Temperament & Tuning

Quote:

"But to 'temperate' a clavier means to tune it. Now the old system of tuning was very different from the modern one. I a modern piano, if you play c sharp or d flat it is the same note. But theoretically they are different notes: the c sharp is lower than the d flat. "

I'm curious about the source of the idea that theoretically a c sharp is lower than a d flat. I'm not a theorist so someone who is will have to clarify. But in playing the Hardanger fiddle which is based on the natural harmonics and the natural scale, the instrument uses quarter tones. The usual practice is to play a sharp that is resolving upward a quarter tone higher than usual. A flat would be a quarter tone lower as it resolves downward. So when you say a c sharp is lower than the d flat, it doesn't ring true with a longstanding and continuous tradition with roots in the Baroque period.

Please explain.

All the best,

Karen

 

Karen:

Welcome!

I know string players use the harmonic scale, and, therefore, they distinguish between major and minor tones and so forth. I also know you divide the octave in up to 53 (am I right?) intervals - how one can do it I don't know, I've always thought strings players have a different brain from everybody else.

And I know that sharps and flats are taken differently dependeing on the harmonic context and the following note they play.

But I believe in a twelve tone keyboard using theoretically pure intervals (sort of - there are no minor or major tones: one just gets the mean, hence the name mean tone temperament) an augmented second is smaller than a minor third.

But perhaps I missinterpreted your post. Comments or corrections please? Temperament is a very complex theme and all I can say is that I like to listen to a mean tone tuned harpsichord or organ, but, as for myself, I always use equal temperament; one doesn't have the beautiful pure thirds, but one can modulate and it is rather logic.

 

natural tunings and quarter tones

This is a digression from the original topic of the Well-Tempered Clavier, but an interesting thread by itself.

The Norwegian composer, ethnomusicologisy, folk musician, Norwegian radio host/producer Eivind Groven did some interesting research on organ tuning as a result of his understanding of tuning in Norwegian folk music.

Some music theorists have taken an interest in what he did. See the project here:

http://www.wmich.edu/~mus-theo/groven/

That's all I'll say about it now. If there is more interest in this discussion I'll go further.

God Jul,
Karen

 

Karen:

I read through the threads (couldn't download the musical examples, but I know mean tone tuning relatively well, so I know the difference between a ET chord and a pure one - and I agree, there is no comparison in terms of beauty). Much of it I already knew (more or less - I'm very keyboard oriented myself, although in my youth I sang some Gregorian) but I agree that the Equal Temperament domination is not always a good think.

I was interested in the 'harmonically context sensitive' organ, but, of course, you lose tracker action if you adopt it (that is, the traction must be electric, and therefore you ca no longer control the attacks and releases of notes).

I am very interested in knowing more. You see, I love Irish music, and, when I listen to it played in classical temperaments it loses most of its magic.

So any discussion, presentation, or further information will be welcome.

 

Re: natural tunings and quarter tones

I said I'd have more to say about natural tunings and it's taken me awhile to get back to the forum. (My 3-year-old will wake up soon and then it's over for me for the rest of the day.)

One thing I find interesting is just how much equal-temperment has taken over and dominated classical music to the point where many are not even aware that anything else exists. Some people--excluding people here--seem to feel it was an improvement over what came before. In reality it is simply a solution to the problem of how to get an instrument tuned in such a way that you can play in many different keys in one piece or in rapid succession without having to stop and tune! Or, in the case of a large ensemble, getting instruments based on different pipe lengths and string lengths to be able to play somewhat in tune together in a circle of keys. (I won't say all keys because 12 is convenient for mathematical purposes, not all that exist. Something classical music has obliterated.)

I know about this problem of retuning first-hand. The Hardanger fiddle has over 20 different tunings, tho 70% of them are in "regular" tuning (sounded pitches from top to bottom are F#-B-E-B with understrings tuned to b-g#-f#-e, and if the fiddle has a fifth string c# or d). This makes the droning effect, the constant sound. This drone would never happen if you tuned to equal-temperment! When I first started as a classical player I wanted to tune the fifths and thirds the way you do in classical music, tighter fifths and thirds. My Norwegian teachers would take the fiddle away from me and retune it saying I didn't get it in tune. So I listened and watched carefully for what they did. Now I tune the understrings to the widest fifths I can stand, with the third below as low as I can stand. Voila! It rings! (It's a bit more complex than that, but the best I can explain here.)

Now it isn't simply a matter of natural tuning versus tempered tuning. Recently I have become aware that Hardanger fiddle tunes should be played with quarter tones and pitches appropriate for the source instrument, be it voice or willow flute or ram's horn, whatever. Each source instrument has its characteristic scales. With careful listening I can create such a different quality of sound from tune to tune, without having to play a piece that's in one of the alternate tunings. I simply change how I use the natural scale that I'm tuned to.

This is all such wonderful stuff to ponder.

God Jul,
Karen

 

Karen:
As you certainly have gathered, I actually agree with you. Not only 12 tones is an artificial limitation, but all the instruments that rely on sympathetic vibration (such as the organ) suffer when tempered equal. For instance, playing Sweelinck (or Scheidt, or even Reincken, or Cabezon or Rodrigues Coelho) in a equal tempered organ produces completely different results from those you get with mean tone tuning.

For once, the mutations (the artificial partials of the organ, that are actually sounded through pipes tuned to that particular partial) sound right and do not beat with the 'tempered' (or 'tampered'!?) fifths and thirds.

That is also true of very bright instruments, such as the harpsichord. A mean tone harpsichord played in C major is unbelievably sweet and mellow *and* bright. With equal tuning one has to withstand the harshness of the upper partials beating.

There are further advantages: every key has its own character. In mean tone, f minor is indeed poignant, whereas with equal tuning it is just – well, the same as c minor but transposed upwards.

But it is true that it is very difficult to build, to tune and to play a keyboard instrument that allows all true intervals – you have to have a lot of keys to each tone, and playing it becomes very difficult.

Of course, with modal music, which doesn't truly modulate, the mean tone system is perfect. But with the transition to tonality you get only two modes (three if you divide the minor) and without modulation music is bound to be boring. Hence equal temperament, which is the consequence of dropping modality.

Now with folk music, based, as it is on melodies which are not necessarily truly tonal – and, of course, very often in different tuning systems – the tempered scale sounds rough and ugly.

But even with baroque music (Bach, the cello suites and the violin sonatas and partitas), I like musicians to use true intervals. In that respect I very much like the last Bylsma record of the 'cello suites. He uses different intervals depending on context (there are also some intonation errors, but that is natural) and the music becomes extremely poignant.

So we agree. Only, you see, I love Bach and Buxtehude and they at least require Kirnberger tuning.

Let's keep this matter up. Temperament and true intervals are one of the most interesting (also one of the most difficult) matters in music.

Best wishes,

 

Natural tuning

Having been trained in the classical conservatory model, it never occurred to me what the gains and losses were to one system or another. Equal-temperment just seemed to be one of the many advances of a superior culture. I don't think I was alone in this bias as I encounter it now frequently when I play for some classically-trained, but unenlightened, folks. Certainly there are those classically-trained individuals who get beyond that bias, but they have to find their way their on their own. So this little bit of "exotic" musical history provides me with a bit of empathy when I hear people from minority cultures in the United States complain about the eye-closed bias of the dominant culture.

That aside, as a Hardanger fiddler I find it a lonely existence. My instrument is tuned to itself, which is generally a whole step above a regular violin. If anyone is willing to play with me it must be in MY key, usually in E or closely related keys. The unique characteristics of the sympathetic strings get buried in an ensemble. To play with a group, I might as well pick up the violin.

I admit the "improvements" are many with equal-temperment, especially if it involves a lot of instruments. It would be nice though if the advantages of natural tunings would be also taught in our music schools when it involves solo playing, playing within instrument families, or playing period music.

God Jul,
Karen

 

Karen:

As a matter of fact, historical tuning is becoming more important in teaching. I knew an organist - as a matter of fact he is an organ professor - that is an expert in tuning.

The fact is, when you consider pre tonal music, you have to get a different temperament. Also, many historic organs are tuned to mean tone. And, again, many choirs sing with more or less pure intervals.

Could you please give me some details of the way you actually perform the intervals? (I listened to your links; I just wanted to know how you conceptualize it).

And, further, do you think there is a particular Irish tuning?

I'll ask the administrator to split this section from the WTC one, as it is strongly diverging.

 

natural tuning

Thanks for splitting this topic from WTC. I wasn't sure how to do that and still maintain the integrity of the thread.

Maybe music schools have become more diverse and have integrated more of a world perspective into their curriculum. It was over 20 years ago that I was in school but I worked at the music school here in the early 1990s. At the time I worked there the new and old perspectives were really a battlefield in the musicology department. As far as I could see the string program was still pretty old school in method and material. Composition was always out front in this regard. I knew little about how keyboard approached their cultural material. Maybe organ training has historically been more sensitive to this subject of tuning.

As for how I think when I play a tune. First, I ground myself in the tonality of the scale. Then the function of the note is obvious. In Norwegian music, the strong beats generally contain the tonic, fifth, thirds, i.e. the more resonant tones of the scale. If the main beat contains a leading tone it is usually functioning to either delay or anticipate the resonant tones. You are always playing double stops. Any finger that is free is used to add an ornament so there is always a flutter of the tone above or below the main note.

The notes that are played as a leading tone, either upward or downward, are the only ones that get "bent" in the direction the line is headed. So in a D pentatonic scale, the C would be used slightly raised but sometimes not quite a C# if it were heading upward. The G would be slightly # toward A. But if you are in D major, the C# would be raised to be as close to D as you can get, same for G#. It really depends on the age of the tune. That is determined by the kind of scale, I think. (It's only by writing this that I have put this much conscious thought to it.) It also depends on the source instrument of the tune.

The guide is always what makes the maximum ring of the understrings on the Hardanger fiddle. In an ideal situation I can tune carefully with wide fifths and the understring thirds just right to maximize the ring. Then if I can quietly play a fyrespel, or prelude, that tries the instrument and gets it vibrating.

A final way I tune the scale--especially in the typical settings of a dance or performance with lots of people and distractions--is the muscle memory of how the fingers go down. This is something I try to make conscious when I have quiet practices! The second finger sometimes needs to be right under the third finger, needing to back out of the way when the third finger plays. Some double stop thirds may be a reach or closer depending on the function.

As for what you hear on my CD, I wouldn't say that I was completely satisfied with the results of my intonation on all tunes, but when you play an instrument with several tones ringing at once, the technician can't fix it afterwards in editing like a single line instrument! (I simply had to live with the results and hope I can make another recording and get closer to the ideal.) The older tunes are more difficult in that regard because the scale is less natural for me.

I don't know much about Irish tunes. They are related to Norwegian tunes but I wouldn't know in what cases they diverge and come together.

That's all I know,
Karen

 

Re: natural tuning

Are they? As someone who likes Irish music (and, worse, who is actually Irish), I've never known of any connection, other than the old pentatonic scale on which all Western music is grounded. The Celtic music culture, I thought, is different to other European cultures, and is still heard in the Celtic areas (Ireland, Scotland, Wales, Brittany). Like the Celtic-originating language, it breaks into two parts, Gaelic (Ireland, Scotland) and Brythonic (Wales, the old Cornish language and Brittany). The Gaelic tradition spread into the border areas and much northern English music has the same jigs and reels as has Scottish music.

Having said that, I've never actually heard any Norwegian music (apart from Grieg!), and I know there was a long history between the Scottish and Norwegian kings (the Orkney Islands were once Norwegian and the cathedral there has the good Scottish name of St. Magnus), but I've never known of any cross-fertilisation in the two musical cultures.

 

Just a note to say that I split this thread off from the Well Tempered Clavier thread (at RdS's request ) as it's developing into a more general discussion about temparment and tuning.

Michael.

 

The even temperament tuning is based on dividing an octave into 12 equal parts. As the fundamental frequency of a note is half of the frequency of the note an octave above, this means that semitones are separated by a frequency factor of 2^(1/12).

Amongst other things, this means that the dominant is reached by moving up seven semitones from the tonic so that the frequency of the dominant is related to that of the tonic by the factor 2^(7/12) or 1.498 - this is a perfect fifth in equal temperament. Similarly, a perfect fourth can be attained by moving down five semitones giving a factor 2^(5/12) or 1.335.

In natural temperament, by contrast, the perfect intervals are related by neater relationships between the frequencies which do not result in the beating which can trouble sensitive ears - a fifth having a factor of (3/2) or 1.5, and a fourth a factor (4/3) or 1.3 recurring.

The most surprising thing is when you hear a really well-trained choir directed by someone with a sensitive ear - when the choir is playing along with a keyboard they'll sing in even temperament, but when they're singing unaccompanied they start singing in natural intervals

 

Thanks Karen, that is very interesting. I know nothing of violin (I mean the family) playing, so I don't follow you on fingering details. But the musical stuff I understand.

Well. No one is ever completely happy after the editing (save Glenn Gould!), but the files I opened seemed OK. Of course, your sense of pitch is far better than mine - i only have to depress the keys, you see (and I am a very bad tuner).

But please explain why it is so difficult to edit your instrument. For instance, with the organ you have a major problem there, because of reverberation. Isn't that similar? Or did I get it wrong?

And, Pete: that is interesting, I noticed that before. That is why what used to be called 'a capella' singing is so beautiful: no tempered instruments to get the voices out of tune (I mean, in a very good choir - with a bad one some kind of pitch support is badly needed, or else the music gets lower and lower, as you know).

 

Here is a good introduction to temperament on the keyboard. Just follow the explanation to each temperament system by clicking the arrows on the right.

 

This is all very interesting. There have been some questions posed to me which I want to answer with some good thought. Just to say I'm still interested in this discussion but may not be back to answer until after the holidays!

God Jul,
karen

 

Karen:

We'll wait! Have a nice time.

Merry Christmas and all that, by the way.

 

Hallo, Karen! Are you still there?

THIS WILL INTEREST ALL ANCIENT MUSIC LOVERS

I became increasingly interested in tuning questions because I have bought a harpsichord (with three sets of strings, two unisons and an octave). I have to tune it fairly often – and, as I said before, I am a lousy tuner. So I gave up trying to tune the instrument by ear (it had got almost a quarter of a tone down and I got very curious thirds!) and bought a tuner.

Now I can tune the instrument to Werkmeister III (the present condition, as I am studying some Bach), to Valotti, and several more – including, of course, mean tone.

That said, with a 12 note to the octave instrument I find if one tunes it to mean tone our approach to harmony and tuning must be completely changed.

In C major or even d minor it sounds very well – gorgeous, really. But when trying to play in f minor (there are several mean tone epoch pieces written in that key) the instrument just sounds hopelessly out of tune. Even a relatively 'easy' key, as b minor sounds utterly horrible.

My first thought was just: 'how on earth could they endure this?? Give me back equal temperament, fast!'

But then I thought that when one is listening to ancient music one has to change one's approach to tuning and harmony. What they get with mean tone is that there is a very big difference between quiet keys – C, d – and anguished keys – f, f# and so on). What this means is that what we call 'out of tune' was seen as 'agitated', 'distressing' and so on. That is, the mistuning of the 'remote' keys was seen as an actual component of the distressing nature of the keys – a very Baroque worldview.

For a trained musician to appreciate this is extremely hard. We call it out of tune; they used to see it as distressing. I found this very interesting but, at the same time, I strongly doubt I will ever tune my harpsichord to mean tone temperament! (I must add that it takes me two hours to retune the instrument, so I cannot just undo a tuning in ten minutes).

 

Thanks for the prompt! I have lurked here in the last couple of weeks but haven't had the time to get my thoughts together in a coherent way. After Christmas I thought I'd have more time but had more performances in January than I have ever had. So I'll just muddle into this subject with whatever time and care I can muster.

That is exactly right. This morning I finally did what I have been meaning to do since this conversation began; I documented what happens with the retunings of the Hardanger fiddle.

Basic tuning for Hardanger fiddle is e1, a, d, A (like violin with G tuned up one whole step) The sympathetic strings (that aren't played but resonate when the top ones are played) are tuned a, f#, e, d, and if the fiddle has a fifth string like mine, B or c#. I have concluded that the tunes played in this tuning can be in D major or D lydian, or A major. (NOTE: actual sounding pitch is 1/2 step to a minor 3rd higher than violin A440 tuning, depending on how the Hardanger fiddle maker "tuned" the hardingfele. For the sake of classical violinists, transcriptions are simply written as if the fiddle strings are tuned to A440. I mention this in case you follow my links to listen to the samples I will give you.) Regular tuning can be heard on my CD www.cdbaby.com/solgard on the tunes "The North Fjord" and "Mountain Fantasy" as best examples. All the tunes are in this tuning actually on the CD except "The Horse that Carried the Dead" mentioned below.

Now, here is the interesting thing related to what RdS was talking about with mean tuning of the harpsichord. The Hardanger fiddle has over twenty different tunings. These are combinations of pitches and relationships between the bowed strings and the sympathetic strings. These different combinations of chords and scales make for different moods of the tune. A player doesn't just play in different keys that have the same relationships of scale to each other. You are actually playing in a different mathematical acoustical combination of sounds. It really defies western classical music theory but I will humbly apply that vocabulary to this system. (I don't know if there are Norwegian Hardanger fiddlers who are music scholars who have worked with this. I wish Eivind Groven were still alive because I'm sure he would have an opinion on this subject. I'll provide the link later as I don't dare loose my text here. You could search on "Groven Piano Project." I might have mentioned it a couple of months ago.)

When I tune from regular tuning to the tuning usually used on violin, e1, a, d, G (understrings: a, g, e, d, B), there is little disturbance to the relationships of the other strings. Other strings need slight adjustment, but not much. I find this tuning is used for more recent tunes that may have origins in Sweden, the British Isles or Germany, places that use regular violin. There are some older tunes in Hardanger fiddle repertoire that do use this tuning. In those cases, the key is more ambiguous between G lydian and D major perhaps or D tetrachord as dominant to G. This is where applying our classical system on the Norwegian music breaks down. I also don't have a large repertoire in this tuning be able to speak with authority so take this with a grain of salt. (Sorry, I don't have any samples to direct you to. I'll have to look for some recorded examples to mention.)

When I tune from regular tuning to c#, a, d, A (understrings: a, f#, e, c#, B), more drastic changes happen to the balance of the rest of the strings. When e1 goes down to c#, the a string rises in pitch but the understring d and A remain stable. Once I retune the understrings, the bowed d goes flat. This tuning is "distressing" in sound. I have a sample on my CD at www.cdbaby.com/solgard, the track labeled "The Horse that Carried the Dead." (The Norwegian title is actually "Førnesbrunen" but that means little to my American audiences so I made the English name tell a bit about the tune subject matter.) How to describe the key is difficult. The tuning itself gives more emphasis to A with 3 strings tuned to it. C# has 2 strings, F#, E, D, B get one string each. The tune goes in stages first on an A drone, then C# drone, next going between A & B. These are not ever complete scales, but more like tetrachords in each "key." It is sort of in A something. I'll say no more.

The next tuning I moved into was retuned from the one above, not from regular tuning. It required raising d to e. The understrings put c# back to d with the low B up to c#. (bowed strings c#1, a, e, A with understrings a, f#, e, d, c#) When I tuned the d to e, the a string goes flat but the understring a goes sharp as does the f# understring. The piece or tune I used for my analysis was "Nøringen," a tune to call the bridal couple down to breakfast after their first night together. With just these two string tuning changes, the character of this piece is dramatically different than for "Førnesbrunen" above. (Sorry I don't have a ready sample for you to hear but it is recorded by Norwegian master Leif Rygg in a duet form. If interested I'll go through my collection and direct you to the recording it's on.) This tuning alternates between A Major and E Major. The number of strings tuned to different notes are 3 A's, 2 c#'s and e's, one d and f#. I notice that when I play this one I need to adjust my fingerings slightly to raise the sharped pitches f#, g# on the e string to make it ring properly with the a string. Curious.

I just wonder if some of these adjustments I mentioned on my nine-stringed instrument might provide some insight about small adjustments you might make for the harpsichord to play in closely related keys. It does seem to be a lot of work though! And I avoided playing in alternate tunings for years on Hardanger fiddle for the same reason!

That's all the time I can spare for now. This discussion is great to spur me on to think consciously about this subject.

All the best,
Karen Solgard

 

Re: Re: natural tuning

The Hardanger fiddle music is much closer to the music of the British Isles than you would get if your only window into Norwegian music is Grieg. The fiddlers of Scottish and Shetland Islands say themselves that the music is related to Hardanger fiddle. I can hear the connection through the form of Irish fiddle tunes but haven't made a study of it. It's closer than you think though!

All the best,
Karen Solgard

 

Thanks, Karen, I consider myself thoroughly corrected! Just ignorance talking (but then, why should today be any different than usual?)