Scale Duets

Edited: December 27, 2017, 3:00 PM · You can download 2 violin duets for scale practice for free at my website https://www.baylor.edu/music/index.php?id=925996 .These are after Spohr's duos in his Violin School. The only one in his tutor are in G, but I have transposed them up to A flat and A natural, and slightly altered the 2nd violin part (the teacher's) so there is a drone tone. They could make it a fun incentive for a student to practice on scales. Enjoy!

Replies (29)

December 27, 2017, 4:39 PM · Hi Bruce, quick question. If you use a drone or duets for scale practice, doesn't that reinforce just intonation rather than the usual Pythagorean scale intonation? I've always wondered about that.
December 27, 2017, 5:28 PM · Bruce -- fantastic! Thank you for adding these to your website.

Paul -- yes, a drone will put you in Just Intonation mode.

December 27, 2017, 5:58 PM · pythagorean intonation is not "usual" for scales, at least in the classical world
December 27, 2017, 7:02 PM · Irene I was following the advice given in the video linked below. Is that incorrect? I guess I thought Sassmanshaus was kind of a authority on stuff like that.

https://youtu.be/buZOs-czOUg
https://youtu.be/QaYOwIIvgHg

Edited: December 27, 2017, 9:54 PM · Let me start off by saying that I have a lot of respect for Saussmanshaus as a pedagogue. I had at one point the pleasure of working with one of the leading figures in the field of tuning systems, Ross Duffin, and one of the most important realizations I came away with was that our conception of intonation as string players doesn't necessarily match up with what we're actually doing. That said, I would characterize what Saussmanshaus is promoting as essentially Casal's expressive intonation, with extreme leading tones. Just for fun, I ran his scale fragment through Audacity, and his D-F# (296hz - 377hz) is even wider than a Pythagorean ditone. Expressive intervals like this are largely a matter of fashion - it was very popular at Juilliard for a long time thanks in part to Bobby Mann - but it's my feeling that the field in general is moving away from this toward a more Just system.

Even more anecdotally, I was told by pretty much every teacher I've studied to keep 3rds / 6ths more harmonious with the tonic (so, away from pythagorean toward Just) - and while I haven't listened to many accomplished players play scales since college, that's what I'm used to hearing. Either way, I think learning to hear and produce the pure intervals is a very important step in anyone's training.

Bruce, sorry for the derail and thank you for the great resource!

December 28, 2017, 12:46 AM · Bravi to Bruce and Irene!

Paul, I highly recommend you read Ross Duffin's book on intonation. World leading expert explaining a difficult subject in a tiny book, hard to find anything better.

December 28, 2017, 4:53 AM · "his D-F# (296hz - 377hz) is even wider than a Pythagorean ditone"

For people like me who don't know the frequencies by heart:

A major third is:

400 cents in equal temperament
419 cents for the frequencies above
386 cents in just intonation
408 cents in Pythagorean (if counted from the tonic)

Edited: December 28, 2017, 5:54 AM · I didn't know about Duffin but I'll definitely read that! Thanks! My own take on Sassmannshaus is that his system is canonical .. sort of as "as far as one would go".

I like Bruce's studies. Should be great for Suzuki families that have 2 violins. Reminds me of the Dont book that has accompaniments, which I loved as a boy.

December 28, 2017, 8:34 AM · There are also 2nd violin accompaniments for the Kreutzer etudes. You can find them on imslp.
December 28, 2017, 12:39 PM · "If you use a drone or duets for scale practice, doesn't that reinforce just intonation rather than the usual Pythagorean scale intonation..."

Paul, while you may be technically right, I don't think it matters on a practical level. When we do these things, like play a drone (or when I advocate for putting a tuner on a certain note as a drone), what we're trying to do is get the student in the ballpark and just get them to listen. Usually the issue isn't fine intonation but gross deficiency and lack of listening and adjusting skills.

December 29, 2017, 12:24 PM · Thanks for reminding us of Spohr's studies: effective and musical!
December 29, 2017, 3:11 PM · There are a large number of duets in Spohr's Violinschule which are pedagogical in nature. Scales, chromatic scales, arpeggios, double stops, violin concertos, etc. http://ks.imslp.info/files/imglnks/usimg/9/94/IMSLP330999-PMLP30640-violinschuleengl00spoh_1878.pdf (this is the English translation by Henry Holmes)

This forgotten resource which could be very useful in contemporary teaching.

December 30, 2017, 6:20 AM · So because of this thread and Dorian Fu I am halfway through Ross Duffins book. It is fascinating and eye-opening. I didn't know anything about alternate tuning systems. Knew about just intonation vs. ET but only in the very narrow context of tuning in the violin and had not considered further implications. Fascinating.

That said... If you do read the book and are fascinated as I was don't bother to try to explain it to anyone unless they have a decent amount of theory already. Thus far I have had three people look at me as though I were explaining how paint dried while we watched it dry.

Edited: December 31, 2017, 7:23 AM · What is the title of Duffin's intonation book? Is it "How Equal Temperament Ruined Harmony (and Why You Should Care)"?

And @Jessy, give it a try: mention some fascinating facts!

I found all that I've read so far about temperaments so far rather boring and usually badly explained. For example: Quarter-comma meantone on Wikipedia: endless fractions and exponents and zero information on who uses/used this system and what people think of the tradeoffs made in this system.

December 31, 2017, 7:16 AM · Hahah.. ok! But I am far from an expert so if I get something wrong be gentle!

So, for instance, the ET Tuning comes about because of the shortening of twelve consecutive fifths by a tiny amount. This then creates octaves that can be divided into 12 equal half steps. Which then creates thirds that are both very wide and very narrow depending on major or minor.

Tuning a piano (in ET) is done by measuring the rate of the beats (beats that we all have heard while tuning our violins) that are created when two frequencies are clashing.

Chords are based on the natural harmonics produced when a single note is sounded. So unless you are intentionally looking for dissonance you construct a chord with notes that "match" those harmonics produced by sounding a single note.

Just intonation is based on that concept. The waves should match in just intonation where in ET They do not.

A piano would probably sound more harmonic if it had split Black keys. This is because the Black keys are mathematically split so that they evenly divide a whole note. However, in actuality , for example, a G# is not the same note as an Ab. The Ab should be higher and the g# lower (based on natural harmonics). This all goes back to the ET Tuning and the modification of the fifths and the subsequent division of an octave into twelve equal semi tones.

There were multiple other tuning systems used as late as the early 20th century and still prevalent in the mid 19th and what are now referred to as cents were referred to as commas. Cents and commas are simply a breakdown of a tone into smaller segments so that you could tune with multiple other people accurately. Many of these systems were referred to by the number of commas they used to divide the tones.

All of the above I learned from that book and there is tons more. I just found it all facinating.

I am still reading it but will be done shortly and I will likely read it through a second time. Perhaps comments and discussion here will help me grasp concepts that I don't understand.

December 31, 2017, 8:15 AM · for example, a G# is not the same note as an Ab. The Ab should be higher and the g# lower (based on natural harmonics).

I have heard this before, but I wonder whether it is really universally true, no matter what place in the harmony the note has. In the intervals Fb-Ab (386 cents) and E#-G# (316 ct) it would be the other way around. And who is to say that the Ab/G# need to be adjusted and not the Fb/E#?

The example is a bit extreme because it involves the uncommon E# and Fb, but consider a Bb in different intervals:

Gb-Bb (386 ct): lower the Bb or raise the Gb relative to ET.
Bb-Db (316 ct): lower the Bb or raise the Db.
G-Bb (316 ct): raise the Bb or lower the G
Bb-D (386 ct): raise the Bb or lower the D

The whole problem of designing a temperament (on a keyboard or fretted instrument) is that it will only work for music in a particular key. On the violin, we can make these decisions on the fly, but the mystery for me is which tone needs to be adjusted if neither is an open string.

I asked my teacher the other day, but she told me not to worry about non-ET intonation yet because my finger positions aren't accurate enoguh anyway. :-)

Edited: December 31, 2017, 8:27 AM · By the way, there are ways to get correct intonation on a fretted instrument:

December 31, 2017, 9:24 AM · I have seen that video before. I am amazed by it!

Now, if I am not mistaken, the note that would be adjusted will depend on the line of Melody (the horizontal) or the chord ( the vertical) or the key in which the music resides. The important thing, if you want to use just intonation is that the major third ( in your example) is a "true" major third.

Now, as for the "extreme" examples you mentioned...E# and Fb I don't understand why you are saying it would be reversed. The Fb would be slightly higher than the E#. Perhaps I am misunderstanding what you are saying?

December 31, 2017, 9:43 AM · I mean: the interval Fb-Ab needs to be reduced from an ET 400 cents to a just 386 cents. You can do that by lowering the Ab or raising the Fb. So, the statement that an Ab is higher than a G# or ET Ab is not generally true.
Edited: December 31, 2017, 10:35 AM · So the Ab in Just intonation tuning would also be lowered. You would not just lower one or the other. They both get lowered.

Let's make it a little easier...Imagine using a keyboard tuned in ET. A C natural to an Eb. That is a minor third. To make a just intonation minor third you would slightly lower the Eb.

Likewise, a Bb to a Db is a minor third. To make it a proper just intonation third you would lower both the Bb and the Db.

These examples are only necessary when you are trying to "translate" from ET to Just. However, if you have already decided to use Just intonation it is not necessary. You simply adjust the pitch to make the most harmonic interval.

December 31, 2017, 10:21 AM · "A piano would probably sound more harmonic if it had split Black keys..."

Yes, the Archicembalo was invented to try this. Didn't prove very popular, though.

It's curious to me that the same people pop out to dissect tuning systems at the slightest provocation. It's simply not necessary (or practical) to worry about this tuning vs that tuning when playing the violin.
Just tune each note for the appropriate resonance, and intervals for least amount of beating.
Anything else is mental something-or-other...

Edited: December 31, 2017, 10:37 AM · @jessy, Ehm, you state that Bb-D is a minor third and Bb-Eb is a major third. I respectfully disagree. :-)

And even if they were, I don't really see an argument why only one of the two tones of the interval is a candidate for adjustment.

@Scott, "Just tune each note for the appropriate resonance, and intervals for least amount of beating." -- do you mean resonance with open strings?
And tuning intervals: I assume that you tune the latter of the two in a sequential interval, but which one of the two do you tune in a double stop?

P.S. if you're referring to me: I'm trying to figure out how violin intonation is supposed to work and I still don't get it. It seems that all violinists want their intonation to improve and on posted videos either intonation is criticized or the poster himself/herself apologizes for intonation. It seems that there is a concept of "correct intonation".

December 31, 2017, 10:32 AM · Oops. You are right. Sorry. But the point is that both would be lowered. Not just one or the other. I'm going to edit that too. I can only bear to look so foolish hahah.
Edited: December 31, 2017, 10:49 AM · I agree with you Scott. I am merely discussing it because I find it facinating and it was brought up. It isn't needed for the violin. Either you are in tune or you are not.

Han, I think that you should just start playing intervals and listening. On the violin you can hear when two notes are not in tune. A minor third (and other intervals) have a much larger "agreement" just like the fifths when you tune them. You can hear when it is not in tune with itself.

Edited to add...I hope that doesn't sound condescending. I am just learning to hear it properly myself. :-)

Edited: December 31, 2017, 10:48 AM · Scott, I agree. But I do think there are some good general rules, such as narrowing of major thirds in double stops, etc. What these rules are called is less important. A bit like knowing the difference between Boyle's Law and Charlie's Law. Important laws, but the names do not make them so.

Somehow I find fourths the hardest to get exactly right. Not sure why.

December 31, 2017, 10:47 AM · Scott - "It's curious to me that the same people pop out to dissect tuning systems at the slightest provocation. "

Well, if people would stop posting misleading or inaccurate information I wouldn't have to.
Personally I find that the most important component of "in tune" playing is consistency of note placement - the ear can adjust to pretty much anything else.

December 31, 2017, 11:03 AM · Irene, thanks for mentioning Ross Duffin's book "How Equal Temperament Ruined Harmony." I read it a few months ago and it was much more accessible and well-written than the few other books I have attempted on the subject. Scott, tunings and temperaments might not interest everyone, but some of us are fascinated with them because they are the technical understanding of why different musical periods have different harmonies and melodic intervals. I became very interested in the subject as my tastes drifted further back in time, to the point where I mostly listen to 17th century and earlier music, though I will creep forward as far as Mozart from time to time.
December 31, 2017, 11:10 AM · Will, while reading that book I couldn't help but wonder if ET isn't the root cause of the current pop music that all sounds the same. If pretty much all keys sound the same (comparitively) wouldn't that explain the limitations and lack of originality in current music?
December 31, 2017, 11:49 AM · Jessy, I recall a line from very early in Mr. Duffin's book where he says he was careful to title the book "...ruined HARMONY" rather than "...ruined MUSIC." I agree with him that equal temperament should be thought of as just one more temperament in the large menu available to us, and we should not resent its dominance in contemporary music since it was a solution to the problem of keyboards and fretted instruments that cannot easily make small frequency adjustments to allow for playing in different keys. After all, it's not just "current pop music" that uses equal temperament, but also virtually all orchestral music at least since the early 20th century (as even Duffin concedes) --though not nearly as prevailing (can't use the word "dominant" here!) in the romantic music as asserted by Stuart Isacoff in his book "Temperament," which mocks as superstitious those who resisted adoption of equal temperament.

Regarding "the current pop music that sounds all the same," I don't think that is attributable to tuning --does all equal temperament orchestral music "sound the same"? It's only true about any genre of music from a distance to those of us who don't appreciate the genre. To my own surprise, I overcame some musical snobbery when I began to discern the "good" old country music from the "not as good" old country music (1950s & 60s). Anyone who likes a certain genre of music will never agree "it all sounds the same" and will have strong opinions regarding the good and bad music in that genre. In current pop music, what makes so much of it all sound the same is that so much of it REALLY IS the same: computer-generated tones, drum machines, synthetic or computer-modified voices --it seems like actually playing a musical instrument has been eclipsed by electronic buttons and dials and touch-screens. The lesson for true artists: don't run with the herd!

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