How to tune an instrument from scratch

[Nutball]

I'm having a bit of difficulty using google to find what I'm looking for, which is often the case in recent years. I'm curious to know how, in the old days, people made an instrument, and tuned it.

For example, if I built a piano, I now have 88 strings sounded by keys. Actually I need a rough idea of how long the strings need to be. I need to be able to find a frequency to base the tuning of all notes off of. I need to then somehow figure out how to make all 12 keys per octave an equal proportion apart in frequency, assuming I'm using the standard scale of today.

With no digital or precalibrated tools, how would I accomplish this? How could I count the frequency of each note, or what method would allow for the precise tuning of the first 12 keys, so that the rest of the notes can be tuned by ear an octave higher than the previous note?

[tpappano]

I have never tried it but in a nutshell, you start with A tuned with a tuning fork as a reference. Then, when that A is played against certain other notes you count beats between overtones, and by doing this you eventually get the first octave in tune by counting beats between various combinations of notes. I think being a wizard helps 8)

[andijah]

what method would allow for the precise tuning of the first 12 keys

Piano tuning isn't accomplished by looking at the first 12 keys of the octave/chromatic scale. So, one would start somewhere, e.g. with the a, maybe using a tuning fork as suggested by tpappano or the inner ear. The challenge is that you have more than one string hit by the hammer and all have to work together. In theory, it might be enough to tune one key after the other, start with the a, then go to a# or b flat, then to b etc. and tune them "exactly" a half tone apart. However, dividing the octave by 12 and hoping the result will sound right works mathematically, but not musically. We hear overtones as well and this has to be taken into account when tuning. There are various ways to tune an instrument (well-tempered, meantone, equal temperament...) and...

For the organ, the pitch is influenced by various parameters, and one is the length of the pipe. And so tuning in the olden days or building the organ from scratch involved a lot of work, trial and error, and measuring and listening... I don't know of a better way to describe this and am not sure you find my ramblings helpful.

Knowledge about length of strings and tuning them is supposed to be very old. It is said by some that the early hunters realised that plucking on the string of their bow made a sound and that they started experimenting. And I guess they also worked by trial and error and over the years people found out how length is related to pitch and for flutes and other wind instrument, how bore etc. made a difference, too.

[regeron]

I would assume that "in the olden days" you wouldn't have just woken up one day saying, "Today I'm going to build an organ" with no previous knowledge or experience. You would have apprenticed with someone. You would have gradually learned about woodworking and metalworking. You would have helped to maintain or repair existing instruments.

You would have learned how to tune. This usually references a specific given pitch. We now use A440 but that only became an international standard in 1955! See the wikipedia article:
https://en.wikipedia.org/wiki/A440_(pitch_standard)

My organ tech, after tuning tenor A on the Great 4' Principal to A440, proceeds by alternating ascending fifths/descending fourths so that he can stay within a range of 12 notes. He doesn't tune them pure; he knows (by hearing) how many beats there should be to be equally tempered.

A up to E down to B up to F# down to C# up to G# down to D# [[[ DOWN to ]]] A# up to F down to C up to G down to D [[[ DOWN to ]]] A.
*** The two disruptions to up-down-up-down are to stay within the octave.

ESTABLISHING THE BENCHMARK PITCH:
I suspect this would be done in a few ways.
- Tuning device - like a pitchfork or a pitchpipe.
- Size - For example, if I were making valveless brass instruments, however they coil on themselves, I just need to know how long the tube should be from mouthpiece to bell. On a pipe organ, my lowest open metal pipe of a particular rank would be 8' from mouth to top of pipe.

I haven't researched this, so would be interested to read if anyone else can share more about the history of tuning.

[andijah]

By the way, my local organ builder tunes from the lowest C upwards, whole tones, one by one. C, D, E, F#, G#, A# and so on and then C#, D#, F, G, A, B.
So there's various ways of doing it.

When you search for "tuning and temperament", there are several resources coming up with some historical information.
Example: https://www.kylegann.com/histune.html

[regeron]

When my organ tech tunes, he sets the temperament on the Gt 4' Principal as I described above. Next, he uses those 12 notes as a reference for tuning that whole rank. Once that is done, he tunes the other ranks, using the 4' as a tuning guide. For those other ranks, he also starts at low C (or tenor C, in which case he tunes the lowest octave of that rank to the octave above.)

In some organs, the pipes are arranged in two rows, end to end. These are known as the C-side and the C#-side, as the pipes go up in whole steps. There are other instances where the pipe work is divided into 3 groups or partial ranks, starting on C, C#, and D respectively, then proceeding up in minor thirds.

[Nutball]

Before checking out your link, I'd assume one could start with A, then with trial and error try to evenly space the tuning of all other notes in the octave based off the slow beating between half steps. At first I was thinking one would have to figure out the math formula to calculate the frequency for all 12 notes, then find a way of counting the frequency to get each note right. I hadn't thought of averaging the out of tune beats between half steps, but that would naturally get you a logarithmic progression.

They say even Tesla was more of a trial and error guy than a mathematician.

[myorgan]

As far as counting beats, one tuner I watched used the interval of a 10th in the higher octaves because the beats were slower (easier to count).

Michael

[andijah]

For those who want to dig deeper: http://www.terryblackburn.us/music/t...ent/stoess.htm

[Coenraads]

Tuning From Scratch: Try it

When I acquired a pipe organ in the 1970s, I tuned it using a Conn Strobo Tuner "liberated" from a dusty corner of the music room at the school where I taught. I have fond memories of the glowing tubes inside the case, and the flashing neon tube behind the spinning disc. But when I acquired a small Sperhake harpsichord, I was determined to use pencil, paper, a calculator, a stopwatch, an A440 tuning fork and my knowledge of physics to tune the instrument from scratch. In an equal temperament, successive notes are in the ratio of the 12th root of two, which a scientific calculator will tell you is approximately 1.059463... (2, y^x, 12, 1/x, =)

Starting at A440 calculate and record the frequencies of the notes above that by successively multiplying by 1.059... You'll know you're doing it right if you get 880 when you reach A an octave higher. Similarly, using successive divisions work out the octave below A 440. Now that you have the fundamental frequencies, calculate the 2nd harmonic of each note (multiplying by 2) and the third (multiplying by 3). As you peruse the three columns, you'll quickly notice that some of the harmonics differ by only a few Hz. Circle these and draw lines between them. What emerges is a pattern of fourths and fifths which will enable you to tune all the notes in a centrally located octave by counting beats.

Physics 101: Number of beats per second = Frequency 1 - Frequency 2

Trying to be accurate, I used a stopwatch to count the number of beats in ten seconds and then proceeded to tune each string in the central octave until each beat rate matched that derived from the chart. When I finished at A880 it was very gratifying to find that it was in tune with the A440 I had started with. Having thus finished "laying the bearings" the remaining notes were tuned by octaves. It was an interesting and instructive exercise and I recommend that all organists try this at least once in their lives. But do try this with a principal stop, which has all the required harmonics, and not a flute which may not.

Having already acquired a compact Yamaha tuner, I'll admit that I 've never used this technique again. Nowadays I rely on the PitchLab app on my iPad. It's an excellent tuner and has the advantage that one can program in a custom tuning such as the one used on the Wolff organ in the local cathedral.
John

[myorgan]

It's odd the title of this thread is "tuning from scratch." With cheaper tuners intended for orchestra or band instruments, I've found they don't work well for a piano when tuning the extreme highs or lows. In such cases, I actually pluck the string with a fingernail rather than using the piano key hammer. It seems to allow the tuner to decipher the pitch better by altering the overtones.

Michael

[Nutball]

My original question was how people would go about tuning an instrument with whatever was available to them at that time hundreds of years ago.

Is your Super Moderator a new status over just Moderator? I just noticed it.

[myorgan]

Nutball,

I never saw it before. New one on me! I think Admin is having fun.

Michael

[Larason2]

Not 100% related, but for piano tuning, I use “Piano servicing, tuning and rebuilding” by Arthur Reblitz. It is a great resource for learning how to tune equal temperament.

As for the original question, the ancient Greeks are credited with inventing temperament. They realized all notes had harmonics, and you could tune one note to another by selecting a frequency where there were no beats when you played another frequency at the same time. They came up with a lot of temperaments, but the only one that really stuck was what we call Pythagorean. Pythagorean is really easy to tune. From whatever your pitch standard is, you tune pure fifths (beatless) up and down until you’ve covered all the notes, then tune octaves up and down from those. For most old organs, the pitch standard was the bottom pipe, which would have been 8 feet long for an 8’ stop, 4 feet long for a 4’ stop, etc. You then tuned fifths up from that and octaves up and down for every other pipe. Later on, meantone temperaments, well temperaments, and equal temperament came along, and each have their own trick to tune, but for almost 1500 years, pythagorean was the main temperament used in the west.

[andijah]

So, back to the historical question. I don't know of any books describing the veeeery early days of tuning, but that doesn't mean there aren't any.
Since the very first instruments that people used were neither the pipe organ or the piano, whatever tuning techniques already existed when these instruments were invented, these techniques will probably have been used.
As for scales, don't forget that the scales we now use aren't that old either, and there are types of music in the world that use totally different scales than "our" major/minor system.
We never had to tune the Gamelan instruments I had the privilege to play during my music college time but if this had been necessary, a standard 440 hz tuning fork wouldn't have helped.

For the history of tuning I guess one would have to look at the history of musical instruments and also at playing together. The solitary flutist of the stone age who built him- or herself a flute from a bone might not have cared about the 440hz a if he/she was the only player

[myorgan]

We never had to tune the Gamelan instruments I had the privilege to play during my music college time but if this had been necessary, a standard 440 hz tuning fork wouldn't have helped.

Good point, Andrea.

I just learned a decade or so ago that A=440 did not become "standard" until the middle of the 20^th century. At the beginning of the 21^st century, I've noticed some orchestras in Canada & the US are beginning to use A=442 as the new "standard" in an attempt to create excitement in the performances. Personally, I wish people would just leave it alone, but I guess some feel they need to change the "standard" to create some sort of self importance and have something to pat themselves on the back for.

I wonder if that was true historically? I am referring to people randomly changing the "standard."

Michael

[Nutball]

Personally I like playing my organ transposed down 3-4 half steps (A= 350-370hz), it just sounds really good, but certain pieces of music are difficult to play transposed because my brain doesn't always adjust for it. Some pieces I seem to memorize with a pitch perfect memory, and can't play transposed by ear, only by looking at the keys.

[andijah]

Oh, I know of at least five different versions of the "standard" A. And, yes, some have to do with experiments to make an orchestra sound "brighter" or clearer. According to various sources, the A was around 410Hz in 18th century France, and Mozart liked 422Hz.
Off to (yet another) video call in a minute, but can write more about this later or whenever.

[Coenraads]

Going back to the original question, "How would people go about tuning an instrument with whatever was available to them at that time hundreds of years ago." This raised in my mind the question of how, in the absence of fancy electronic devices, one measures the frequency of a sound. It turns out Galileo had already figured that one out and reportedly used a "cogged wheel." This sounds very much like Savart's wheel which was originally developed by Robert Hooke.

As a retired physics teacher, I kick myself for not thinking of this. Savart's wheel is a staple of most physics labs and I have used it many times to illustrate the connection between vibrations and frequency. Savart's wheel has serrations on its outer edge like a saw blade. When the wheel is spun and a piece of cardboard is held against the edge, a tone of a distinct pitch is heard. The wheel also has circular rows of holes punched through the disc and a sound can also be produced by blowing a narrow stream of air through the holes.

Once accurate clocks with second hands were available, it would be easy enough to turn the wheel at a rate that produced a sound that matched that of an organ pipe say. Counting the number of revolutions per second, a simple calculation would yield the frequency. Clever!
John

[Piperdane]

A piano tuner I knew in the 60's would tune the piano completely by ear. He would start by dampening two of the three strings using a long felt strip. Then tune the single "A" string using a tuning fork. He would then tune by fifths and fourths below A (A and D, A and E). Once D and E were tuned they could be used as the reference point to tune 5ths and 4ths from it, and so forth and so on. Once the one set of strings was in tune, he would remove the felt from the other strings and tune them to each other. He could tune a piano in about an hour ... and he had the contract for doing all the pianos at Disneyland (Anaheim, CA) for about 10 years ... working there myself I would run across him tuning a piano in the park before opening hours.