Tuning Fifths in Just IntonationTechnique and Practicing: Which notes need to change in pitch according to harmonic function.
From Michael De Sapio
From John CaddYou need to read all you can about historical temperaments to get a better picture. What you ask is a balance between wanting to sound natural like a singer and worrying about clashes as if you were playing a fixed note instrument such as a piano which most likely would be in Equal temperament. Check out all those circular graphs comparing temperaments with modern tunings to see where the differences lie. A very odd thing happens if you have a piano tuned to one of the temperaments used in Bach`s time. Any recordings made with a standard modern tuning begin to sound ugly and out of tune. ( Which they are ).It`s a big commitment to make the change. Not quite dissorientating , but you become convinced that all the rest of the world is out of step. Spend a few weeks on that topic to get a perspective . It`s not something I could say in a sentence to convince you either way .
Posted on April 26, 2012 at 08:22 AM
From Adrian HeathTwo extremes:
Posted on April 26, 2012 at 09:07 AM
- "Meantone", lovely smooth pure major thirds, highly compromised fifths;
- "Pythagorean", pure fifths, gritty major thirds, (and maybe, stretched octaves...)
What to do?
Fifths are "spatial", thirds sensual..
In double-stops, I have sometimes had to raise the lower note of a major third, rather than lower the upper note, e.g. C with open E.
A comma in first position is good 1/8th inch wide, wider than my usual romantic vibrato!
A surprising number of musicians don't understand what on earth we are talking about!
Take frequent breaks for a nice cup of tea!
From John CaddI forgot to mention the magic phrase; Key Colours. You would be surprised at the way they enhance the musical impact . You don`t even need to wear sandals to get the benefit. Also read the essay ;A History of String Intonation , by Hasse Borup . It will all help. Unfortunately the Piano is the best instrument to show key colours but the subject has been effectively buried alive for the last 100 odd years by Equal Temperament .In a way the violin is too adaptable and so it misses the chance to use key colours unless you work hard to find a way to find and use them . The frequency comparisons between Equal Temperament and any Historical Temperament will show you where to look for solutions to your problems . Certain notes (4 or 5 of them .I pick F , G , Bb , and C as the main suspects ) will become the keys to open a few doors .
Posted on April 26, 2012 at 10:09 AM
If I was a Physics teacher I would show a wave pattern of one note showing each peak and trough . Then I would superimpose another note of a different frequency on top. It would take minute adjustments in frequency for the sound to alter . The Historical Tuning frequencies were chosen to accentuate the beauty of the sound whereas Equal Tuning was imposed regardless and has certain glaring out of tune notes that we have become used to for over 100 years. Technical tuning reasons were the cause in the past. Arguments about the best or worst temperament among the Historical afficionados will probably ensure that Equal tuning remains as the permanent fallback choice.
From Michael De SapioMaybe I wasn't entirely clear in my original post on what I was looking for. I am conversant with just intonation principles and have progressed beyond "equal temperament ears", having played baroque violin for several years now. What I'm asking is, objectively speaking, which notes of the scale need to be differently pitched when functioning as a fifth instead of a third.
Posted on April 26, 2012 at 11:11 PM
I am not concerned here with keyboard temperaments; these, as I understand, of necessity have variable fifths (some wider than perfect/pure, some narrower than perfect/pure). I'm concerned solely with just or pure intonation and perfect or pure fifths.
To put the question as precisely as possible, should, e.g., F be played differently as the fifth of B flat than it should be as the third of D? When I play F as the third of D I play it quite high so as to make a wide and pure minor third. Should this pitch then be exactly the same to tune a perfect/pure fifth with B flat? This is the crux of my question.
From Corwin SlackMichael, I think this (just intonation) is the most difficult subject in music. There are examples on line (I will post later) that demonstrate that you can either play linear motio justly or you can play harmonies justly but you cannot do both. You cannot even tune 4 successive thirds without some compromise. My guide on this subject is figuratively a full professor Nobel Laureate to my Pre-K but I have come to believe that this is the Mount Everest of artistry. Good luck! You will need it.
Posted on April 27, 2012 at 04:40 AM
From Adrian HeathAll right, let's take A in the key of C:
Posted on April 27, 2012 at 07:02 AM
If the root of the chord is D, it's a pure perfect fifth;
But to answer your question (!), in a B-flat chord, F should be a pure fifth above; in a D minor chord, the F must adapt, as we go along, to the D & A. All this depends on where the B-flat came from: probably a pure 3rd below open D? Or A pure 5th below F a pure 4th above C? And so on and so on..
Every note of every scale, is subject to this dichotomy; but as I suggested above, we should usually "build" with fifths and "enjoy" the thirds.
In one chamber-music workshop, (a Haydn quartet in C major), the instructor asked us to tune the E & A strings down one comma: the D-A 5th was horrible but C and G chords were lovely!
Semitones are often wider than people think: a B leading-note to C is very often a pure third above G; a melodic B may be much higher.
One other thing: in a context favoring pure thirds, G-sharp is usually lower than A-flat.
From John CaddMathematically you cannot square the circle in the way you want to . If you were playing a fixed note instrument it is out of your hands , unless you have your own tuning fork . But on a violin you can easily cheat and play what sounds best at that moment. Each moment in a piece allows you to do alterations on a moving scale that can disregard intervals played 2 or three seconds ago . Listeners have short memories like that . Chopin played with that idea . It`s what made his music so interesting.
Posted on April 27, 2012 at 01:45 PM
From katrina thurlowIs this the case in all tunings? If you were tuning to A 412, 415,435, 444, 455 is the principal still the same? If the instrument resonates differently, would things still turn out?
Posted on April 28, 2012 at 08:50 PM
Can you this while in scordatura? Say you are in A major and you bring your g and d up one tone, you should tune those strings in 5ths, and you tune your e string a perfect octave from the d string, dosn't that do enough?
Was this only done in the baroque? It seems to give the music an entirely different sort of voice; and give more artistic freedom! Has anyone ever done this with adagio from bach sonata no.1? How did it work out!
From Adrian HeathKatrina, I confess I haven't used much scordatura, except for a brief flirtation with the viola d'amore, which is usually tuned to a chord of D minor - or D major! How to tune the F/F# string in a way that allows modulations? I had to examine the pieces carefully beforehand.
Posted on April 29, 2012 at 05:48 AM
But the same constant adjustments to fingered notes apply to any tuning - and any tuning fork. Playing with gambas (adjustable frets) or lutes (fixed frets) complicates life even more..
The composer's style comes into play as well: Vivaldi loves to use the ringing of open strings, either bowed or "sympathethic"; Bach's complex and ever-changing motifs don't give so much time for listening to resonance.
Minor keys are also a problem; their tuning often derives from the relative major, but not always. And the final chord is often an open octave or fifth, or even a "Picardy" major chord.
In his 5th solo 'cello suite in C minor, Bach lowers the A-string to G: a more silvery resonance, and perhaps a remeniscence of the (preceding?) version for lute.
Try playing Vivaldi's (in)famous A minor concerto in G minor, without retuning: it looses its "bloom", and becomes almost plaintive. Now tune the violin down a tone but play normally: the lower tension lets the strings "shimmer", and the open strings and their harmonics ring out.
At least "baroque" performance practice makes us really listen!
From John CaddIf you practice a piece long enough , your fingers will get used to landing in certain positions as you continuously monitor the sounds that you want. In a different piece in a different key the monitoring process and the influence of practise will possibly see your fingers landing in different places for the "same note " if you carefully compared recordings of both pieces . Is it likely that the "different finger positions " are being taken care of without our being conscious of that "fact "?
Posted on April 29, 2012 at 12:46 PM
You ask an interesting question in search of a kind of rule . How do you like the comparison of the actual sounds in the cases you have mentioned ? Would a logic box be useful for sorting out the options ? Allow for "technically correct but sounds wrong " and "technically wrong but sounds good ". Would the informed audience intuit which was which. If there is a repeat , test them with both .
I wrote inuit first but realised that was an Eskimo .
From Michael De SapioI am going to continue to do intonation experiments with my group to examine this issue. I am going to sound a note, say F, and keep it constant while the cellist plays first third (D) and then a fifth (B flat) and see whether my F (which I will not have changed) sounds good in each context. I will do this with various notes.
Posted on April 30, 2012 at 05:19 PM
One thing I've seen in discussions about violin intonation is that people make a distintion between "melodic" and "harmonic" intonation. With my baroque training, I am not inclined to agree with this distinction. My training has taught me that every melodic note fits into a harmonic framework, and to my ears just intervals sound perfectly fine in a linear context as harmonically. The example of "melodic" intonation that is often used is that of the sharpened leading tone, but this is a modern notion originating with Casals. I don't see it having any application to earlier music.
From Adrian HeathMichael, I quite agree about the dominance of the harmony, but there can be magic moments when the melody escapes to have its own logic,e.g. quick passing notes, échappés and cambiati etc. Or in Purcell's Fantasias where a rising B-natural can clash with a falling B-flat..
Posted on April 30, 2012 at 06:48 PM
My favorite demonstration with students:
All quite wierd to my "tempered" ears, but a kind of expanded conciousness..
From John CaddDid some composers get these things wrong and leave the mess to be sorted out by players?
Posted on May 1, 2012 at 01:26 PM
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