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Early Tuning. How Was It Done?


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Inventor's pitch pipes sounds very plausible.


I wonder if people who had perfect pitch played a role in communicating tuning. I imagine that would a valuable skill in those days. Maybe Pythagorus had perfect pitch and that allowed him investigate the relationship between pitch and frequency.


All speculation of course, but maybe members who have perfect pitch could chime in.

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Good thinking...


There is a 64ft pipe in a local organ, one of only two in the world and I believe organists playing the other one are not allowed to use the 64ft as it has compromised the structural integrity of the building. The reason for this seeming discursion is the 64ft pipe is excited in some way by a free reed. The reed tongue may be made of wood. There are pictures but not a lot of explanation here http://members.ozemail.com.au/~googong/sydneyt.html

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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.




Ah, but whose foot did you use?

If I recall correctly what I've read on the history of shipbuilding, before the introduction of the Metre, England and each continental shipbuilding city had its own foot, which could vary a bit from the others. I wonder if this could be the reason for there being different concert-pitch tuning forks in different European cities. They might all reflect the pitch of an organ-pipe a foot long, but a different foot ...




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Since this has gone almost totally off topic, (I like the duscussion and I am learning a few things) whenever temperaments are mentioned I like to recommend the book:


How Equal Temperament Ruined Harmony: And Why You Should Care

by Ross W Duffin


Reed scaling is also a fascinating topic. Many concertinas will use the same reed frame size for up to 7 different notes to save money while some manufacturers (Wakker for example) will use a frame size for only 2 notes.


I've tuned many pianos over the years and first started by counting the beats of the overtones. I am just about to begin tuning concertina reeds and while I understand much of the theory and have enough experience to know what a good concertina should sound like, I have no idea how to physically profile a reed tongue. The best wisdom I think will be, at least at first, to just copy the existing profile, then experiment and just hope I don't ruin too many reeds.


The timbre of an instrument is a mostly a result of the number of overtones and the amplitude of overtones. This is why a flutte, trumpet, guitar, concertina sound different even though playing the same note. inharmonicity is simply that the overtones can be out of tune with the fundamental. The stiffness of a string at the ends causes higher overtones to be flat. Pianos are stretch tuned to compensate for this. Higher notes are tuned sharper, lower notes are tuned slightly flat. Apart from scaling (the physical size of the reed tongue in thickness, length, etc.) I understand the profile of a reed drastically affects the number of overtones (harmonics), amplitude of these overtones, therefore tone... the inharmonicity of these overtones.


I know that the reed must be filed perfectly flat or it can vibrate in a figure 8 pattern.


Oops, must go... to be continued...



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Thanks very much to Alex Holden and Inventor whose contributions have. for me at least, really got to the crux of this question of how Pythagoras was able to formulate a sophisticated system of tuning without the aid of a smart app. Their examples of the monochord and organ pipes measured in feet has brought home to me the precise but essentially simple mathematical relationship between length and pitch. That is, double the length of the pipe or string and drop an octave. Halve it and raise an octave. This means that note intervals can be readily quantified by physical measurement and calculations of relative pitch and temperament can be made based on length values, without needing to know the Hz values of the notes. This makes the whole thing possible a couple of thousand years before the electronic tuner. Then, as Anglo Irishman pointed out, all that was needed was for everyone to agree which philosopher's foot should be used to calibrate the tape measure!

Edited by catswhiskers
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Temperaments are tuned by counting the beats. One easy way to do this is to set a metronome to 105 and count 4 beats per tick, then you will be counting 7 bps (105x4=420), (420/60 = 7).

Set the metronome to 120 and count 4 beats per tick for 8 bps.


Set the metronome to 136 and count 4 beats per tick, that is 9 bps.




To answer the OP's original question... This method may also may be used to calculated A=440 or even old high French opera pitch A=453. As a side, we could even use 60 or 50 Hz AC hum today as a reference these days.


The temperament reference octave is then tuned using third, sixth and fifth intervals, tuning them to specific beat rates. The fifth and fourth interval for later used for testing. You can do this the other way around of course.


I digress again... Still, the biggest mystery to me is reed inharmonicity! Piano strings have a fixed inharmonicity based on the length of string, string material, bridge design etc. so that the stretch or leveling can be easily predicted and the stretch tuning of each string calculated using software. I use TuneLab.


Problem: A free reed tongue's inharmonicity is controlled by the profile shape of the tongue which is varied while filing it. Wanted overtones are tuned and enhanced, while unpleasant overtones are suppressed. I have yet to find any info on how to file a reed to adjust the pitch and amplitude of it's harmonic overtones.



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John, the natural harmonic series of the cantilever beam whether profiled or uniform thickness is non musical and non linear, unlike that of an "ideal string ". Having tuned pianos you understand how the string stiffness tends to sharpen the overtones and the lengths they have gone to with multi layer windings to try to add mass without adding too much stiffness. There is no such remedy for free reeds. The second harmonic is much sharper than an octave, the third harmonic is as much again sharper than the fifth ( off by a few notes I seem to recall ). If you plot the harmonics of the musical series 1X 2X 3X... You get a nice straight line. If you plot the natural harmonic series of a reed, you get something that looks like a steep sided parabolic curve. ( talk about inharmonicity! ). You can perturbe these natural harmonics by varying the thickness in different places, but it is a complete waste of time.

AS I HAVE SAID, the natural harmonics ( which you can excite these by slowly sweeping a variable oscillator connected to an amplifier and small speaker ) that represent the multiple wiggling modes of the reed analogous to the vibrating antinodes of a string and are at least in a long reed, quite visible with a strobe, ARE SIMPLY NOT PRESENT when the reed is driven by the air flowing through the reed. Instead when you look on a spectrum analyzer, you get a very clean musical series with little or no deviation, regardless of profile. Profile does affect the strength of the overtones, but not the frequency, as does the gap between the reed and the frame, as does the aspect ratio of the reed and numerous other factors that affect the timber much more than the reed profile.

Simply said, your concerns with profile do not need to deal with produced inharmonicity. Concertinas are not pianos where string vibration is amplified by the soundboard. The reed acts as a valve, not as a driver. The sound energy is in the pressurized air it controls.

Reed profiles are designed to produce the desired pitch in a reed whose length is limited by the available space. Low reeds taper to thick tips to add mass where the reed moves the most, reducing it's frequency over that of a level reed. High reeds taper to thin tips to allow a longer reed ( needed for balanced volume ) to reach a higher pitch, which would otherwise need an overly short , even tiny reed. The center section of the reed is more or less neutral, since the pitch raising effect of subtracting mass is balanced by the pitch dropping reduction in stiffness. This section allows you to adjust the overall reed stiffness ( needed to have all reeds sound at close to the same pressure level ) to create a balanced set. Since thinning near the center of the profile has little effect on pitch, tuning an already profiled reed by removing material in the neutral area will only weaken the reed, leaving it more susceptible to blowing flat under pressure, or choking without a large set gap and a reduction in maximum volume. Removing material where it affects the pitch most once the reed's proper stiffness is set is where you want to tune. General rules are: spread your thinning out a bit, don't make it too local, or the reed bending will focus there. Reduce the tip to raise pitch, reduce the root end to lower. For some mid and low reeds, that may have seen poor tuning, thinning at the root may cause excessive bending. For these, applying a thin coat of lead free synthetic rosin core solder at the tip will lower the pitch enough so you can remove nearly all of it to bring the reed back up to pitch. High reeds are often paper thin at the tip, but these generally require only the removal of a tiny bit of dust less than a millionth of an inch to change their pitch, but need extreme care, since it is so easy to overshoot in either direction, in contrast to low notes that change pitch much more slowly when material is removed.

There are a number of ideas about reeds that have been promoted over the years that are the result of people comparing concertinas to instruments from other families. They sound good and are usually valid for the other instrument, but don't have analogs in concertinas. Concertinas have more in common with brass or woodwind instruments, than strings, but even there, the commonality of function is minimal.


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