Brass age hardening

[Ben Thackeray]

I have just been tuning a friend's Wheatstone 48key English which he says was made in about 1870. It has brass reeds which do not look as if they have been tuned since new. The instrument was in a bad state when he got it and had plainly not been played for a very long time. I do not know the likely pitch it was originally tuned to but might guess A=442 or 444.

At A=444 the deviation from A=440 would be about 16cents at that frequency. (If I got my calcs right). What amazed me was the enormous range of deviation from assumed correct pitch. Many of the reeds were between 30 and 40 cents sharp. See attached chart which is with reference to A=440. These were measured with the reeds in the instrument. The deviations were spread randomly between low and high reeds. The difference between in the instrument and on the tuning table was very small. 0-3 cents. My question is - is this huge disparity normal for old instruments. In trying to account for it I wondered whether the brass in the reeds was subject to age hardening which would I assume raise the pitch. I would be grateful for comments.  

1870 Wheatstone.pdf

[Little John]

If it hasn't been tuned since 1870 then it will almost certainly be in a mean tone temperament - probably quarter comma. You can check this easily: first play the same note at different octaves together. You would hope that they sound good, indicating the instrument is basically in tune. If that's the case, now try playing Eb and D# together. If they are horribly different it indicates mean tone tuning. (Likewise Ab and G#.)

 

If possible leave it alone!

 

LJ

[Little John]

4 hours ago, Ben Thackeray said:

What amazed me was the enormous range of deviation from assumed correct pitch. ... The deviations were spread randomly between low and high reeds.

 

The way I read your chart is that, with two exceptions, the deviations from equal temperament are uniformly distributed across a range of about 45 - 50 cents. That's exactly what you would expect from quarter comma mean tone tuning.

 

As to the outliers, the one shown at -50 cents is probably misrepresented. It is probably the note a semitone lower 50 cents sharp (and therefore almost within the expected band). The note shown as 60 cents sharp is probably the only one that is actually out of tune!

 

LJ

[Ben Thackeray]

Many thanks Little John. I don't have any experience of anything other than equal temperament so I think some reading up is indicated. That would probably account for the relative closeness of the pairs of reeds which did puzzle me. The outliers were just that, not misidentified. I do not have the instrument now so I can't check as suggested. I have just tidied up the worst inconsistencies to make it acceptable to play.

[Little John]

You're welcome, Ben. Tuning temperaments are an interesting subject, to a few of us, at least! You can find lots of information on the internet, and lots of discussion of it on this forum.

 

One key factor is that in equal temperament the major thirds are 14 cents sharp of a "pure" third. Because of the strong overtones in a concertina this can make it sound quite harsh. Quarter comma mean tone tuning makes them pure and hence much sweeter sounding. Most, or probably all, early concertinas were tuned this way.

 

During the 20th century equal temperament gradually took over but there is a minority of concertina players reverting to mean tone tuning - usually fifth comma in which the thirds are not quite pure but still much sweeter than ET.

 

I read in another context (tuning church bells) that most people can't distinguish a difference of 20 cents. An English concertina tuned to fifth comma mean tone with A = 440Hz will have a maximum deviation from ET of about 17 cents (the Ab). Players of mean tone tuned concertinas on this forum have never had anyone say "you're out of tune"!

[Paul_Hardy]

As others have said, this was almost certainly tuned meantone, not equal temperament. I retuned a similar one recently, and put it in 1/5 comma meantone - see https://pghardy.net/concertina/lachenal_27590/lachenal_27590.html for details. It sounds sweet, and is within 9 cents of ET for the main keys I play in, so nobody will hear it as out of tune in a session. That link has a table of frequencies and shifts from ET.

[d.elliott]

Little John,

 

I agree that you are looking at an unequal temperament scale. However the bell tuning comparison with respect to free reeds is probably a bit misleading, one being a pulse, decaying, the other being a continuous tone emission.

 

On continuous notes, most players can pick out a 10 cent error, quite a few 5 cents. There was a debate on this forum about tuning tolerances some years ago. Whilst some players were of the opinion that with modern tuning meters, Zero Error through out the instrument from any note's nominal value was the only acceptable deviation. Obviously poppycock. Based upon reading audiological information, I chose to tune to +/- 1.5 cents from nominal, although this cannot always be achieved, it usually can. You need a meter that displays error in tenths of a cent, thus resolving to not more than 0,02 of a cent. I find that analogue meters or graphic analogue displays are too imprecise.

[Ben Thackeray]

Thanks again to all. It has been an education for me. In recording the reed frequency deviation from A=440 I adapted  another spreadsheet normally used for equal temperament accordion work where G# and Ab, and D# and Eb, are the same. This initial table of recorded deviations ( attached ) shows well the differences that mean tone produces. It is not however clear to me what the fundamental tuning frequency would have been.

Matthew's Wheatstone as found.pdf

[Little John]

On 2/23/2021 at 1:55 PM, Paul_Hardy said:

As others have said, this was almost certainly tuned meantone, not equal temperament. I retuned a similar one recently, and put it in 1/5 comma meantone - see https://pghardy.net/concertina/lachenal_27590/lachenal_27590.html for details. It sounds sweet, and is within 9 cents of ET for the main keys I play in, so nobody will hear it as out of tune in a session. That link has a table of frequencies and shifts from ET.

 

I went through exactly the same thought process and calculations before having my new Holden Crane tuned in exactly the same way: fifth comma mean tone with A = 440Hz.

 

I would endorse your recommendation of Ross Duffin's book on temperaments. The only slight annoyance is that he talks more about sixth comma mean tone than fifth comma. I can't imagine why anyone would choose sixth comma.

 

One comment: you refer to equal temperament as being 1/11 comma. Logically it is 1/12 comma with reference to the Pythagorean Comma (produced by 12 stacked perfect fifths, so reduce each by a twelfth and Bob's your uncle - ET), which is approximately the same as 1/11 comma with reference to the syntonic comma.

[Stephen Chambers]

8 hours ago, Ben Thackeray said:

 It is not however clear to me what the fundamental tuning frequency would have been.

 

That would be the pitch of A (or the relative A on a transposing instrument) which is A-444 = "Medium" or "Society of Arts" pitch, which was established in 1860.

[Ben Thackeray]

Paul - I like your review of your Lachenal tuning work thanks. I am curious as to why you didn't centre the temperament on G rather than A, being more central within your ( and my) preferred keys. Having had my curiosity stirred I have ordered a copy of the Ross Duffin book. Best wishes.

[Paul_Hardy]

1 hour ago, Ben Thackeray said:

I am curious as to why you didn't centre the temperament on G rather than A, being more central within your ( and my) preferred keys.

 

I wanted to be able to give an accurate concert pitch A=440, so that others could tune to that. There is a tradition in orchestras and string groups that everyone tunes to a given A.

[Stephen Chambers]

2 hours ago, Ben Thackeray said:

 I am curious as to why you didn't centre the temperament on G rather than A, being more central within your ( and my) preferred keys. 

 

If you centre the temprament on A, then the keys of A, Bb, C, D, F and G are all very good (whilst B is poor, and C#, F# and G# are intolerable), but if you centre it on G, then the key of A becomes poor...

[Little John]

16 hours ago, Ben Thackeray said:

I am curious as to why you didn't centre the temperament on G rather than A, being more central within your ( and my) preferred keys.

 

15 hours ago, Paul_Hardy said:

I wanted to be able to give an accurate concert pitch A=440, so that others could tune to that.

 

This is one good reason to centre on A, but there's another. It may seem counter-intuitive but centring on A actually minimises the deviation from ET in the popular keys of G and D.

 

14 hours ago, Stephen Chambers said:

If you centre the temprament on A, then the keys of A, Bb, C, D, F and G are all very good ...

 

I suspect there's a bit of confusion here (which also arose in an earlier discussion of temperaments). Ben, Paul and I are using "centred" in the sense of "matching ET" and tuning the other notes relative to that. The other notes will move increasingly far from ET as you go round the circle of fifths.

 

Eleven iterations round the circle of fifth brings you back to the note you started with if you're using ET. (That's the whole point of ET.) Using pure (Pythagorean) fifths the final fifth is too small. Using 1/4 or 1/5 comma mean tone the final fifth is too wide. It's referred to as the "wolf fifth". Because it sounds so awful you can't really play in keys that involve the wolf fifth. This limits you to six good keys (anglo or duet) or eight good keys (English).

 

"Centred" is sometimes used to describe where you place the wolf fifth, or the point in the circle opposite (really a pair of notes rather than a single note).

 

Where you place the wolf fifth, and hence which keys you can play in, is a decision which is independent of which note you have perfectly in tune with ET. It's equivalent to deciding which sharps and flats you want. The English system gives you four sharps (F, C, G, D) and three flats (B, E, A). On a duet or anglo the choice is really between four sharps (F, C, G, D) and one flat (B) or three sharps (F, C, G) and two flats (B, E) if you have a bias towards flat keys for song accompaniment, for example.

 

LJ

 

[David Barnert]

3 hours ago, Little John said:

Eleven iterations round the circle of fifth brings you back to the note you started with if you're using ET.

Twelve, surely. There are twelve notes to tune. If you start with one index note arbitrarily tuned to an external source, eleven iterations will tune all the others to that note, but it’s the twelfth that will (hopefully, if you’re using ET) take you back to the index. Like the 12 numbers on a clock. It takes 11 hours for the hour hand to point to all the numbers, but 12 to bring it back to where it started.

[Little John]

9 minutes ago, David Barnert said:

Twelve, surely. ...

 

You're right, of course, David! The mental image I had was that eleven iterations brought you to the twelfth note, leaving an interval of a fifth to return to the start note; that fifth being equal to the others only if the tuning is ET. That's what I was trying to describe in the rest of the paragraph.

 

Your clock analogy is nice. In ET the hours are the same length. Mean tone tuning (1/4 or 1/5 comma) makes the last hour too long while Pythagorian fifths make it too short.

[Theo]

No, it is 11 steps.  There are 11 intervals between 12 notes. 

[David Barnert]

5 hours ago, David Barnert said:

Twelve, surely. There are twelve notes to tune. If you start with one index note arbitrarily tuned to an external source, eleven iterations will tune all the others to that note, but it’s the twelfth that will (hopefully, if you’re using ET) take you back to the index.

 

1 hour ago, Theo said:

No, it is 11 steps.  There are 11 intervals between 12 notes. 

No, I stand by what I said: Twelve. Read it again, more carefully this time. It would take eleven steps to hit each note once, but we are talking about doing that and then returning to the first note (albeit seven octaves higher). That takes an additional step. Again, the clock face: From the XII, take a step to the I and then the II and continue to the X, XI, and back to the XII. You’ve taken 12 steps.