Just Intonation Suggestions

[JimLucas]

I still have vivid audio memories of hearing some of Paul Groff's concertinas.  Perhaps it was the room.  Perhaps my inexperience.  Perhaps the way Paul played.  I don't know for sure which, if any of the concertinas, were in alternate temperments.  I do know that the thirds and the chords that Paul chose were exceptionally pleasing.

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I've had the pleasure of more than one visit to Paul in which he took instruments in different tunings and played specific arrangements on each to highlight its advantages for particular styles. In some instances he then played the same arrangement on instruments in other tunings, which showed that they didn't "fit" as well. He demonstrated quite clearly that there was no one tuning that was best for everything.

 

But perhaps the question should be:  If equal temperment compromises thirds and some concertina styles favor thirds why not dedicate a solo concertina to 1/4 comma mean tone or Werkmeister III?

If you mean some individual's particular instrument, I suspect it's been done, though maybe not recorded a whole CD's worth. (How many anglo CD's are done entirely on only one instrument?) If you mean that some maker should produce a separate model that uses such a tuning, it might be interesting to see what the market would make of it. But I think any of the current makers of mid- or high-range instruments will tune an individual instrument to whatever standard the buyer requests. (How about a MIDI concertina able to switch among 17 different "temperaments"? )

[David Barnert]

But a deeper question might be whether Pythagorean thirds are important or even intended in music where "chords" usually consist of at least 4 and often 6 or more steps of the chromatic scale (ignoring octaves, though that's something that really can't be ignored without drastic effect).

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I'm not sure just what you mean, here, Jim.

 

Pythagorean thirds are a whole 'nother concept from what we've been discussing. Not equal tempered, not pure, not any of the temperaments that preserve or approximate the "lower than equal temperament" nature of thirds, Pythagorean thirds are actually sharper than equal temperament.

 

Pythagoras never considered the 5th harmonic, to which pure 3rds are tuned (5/4). He only used the first 4, giving 5ths and octaves.

 

To tune a 3rd in Pythagorean tuning, you have to go up a 5th (3/2) four times and down two octaves (1/4), yeilding 81/64, or 1.265625. Pure 3rds (5/4) have a frequency ratio of 1.25, while equal tempered 3rds (irrational) have a frequency ratio of 1.2599...

[JimLucas]

But a deeper question might be whether Pythagorean thirds are important or even intended in music where "chords" usually consist of at least 4 and often 6 or more steps of the chromatic scale (ignoring octaves, though that's something that really can't be ignored without drastic effect).

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I'm not sure just what you mean, here, Jim.

Pythagorean thirds are a whole 'nother concept from what we've been discussing.

Pythagoras never considered the 5th harmonic, to which pure 3rds are tuned (5/4). He only used the first 4, giving 5ths and octaves.

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I think I meant "pure" thirds. I thought the two were synonymous. My mistake, it seems.

 

What I "know" of Pythagoras and music is that Pythagoras' philosophy of music (and of the universe) was based on simple integer ratios. I've read that in several places, without any of the sources (that I've read) going further than that, e.g., dealing with possible compromises.

 

In any case, what I meant was a third represented by the smallest such ratio, which I think is what you mean by "pure". Then what I was trying to express was that in chords which include 4 or more degrees of the scale the equal-tempered scale may produce as close to "pure" results as anything else, if one takes into account all the intervals comprising the chord. Furthermore, that some composers/compositions may even be trying to create or manipulate dissonance, rather than minimize it.

[allan atlas]

I use concertinas tuned to three different temperaments during the course of my lecture-recitals: there's one in equal temperament, another in meantone (this instrument likely belonged to the William Peel, sone of the prime minister), which i use to play unaccompanied stuff. . . .it produces a real "twang" when used against the piano. . . . .and the instrument that i use most was recently retuned according to Thomas Young's "Well Temperament No. 2", which he describes in his essay on acoustics from 1800. . . . . .briefly: the major third C - E is narrow. . . .then the thirds grow wider and wider as we go around the circle of fifths simultaneously in both directions. . . .so the thirds G - B and F - A will be wider and equal to one another. . . .the thirds D - F sharp and B flat - D will be wider still and equal to one another. . . . .and so on and so on until one reaches the widest third with F sharp - A sharp (= G flat - B flat). . . .one of the pieces that we (the NY Victorian Consort) do is a piece by the Italian-born Angelo Mascheroni, who immigrated to London. . . .the piece is called "For All Eternity". . . .it's in E flat. . . .but modulates to G flat. . . .that passage has the voice and the obligato part (which i take on the concertina) in unison. . . .and we find that it causes some real "tension"........allan

[Dan Worrall]

I wonder why equal temperament seems to be the standard with concertinas made or retuned today....why shouldn't mean tone be the standard and not the exception?

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Because people play together?

 

...fretless strings can indeed adjust to any "temperament" -- or shading of any individual note -- except on the open strings. But fretted strings can't.

 

...for all-around use -- including accompanying the singer-guitarist in my local session who has capoed up to the key of C# -- I'll stick to equal-tempered, if only because otherwise the other musicians would accuse me of being "out of tune".

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Jim,

Down here on the Gulf Coast....it must be the heavy air....people have a slightly different take on that. Cajun accordions are tuned to remove the beating in their main chords....a local version of unequal temperament. There are scores of Cajun bands where this mean tone instrument is paired with fretted guitars and unfretted fiddles, and they seem to get along just fine playing together....but maybe that is the beer!

 

ps. A bit of an aside on temperament:

Harold Herrington showed me an exceptional DVD put out by the Cajun accordion maker Marc Savoy (called "The Gospel Accordion to Marc", vol 2) where Marc discusses in great detail not only temperament but tuning techniques....and it has a certain resonance (no pun intended) with what conditions and decisions early concertina tuners must have been faced.

They had no electronic tuners in nineteenth century Louisiana of course, and early Cajun accordion tuners were also not trained in music theory (most could not even read music). To tune an accordion, they first tuned to one reference note...usually C (maybe they had a tuning fork, otherwise they just got close). Everything else was done by ear relative to that reference point, a la 'do re mi' etc and by tuning intervals. On a diatonic instrument, on the push or pull you have (mostly) third and fifth intervals, so they concentrated on tuning with those found naturally on the keyboard. Remember they had no training, so absolutely perfect equal temperament was out of the question (to tune to equal temperament without an electronic tuner, you'd have to carefully count beats per second in various intervals...beyond their ken or skills). When they got to the main chords for key of C (the CEG, GBD, and FAC major triads), they wanted a pure, non-beating sound. Fifth intervals in equal temperament have almost no beating, as you know....so they tuned those fifths for those chords perfectly pure, by ear. But the thirds beat like crazy of course in anything close to equal temperament....so they would take a C chord (CEG, on the push) and flatten the third (E) until all beating was gone in it too, by ear (in today's parlance, about 15 cents lower than equal). They then repeated this for a G chord (GBD), flattening the B about 15 cents. With the F chord (FAC), they didn't like to flatten the A, because it ruined a few characteristic partial chords they liked to play in Cajun music, according to Marc...so they lived with the beating of the A in near-equal temper. Voila...Cajun unequal temperament.

 

The early anglo concertina tuners perhaps operated similarly. This was a cottage industry. A reed tuner would work out of his house on a piecemeal basis. He was not likely to have been finely trained in academic music theory, but had more practical street ears. He probably had a tuning fork or some such standard to tune from, but little else. Unequal temperament of some sort would likely have been the best way he could cope. As Marc Savoy says, the early Cajun tuners couldn't count precisely how many beats per second to get an equally tempered interval like a third....but they could certainly take ALL the beating out of it; and since the diatonic keyboard naturally gave them thirds and fifths, they concentrated on making these intervals sound pure and dry. On a diatonic instrument in the key of C, if you first tune the 6 notes for the C and G chords, which are those most commonly used when playing in the key of C, you have thus tuned all the notes of the scale except A. Adding the second (G) row on an anglo means they had more hard choices to make than the Cajuns. Obviously, some wolf-ish fudges would have to be made, depending on what sort of sounds the English tuners themselves had in mind (e.g., were they perhaps looking for a two-row chorded style a la Minasi or Hoeselbarth or Kimber, or were they looking for a more upscale 'fully chromatic' instrument playing complex melodies in all keys, a la Jones' vision?). I would guess that, this being an anglo, their choices would still heavily favor tuning relative to the main chords played in the keys of C and G for a CG instrument (happy to be proven wrong if anyone has data on this!). The experience of the Cajuns shows us that this pre-digital, non-music trained process would naturally drift to an unequal temper of some sort.

This all gets way off the point of Jim's post of course, but might give a bit of insight in explaining the popularity of unequal temperament for these diatonic instruments in the nineteenth century, beyond the simple fact that unequal (in its varieties) was the prevalent temperament of the time. In a similar fashion, the English measurement system is based on twelves, which are very easily subdivided into thirds, halves, and fourths....much easier for people who had no digital calculators. Some of us still prefer the coziness of feet and inches....and the purity of unequal temper. To each his own!

 

ps. edited to clarify terms used

Edited October 14, 2005 by Dan Worrall

[JimLucas]

...the English measurement system is based on twelves, .... Some of us still prefer the coziness of feet and inches....

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And dozens. Don't forget dozens. A box of 10 eggs just doesn't have the same appeal.

[Stephen Chambers]

Harold Herrington showed me an exceptional DVD put out by the Cajun accordion maker Marc Savoy (called "The Gospel Accordion to Marc", vol 2) where Marc discusses in great detail not only temperament but tuning techniques....and it has a certain resonance (no pun intended) with what conditions and decisions early concertina tuners must have been faced.

They had no electronic tuners in nineteenth century Louisiana of course, and early Cajun accordion tuners were also not trained in music theory (most could not even read music). To tune an accordion, they first tuned to one reference note...usually C (maybe they had a tuning fork, otherwise they just got close). Everything else was done by ear relative to that reference point, a la 'do re mi' etc and by tuning intervals. On a diatonic instrument, on the push or pull you have (mostly) third and fifth intervals, so they concentrated on tuning with those found naturally on the keyboard. Remember they had no training, so absolutely perfect even temper was out of the question (to tune to even temper without an electronic tuner, you'd have to carefully count beats per second in various intervals...beyond their ken or skills). When they got to the main chords for key of C (the CEG, GBD, and FAC major triads), they wanted a dry sound. Fifth intervals in equal temper have almost no beating, as you know....so they tuned those fifths for those chords perfectly dry, by ear. But the thirds beat like crazy of course in anything close to equal temper....so they would take a C chord (CEG, on the push) and flatten the third (E) until all beating was gone in it too, by ear (in today's parlance, about 15 cents lower than equal). They then repeated this for a G chord (GBD), flattening the B about 15 cents. With the F chord (FAC), they didn't like to flatten the A, because it ruined a few characteristic partial chords they liked to play in Cajun music, according to Marc...so they lived with the beating of the A in near-equal temper. Voila...Cajun mean temperament.

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Dan,

 

Thanks, that sounds like a much more detailed version of what he told me at Michaelstein, but my understanding was that he was talking about when the Cajuns started to build their own accordions, in the early 1950's. Prior to that they would have been tuned (like harmonicas) nearer to "just" by the factories in Germany, and probably wouldn't have lasted long enough to be retuned in Louisiana ? (After all, we know that the life expectancy of a German concertina that was played all the time, and maintained every week, was only 3 months, and you hear stories of one being bought for a "house dance" in Ireland & being put on the fire in the morning, it was so wrecked. The melodeons were no better.)

Edited October 13, 2005 by Stephen Chambers

[Robin Harrison]

............I wonder how important exact tuning is anyway, in a group setting ( ie session) if the difference between the instruments is only 14 or so cents. I ask this question based on two observations.

I used to take my two children to Suzuki violin group sessions and recitals. There would be 40 or so kids hacking away in all sorts of tuning. The sharp kids counter-balanced the flat kids. To my ear it never sounded out of tune..........just a great big sound of people playing together. It reminded me of my three voiced melodion; one reed spot on, one sharp and one flat, producing a distinctive sound. The equivalent really of two out of tune accordions playing with one in tune.

The central issue is playing together in a group, such as a session, and not how exact the tuning sounds to others...........it's not a recital.

My 14 cents worth !

Robin

[Paul Groff]

Hi everyone,

 

It warms my heart to see such interest and enthusiasm for tunings "outside the equal-temperament box"!

 

I would like to caution those new to this subject (and maybe some who are not) that in the preceding discussion some technical terms have been used haphazardly or even incorrectly. Anyone who would like to learn more about tuning and temperament can find excellent books and articles on the subject in any music library (or email me for particular references). Some of this books have very useful glossaries that I recommend.

 

A few specifics: "meantone" is not equivalent to "unequal temperament," or to "just intonation."

 

There is only one "equal temperament (with 12 tones to the octave)." There are many, many unequal temperaments and tunings, some of which are meantone and some not, some of which have more or fewer than 12 tones to the octave.

 

In my own work I always emphasize the difference between a tuning or temperament that includes one or more pure intervals, and a "just tuning," some times called "just intonation." In fact my personal view is that the concept that there is only one "just intonation" is flawed, especially as applied to traditional music and instruments such as the german/anglo concertinas or the diatonic accordion family.

 

Thus, as Theo noted, 1/4 comma meantone (but NOT other meantone temperaments) has major thirds that are pure or just, but it is not what is normally considered to be "just intonation." The fifths in meantone temperaments are narrow, as has been noted.

 

As David points out, the theoretical concept of "Pythagorean tuning" has major fifths that are pure or just, but the thirds are wider than in ET and very harsh.

 

Stephen makes an important point, implicitly -- perhaps suggesting that the "cajun accordion tuning(s)" used by Louisiana builders today may well have a partial ancestry in the unequal-tempered tunings of the prewar German accordions such as the Monarch etc? That has always been my speculation also. These older German accordions (I don't mean the later version of the Hohner 1 row) were still being played by some cajun musicians during the time that the first Louisiana-made instruments were being developed. The cajun tunings are different than the German tunings (e. g., I have heard that some makers actually sharpen the F for a pure F-A), but both share very pure triads on the tonic and dominant chords in the home key of the instrument. It may ALSO be true that the cajun fiddlers independently preferred pure fifths and/or thirds, as do many traditional fiddlers, and perhaps the fiddle styles favored such intervals even before the accordion was introduced into this music. Marc Savoy knows more about the cajun instruments and their history than I may ever learn, but it surprises me that the old German accordion tunings are rarely given credit for their possible contribution.

 

Back to the question that started this discussion.There is a scale for "just intonation" that has sometimes been published in the context of tuning the Irish pipes. Basically, this is a scale for the D major diatonic scale, plus the note C natural, and is designed so that the following fifths are pure:

 

C-G, G-D, D-A, A-E

 

And the following thirds are pure:

 

D-F#, G-B, A-C#

 

This scale allows the fifths and major thirds most commonly played on the Irish pipes (including regs and drones) to be pure.

 

In deviation (cents) from equal temperament, this is one version:

 

D-0, E-+3.9, F# -13.7, G -2, A +2, B -15.7, C -3.9, C# -11.7.

 

 

Note that this leaves the fifth E-B and the third C-E very raucous!

 

You can certainly tune your concertina to this scale and it will sound BRILLIANT for much Irish traditional music played in the traditional keys, especially if you play with pipes or other drones.

 

But this scale does not tell you how to tune D#, G#, Bb, F natural. And no matter how you tune these latter notes, if you "pipe-tune" the keys of D and G, playing in some of the other keys often used on the anglo will sound pretty wild.

 

If you want to sweeten the tone of a concertina without going all the way to "pipe tuning," the various mean-tone and well-tempered scales are alternatives, as are some special tunings that were actually used in the 19th century by the anglo makers themselves, and that are the subject of my ongoing research. I have also invented some new tunings and temperaments that can be useful for particular purposes.

 

Ultimately the choice of how you tune your instrument is part of your musical expression, and the comments by Jim, Allan, Geoff, and others illustrate that this choice also needs to be considered in the social context of your music making.

 

I do want to salute the pipers, though. For the most part, they have been loyal to the traditional sound of their instrument, which is really inseparable from its unequal-tempered tuning, and this shows great integrity. The same for the cajun accordionists. In a way, I wish the anglo players had shown more loyalty to the old sound, rather than going so heavily for equal temperament in the 20th century. But that is just my personal opinion – and I do use ET myself very often.

 

One last point - pipes do have an advantage over concertinists in that the pitch of notes played on the chanter is much more adjustable by the player in real-time, using alternate fingerings and subtle pressure changes. This gives a good piper the ability to fit fairly well with fretted instruments if desired, and then to play a solo spot with drones and regulators with the most splendid pure harmonies.

 

Paul

 

 

Edited only to add: I see that now some of those who misused technical terms have edited their posts (above in this thread), subsequent to my original post here. This is good if it reflects a learning curve, but it does make the original course of the discussion here hard to follow now! PG

Edited October 23, 2005 by Paul Groff

[Doug Barr]

Paul, You should really publish your findings. Many of us are interested in what you have found. Doug

[Paul Groff]

Hi Doug,

 

Thanks for your interest. Would you or anyone who owes you a favor like to hire me as a professor, musicologist, curator, or even librarian so that I can make a living doing this?

 

 

Seriously, I am glad if you (or anyone else) have found my contributions to these discussions helpful. It is my pleasure and my nature to teach and to be forthcoming with information. But in this country, where expenses for raising children are so great and where support for my kind of art and research is so meager, it would be irresponsible to my family for me to give everything away. I do have a business and if you ever were to patronize it you might find that I am even more generous and helpful to my customers than to the public at large.

 

I do promise it all will be published someday!

Edited October 13, 2005 by Paul Groff

[Chris Allert]

Back to the question that started this discussion...

 

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at last

 

so paul, what do you do about the other notes? do you just leave them in equal temperment? there are a few tunes that use the g#. also, the chanter is fully chromatic, isn't it? is there a standard for how the rest of the notes are tuned?

[Paul Groff]

Chris,

 

Despite my efforts one year, I don't play the Irish pipes. Peter Laban may have some good advice for you here.

 

But it is my understanding that, on an unkeyed chanter the pitch of the notes D# (or Eb, which is of course a different pitch in some temperaments and tunings), G# (Ab, ditto), Bb (A#, ditto), and F natural are mainly controlled by the tuning of the other notes I mentioned, plus the particular fingering and bellows pressure used. SO they would not be independently tuned by the maker....except in that the bore, reed, and hole positions and dimensions relevant to those notes might cause a compromise in the "set" tuning of the 8 notes I mentioned in my previous post. (The D#/Eb note might be an exception here but I haven't seen a reference to any "standard" target pitch for this).

 

Again, keep in mind that the player of Irish pipes has some latitude to push each pitch around while playing.

 

On a keyed chanter, there will be separate holes for some or all of these "extra" notes. For the "target pitches" used to size and position those holes, you will have to consult one of the makers.

 

G# could be tuned pure with E, Bb with D, F with A (or with C!) , D# with B (or Eb with G)....there are many possible ways to continue to make "just intervals" as you fill in the scale. But remember, as I noted before, even within the 8 notes I gave before there are already the "unjust intervals" E-B and C-E, so from that point of view it is really not the whole tuning that is "just."

 

Pipe tuning merely includes MANY just fifths and major thirds.

 

Best wishes,

 

Paul

 

(Edited for spelling and greater clarity. I now see that I also made some typos in my other posts but don't like to edit a post once there has been a response. Hope the meaning is clear.)

Edited October 13, 2005 by Paul Groff

[allan atlas]

FOLKS: the literature on tuning and temperaments (and they are really NOT precisely the same) is V A S T.....................two items that i've found useful are:

 

Charles A. Padgham, The Well-Tempered Organ (Oxford: OUP, 1986) and

 

the classic study by Owen H. Jorgensen, Tuning. . . (East Lansing, MI: Michigan State UP, 1991)

 

there is an interesting discussion by a fellow named Ross Duffin called "Why I Hate Vallotti" (or something very close to that). . . .it's available on the web. . . .just google up "Ross Duffin" and you should find it. . . .and there are audio examples that demonstrate various temperaments. . . . .

 

one might also look around for material by Mark Lindley. . . . .

 

in the end, it's a hornet's nest. . . . .

 

concertinists in particular should look at Wheatstone's "Harmonic Diagram" and its accompanying discussion in the volume of his scientific papers. . . . the Diagram itself is reproduced in my book, The Wheatstone English Concertina. . . .it shows in very clear fashion "where his head was". . . . .and why, in the second edition of his treatise on orchestration (1855) Berlioz scorned that aspect of the instrument...............Allan

[Chris Allert]

concertinists in particular should look at Wheatstone's "Harmonic Diagram" and its accompanying discussion in the volume of his scientific papers. . . . the Diagram itself is reproduced in my book, The Wheatstone English Concertina. . . .it shows in very clear fashion "where his head was". . . . .and why, in the second edition of his treatise on orchestration (1855) Berlioz scorned that aspect of the instrument...............Allan

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on the concertina.net links page there is a link to something about wheatstone's harmonic diagram here:

 

http://www.ghg.net/bdwright/CW/Harmonic.html

 

but this link no longer works. does anyone know where this page may have moved to?

[Chris Allert]

for people who may not know what we're talking about in this discussion, i just found a very good introduction to the topic of temperments here:

 

http://www.dolmetsch.com/musictheory27.htm

[Paul Groff]

Chris,

 

Thanks for the link - that's a very useful website. Its detail might intimidate some, and some technical niceties might confuse the novice. E.g., it is technically true that "equal temperament is a special class of meantone," but in ordinary usage most of us find it clearer to employ the term "meantone" only when referring to the non- (equal temperament) meantone scales.

 

Let me know what tuning you choose (in the sense of, “how you choose to have your instrument tuned”) and how it works for you!

 

 

 

Allan,

 

Those are also great references that I too recommend. Like you, I distinguish between the terms "tuning" and "temperament" (see my posts in previous threads on this site), although the former term has multiple meanings. Specifically, a scale based on “just intonation” is a tuning, but not a temperament. But your clarification may help some readers here -- I realize that when I wrote "tuning(s) or temperament(s)" some might read this usage as implying equivalence, when I meant it to imply two alternatives.

 

Paul

[Chris Allert]

Let me know what tuning you choose  (in the sense of, “how you choose to have your instrument tuned”) and how it works for you!

 

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well, after all this i'm going with equal temperment for now since i'm not really sure what i want yet.

 

i haven't played since early 2002 since i don't have an instrument. (if anyone sees suttner #128 around, let me know. it's probably in ireland somewhere.) bob tedrow will be done building me a new instrument any day now. it will take me a while to get my repertoire back so i don't think i'll be playing chords for a while.

 

when i get a couple more nickels to rub together, i may get a low tuned instrument (Ab/Eb or so) and have it tuned with a traditional piping scale on D (or Bb since it's low). i really like the low-tuned pipes that willie clancy plays on his recordings and it would be nice to have an instrument tuned to match them.