meantime, try this if you're not familiar with the overtone series:

Depress as many keys on your piano as possible without them sounding (white keys are usually easiest).  Hold them down.  Now, hit one of the bass keys (white key) hard and staccato, and then listen.  You might expect that would get all the notes vibrating, as there are no dampers to stop it, but what you'll hear is that it "excites" the notes that are closest to the overtones of that original note.  Kinda cool.

To be continued...
:)

JH 


Offline davidjosepha

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Re: Equal Temperament vs. Well Temperament
«Reply #8 on: August 01, 2012, 01:04:49 AM »
Depress as many keys on your piano as possible without them sounding (white keys are usually easiest).  Hold them down.  Now, hit one of the bass keys (white key) hard and staccato, and then listen.  You might expect that would get all the notes vibrating, as there are no dampers to stop it, but what you'll hear is that it "excites" the notes that are closest to the overtones of that original note.  Kinda cool.

I did this again for fun, but as a drummer who has to deal with snare buzz when tuning, I'm pretty familiar with the concept of sympathetic vibration!

I don't know the exact notes that resonate with each note, but let's say a G resonates when a C is played. Do you define the G (or 5th) in that chord by the overtone that sounds when C is struck? So you would tune your G in the key of C to that overtone?

Thanks so much for the detailed responses. I eagerly await the final chapter in this explanation!

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #9 on: August 01, 2012, 05:57:42 AM »
Essentially, yes.  That's where you get the G (perfect 5th from C, and the strongest overtone aside from another C).   
But let me back up a bit.  The overtone series is as follows (starting from the lowest note, which is the note you play and hear - the fundamental, and proceeding up an imaginary keyboard.  The strongest overtones tend to be the first ones in the series.):
C (fundamental)
C (octave above fundamental)
G (fifth above previous C... etc.)
C
E
G
Bb
C
D
E

It goes on, but the theory goes that we can't hear all that.  Actually, people usually can't or don't perceive as far as this a lot of times, I think.  Again, hard to say, as sometimes what we "hear" we can't quite define other than in terms of its overall effect on us.

So, yes, in simple terms, we use the harmonic series to determine the notes and what goes where, but it's more than just following nature - it's how the notes interact with each other because of that natural set of vibrations.  When you play a fifth, for example, both notes will have overtones going within the tone.  Just like your piano that vibrates sympathetically with the overtones (when they're close to the natural ones), the two notes of a fifth will likewise gel with each other where the overtones are close (where they aren't, they are too far away for us to really hear the interaction of the vibrations). 

If you tune a perfect fifth (C-G), or a G that corresponds exactly with the G overtone of C, the vibrations won't "fight" with each other - you get a pure, smooth, laser-like sound with no interference.  If, however, you tune a G that is vibrating at a slightly different rate than the harmonic (perfect fifth), the vibrations don't mesh - they "fight" with one another and produce "beats" - a sort of "wah-wah-wah" sound at the level at which the tones are "fighting" - in this case, at the G. 

Not everyone hears beats, specifically, but we do perceive something - sometimes this sound is described as rough, or wobbly, or muddy.  The further away from matching the G is from the harmonic, the faster the beats go, until you lose track of the beats and it just sounds, well, melodically out of tune.

So, lets take the third, now, which is a little more complex.  You have to go up the series a bit further to hear where the beats are happening, but they happen.  I'll try to illustrate below:
 


    E

    E

    B


E--E

This last E is where you will, theoretically, hear the note beating if it is close to, but not quite, a pure third.  Again, you may perceive this beating somewhere else or as a different sort of sound or sensation, but this is where it's happening.  This is where I learn to listen, as a tuner, at least at first.  After a while, you can kind of back up again and just hear the purity of the interval without having to seek out the beats at a particular overtone.

So why not tune everything pure? Because it doesn't work out evenly.  Nature is "flawed" and if you tune a circle of perfect fifths, you'd expect to come back around to your original tone, but you don't.  Therein lies the conundrum that creates the need for tempering, or adjusting the notes so that this "leftover" interval is absorbed in a strategic way in the span of an octave to make music (or, at least keyboard music) possible.  Early temperaments didn't temper the notes much in the base keys, and they tended to stick to these keys and enjoy the beauty of it.  Equal temperament makes all keys sound exactly the same by making a mathematically "perfect" division of tone, but in the process (as I said originally) it makes everything but the octaves equally out of tune in all keys and much is lost, in my opinion, particularly with earlier music that really uses tuning as an integral part of the music (again, in my opinion).

So.  There's my summary (kind of) version of things.  Still interested after all that?  :)
Hope so. This stuff is fascinating (to me anyhow), and does bring "old music" to life in a much more invigorating way, as far as I'm concerned.

What do you think?

By the way, to "lovetheboy...", I'm glad you found my initial explanation helpful, and in regards to that book of yours - it seems you answered your own question by noting you already have found plenty of typos and errors, yes?  :)  Keep up the questioning and research and you'll do fine, I'm sure. 

JH


Offline davidjosepha

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Re: Equal Temperament vs. Well Temperament
«Reply #10 on: August 01, 2012, 11:37:14 PM »
Thanks, this has all been very interesting! So you're saying that if I played a C and then the third E up after the C, I'd hear beats on a piano because of the equal temperament? That's pretty cool.

I have one more question. People with perfect pitch. Why aren't they (or are they) completely annoyed by a piano since the piano is slightly out of tune? Did they develop perfect equal-tempered pitch, or what?

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #11 on: August 02, 2012, 01:31:05 AM »
I was speaking from a harpsichord perspective, where everything is more clear and obvious to hear, but yes, the modern equal tempered piano is full of beats, as well as all kinds of other sorts of interference, inharmonicity, etc.  The equal tempered third is very much out of tune (I still hope to demonstrate in some recording what a pure third sounds like - you'll see...).

Perfect pitch. (I love your line of thinking and questioning!) Unlike what a lot of people think, perfect pitch is not something one is born with.  Not in the way we tend to think of it, anyhow.  No one comes out of the womb "knowing" that 440hz is called an "A", because 440hz was not always an A.  No one comes out of the womb "knowing" that 440 even IS a pitch that has a name.  What they DO come out of the womb with, I think, is a particularly strong pitch memory, and they learn to associate whatever pitches they are exposed to with the labels associated with them.  That is all.  So, in terms of an equal tempered piano, I'd say that if that was what someone with "perfect pitch" has been exposed to all their life, their "perfect pitch" relates to those particular pitches.  Anything ELSE might drive them crazy, really. 

But I'm just theorizing here.  I don't have "perfect pitch" in the traditional sense (though I have some pitch memory and can sing a favorite piece or song in the "right" key, say.  I think probably lots of folks can do this sort of thing).  You'd have to ask someone with true "perfect pitch" to really answer your question, I guess.

Thanks for the discussion!  Have enjoyed it!  :)
JH

Offline thinkgreenlovepiano

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Re: Equal Temperament vs. Well Temperament
«Reply #12 on: August 02, 2012, 06:33:37 AM »


By the way, to "lovetheboy...", I'm glad you found my initial explanation helpful, and in regards to that book of yours - it seems you answered your own question by noting you already have found plenty of typos and errors, yes?  :)  Keep up the questioning and research and you'll do fine, I'm sure. 

JH



lovetheboywiththebread isn't the only one who found your explanation helpful! I did as well! (I'm her sister)  Thanks :)
Anyway, I've noticed that the book is filled with grammatical/syntax errors and typos, but I'm not sure if the author made mistakes about the facts... maybe we are misunderstanding her explanation of equal temperament... ? :/ Because strangely, the RCM syllabus does not include well temperament.

What you said about perfect pitch was also really interesting! I've always wondered about that, because lovetheboywiththebread up there has perfect pitch, and your explanation makes perfect sense!
"A painter paints pictures on canvas. But musicians paint their pictures on silence."
~Leopold Stokowski

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #13 on: August 03, 2012, 04:48:30 AM »
Sat down at the harpsichord today to try to capture some quick examples of what I talked about here. What you will hear is the following:

First, two chords consisting of only the notes of a pure third - A and C#.  It may sound out of tune to those so used to Equal Temperament, but this is, in fact, a real, pure major third (or pretty darn close - I'm not perfect).  Note the pure and focused sound which is possible when two notes mesh well together and do not "fight" with one another. The "fight" that happens where overtones clash causes beats - that wah-wah-wah sound that some people hear as that, and others simply hear as "muddiness" or "roughness" or "shimmery" or whatever.   

The second two chords simply add in the fifth to the mix.  In theory, because the fifth is slightly tempered, it should add a little turbulence to the sound.  It's not tempered much, though, and the sound is still pretty good.  This is the sort of sound you get from certain keys in meantone temperament. 

Now the ugly begins.  The third set of intervals is an example of what happens when you try to place a C# with an F - these do NOT make anything near to a harmonious third - only a Db can do that.

Next, you will hear me tune the C# up to a Db (yes, C# is LOWER than Db) such that it becomes a harmonious third - Db - F.

Then I will compare the C# that still remains an octave away with the Db -  quite the discrepancy.  Yes, they really are two different notes!

Then you'll hear me play a few broken octaves until I resolve back into A major (with C# of course).

Hope this helps!  :)

JH

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #14 on: August 03, 2012, 04:53:12 AM »
P.S.  Glad to hear from you too, thinkgreenlove... and happy you found some use in my post, too!  Hope you enjoy the recording, also.

I'm not sure what to make of your history class leaving out discussions of tuning and temperament, or, even worse, possibly providing misleading or unclear or even inaccurate information?  Not sure what to say to that, but I'm glad you two are exploring the subject on your own!  Makes a big difference, in my opinion. 

JH

Offline davidjosepha

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Re: Equal Temperament vs. Well Temperament
«Reply #15 on: August 03, 2012, 03:54:36 PM »
That recording really helped me understand a lot of what you're saying. Thanks for taking the time to make it!

So, in your opinion, is the tradeoff made when using equal-tempered tuning worth it for the convenience of being able to play in any key and have the intervals all sound roughly correct, but never quite perfect?

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #16 on: August 05, 2012, 05:17:00 AM »
That recording really helped me understand a lot of what you're saying. Thanks for taking the time to make it!

So, in your opinion, is the tradeoff made when using equal-tempered tuning worth it for the convenience of being able to play in any key and have the intervals all sound roughly correct, but never quite perfect?

Glad the recording was helpful. :)

As far as your second question, I guess the short answer would be that I do not favor equal temperament for anything, for the most part, because a gentle well temperament can accomplish the same thing with more pleasing results, in my opinion. 

ET is really a mathematical solution whereas a good well temperament is an artful, musical one.  I had a great tuner for a time who tuned "equal" by ear, and what resulted was, in effect, a good well temperament.  He did not do the "whang whang WHANG!" thing that so many tuners do, nor did he use a computer to measure himself.  He simply used his ears, his experience, and listening to him tune was as lovely as the result.  I miss him.

Anyway, as far as the "trade-off" is concerned, the same question might be asked of a good well temperament, and my response to that would be that music history dictates, for me, what is most appropriate, and where the "trade-off" is relevant or necessary - or artful, really.  Culture decided over time that the trade-off was necessary and important, and composers wrote music accordingly. I will go along with that, happily.  I simply favor the temperament and instrument that really best suits the music.  I would not try to play Chopin on a harpsichord, or on any instrument tuned in a meantone temperament.  It would just be... well... wrong. Wouldn't do justice to the music, to the instrument, to anything, really.  By the same token, I would never play Couperin or Froberger on an equal tempered piano.  Again, wrong for the same reasons. 

Equal temperament may have been talked about as a theory for a long time, but as a reality it was completely irrelevant to early music - at least as far as the keyboard is concerned.  There IS no trade-off to be made there - there is no need for ET back in those days because, as I mentioned previously- they tended to write in certain keys.  THEY decided that the tradeoff of compromising that tuning to play in all keys was not worth it at the time, so I'll go along with that too  - again, happily.

So I guess it's a question of context and circumstances. 

Many argue that ET only becomes truly relevant as a reality in the mid 20th c. It's great for 12-tone music.  But I'm not a fan of 12 tone music. 

What are YOUR thoughts on all of this, if I may ask? :)

JH



Offline davidjosepha

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Re: Equal Temperament vs. Well Temperament
«Reply #17 on: August 07, 2012, 12:04:52 AM »
What are YOUR thoughts on all of this, if I may ask? :)

Well, it's hard for me to judge given that I haven't heard enough music played on a well-tempered instrument, but my initial thoughts were close to what you said, about how you wouldn't play Chopin on anything other than equal temperament because it was written for an equal-tempered instrument. I would assume lots of music written for equal temperament would sound abysmal on a well-tempered instrument, although I don't know that.

However, I do know that I have more than once played a chord (1 5 8) on a piano and it just felt slightly...empty, in a way, like it wasn't quite right. I thought it might have to do with the tuning, although I didn't really understand anything about a piano's tuning other than that it was never exactly in tune. Each note individually sounded in tune, but together they didn't seem to mesh quite right, just a tiny bit off from what my ear wanted to ear. When I heard your recording, I instantly knew that was what it was supposed to sound like, that was the right sound.

So, I've been quite torn when reading this thread. It really is a situation where there's no perfect solution (I don't think). However, I thought about it quite a bit, and thought about all the beautiful music that wouldn't have been written and couldn't be played if not for equal temperament (or, at least not without having some sounds like the nasty ones in your recording) and how I really only noticed the 5th sounding a little funny when playing a chord that lasts a long time where all you have to think about is that chord--I would never (consciously) notice something like that in the context of a piece (except maybe an ending chord)--and ultimately decided I'm fine with equal temperament, given the tradeoffs. What you said about your piano tuner having a slight well temperament was very interesting though, I'd be interested in trying that.

But for now, I'll leave pure intervals to string players and they can leave the ability to, ya know, play multiple notes, to me ;D

Offline lhorwinkle

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Re: Equal Temperament vs. Well Temperament
«Reply #18 on: August 07, 2012, 12:38:18 AM »
If you play 1-5 ... it's supposed to sound "empty" and haunting. It can be used to good effect.

Offline davidjosepha

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Re: Equal Temperament vs. Well Temperament
«Reply #19 on: August 07, 2012, 12:46:11 PM »
If you play 1-5 ... it's supposed to sound "empty" and haunting. It can be used to good effect.

Sorry, yes, I know that, but I meant...empty in a "this actually isn't right" kinda way.

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #20 on: August 08, 2012, 05:27:08 AM »
Oh no no no!  You misunderstand.  I would NOT play Chopin on an Equal Tempered instrument, given the choice.  I would play almost nothing on an Equal tempered instrument if I had a reasonable alternative (which well temperament DOES provide.  Chopin did NOT write for equal temperament, nor did any of his contemporaries - so I would argue strongly.  Oh my my my.  No no no. 

For the poet of the piano, so enamoured with the intimate subtleties of sound that he elicited from his cottage Pleyel, to homogenize (and bastardize?) the sound with an equal temperament (which would have been theoretical at the time anyway) would be unmusical, in my opinion, or at least antithetical to what Chopin created.  Can Chopin be played in equal temperament to good effect?  Sure.  Happens all the time.  I would argue that it is not only better, more artistic, more poetic with a well-temperament, but also more appropriate. 

Historical trend determined that the trade-off for spreading out the interval discrepancy amongst all keys such that they all coudl be played was a real thing- but NOT done by equal temperament.  No No No.   A gentle well will NOT have the horrid sorts of intervals so obvious in that recording.  It will have subtle differences between keys - ones that many might not even notice on a conscious level, but I do believe that they nonetheless affect us.

Where history favors well-temperament, so do I.  Same for earlier meantone temperaments.

Just wanted to clarify...

JH

Offline j_menz

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Re: Equal Temperament vs. Well Temperament
«Reply #21 on: August 08, 2012, 06:03:11 AM »
Hate to disppoint you, but Chopin's piano was almost certainly tuned to equal temperament. It was the preferred temperament from the classical period and had become pretty much universal by the first quarter of the eighteenth century.
"What the world needs is more geniuses with humility. There are so few of us left" -- Oscar Levant

Offline lhorwinkle

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Re: Equal Temperament vs. Well Temperament
«Reply #22 on: August 08, 2012, 02:57:40 PM »
Nope. Widespread use of equal temperament is a twentieth-century phenomenon. Well temperament was king throughout the nineteenth century.

Offline justharmony

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Re: Equal Temperament vs. Well Temperament
«Reply #23 on: August 08, 2012, 04:22:18 PM »
Welcome to the discussion, j_menz, but Lhorwinkle is right. Equal temperament was NOT what Chopin was composing with, nor anyone else of the era (at least, as far as keyboards are concerned).  From where are you getting your information?  I am curious...
JH



Offline latrobe

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Re: Equal Temperament vs. Well Temperament
«Reply #24 on: December 02, 2019, 04:18:20 PM »
The Concours International de Piano de Nice is the first Piano Competition to have adopted unequal temperament as its standard - here's the recording of the final concert on a Fazioli tuned to "High Definition" tuning, a Kellner based well temperament with my particular twist in tuning it.



And in response to one of the answers above Chopin was most certainly not writing for equal temperament. He practised on a Pantalon which would have made a terrible noise in modern tuning without any dampers. It relied on the resonance of unequal temperament.

Best wishes

David P
David Pinnegar BSc ARCS
Promoting keyboard heritage http://www.organmatters.co.uk and performers in Unequal Temperament http://www.hammerwood.mistral.co.uk/concerts.htm