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Early Tuning. How Was It Done?

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In our computerised age even those with limited talent can achieve what was once the preserve of specialists and craftsmen. I'm fairly musically illiterate yet I have successfully tuned two anglos, one to ET A440, another to Society of Arts pitch, quarter comma meantone - with the aid of a tuning app on my smartphone! What intrigues me is how the same or greater degree of accuracy and complexity was achieved by tuners working in the nineteenth century or earlier. How did they do it? How did they measure the small variations in vibrations between notes in different pitches and temperaments? Did they have super-accurate pitch recognition? Or did they rely on an extensive range of tuning forks or pitch pipes, and if so, how were these calibrated in the first place? I would be very interested to hear if anybody has any knowledge of this subject. Thanks. John

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What I have noticed is that piano tuners nowadays tune only the central octave of a piano using an electronic tuner, and tune the upper and lower octaves from it by ear. They don't aim for an exact Herz value in the upper and lower ranges - they "stretch" the octaves, making the highest notes slightly sharp and the lowest notes slightly flat. They sound more "in tune" that way.

I've noticed the same with my autoharp. If I have the highest couple of strings dead on the tuner, they sound (ever so slightly) flat and lacking in brilliance when I play them as part of a long strum.

 

Perhaps because of this experience, I find that free reeds - specifically my (professionally tuned) Lachenal Crane duet and Hohner mouth organs - give me an uneasy feeling when I play the very highest notes on them.

 

Perhaps electronics make things easier - but not better?

 

Cheers,

John

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What I have noticed is that piano tuners nowadays tune only the central octave of a piano using an electronic tuner, and tune the upper and lower octaves from it by ear. They don't aim for an exact Herz value in the upper and lower ranges - they "stretch" the octaves, making the highest notes slightly sharp and the lowest notes slightly flat. They sound more "in tune" that way.

I've noticed the same with my autoharp. If I have the highest couple of strings dead on the tuner, they sound (ever so slightly) flat and lacking in brilliance when I play them as part of a long strum.

 

Perceived pitch does not always precisely correlate with absolute frequency. Maybe this is an example of that? The example I'm most familiar with is from playing an instrument -- whistle or concertina -- on a subway or railway platform as a train roars into the station. The presence of the background noise can cause the perceived pitch to change by a semitone or more. (At least it did for me, and I've tested it multiple times in multiple stations.)

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When members of a classical orchestra have a final brief tune-up on stage, immediately prior to embarking upon a performance, they are each ultimately relying upon there own ears to be the final arbiter and it will be the ears of others that they will be hoping to satisfy ?

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In our computerised age even those with limited talent can achieve what was once the preserve of specialists and craftsmen. I'm fairly musically illiterate yet I have successfully tuned two anglos, one to ET A440, another to Society of Arts pitch, quarter comma meantone - with the aid of a tuning app on my smartphone! What intrigues me is how the same or greater degree of accuracy and complexity was achieved by tuners working in the nineteenth century or earlier. How did they do it? How did they measure the small variations in vibrations between notes in different pitches and temperaments? Did they have super-accurate pitch recognition? Or did they rely on an extensive range of tuning forks or pitch pipes, and if so, how were these calibrated in the first place? I would be very interested to hear if anybody has any knowledge of this subject. Thanks. John

 

What I have noticed is that piano tuners nowadays tune only the central octave of a piano using an electronic tuner, and tune the upper and lower octaves from it by ear. They don't aim for an exact Herz value in the upper and lower ranges - they "stretch" the octaves, making the highest notes slightly sharp and the lowest notes slightly flat. They sound more "in tune" that way.

I've noticed the same with my autoharp. If I have the highest couple of strings dead on the tuner, they sound (ever so slightly) flat and lacking in brilliance when I play them as part of a long strum.

 

Perhaps because of this experience, I find that free reeds - specifically my (professionally tuned) Lachenal Crane duet and Hohner mouth organs - give me an uneasy feeling when I play the very highest notes on them.

 

Perhaps electronics make things easier - but not better?

 

Cheers,

John

 

This may be of interest Tuning.doc

 

However, what was used to accomplish tuning of tuning forks etc., I have never found a definitive answer.

 

Geoffrey

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Stretch tuning on a piano with 8 octaves is needed due to the large range in pitch. I doubt however if the experience is a linear one, but instead feel like the perceived flatness increases in the highest octaves more than lower ones. While concertinas don't have that range, lots do go very high, C7 and above. So they are still vulnerable to the effect. Tuning is always a compromise though, and what sounds best often depends on the kind of music played. If you just play single note melody, slightly sharpening the upper octave might be a good idea, but if you use the higher notes in chords, pairs or octaves, such out of tuneness becomes quite noticeable, especially since the beat rate for octaves that are only off a cent is much higher in upper octaves than lower ones. Throw in the problem of reeds not being pitch stable like tuning forks, but varying in pitch with playing pressure, bellows extension and the like, and your best tuning efforts might produce results that vary from session to session. ( though not by a lot )

My piano tuner still just uses a tuning fork, but does a brilliant job. They all have to take tests to be able to accurately gauge the number of beats per second in intervals by ear to determine the stretch among other things. I cringe at sessions when people bring out the little electric box. Being able to tune by ear is seeming to be becoming a lost art. Heaven forbid your batteries are dead!

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It does appear that tuning by ear may be becoming a dying art. Of course, electronic tuners do have their uses, especially when on stage. Tuning a hammered dulcimer by ear from a tuning fork was a laborious and slow process (how long does it take to tune a dulcimer? - no one's ever found out) and an electronic tuner makes it much easier. However when tuning my guitar I prefer to use a tuning fork for the A string and tune the others by ear. The electronic tuner may give an exact pitch but it doesn't always sit right with the other strings.

 

I have no experience of tuning concertina reeds but I find it significant that both Geoff Crabb and his father preferred to tune by ear.

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Tuning a hammered dulcimer by ear from a tuning fork was a laborious and slow process....

I was working once with a hammered dulcimer player who needed to tune his instrument. He was surprised, but quickly enthusiastic that I was able to supply each and every note from my concertina (and in any order requested). Said he'd never managed to tune his instrument so quickly before.

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Dulcimers are frustrating things to tune. With courses of 4 strings, all supposedly tuned in unison, the only string which is not quite in tune seems to outvote the others which are. To add to the fun, the treble courses run across a bridge, so they each play two notes, but both sides are tuned from the same set of tuning pegs and you have to try to tune one side of the bridge without upsetting the tuning of the part of the string on the other side :( .

 

Whereas my concertina I just take out of its box and start playing :) . Of course, when that needs tuning ...

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I used to build Hammered Dulcimers, so am familiar with the beast, though I found them very natural to tune if the bridges were properly placed. I use a decent electronic piano tuner for my concertinas because it only listens to the pitch to be tuned and isn't dragged of by strong harmonics which can be trouble in both low and high notes. ( I don't use the FAC stretch function though )

Regarding something Geoff mentions in his excellent article about inharmonicity in reeds. I have found my reeds to be remarkably "harmonic" ( unlike piano strings ) through their audible range. I don't think this is due to something special about my reeds, but wonder if the issue isn't that each reed's harmonic series uses itself as its root note, and even if it is in perfect tune with itself, it isn't going to be tempered in any way at all., so is bound to clash with some other notes. Since the first three or four harmonics in reeds are quite strong ( though they quickly become inaudible in the higher notes, ) you can only count on the second harmonic ( octave ) to have the same relationship to the rest of the notes as the fundamental. Making judgement calls as to how to "level" the instrument would seem then to make key choices about the notes to adjust, especially since you can't single out a harmonic to tune in exclusion to the rest of the reed. ( reed harmonics in playing are not caused by the reed vibrating in different modes like a piano string or even the cantilever bar it is, which has no musical harmonics at all, though the second is close to the octave if sharp. A plucked reed can vibrate in those modes, but when air driven, they don't appear. )

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They used a tuning fork as a starting point reference then compared similar harmonics counting the beats to get the correct temperment. Once the middle octave was in tune to the correct temperament, this was used as a reference for the rest of the instrument. Please look up "inharmonicity" and "Pythagorean comma" for more interesting info on this topic...

 

I've heard that Lachenal supplied complete sets of in-tune reference reeds to sub-contractors who would then tune raw reeds to the reference reed pitches. The pitch of the reed out of the instrument is different from when it is in the instrument. The mystery to me is how they got the right profile of the reed tongue enhancing/suppressing certain harmonics and tuning these harmonics is the big mystery to me. See inharmonicity on Wikipedia.

 

Thanks,

John

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They used a tuning fork as a starting point reference then compared similar harmonics counting the beats to get the correct temperment. Once the middle octave was in tune to the correct temperament, this was used as a reference for the rest of the instrument. Please look up "inharmonicity" and "Pythagorean comma" for more interesting info on this topic...

 

I've heard that Lachenal supplied complete sets of in-tune reference reeds to sub-contractors who would then tune raw reeds to the reference reed pitches. The pitch of the reed out of the instrument is different from when it is in the instrument. The mystery to me is how they got the right profile of the reed tongue enhancing/suppressing certain harmonics and tuning these harmonics is the big mystery to me. See inharmonicity on Wikipedia.

 

Thanks,

John

Inharmonicity generally refers to the lack of tracking of the produced harmonics with the idealized series, where the harmonic frequencies are in whole number multiples of the fundamental. In stringed instruments, the inharmonicity results from the inherent stiffness in the string material, which tries to make it vibrate as a bar, who's natural harmonic series rises much faster than whole number multiples and is not linear, producing a sharpened harmonic from the ideal string, which has no stiffness, ( stiff low piano strings have high inharmonicity, while nylon or fiber core strings have a relatively low inharmonicity.

While free reeds do have a harmonic series that is created by the feed vibrating in multiple modes ( single where the end moves up and down, double where the reed moves in a modified S shape, and higher modes where the reed vibrates in varoisly humped wiggles. ) the frequencies of these bear no resemblance to the linear musical harmonic series and are non linear. Varying the profile does affect these harmonic frequencies as the thin and thick parts of the reed come into and out of congruence with the bending parts of the reed. However as mentioned in my previous post, , when reeds are activated by airflow, the natural frequencies the reed is capable of vibrating in do not occur except in rare circumstances with a low set reed that starts as a high whine, not the fundamental. Instead, the reeds/airflow combination produces a remarkably true linear harmonic series, which profile variations only affect with regards to the strength of the harmonics, not the frequency of them. This is not theoretical stuff, but from experiments that produced that produced results that were completely different than I expected. Benade attributes this difference between natural and air driven frequencies as the results of hetrodyning. Other people disagree. I have not seen anything I consider definitive about why the air driven series is the linear musical one and not the cantilever bar one.

Regardless, it is plain as you say, that a tempered octave will produce higher and lower tempered octaves, what this has to do with Geoff's " leveling" process, I don't know. It was my understanding from his article that the leveling process corrected errors that strict octave tuning produced.

Dana

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There's a book about the evolution and history of the many approaches to tuning -- not specific to concertinas, admittedly. It's called "Temperament" by Stuart Isacoff, Alfred A. Knopf, NY, 2001. Yes, it goes into great detail about the many ways that musicians dealt with tuning over the centuries -- philosophical, practical, aesthetic, mathematical, and so forth. Can be rather heavy reading, tho' it does cover a lot of the ground discussed above.

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And there is a huge amount of information on the web about tuning. Searching for "historic temperaments" will get you started.

 

But back on topic: Accordion tuners also used the method of having a set of reference reeds covering an octave, or sometimes a little more. These were fitted into a tuning table with simple hand operated valves to send the air to the required reference reed. There are pictures of one on Johann Paschers web site

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Thanks to all for the many interesting replies, some of which have gone far beyond my original, essentially practical question, and some, I have to admit, a little above my head! Nonetheless all fascinating stuff and I for one have learned a lot. I think my original question as to how tuning was done in the nineteenth century has been pretty well answered. But not the question of how the tuning aids they used were originally callibrated. Or going back a bit further, how for example did Pythagoras measure the precise frequencies of notes in order to calculate the complex mathematical relationships within music? Unless I've missed something I think those questions still remain unanswered - but I'm sure someone out there knows.....

John

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I thought the most interesting part of your question was 'how were early tuning forks calibrated' and was hoping someone would reply with the answer. There was no way they could have counted 440 hz but perhaps a very low note was analysed by some method such as allowing the bottom of the fork to agitate ripples in a body of water which could be counted arriving at the other bank because they had grown larger. Or counted by using a strobe such as a rotating disc with holes (which would only need to be a candle powered) to visually stop the wave motion. This low note/low count could be scaled up in frequency using beat counting.

 

It is possible no precise calibration was needed. As long as everyone agreed a particular fork was "the one" then you could call it A, everyone could copy it and no-one could argue. When precise metering was available the note could be shifted to conform, much like the metre changed from being the length one of a steel bar in a Parisian vault to a number of wavelengths of a emission line of krypton-86.

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I think Chris is right, until relatively recently the 'standard' pitch would be decided by a group of musical big-wigs getting together and agreeing what it ought to sound like. It varied from city to city and changed over time (apparently 'pitch inflation' was a much-debated problem).

 

There is a tool called a monochord (constructed a bit like a one-string guitar) that has historically been used to experiment with different temperaments.

https://en.wikipedia.org/wiki/Monochord

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It occurs to me that organ builders refer to the pitches of the various "C"s as - 1 foot., 2' (middle c'), 4' (tenor c), 8' (bass C), and so on; corresponding to open organ pipes of that length. Is it possible that the original reference was not a tuning fork but a pitch pipe, one foot long. This could not only be easily carried around, and sounded loud enough for a choir to hear; but could be reproduced to approximately the same pitch, without any direct reference to someone else's one foot pitch pipe.

 

Inventor.

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