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Dan Stener

Timing Of A=440 Tuning

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Hello,

 

I seem to recall reading a piece that indicated when the A=440 tuning became the "standard" but cannot recall its title or location.

 

I am curious if anyone can advise if - and when - the concertina makers began tuning to the A=440 standard.

 

I will also appreciate any listing of links or other references to this topic.

 

Thanks.

 

Be Well,

 

Dan

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The international "concert pitch" of A 440 Hz was only adopted at the International Standards Association conference in May 1939. Up until then there had been no less than four pitch standards in use in England alone (at the same time !). However, the owners of instruments in the old "New Philharmonic" pitch of A 439, introduced in 1896, could almost be excused for thinking they were in "concert pitch", it being very close to 440.

 

I would suggest you take a look at Wes Williams' "Notes on Concertina Pitch" on C.net.

Edited by Stephen Chambers

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DAN: As Stephen pointed out, things were not as simple back in the nineteenth century. Note the following, however:

 

(1) a Wheatstone price list from the 1910s says that unless otherwise ordered, the concertina will be tuned to c'' = 540Hz, which puts the a' (the note that the oboe player sounds when the orchestra tunes up) at 452.5Hz;

 

(2) a' = 452.5 was the tuning that the piano manufacturer Broadwood used from at least 1852 to at least 1874; it was also the frequency to which the Philharmonic Society Orchestra tuned most often (both Broadwood and the Phil Soc Orch were in London);

 

(3) a study that's still very useful is Alexander John Ellis, "The History of Musical Pitch," Journal of the Society of the Arts, vol. 28 (1880); this has been reprinted in Studies in the History of Musical Pitch: Monographs by Alexander J. Ellis and Arthur Mendel (Buren [NL], 1968); note that Ellis himself played the concertina (he is listed in the Wheatstone ledgers), and actually had an instrument specially tuned to "just" temperament for him by Lachenal.

 

Allan

 

P.S.: Not only were there a number of different tunings in use at the same time (in terms of the frequency to which this or that note was tuned), but there were also different TEMPERAMENTS in use. Note that equal temperament (to which we are accustomed and in which all half-steps are equidistant from one another [100 cents], so that all keys sound the same), was slow to become the norm in England. The Broadwood piano company adopted it as their customary temperament only in 1846, and many an English church organ was re-tuned to it only later. Until that time, the situation is rather precarious. Some instruments were no doubt tuned in MEANTONE (the concertina was so tuned until [probably] the mid- to late 1850s, when the nature of the music that was being written for it would not longer have been playable in meantone, especially against an equal-tempered piano); other keyboard instruments, though, were probably tuned in one or another of the various WELL TEMPERAMENTS, with Thomas Young's well temperament No. 2 perhaps having been particularly popular. All in all, it is a hornet's nest, about which a gentleman in Bristol named Alexander Mackenzie of Ord has done important research. I write about the entire problem (though somewhat briefly) in a forthcoming article titled: "The Victorian Concertina: Some Questions about Performance," which, if everything goes right, will appear in a new journal called Nineteenth-Century Review, vol. 2 (2005).

Edited by allan atlas

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Apologies for a thread creep, but 'they were all related, or knew each other' comes in again - Thomas Young (of modulus fame) was a generation earlier than Wheatstone, but made his name in London scientific circles. He was born at Dulverton, Somerset to a Quaker banking family, about five miles from Taunton, where Wheatstone's wife Emma was born, and her father was a merchant.

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... equal temperament (to which we are accustomed and in which all half-steps are equidistant from one another [100 cents], so that all keys sound the same),...

Apologies to Allan, but I think this needs some clarification, since it doesn't say in what manner the musical half-steps are equidistant. Specifically, the half-step differences between notes are not equal numbers of hertz (1 hertz = 1 cycle per second), they are equal ratios of the notes' frequencies. They do not add; they multiply.

 

An octave is a doublling of frequency, so the octave above A440 is A880 (the number is the frequency in hertz) with the octave covering a difference of 440 hz ("hz" is the abbreviation for "hertz"), while the octave below A440 is A220 and that difference is only 220 hz. But 880/440 = 440/220 = 2, which is what matters. There are 12 chromatic half steps to an octave, but the differences between them in an equal tempered scale aren't equal numbers of hertz; rather it is the ratios that are the same. And what ratio is that? The number that multiplied by itself 12 times will give a final result of 2. That's called the 12th root of 2, and it's approximately 1.0595.

 

As for "cents", of course there are 100 of them per half step, because "cent" means 1/100. A cent is defined as 1/100 of the half-step interval, but in terms of hertz, the cents are different for each half step. Each cent between A880 and the A# above it will be twice as many hertz as between A440 and the A# above it.

 

If you're technically minded, you may be wondering whether the division of the half step into cents is additive (each cent with the same number of hertz) or multiplicative (equal ratios, each the 1200th root of 2). I believe it should be multiplicative, but with divisions that small the difference between the two would be hard to detect. The error from using the equal-numbers-of-hertz assumption in the range just above A440 is less than 1/100 hz per cent, and less than 0.2 hz (one cycle every five seconds) in the middle of the half-step interval.

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An octave is a doublling of frequency

Unless you are a piano tuner, in which case it is normal to "stretch" the octaves so that they are progressively slightly flatter in the low range and sharper in the high range of the keyboard !

 

But I think we have gone a long way beyond Dan's simple initial question. The subject is more than complex enough to justify a "Tuning.net" forum of its very own.

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This history of tuning and temperment is an excellent resource for those curious about the various types of tunings.

 

If you want to play with alternate tunings, by far the easiest way is with a synthesizer, since many even mid-end synths will let you adjust the tuning fairly trivially.

 

--Dave

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WES AND DAVE AND FOLKS: didn't realize that Young and Mrs Wheatstone were "paesani". . . . . .

 

i certainly did not mean to imply that Hz and cents were the same. . . .obviously they are two quite different -- and even unrelated -- things. . . . . . . .the former measures the absolute frequency to which things are tuned (if i may put it so crassly), while the latter measures the distance between the half steps. . . . . .

 

thus in equal temperament, from c natural to c sharp is 100 cents. . . . ..in quarter comma meantone it's only 76 cents. . . .so that if one plays a D-major scale that "leading tone" is going to sound rather flat. . . . . . .

 

Wheatstone, of course, got around some of the meantone "problems" (they are problems only to our equal-tempered ears) by giving alternate buttons and pitches for the D sharp/E flat and G sharp/A flat. . . . .which is why a number of the tutors from the period can offer the opinion that the concertina is more in tune than any other wind instrument. . . .. but this is another story entirely..........one having to do with the juxtaposition of a keyboard instrument against a violin, wind instrument, or voice..............

 

clearly, one could have meantone temperament or equal temperament or any other temperament regardless of whether the a' is tuned to 440, 452.5, or anything else. . . . . . .

 

what is also interesting is the tolerance that audiences must have had back then. . . . . .for instance: in 1846, Regondi gave a recital in Dresden, accompanied by Madame Louis Dulcken (piano teacher to the royal family). . . . .one must presume that she played an equal-tempered piano (that temperament having been in use for quite some time on the Continent). . . . . .on the other hand, there is no evidence that Regondi used anything other than a meantone concertina (no one seems to think that Wheatstone and the other manufacturers converted from meantone to equal that early). . . . . .yet never did any of the reviews even hint that the concertina and piano were out of tune. . . . .one reviewer mentions that the concertina is truly chromatic (that is, differentiates between D sharp and E flat and between G sharp and A flat). . . . . .but that's all he has to say. . . . . . .

 

i often demonstrate my meantone concertina using a piece by George Alexander Macfarren titled BARCAROLE. . . . .here Macfarren has the concertina sounding an "a flat" (moving towards the a natural) against a C-augmented triad (C - E -

G sharp) in the piano. . . .now even if the English piano against which the concertina was playing was in meantone (still another separate problem), the piano's single note for the G sharp/A flat pair would almost certainly have been G sharp. . . . . . .thus when the concertina player hits the A flat, there's a forty-one-cent twang between the two notes. . . . .the twang, however, is over in an instant. . . .and the ear takes it in stride. . . . .i know this because i've sometimes used the same instrument to play the "Prayer" from Molique's Six Characteristic Pieces. . . . .the Prayer is in E major. . . . . . . .and, after telling the audience what they're in for, i will play the piece sometimes using the G sharp, sometimes using the A flat. . . . . .no one ever winces more than once...................

 

Berlioz, on the other hand, railed against the instrument's meantone temperament. . . . saying that it was the work of scientists, not musicians. . . . . .remember that he would have come to know the concertina when he served as a judge at the exhibition of musical instruments in 1851. . . . . .

 

as for Young's well temperament. . . . . i've recently had wim wakker tune a late 1860s instrument to Young's well temperament No. 2. . . . . . .i use it when i take obbligato parts in performance with the New York Victorian Consort. . . . . . the audience reaction has been altogether positive. . . . .they have said that it provides the concertina with a little "distance". . . . .keeps it from being swallowed up by the piano and the voice when we're all in unison. . . . . .on the other hand, i do not use the instrument in a piece that has two long passages in G-flat major, at which point Young's temperament is furthest removed from equal temperament. . . . .when we play in unison here, it begins to sound a bit "edgy". . . . . . . . . .

 

the entire problem is a very knotty one. . . . . . .especially in terms of what temperaments were in use when. . . . . . .specialists still argue vehemently about what temperament Bach had in mind when he wrote the Well-Tempered Clavier. . . . . . there is more than a little evidence that it was NOT equal temperament. . . . .nor does "well-tempered" imply equal temperament. . . . .it implies that he used one of the various "well" temperaments. . . . . . .nothing more than that...............allan

 

POSTSCRIPT: one of the things that i've found most enlightening is moving away from theoretical discussion and actually using the meantone and Young-tuned instruments in action, both unaccompanied and against equal-tempered pianos. . . . .as i said. . . ..the ear adjusts very quickly. . . .AND NONE OF THIS, OBVIOUSLY, HAS ANYTHING TO DO WITH HZ 440 or 452 or anything else.......allan

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. . . . . .on the other hand, there is no evidence that Regondi used anything other than a meantone concertina (no one seems to think that Wheatstone and the other manufacturers converted from meantone to equal that early). . . . . .

Though I recall seeing a reference, in one of the old Free Reed magazines, to Regondi having both meantone and equal-tempered concertinas. Unfortunately the magazines are in Kilrush, and I am in Dublin at the moment, so I cannot be more precise.

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STEPHEN AND FOLKS: though he may well have had both kinds of instruments, i would ask one thing and note another:

 

(1) when did he have both kinds of instruments, in other words, how far back can we push the conversion -- even on a limited basis -- to equal temperament. . . . .Berlioz, describing what he saw and heard in 1851, talks only about meantone instruments. . . . . .

 

one of the signals that the conversion is taking place appears in THE MUSIC ITSELF. . . .(AND WE MUST START PAYING GREATER ATTENTION TO THE MUSIC). . . . .in other words, starting in the mid- and late '50s, music for the english concertina begins to break out of its C-, G-, D-, and A-major rut (which it had, to a large extent, been stuck in). . . . .pieces begin to explore more "distant" tonal regions. . . .modulations go further afield. . . .none of which would happen, i think, if the composers were writing with a meantone instrument in mind. . . . . . .there are sections of the Molique sonata in B flat, for example, particularly in the second movement, that would sound absolutely awful in meantone. . . . .even Regondi's own MORCEAU DE SALON: ANDANTINO ET CAPRICCIO-MAZURKA (Wessel, 1855) has passages in which a meantone concertina would sound awfully rough. . . .i know. . . . .i've played them on the meantone instrument. . . . .and i've played them against an equal-tempered piano. . . . . . . .my own best guess is that they started converting in the mid- to late '50s. . . .perhaps not all at once. . . .and perhaps equal temperament didn't become the customary temperament until circa 1860 or so. . . .in any event, we know that at least some manufacturers continued to produce instruments with meantone temperament. . . . .there's plenty of evidence for that. . . .Cawdell says so. . . . .the Wheatstone publicity material says so. . . . . . .Ellis says so. . . . .Ward says so. . . . .in fact, Wheatstone brags about their instruments being in equal temperament while other lesser manufacturers continue to produce meantones.....................

 

 

(2) the recital in Dresden in 1846, with L. Dulcken at the piano, was definitely on a meantone instrument. . . . .the german reviewer even makes a special point of noting that there is a difference between D sharp and E flat, on the one hand, and between G sharp and A flat, on the other. . . .this is what leads him to write that the instrument is "truly chromatic" ("wirklich Chromatik". . . or something to that effect). . . . .

 

 

as i said, it's a knotty problem. . . ..but it might only be a problem from the point of view of our ears being so accustomed to equal temperament that everything else sounds "out of tune", as it were. . . . . .flip the coin over: to audiences that were brought up with non-equal temperament, that's what would have sounded out of tune. . . .indeed, there was a famous English organist (i just don't remember his name), who, after hearing organs that had been retuned in equal temperament, vowed never to go into a church again!!!!!. . . ..he couldn't stand the way they sounded..................K N O T T Y...................allan

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A cent is defined as 1/100 of the half-step interval, but in terms of hertz, the cents are different for each half step.

Reading stuff on this a while back seemed to suggest that the cent is defined on a logarithmic scale, rather than linear?

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If we define pitch as a number so that each semitone is 1 unit higher than the previous note, setting the origin at A440 = 0

so ... A220 = -12, ..., G=-2, Ab=-1, A440 = 0, Bb=1, B=2, C=3, ...A-880 = 12, ...

 

then we can convert frequency (f) to pitch (p) by the formula:

 

p = 12 log2 (f/440)

 

where log2 means logarithm to base 2.

 

On this scale, a cent is 0.01.

 

So cents (and semitones and any other interval you choose) are logarithmically related to frequency.

 

If you want to implement this on your calculator or spreadsheet using the log function (where log is logarithm base 10 or log base e - same formula does for either so long as you are consistent), then use the formula:

 

p = (12/log 2) log (f/440)

 

where in this case log 2 means the logarithm of 2 in the selected base.

 

Or in reverse

 

f = 440 exp ((p log 2)/12)

 

where exp is your appropriate anti-logarithm.

 

We can use the formula to calculate the pitch number of 660 Hz (a perfect perfect fifth above A440, ratio 3/2) as 7.01955. So a perfect perfect fifth is nearly 2 cents sharp of an equally tempered fifth. Take 12 of them (12 fifths should be 7 octaves), and you are now about 23.5 cents sharp, nearly a quarter of a semitone, which is the amount a piano tuner is out over the (just over) 7 octave range of a piano when using perfect fifths to tune by ear, which he then has to "temper" to put the octaves in tune.

 

By the way, it is my understanding that Russian orchestras play (or at least recently still played) in a different pitch from A=440. I was at a prom concert about 10 years ago when one of the big Russian orchestras was accompanying a piano concerto. An announcement was made apologising for the state of the piano, which the tuner had tuned to 440, and on learning of his error had only half an hour or so to correct it to Russian pitch, which therefore had not been done perfectly. Not that we could notice anything of course. Though it did strike me as odd that the orchestra couldn't play to the piano's pitch (pace any xylophonist or celesta players) - what do they do when playing with an organ?

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Reading stuff on this a while back seemed to suggest that the cent is defined on a logarithmic scale, rather than linear?

That's what I was describing, though without using that big word. :)

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FOLKS: many orchestras tune to a frequency higher than a' = 440. . . . .it makes them sound more "brilliant". . . . .i forget which soprano it was who always insisted that the orchestra tune a little higher in order to make her voice sound more "BANGO!!!".............

 

AGAIN: one can tune the a' to any frequency one desires. . . . . .the issue cuts across questions of temperament..........allan

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