Unequaly Temper Tuning

[d.elliott]

This is by way of sharing information:

 

Wheatstone serial 6725 came a visiting today, it is in amazing coindition, and in its original pitch and tuning.

 

 

I calibrated my meter to the 'A's of the instrument, so all the 'A's were within 2 or three cents of 0 in both directions of play. As were 'E's, and 'D's.

Now the G's all read about +10 cents, as did 'F's and 'C's. Whilst the 'B's read -10 cents, consistently!

 

So far so good,

 

Now enharmonics:

 

in all cases the 'lower' note accidental was 20 cents flatter than I would have expected an equal temprement to be, and the 'upper' note 20 cents sharper.

 

I.E.

 

G# is 20 cents flatter than equal temprement, and Ab 20 cents sharper.

D# is 20 cents flatter than equal temprement, and Eb 20 cents sharper

 

Interestingly C# was also 20 cents flatter than I would have expected.

 

this instrument sounds sweet, is chords are beautiful, and all these comments apply and are consistent through out 6725's octaves. There was no real difference on most notes (+/- say 2 cents) between the bellows in or out directions.

 

Unfortunately 6725's owner is bigger than I am, so it went away again.

 

Dave

[Paul Groff]

Dave,

 

I understand and respect your unwillingness to claim a "false precision" for your measurements of the pitch of these notes; all seem "rounded" quite a bit to the nearest 10 cents. If you still had the instrument at hand, I would ask you to play through the circle of fifths and see if you can detect subtler movements of your meter, that are consistent for all the duplicate of the notes concerned. Something closer to the following (again this is rounded) would be expected for 1/4 comma meantone, given A as a zero point:

 

 

D# -20.5

G# -17

C# -13.7

F# -10.3

B -6.9

E -3.4

A 0

D +3.4

G +6.9

C + 10.3

F + 13.7

Bb +17

Eb +20.5

 

 

Another way to test this is by checking major thirds, which should be beatless in 1/4 comma, and fifths, which should all be about equally "bad." If some thirds are noticeably worse than average and some fifths are a little better, you may have a "modified meantone" temperament.

 

When you calibrated your meter to A, where was your pitch? I have frequently found A = 446-7 on these, which may be "Society of Arts meantone pitch" used in the mid to late 19th century.

 

Many thanks for your interesting observations!

 

Paul

 

edited to change the absolute values for Eb and D# from 20.6 (as originally posted) to a more accurate 20.5

Edited December 13, 2003 by Paul Groff

[d.elliott]

I only had around 1/2 hr to make the observations, also with people talking in the bacj ground, the 20 cents above and below zero for the enharmonics was uncannily precise, although there was some small drift between notes on opposite bellows directions I think the figure stands.

 

The 'A', 'D', and 'E' all registered as close to zero as made little difference, the 'F's were actually all closer to +12, and the 'G's closer to +8; but the conditions for measuremnet were not ideal so I rounded them a little.

 

I have looked at your scale, and I need to work it out, I am not up on things like 1/4 comma meantone, I have never heard of this before.

 

I have handled concertinas with unequal tempered tuning before, but this was my first attempt to record some data, I expected the difference, but not the degree, in the enharmonics, but not in the note fequencies

 

Dave

[d.elliott]

Sorry Paul,

 

In the distraction, I forgot to note the 'A' pitch varience, I think it was around 15 cents sharp (ish).

 

Dave

[d.elliott]

Paul looking at your scale,

 

Where is Ab? compared to G#

 

Dave

[Paul Groff]

Dave,

 

If "A" is taken as a point of reference, the value for Ab (in a 1/4 comma meantone scale) would be around + (sharp) 24 cents.

 

It was my mistake to omit this from the table above. I also was working from memory and got the values for Eb and D# slightly wrong as noted. I am making the addition for Ab here instead of in the edited table to preserve the sense of our discussion in this thread.

 

Note that all the fifth intervals are just slightly flat of equal temperament ( around 3.42 cents flat or narrow from equal-tempered fifths; of course equal tempered fifths are themselves a little narrow from pure). The major thirds, when correctly "spelled" (a-c#, f-a, c-e, d-f#, eb - g, e-g#, etc. -- but NOT e-ab) are pure as noted above, and much more beautiful than the wide thirds of equal temperament which are about 13.7 cents wider. There are some good discussions of this and other non-equal-tempered tunings and temperaments on the web, easily found if you "google" meantone, temperament, etc. David Barnert also referred us to a great site on "well-temperaments." (Search this New Forum for discussions among David, Jim, Allan Atlas, and myself for this and some additional references). In my view, the concept of "well-temperament" is not very well-defined for keyboards -- like the english concertina -- with more than 12 tones to the octave.

 

In any case, since the concertina you measured has "wolf fifths" that would not be musically useable (e. g., D# to Bb), and there are two sets of alternate enharmonics, I would include its temperament in the meantone family. If the numbers were exactly as you describe, it would be an irregular meantone temperament in which the fifths were not equally narrow. However, within the limits of measurement error, drift over time, possible retuning over the last century and a half, and even the initial tuning accuracy, I think it is very possible that the original INTENT of the maker was to put it into something close to 1/4 comma meantone (i. e., with values as noted in my table). It is also possible that some other specific temperament was intended, but of the common ones, 1/4 comma may be the best fit. But more data would be helpful (including raw data for all the duplicate notes, notes on evidence of prior tuning, evidence of reed corrosion, even valve condition or prior replacement). We will never really know EXACTLY how they were tuned when new, but with an "archaeological" approach we can make some reasonable inferences, within limits.

 

Now, I want to congratulate you for providing a great "blind trial" of this notion of measuring old temperaments. Since you apparently did not know which values to expect for this instrument (as I didn't the first time I measured one), there was little possibility of bias when you read your meter. I worry sometimes whether at this point I'm seeing what is really there (when I measure pitch values), or what I have come to expect to see! Any tuner knows that pitch is sensitive to pressure and many other factors, so if one did not always struggle to be as scrupulously objective and fair as possible, there could be a risk of getting the instrument to produce the pitches you are looking for... Anyway, I at least find that I have to make an effort to retain an open mind. And the result is, I find that different instruments (even by the same maker) seem to be tuned slightly differently.

 

Thanks for this really interesting study and for your willingness to share it. I gather you liked the sound of this tuning?

 

Paul

[d.elliott]

Wow, Paul

 

I have not taken this instrument apart, It was brought to show me by some people for whom I had done some work, on another instrument. I took the opportunity to handle the concertina, nip off and grab a meter, Seiko ST-1100, (around £100 in the UK, probably 2/3 of that in the US so not a cheapo).

 

Our wives were chatting, and we were half joining in, so there was distraction and background noise. I will see these people again in the Spring, and will try to conduct a more measured study.

 

I checked duplicate notes, saw some but little differences, and simply though of age, and that the tuning was fairly consistent say between the 'G's or the 'C's. I shall know what to look for next time and record precise values in all cases.

 

The instument is in very fine fettle, and I do not suspect any form of abuse, but as to reed condition, you never know until you look!

 

Thanks for the interest, I clearly am not up on the mathematics and the implications of my readings, or their degree of imprecision as first reported. Home work required!

 

 

 

Dave

[Paul Groff]

Dave,

 

Just to make absolutely sure you understand I mean *no* criticism whatever of what you recorded, found, and shared with us! It is very rare indeed for anyone to try this and the results are always interesting. I am very willing to accept that all your figures are exactly on the money, but wanted you to know how they compare with a "standard" unequal temperament that was used through the 1850s, and to suggest further directions that *might* be pursued.

 

As a former scientist and veteran of many research seminars (both presenting and listening) I know it is the easiest thing in the world to suggest that someone else do more research. As a practical matter this is not always possible. I myself have not had the time or resources to do the documentation I would have liked on the few (and every day fewer) concertinas remaining in original condition.

 

One reason I specified some other forms of evidence that can help us interpret the temperament of old concertinas is that some well-known concertina authorities have been sceptical that one can determine anything about how they were originally tuned. "They're all out of tune," or "the valves are always bad and when you revalve them you change the tuning" are two of many comments from one authority who I respect very much. But I disagree with him that we can't make some claims about the intent of the original tuners. We just have to be systematic, cautious in our assumptions and claims, and take the time to thoroughly assess the instrument as it arrives in our hands before leaping ahead with restoration and "corrective" reedwork. I have sketched out some supplementary clues that might help you decide which of two or three different values for a given note might be most original.

 

One explanation for your figures, if they are exact and not rounded estimates, is that the instrument might have been in 1/4 comma meantone or something close to it, then at some point the tuning drifted and at a later date a tuner not trained in the details of meantone "regularized" a few out of tune notes so that they were in tune with one another but perhaps not quite at their original values. If the D were originally "0" and the G "+8" cents, the fifth G-D would be extremely narrow and harsh. Again, if E is "0" and B "-10" then the fifth E-B would be even narrower and more unpleasant. Not to say this could not have been done, but with an overall range of -20 to +20 cents for the 14 notes D# to Ab (as you report), such narrow fifths could have been avoided. But if the E were a little flatter and the B a bit sharper (as shown in my chart), the thirds in which these notes participate (c-e, e-g#, g-b, b-d#) could be pure and the fifths much better than the reported values. If you are willing to compromise the purity of the thirds, you can improve the fifths even more (e.g., 1/5 comma and 1/6 comma regular meantone), or alternatively you can use an irregular meantone in which not all fifths and thirds are equally consonant.

 

Again, good work and many thanks. I think it's great that this instrument's owner has been able to enjoy it without (yet) thoroughly modernizing its pitch and temperament. If you are interested in further study of this and related tunings, you could easily find a cheap brass-reeded tutor 48 to experiment with meantone, etc. If it is not a high quality one, if it's overall condition is well-worn or even wrecked, and if the reedwork is not original, what's the harm in using it as a guinea pig? You might even find another early one in high pitch that's still more or less in an old temperament.

 

Paul

Edited December 14, 2003 by Paul Groff

[john]

I just noticed this book from Dover books catalog. Don't know if it will be of any interest but here it is:

 

Tuning and Temperament: A Historical Survey

 

J. Murray Barbour

Our Price $13.95

Availability: In Stock

(Usually ships in 24 to 48 hours)

Format: Book

ISBN: 0486434060

Page Count: 240

Dimensions: 5 3/8 x 8 1/2

The demands of tuning (attaining the perfect scale) and temperament (the compromises necessary for composing in every key) have challenged musicians from the earliest civilizations onward. This guide surveys these longstanding problems, devoting a chapter to each principal theory and offering a running account of the complete history of tuning and temperament. Organized chronologically, the book features a helpful glossary and numerous illustrative tables, and it requires minimal background in music theory. This new reissue is currently the only edition in print of a much-quoted classic. 9 figures. 180 tables.

[Theo]

Dave, paul

 

I have read this thread with great interest

 

My first instrument is a two-row melodeon/diatonic accordion. It has always struck me as a completely unnecessary musical compromise to use equal temperment for an instrument in which it is impossible to play in all keys! I have strted reading some of the literature on historical temperaments and plan at some satge to start experimenting with non-equal temperaqment tuning.

 

I have been prompted to go in this direction by an apparent increase in sensitivity to mistuning since I stared runing and repairing instruments over the last 2 or 3 years.

 

My question is where to start. There are several well documented tmperaments to choose from, and there is also the question of the "based" key to which the temperament is related. All the literature I've seen so far is written for piano type keyboard tuning, where C is the starting point. I'm asuming that on say a D/G diatonic instrument it would be more sensible to use D or G as the starting point.

 

Am I on the right lines?

 

Theo

[JimLucas]

...I stared runing and repairing instruments over the last 2 or 3 years.

The word you typoed was "tuning", not "ruining". Right?

[A.D. Homan]

[...] there is also the question of the "based" key to which the temperament is related. All the literature I've seen so far is written for piano type keyboard tuning, where C is the starting point. I'm asuming that on say a D/G diatonic instrument it would be more sensible to use D or G as the starting point.

 

 

 

Hi Theo,

I'm really interested in this, too, and I'm going to start a thread over on melodeon.net so that we don't get too far off-topic here on c-net. (Since a C/G concertina, for instance, is often used to play in D, which would be considered to be pretty far off the beaten path for G/C melodeons, for instance.) See you over there...

-A.

[Mark Stayton]

I just noticed this book from Dover books catalog. Don't know if it will be of any interest but here it is:

 

Tuning and Temperament: A Historical Survey

 

J. Murray Barbour

Here's another for the historical tuning aficionados in the audience:

 

Tuning: Containing the Perfection of Eighteenth Century Temperament, The Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament

 

Complete With Instructions for Aural and Electronic Tuning

 

Owen H. Jorgenson

Michigan State University Press, 1991

ISBN: 0870132903

798 pp

 

 

Cheers,

Mark

[Jamie Boorer]

The above is currently on amazon.co.uk for 5 pence less than £200 - Jamie.

[A.D. Homan]

The above is currently on amazon.co.uk for 5 pence less than £200 - Jamie.

 

 

Sounds like a job for "interlibrary loan," not Amazon.