# Strings, just intonation, equal temperament and favorite keys?



## Weston (Jul 11, 2008)

A question came up in another thread about the possibility of strings -- maybe vocal ensembles too -- automatically leaning toward just intonation when not playing with a keyboard, e.g. a string quartet. Is this true and does key favoritism make more sense in this context?

There have been other threads and polls about favorite keys, but we want explore the concept more deeply. In equal temperament it doesn't make much sense to favor one key over another except regarding the efficiency of an instrumental range. The idea of moods or tone colors of different keys would seem to defy logic in our modern tuning, yet throughout history composers have been using D as a martial key, C minor when they want to channel Beethoven, etc. What is it that led composers after Bach to think different keys have different timbres or colors?

As you can see I'm having a little trouble with the focus of this topic, mentioning several vaguely relating things. My apologies about that. With luck, you'll get the gist of what I'm asking or be able to redefine the question.


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## Ukko (Jun 4, 2010)

Fortunately, _Weston_ has left the drift door wide open.

My understanding is that equal temperament is used to avoid 'wolf' chords on keyboard instruments. My, ah, less-than-perfect understanding is how this relates to non-fretted, bowed string instruments 1) when tuning the strings and 2) when playing a duet with a keyboard instrument that is using equal temperament.

There is also a question about the built-in tuning of woodwinds. They don't need to make chords, but they do need to be in tune with the piano, eh?


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## Mahlerian (Nov 27, 2012)

Well, the keys are slightly different in that they rest in different ranges for the instruments involved, make use of different open strings (or none), and other such minutiae. What is no longer different is the spacing between the intervals, so the differences are less obvious.

Still, I do find that certain keys tend to at least be used for certain affekt, even after even-temperament.

A favorite key of mine is B minor, which has a dramatic quality to it, not as stormy as D minor or as dark-hued as B-flat minor, but plaintive like an opera aria. Another favorite is E major, which is very bright, not necessarily cheerful like G major or happy like C major, but bright and sparkling.


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## millionrainbows (Jun 23, 2012)

Get the book "How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross W. Duffin. It shows violin charts with alternate positions for Gb/F#, etc. It discusses ET and keyboards. Ironically, fretted instruments are partially responsible for the rise of ET. There is a useful chart in back, which shows just, ET, and other notes with their cent values.

Know what the cent system is, why it was developed, and how it differs from Hertz (cycles per second, C.P.S.), a scientific nomenclature. Know how intervals are expressed as ratios.

"Temperament" means the adjustment of internal intervals within an octave.

In ET, our adjusted fifth is only 2 cents flat, so it's the major third in ET (14 cents sharp) that is most 'unnatural.' Mean-tone temperament was developed to get purer major thirds. This works in two directions, within a limited range of keys. The ones "out of range" are the ones with "wolf" or bad fifths.

The Bach/Lehman tuning is an early prototype of ET, although true ET was not achieved until 1917. The Bach/Lehman tuning is "well" tempered, meaning it sounds good in all 12 keys.



> In equal temperament it doesn't make much sense to favor one key over another except regarding the efficiency of an instrumental range. The idea of moods or tone colors of different keys would seem to defy logic in our modern tuning...


True. Enough said about ET and "affekt," which doesn't exist in ET. Affekt was only found in "adjusted tunings" in which the internal relations were different from key to key. For example, in Mean-tone, G major might have a sharper Maj3 than E major, but E major might have a better b7 or fifth. Minor thirds would differ, too. Certain keys (like Gb) would be unusable.


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## Ukko (Jun 4, 2010)

Your description of that book is convincing; I am convinced that I would dislike it more than moderately.


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## Taggart (Feb 14, 2013)

Slightly off topic:

http://www.bbc.co.uk/news/magazine-22094279


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## Ukko (Jun 4, 2010)

Taggart said:


> Slightly off topic:
> 
> http://www.bbc.co.uk/news/magazine-22094279


_Taggart_, you have the soul of a poet.


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## PetrB (Feb 28, 2012)

I've heard it in recordings, especially those post WWII coming out of the east block, The Hungarian String Quartet performing Mozart's Adagio and Fugue, for example, or the Kodaly Girls Choir of the same period, and the intonation seems quite 'reflexive.'





Unless I am projecting what I hear, I think later performances from those Hungarian choirs and orchestras became more 'evened out' in their intonation, much like much architecture lost 'local distinction' via the adaption of 'international style' which began after WWII and reached a sort of peak in the late sixties. That much of the 'older regard toward intonation' which was lost or altered, happened to tuning over a few short decades.

ADD: Unless I am having auditory hallucinations, I believe this is a later recording, the intonation 'ironed out,' and it really loses resonance and 'bite.'




END ADD.

Presently, I don't think key, however, has much to do with it, the fact that in the 20th century the instruments are 'modern,' and key choice in earlier repertoire was influenced / determined by the limitations of the instruments, and for keyboards, whichever 'base key' the instrument had been tuned at. So we'll now hear the intonation in contemporary performance, as you've noticed, applied in keys the earlier composers never wrote in 

The premise that equal temperament 'Ruined Harmony' is rather after the fact and silly, imo. It certainly altered harmony and made a modulation less 'distinct,' key areas losing an 'individuality,' the trade-off is equal temperament allowed for a greater mobility to modulate to more places, the former 'restricted,' i.e. go too far away from tonic or the stronger areas / chords in that key in just intonation and it really begins to sound awful and awfully out of tune.

Only a few who call themselves 'purists' would lament the past so greatly, scorn the later eras or all that came from them, made possible by the new tuning, and the technological adjustments and improvements in instruments which made that later music possible, or even 'thinkable.'

Purists some (their prerogative) and to me, the other near or real 'nutters.' A happy answer, and 'to address' intonation, is to render the music written with that tuning in mind in that tuning. Contemporary works which are conceived of for the older or alternate tunings, and now, we have people working new music with old tunings in mind, or using both for further depth of sound, subtle beats between the same pitches as inflected in the different ratios.

If you've been a student in university music departments or a conservatory there is almost always at least one of this type in each class:
Perfect pitch and or an innate and canny ability to track and name 'chord changes.' 
...that ability almost always limited to Baroque, or as far 'up to' early middle classical.
...harbors a major self-conceit about their gift of having that knack. 
...when courses get to either the later classical or romantic era -- some lasting as long into the late romantic, they are the first to pipe up with that non sequitur, *"But what about tonality."* -- usually inflected with a whine implying personal pain and injury. -- What is most injured is their self-conceit and PRIDE over that ability to track chord changes, their limit reached in music of the earlier era, finding themselves lost or unable to track and label the harmonic changes in later music. [The irony of 'perfect pitch' is that it is remains always relative: The present A for those with perfect pitch being more toward Ab for even the late romantics, closer to a full half-step lower Ab for Mozart, and very near a G for J.S. Bach. -- so much for 'perfections.']

I sometimes think people very preoccupied with tunings are more lab rats than musicians, actually avoiding music, music performing and listening, their real interest more in clinical acoustics, which is not an invaluable area of research and study, but more about the workings of the automobile and being far less interested in the ride.

There are 'non-lab' real musicians with real interest and more 'practical ' and inventive use of tunings, more 'to a point' than running numbers in an electronic meter.

Sadly, at least in fora, I often hear about it more from an inbetween the lines, "I'm so sensitive I hear this while you / others do not." (Boo-hoo and my commiserations, sorry to inform that many, even those without 'perfect pitch' hear it just as audibly and are just as sensitive to it, but have not gone out of their way to make it a vanity point to draw attention to themselves.)

There is not, or should not be, any real war going on about this, while some would make of it near that 

Returning the floor to anyone who wishes it....


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## millionrainbows (Jun 23, 2012)

> Your description of that book is convincing; I am convinced that I would dislike it more than moderately.


I'm not interested in who may like the book; it has the information in it the OP asked about. I do not advocate the book's position on ET as inferred from the title.

I did not choose the title for the book. I am not an advocate or detractor of ET; nor do I wish to debate the issue.


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## millionrainbows (Jun 23, 2012)

> Presently, I don't think key, however, has much to do with it, the fact that in the 20th century the instruments are 'modern,' and key choice in earlier repertoire was influenced / determined by the limitations of the instruments, and for keyboards, whichever 'base key' the instrument had been tuned at. So we'll now hear the intonation in contemporary performance, as you've noticed, applied in keys the earlier composers never wrote in
> 
> The premise that equal temperament 'Ruined Harmony' is rather after the fact and silly, imo. It certainly altered harmony and made a modulation less 'distinct,' key areas losing an 'individuality,' the trade-off is equal temperament allowed for a greater mobility to modulate to more places, the former 'restricted,' i.e. go too far away from tonic or the stronger areas / chords in that key in just intonation and it really begins to sound awful and awfully out of tune.
> 
> ...


I think we should leave these kinds of characterizations alone and decide whether or not we are going to discuss intonation per the OP's request. I don't care if people think they have perfect pitch or not, or if a discussion of intonation makes anyone come across as a lab rat; and that's not a very encouraging inducement to discussion. These kinds of non-specific negative generalizations tend to create unease among "sensitive" classical music listeners.

I think discussions of acoustics and intonation would be interesting; much more interesting than someone's opinion about the 30,000th Mahler symphony they bought.


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## Klavierspieler (Jul 16, 2011)

Weston said:


> A question came up in another thread about the possibility of strings -- maybe vocal ensembles too -- automatically leaning toward just intonation when not playing with a keyboard, e.g. a string quartet.


Well, it's really not about leaning, it's about playing in tune. String players are taught to adjust their intonation to the key they are playing in, unless they are playing with a pianist.


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## millionrainbows (Jun 23, 2012)

> Well, it's really not about leaning, it's about playing in tune. String players are taught to adjust their intonation to the key they are playing in, unless they are playing with a pianist.


So I take it that you do not think the ear is naturally drawn or "leans" towards pure intervals in choral groups and string players, but is strictly the result of training?

By "pure" intervals, I mean intervals with no "beating" which are acoustically smooth: perfect fifths which are 2 cents sharper than ET, and major thirds which are 14 cents flatter than ET. You don't think the ear is drawn to smoother consonances?


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## KRoad (Jun 1, 2012)

millionrainbows said:


> I think we should leave these kinds of characterizations alone and decide whether or not we are going to discuss intonation per the OP's request. I don't care if people think they have perfect pitch or not, or if a discussion of intonation makes anyone come across as a lab rat; and that's not a very encouraging inducement to discussion. These kinds of non-specific negative generalizations tend to create unease among "sensitive" classical music listeners.
> 
> I think discussions of acoustics and intonation would be interesting; much more interesting than someone's opinion about the 30,000th Mahler symphony they bought.


Your reply has the unsavoury whiff of a personal (and unpleasant) hidden agenda. No thank you. I for one enjoyed the digression. Concerning the OP... one aspect of which was the subjective emotional associations given over to certain keys - not exactly acoustics or intonation strictly speaking you'll agree. I'd be interested in discussion on this having pondered the issue myself on more than one occasion.


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## Ukko (Jun 4, 2010)

millionrainbows said:


> So I take it that you do not think the ear is naturally drawn or "leans" towards pure intervals in choral groups and string players, but is strictly the result of training?
> 
> By "pure" intervals, I mean intervals with no "beating" which are acoustically smooth: perfect fifths which are 2 cents sharper than ET, and major thirds which are 14 cents flatter than ET. You don't think the ear is drawn to smoother consonances?


_millions_, you have taken the bit in your teeth. If I caused that by knocking your book, I am sorry. Personally, I was once interested in the effects of piano tunings on chords - chords within the 'comfort range' of the tunings. Then I obtained a CD of examples, pieces played on variously tuned pianos, and discovered that they all sounded good to me.

My own question in this thread has been answered. Looks like you don't have questions... hmm. I think I may be edging close to something in a footnote on Stone Tablet #3. Gotta tell you, friend, it ain't _always_ great to be a hillbilly.


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## millionrainbows (Jun 23, 2012)

> Your reply has the unsavoury whiff of a personal (and unpleasant) hidden agenda. No thank you. I for one enjoyed the digression. Concerning the OP... one aspect of which was the subjective emotional associations given over to certain keys - not exactly acoustics or intonation strictly speaking you'll agree. I'd be interested in discussion on this having pondered the issue myself on more than one occasion.


Uhh, OK, but I thought you were on to other topics. If I had an "agenda," you'd think I'd be pushing it. Right now, I'm just responding to a couple of unpleasant posts.


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## millionrainbows (Jun 23, 2012)

> _millions_, you have taken the bit in your mouth. If I caused that by knocking your book, I am sorry. Personally, I was once interested in the effects of piano tunings on chords - chords within the 'comfort range' of the tunings. Then I obtained a CD of examples, pieces played on variously tuned pianos, and discovered that they all sounded good to me.
> 
> My own question in this thread has been answered. Looks like you don't have questions... hmm. I think I may be edging close to something in a footnote on Stone Tablet #3. Gotta tell you, friend, it ain't _always_ great to be a hillbilly.


As I said, I don't advocate the book; I simply quoted its title. The post #5 was one of those posts that is so short that it seems to invite misinterpretation. If anybody cares to discuss the subject in a more in-depth way, I'm all for it.


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## Klavierspieler (Jul 16, 2011)

millionrainbows said:


> So I take it that you do not think the ear is naturally drawn or "leans" towards pure intervals in choral groups and string players, but is strictly the result of training?
> 
> By "pure" intervals, I mean intervals with no "beating" which are acoustically smooth: perfect fifths which are 2 cents sharper than ET, and major thirds which are 14 cents flatter than ET. You don't think the ear is drawn to smoother consonances?


Well, not necessarily. It could a bit of both.

Also, in running lines, you normally exaggerate the key that you are in, i.e. raise the third and leading tone even more than "pure" intervals would call for. Of course, this may just be the way I was taught, but I don't think so.


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## millionrainbows (Jun 23, 2012)

I do think choirs are more naturally drawn to "pure" fifths, and this is a long tradition which dates back to early Gregorian Chant, where fifths were frequently used, and modulation did not matter. I think this is also true of violin players in string quartet contexts. 

There. I dared to actually say it.


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## Kazaman (Apr 13, 2013)

millionrainbows said:


> I do think choirs are more naturally drawn to "pure" fifths, and this is a long tradition which dates back to early Gregorian Chant, where fifths were frequently used, and modulation did not matter. I think this is also true of violin players in string quartet contexts.
> 
> There. I dared to actually say it.


I thought that was commonly known.


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## Minona (Mar 25, 2013)

It's not simply a matter of tunings 'sounding good', it's that composers used key colors of meantone tunings/well temperaments for expressive purposes. Equal temperament discards this information that the composers wanted. 

Equal temperament is used because it's practical, not because it's musically better or reflective of the composers wishes.

Meantone tuning allows purer thirds, sacrificing pure 5ths (because they are further apart and so don't cause such noticeable beating). Well temperaments have a wider range of thirds and 5ths to enable acceptable purity in all keys.


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## Mahlerian (Nov 27, 2012)

Minona said:


> It's not simply a matter of tunings 'sounding good', it's that composers used key colors of meantone tunings/well temperaments for expressive purposes. Equal temperament discards this information that the composers wanted.
> 
> Equal temperament is used because it's practical, not because it's musically better.


For Baroque music and earlier, unequal temperament adds an interesting dimension that is undoubtedly lost when the music is played in equal-tempered tunings.

For some kinds of music, though, it is not just better, it is musically required. Beethoven would occasionally write simultaneous enharmonic relations between notes (C-sharp and D-flat), and there's no reason to think he wanted them to be clashing dissonances. Any music that defines itself by the use of symmetrical scales, such as Impressionism, Expressionism, or Serialism, would become nonsense in anything but equal temperament.


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## superhorn (Mar 23, 2010)

Purists about tuning are such ill-tempered people .


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## millionrainbows (Jun 23, 2012)

So did I, and I thought the threads would indicate what is going on. This is a very unfocussed discussion, and the peppering of unhelpful comments isn't helping either. I'd like to see someone else contribute something useful.


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## millionrainbows (Jun 23, 2012)

Meantone was developed to produce better thirds, but it doesn't "sacrifice" _all_ fifths; some are pure, some deviate. Within a range of keys, both intervals are good; it's only when going out of range that fifths become unusable or "wolf."


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## millionrainbows (Jun 23, 2012)

It can be said that purists about tuning are ill-tempered people; however, if one also identifies advocates of equal temperament as "purists" based on the smugly complacent negative feedback regarding this issue, then the statement is inconsistent, especially if the strategy of calling purists "ill-tempered" is attempting to restrict that negative reference to advocates of those tuning systems _outside_ of ET. It was a very snappy try, though.


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## Minona (Mar 25, 2013)

For me, I have unpredictable demands on my time so I may seem abrupt.

But, when you regard such people as 'purists', it's obvious you don't know what they're trying to say.

Anyway, it's not so much about tuning being 'pure' anymore than it was for Harry Partch. Some keys are actually less pure than ET and they have useful properties that can serve composition. It's ET-only advocates than are the real purists! What's the problem...?

Alternative tunings are about freedom and expression in music through intonation, in this case for music that was written with certain tuning it in mind.

Saying it doesn't matter is a bit like having a print of a Rembrandt and claiming it's as good as seeing the original even though it's flat and the colors and contrast aren't right.

Furthermore, ET isn't the most practical method to tune, only to _use_ if all instruments have it.

C.P.E Bach discribed his father's tuning in his famous essay on keyboard playing, which had _most_ (not all!) of the 5ths were slightly tempered. J.C Bach in London was still importing split-key pianos, so it wasn't the only tuning used for keyboards.

There seems to be a lack of data regarding this subject, which I suspect it due to a lack of interest rather than because the data isn't there.

For example, documents and records relating to J.S Bach's are only now being fully explored.

Joseph Haydn _"The collected correspondence, and London notebooks"_ is out of print.

Mozart's lessons for Attwood clearly reveal his intended tuning, and yet scholars continue to claim he used ET.

I'm not sure about Beethoven, but I don't think you can simply go off notated practices. Chopin also was indesciminate with #/b on score, but he is thought to have used an rather extreme form of meantone for expression. For piano scores, it wouldn't matter too much how you spell the notes because the keyboard will have fixed tuning which the composer or oppointed tuner would set.

Any composition involving natural horns and trumpets is likely to have been in a meantone setting suitable for those keys. (I don't know what sort of effect this had on note spellings but [bb] and [##] were not employed just to complicate things or adhere to theory.)

You know, Michael Haydn (J's brother) actually invented a notation modification to account for naturals, sharps, flats and, double sharps and flats.

I think in the next 20 years, things might open up a little and we might get technicolor Bach (back).

Thanks


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## millionrainbows (Jun 23, 2012)

Minona said:


> Alternative tunings...Saying it doesn't matter is a bit like having a print of a Rembrandt and claiming it's as good as seeing the original even though it's flat and the colors and contrast aren't right.


I agree completely with Minona's entire post. And how could tuning _not_ matter? Bach was known to carry more than one keyboard instrument to "gigs" in his trailer of hay, because he needed backup, and also because he might have several alternate tunings ready for different situations: playing solo, with choral groups, with fretted instruments, or with string players. Of course, Bach did his own tuning chores.

But, Bach and other serious composers did desire to play in every key, so equal temperament was something that became a universal goal. In these times, tuning was done by counting the rate of beats (per second) using stopwatches. Many claims were made of equal temperament being achieved, but it was not until the 1917 that true ET was achieved. WIK supports this:

[A precise equal temperament is possible using the 17th-century Sabbatini method of splitting the octave first into three tempered major thirds. This was also proposed by several writers during the Classical era.

Tuning without beat rates but employing several checks, achieving _virtually_ modern accuracy, was already done in the 1st decades of the 19th century.

Using beat rates, first proposed in 1749, became common after their diffusion by Helmholtz and Ellis in the second half of the 19th century.

The ultimate precision was available with 2-decimal tables published by White in 1917.]


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