Just Intonation Suggestions

[allan atlas]

FOLKS: with respect to choosing a temperament: if you have only one instrument, equal temperament is probably the best -- at least the most USEFUL -- choice. . . . .it is after all, THE STANDARD these days. . . . .and if you're going to be doing a lot of playing with piano accompaniment (as i do), you'll be hard pressed to find a piano that uses anything else. . . . . .

 

of my five instruments, three are in equal temperament, one is in 1/4 comma meantone with 41-cent differences between A flat and G sharp, on the one hand, and E flat and D sharp, on the other (and remember: it's the FLAT note that's the higher of the two), and one is in Thomas Young's "well-temperament" of 1800, which i described the other day. . . . .i find that i can play just about anything against a piano with that instrument. . . .reactions among keen-eared musicians is not that it's out of tune with the piano, but that it "stands out" a bit. . . . .even in the keys with four or five sharps or flats. . . . .it was tuned for me by Wim Wakker about two years ago, and it's become my favorite instrument. . . .i probably use it about eighty percent of the time now.................on the other hand, the meantone instrument against an equal tempered piano really will cause some twangs........

 

Allan

[Guest Peter Laban]

FOLKS:  with respect to choosing a temperament:  if you have only one instrument, equal temperament is probably the best -- at least the most USEFUL -- choice. . . . .it is after all, THE STANDARD these days. . .

 

 

Allan

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I think you will have to take into account what music you are planning on playing. One of my locals is the up and coming Irish concertinaplayer, she has a Jeffries which was obviously tuned to equal temperament. Now she uses chords and two part harmonies a good bit and anyone at the Willie Clancy concertina concert this year will have heard her playing Paidin O Raffartaigh. In this tune for example the df combination she used was one I found grating (not in the sense the tuning was out but the harmony was particularly harsh), having the f down from equal temperament would have made for much, much nicer sounds.

 

Personally I think you should go for the sweetest, best sounding harmonies you can get for your given situation and choice of music. Equal temperament is not necesarily 'the standard' in every kind of music.

[David Barnert]

...she has a Jeffries which was obviously tuned to equal temperament. Now she uses chords and two part harmonies a good bit and anyone at the Willie Clancy concertina concert this year will have heard her playing Paidin O Raffartaigh. In this tune for example the df combination she used was one I found  grating (not in the sense the tuning was out but the harmony was particularly harsh), having the f down  from equal temperament would have made for much, much nicer sounds.

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Sorry, I can't let that pass. The df interval is a minor 3rd and you are suggesting it should be made narrower than an equally tempered minor 3rd by lowering the f.

 

An equally tempered minor 3rd (3 half steps) has a frequency ratio of [the 12th root of 2] cubed, which comes out to about 1.19

 

A pure minor 3rd (up a perfect 5th (3/2) down a major 3rd (5/4)) has a frequency ratio of 6/5 = 1.2

 

So an equally tempered minor 3rd would have to be made wider (1.19 to 1.2) to make it sound more pleasing by making the frequency ratio closer or equal to the ratio of small integers.

 

Did you mean f# instead of f? Or "having the f up" or "having the d down"? Any of these would make arithmetic sense, but the statement as you've made it does not, unless you like your minor 3rds with a frequency ratio of less than 1.19.

[allan atlas]

I agree that the choice of temperament may be dictated by the repertory played. . . . .mine is mainly the Victorian classical repertory for the "English". . . . and it means playing with a piano most of the time. . . . . .so equal -- or something close enough to it (in my own case, Young's No. 2) -- is probably best. . . . .

 

in fact, one could make a case for Young's No. 2 also being every bit as much suited for the English country dance repertory. . . . .bear in mind, that England was rather late in adopting equal temperament. . . . .the Broadwood piano firm (the largest in England) did not adopt EQ as its standard until the mid-1840s). . . . .prior to that time, it's likely that the various "well"-temperaments (and these are not meantone temperaments) prevailed. . . . .there are two very good essays about just this by a fellow named Alexander Mackenzie of Ord in THE JOURNAL OF BRITISH ORGAN STUDIES. . . . one article is from 1979 (i think), the other from the '90s. . . . . .

 

there is also a fascinating document drawn up in the late 18th c. by the violinist Gemignani (i think he was the one). . . . .it shows the neck of the violin and the four strings running along its length. . . . .then it shows where to place the fingers for the various notes (and does so "in scale", so to speak). . . . .what is very clear from the places at which one should put one's fingers is this: G. is not describing EQ. . . . . .if anyone wants to know where all of this is. . .. .let me know, and i'll post it. . . .would have to dig it up...........allan

[Paul Groff]

David,

 

There is a habit in Irish music of omitting the "#" when writing the notes "F#" and "C#." This is not universal, but common enough that it is a “slang” that needs to be understood to communicate with many excellent players.

 

This may have come about through the illiteracy, or near-illiteracy, of some players and teachers (to be fair, for hundreds of years a good few of the best players of Irish traditional harp, pipes, and fiddle were blind), and from the emphasis on the natural scale of D as a point of reference, rather than that of C for “standard” (European) written notation.

 

Thus the Irish have often notated the D major scale: D E F B A B C d. I think the Scottish highland pipers use a similar shorthand. Keep in mind that in both cases (highland pipes and Irish pipes) we are talking about a very characteristic set of pitches that do not correspond exactly with the pitches that most contemporary keyboard players would have used, even back when those keyboards were also not in ET, so in a sense to notate this scale D E F# G A B C# d might also have been misleading!

 

At any rate, in his discussion of the ET'd concertina he heard I believe Peter was referring to the notes you would call d and f#.

 

Note that I do not imply by illiteracy any lack of quality! Remember Homer, et al. The finest tradition of Irish instrumental music has been described by O'Riada as an "orally transmitted art music" (i. e., not a "folk music"), analogous to the art music of India. The failure to adhere to a particular notational convention should not draw attention from the brilliance of the Irish piping tradition, in its own terms.

 

 

 

Allan,

 

One interesting source that compares several of the historically significant microtonal/enharmonic/syntonic/meantone fingering charts published for violin is P. Barbieri's article "Violin intonation: a historical survey," published in Early Music in 1991. Barbieri reproduces and analyzes the chart by Geminiani, but also those by Galeazzi, Warren, Loehlein, etc. A very interesting issue (and very relevant both to "fine traditional" and "amateur folk" fiddling) is whether the open strings were/are tuned to pure, or ET, or 1/4 comma -narrowed (etc.) fifth intervals. I'm sure there are many other reproductions and discussions of these charts but that is one article I have to hand.

 

PG

[Stephen Chambers]

There is a habit in Irish music of omitting the "#" when writing the notes "F#" and "C#." This is not universal, but common enough that it is a “slang” that needs to be understood to communicate with many excellent players.

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Agreed, indeed they likewise commonly tend to refer to "D and D" accordions, when they are referring to those in D/D#, "C and C" for C/C# and "G and G" for G/G# etc.

 

At any rate, in his discussion of the ET'd concertina he heard I believe Peter was referring to the notes you would call d and f#.

That was my understanding too. The note F natural would not normally be heard in Irish music, unless someone was playing in "flat pitch" (as opposed to "concert pitch" = D) in which case the instrument would then tend to be treated as a "transposing" one and still be described as though it was pitched in D.

Edited October 15, 2005 by Stephen Chambers

[David Barnert]

David,

 

There is a habit in Irish music of omitting the "#" when writing the notes "F#" and "C#." This is not universal, but common enough that it is a “slang” that needs to be understood to communicate with many excellent players.

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Thanks, Paul. I hoped it would turn out to be something like that, and even mentioned the possibility toward the end of my post:

Did you mean f# instead of f?

but I was not aware of the practice. I don't play traditional Irish, although many of the tunes make great contradance tunes and I play them in that context.

[allan atlas]

PAUL: thanks for the note about the Barbieri article. . . .i can get hold of that easily enough. . . . .

 

by the way: the very next issue of Early Music (due out in november or early december) will have my article about an emendation that i believe is necessary in the text of Regondi's Serenade. . . .and i use the 41-cent difference between D sharp and E flat as the basis of the emendation. . . . .would be interested to get your reaction.......Allan

[Guest Peter Laban]

The note F natural would not normally be heard in Irish music, unless someone was playing in "flat pitch" (as opposed to "concert pitch" = D) in which case the instrument would then tend to be treated as a "transposing" one and still be described as though it was pitched in D.

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At risk of complicating things a lot more: the F natural does appear in Irsh music at times, both as an f natural as understood by classical musicians as well as what I like to call the f neutral which isn't quite the f natural you'd get from a fixed pitched equal tempered instrument.

Concertinaplayers especially have to make choices here where pipers, fluteplayers and fiddlers can use the intonation desired for the tune at hand. Tunes like the Chicago reel is one common example where the f natural has taken the place (in the playing of some players at least, others may play f#) where an 'f neutral' would probably be more fitting.

It is also interesting to compare concertina players' versions of Paddy Fahey's compositions with the man himself playing them of the fiddle. Hearing Paddy Fahey made me acutely aware he is not playing in equal tempered scales.

 

And I was following the common practice of 'thinking' in the key of D when making my d-f comment.

[Stephen Chambers]

At risk of complicating things a lot more: the F natural does appear in Irsh music at times, both as an f natural as understood by classical musicians as well as what I like to call the f neutral which isn't quite the f natural you'd get from a fixed pitched equal tempered instrument.

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Peter,

 

And there was me trying to keep them "simple" , but that's one reason I was careful to use the word normally in my statement.

 

As you say, it has not always been possible to play the "right" note on fixed pitch free reed instruments, especially on the simple 2-row German concertinas, and on 10-key melodeons, where choice was limited and there has often been some "fudging" going on anyway. But the appearance of more chromatic instruments in the last 70-odd years has complicated matters further by offering choices that may not have been previously available, and ornamentation that can be harmonically "wrong".

 

It's a "can of worms" ...

[Guest Peter Laban]

And there was me trying to keep them "simple"  , but that's one reason I was careful to use the word normally in my statement.

 

 

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I know, initially I was actually more thinking of tuens like some of Sean Ryan's compositions like The Blockers which does move between f sharp and f natural but as I am more at home in the territory where notes aren't as clear cut I ended up there.

 

You're right there about the 'fudging' though, Kitty Hayes and myself have dropped the third part of Over the Moor to Maggie because of approaches C naturals that could not be made to match

[Dave Weinstein]

By "f neutral" do you mean the quarter-tone between f and f#?

 

I always liked "f supernatural" for that one.

 

If you see transcriptions of fiddle tunes that use the f and f#, that's usually a good sign that the original source was playing a non-evenly tempered note between f and f#.

 

--Dave

[JimLucas]

If you see transcriptions of fiddle tunes that use the f and f#, that's usually a good sign that the original source was playing a non-evenly tempered note between f and f#.

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Not in Swedish music.

 

I spent last Friday evening with musicians -- mostly fiddlers -- in Skåne (southernmost Sweden), playing tunes from the local folk repertoire. I'd say that at least 1/3 of the tunes they played shifted deliberately back and forth between pairs like G & G#, C & C#, F and F#, with the chords (2- and 3-fiddle harmonies) shifting as well, e.g., between G and E, C and A, Dm or F and D (major) or Bm. Several tunes included more than one such pair. But there were also a couple of tunes where an in-between pitch was definitely and consistently used, so they clearly knew the difference and made the distinction deliberately.

 

(Now what was the thread where somebody recently said that a 20-button anglo should be fine for playing Swedish music? )

[Chris Allert]

here are my ideas for a low tuned concertina:

 

on a lot of willie clancy's recordings, he plays a low set of pipes were d is about 480 Hz. this is a little lower than b (493.8833 hz) on an equal-tempered scale with a = 440 Hz.

 

here are the ratios for a just tempered scale:

 

unison: 1/1

minor second: 16/15

major second: 9/8

minor third: 6/5

major third: 5/4

perfect fourth: 4/3

augmented fourth: 45/32

perfect fifth: 3/2

minor sixth: 8/5

major sixth: 5/3

minor seventh: 16/9

major seventh: 15/8

 

with d=480, this translates to the following values in Hz

 

D: 480

Eb: 512

E: 540

F: 576

F#: 600

G: 640

G#:675

A: 720

Bb: 768

B: 800

C: 853 + 1/3

C#: 900

 

i think the augmented fourth for the G# is a better choice than the diminished fifth (64/45) since tunes in A will work better with it. my idea for a low-tuned concertina is the basic c/g layout with the above values for each of the notes. so in this system, middle c is 426 2/3 Hz. I guess this would actually be an A/E instrument with a wierd tuning, but it seems less confusing to think of it as C/G.

[Paul Groff]

Chris,

 

There are a lot of good reasons to prefer the "cents" notation and I for one am more familiar with it.

 

So, I won't comment on your "just tempered scale" except that 1) Just intonation is not tempered, by definition, and 2) so-called "just scales" in common use (with 7 notes for a major scale or 12 notes for the 12 notes/octave of a piano keyboard, etc.) actually contain some "unjust intervals," that while not tempered, are not very useful musically. The second point is the one that I made previously re: the intervals E-B and C-E. It is also the reason that I am suspicious of the frequently published statements such as "the scale in just intonation is...."

 

In fact "just intonation" refers to the purity of harmony at any one time in the music, and for many types of music, no single tuning for instruments of fixed pitch will insure that the music played will always be in just intonation.

 

Finally, it looks to me as though 480 Hz is more than "a little lower" than the B corresponding to A 440 in ET. More like about halfway between Bb and B. With this in mind, you might want to look around for an old-pitch concertina in Ab/Eb high pitch (A =453 or so) as a starting point. Jeffries made some great ones, but there are Lachenals around in that key and pitch also.

 

I'm not trying to undercut your efforts here, only to help you refine them.

 

Good luck!

 

Paul

[Chris Allert]

Chris,

 

There are a lot of good reasons to prefer the "cents" notation and I for one am more familiar with it.

 

So, I won't comment on your "just tempered scale" except that 1) Just intonation is not tempered, by definition, and 2) so-called "just scales" in common use (with 7 notes for a major scale or 12 notes for the 12 notes/octave of a piano keyboard, etc.) actually contain some "unjust intervals," that while not tempered, are not very useful musically. The second point is the one that I made previously re: the intervals E-B and C-E. It is also the reason that I am suspicious of the frequently published statements such as "the scale in just intonation is...."

 

In fact "just intonation" refers to the purity of harmony at any one time in the music, and for many types of music, no single tuning for instruments of fixed pitch will insure that the music played will always be in just intonation.

 

Finally, it looks to me as though 480 Hz is more than "a little lower" than the B corresponding to A 440 in ET. More like about halfway between Bb and B. With this in mind, you might want to look around for an old-pitch concertina in Ab/Eb high pitch (A =453 or so) as a starting point. Jeffries made some great ones, but there are Lachenals around in that key and pitch also.

 

I'm not trying to undercut your efforts here, only to help you refine them.

 

Good luck!

 

Paul

 

thanks for the comments. i was trying to base this on earlier comments about how pipes are tuned and i'm not really worried about intervals that wouldn't be played together on the regulators in irish music. as you point out, there is no "perfectly just" scale. ironing out some intervals will make other rougher. the scale mentioned earlier gives pure I, IV, and V major and minor triads in the main key. and you're right about my d being more than "a little" below b.

 

here are the values in cents taken from the music theory link i gave earlier (the last column is the difference in cents from equal temperment):

 

unison = 1/1 = 0.000 cents = same as equal temperment

minor second = 16/15 = 111.731 = 11.731 sharp

major second = 9/8 = 203.910 = 3.910 sharp

minor third = 6/5 = 315.641 = 15.641 sharp

major third = 5/4 = 386.314 = 13.686 flat

perfect fourth = 4/3 = 498.045 = 1.955 flat

augmented fourth = 45/32 = 590.224 = 9.756 flat

perfect fifth = 3/2 = 701.955 = 1.955 sharp

minor sixth =8/5 = 813.686 = 13.686 sharp

major sixth = 5/3 = 884.359 = 15.641 flat

minor seventh = 9/5 = 1017.596 = 17.596 sharp

major seventh = 15/8 = 1088.269 = 11.731 flat

 

so if i'm specifying an Ab/Eb instrument, then, following my earlier post, i might specify that Bb = 480 Hz and that Bb = unison in the above list. of course this is all specified far more accurately than a concertina can be tuned.

 

P. S.

 

in addition to major and minor triads being beat-free, all intervals relative to the drones are also beat-free

Edited October 19, 2005 by Chris Allert

[Stephen Chambers]

... of course this is all specified far more accurately than a concertina can be tuned.

Or any other instrument for that matter ...

[Frank Edgley]

All very interesting from an academic point of view. The last time I visited Colin Dipper, he played his own button accordion (yes, he does play one!) which he had tuned in some just tuning or other. I have to admit that it sounded great, as you would expect, coming from Colin. This is all well and good for someone with a keen ear, and playing solo, but not necessarily all that beneficial when playing with others, unless they, too are tuned that way; and unless you are playing with first-rate musicians, variations in playing styles and abilities might tend to cancel out benefits of any just tunings. I know ther are many musicians out there who are very skilled and may pull it off, but personally, I'm just as happy with a well-tuned instrument in the more usual tuning.