Learning to tune ...

[Paul vdV]

After doing some small scale revalving and rewaxing I wanted to make the next step: tuning an accordion.
Some time ago I bought a cheap Hohner Club IIB (Yes a melodeon, but not too big. The construction was another puzzle, but has been solved, too.) Sounding the thing made it clear that all the reeds were sounding, but way out of tune, no music could be played. Fine experimental instrument to me. The bass side is working now, so time for the treble side.

So for the last weeks I have been searching the web (including this fine forum!) for information, especially on the musette tuning for the offset reeds.. There is a lot of information. Still things kept being vague to me. Then I came across the the videos bij Lester Bailey. He has a great series on hot rodding a Hohner Melodeon. (In my opinion, maybe the best series on YouTube at this moment on free reed instrument repair?) In the installment on tuning the treble reeds he links to the table he uses for tuning the offset reeds. It is this link.


On this there are three rows with numbers that give the amount of cents you have to tune the offset reeds higher to reach a certain amount of musette. Analysing the three rows I realised that there are two factors in play: the amount of tremelo you want, indicated for the A4 reed (which can be anything between 435 Hz and 445 Hz) and the rate in which one wants the tremelo to be in the higher and lower reeds. The Hohner row lowers the amount of cents by 6 each octave. The other rows on the table use different amounts, though this doesnt seem to be an arithmetic relationship that I can discern.
To check myself I, I downloaded the Instrument-tuner. This enabled me to see in wave form two sounding reeds in an accordion and made notes of the values I saw. Since I started to get into accordions 2 years ago I was given several accordions by friends. I have about 7 now, one bough second hand. Although most are in need of tuning, the tuning patterns were clearly visible. All this information, together with the formula to calculate the next note from an original note, was compiled into Excel. I introduduced the 3 variables mentioned in the worksheet. Doing this I was perfectly able to reproduce Lester Baileys tuning chard for the 3 tunings it contains. Furthermore I was able to reproduce a very nice tuning a professional did in my Hohner Tango II, as well the standard tuning Hohner has used for the 2-reed musette sound. The results are included in the Excel sheet. So, by putting all this together, one can calculate the several musette tunings which are mentioned on the internet for tuning purposes.

I know that it is perfectly doable to tune the offreeds by counting the beats, doubling this for the octave and subdividing for the notes in between, it is just me wanting to understand how this all works ...

This all leaves some questions open:

• Am I missing things?
• The amount of cents that goes down with each climbing octave: is there some reasoning behind this that someone can explain?

The Excell sheet is below

For those who want to improve on the file: the unlocking code is accordion

 

[debra]

First of all you need to ensure that the non-offset reeds are tuned "perfectly" (ideally within 1/2 cent, allowing for more tolerance on very low notes).
You need to ensure that when you play octaves together there is absolutely no beating. Professional tuners not only use a measuring device but also check by ear in the "standard" octave that the quarts and quints have the same slow beating.
For the tremolo you first have to decide how much tremolo you want. All your accordions are probably different. Decades ago the general trend was for more tremolo than nowadays. There is no absolute consensus on how the tremolo changes as you go up the scales. Two extreme approaches are:
1) Keep the number of beats you hear constant. That means the deviation in cents one octave higher is 1/2 of what it was. So if A4 has 10 cents tremolo A5 has 5 cents.
2) Keep the octaves 100% dry in the offset reeds, which means keeping the deviation in cents constant. A5 then has twice as many beats as A4.
Real world tuning sits in between these two extremes. What you do is that when you go up one octave you keep about 2/3 of the deviation in cents. So if A4 has 10 cents tremolo then A5 has around 6.5 cents (and A6 has just over 4 cents). When you go down in frequency you "max out" the deviation in cents. So if A4 has 10 cents tremolo then A3 will not have 3/2 or 15 cents but a bit less.
The table you posted reflects this real world tuning.
What the table does not tell you is that the final judgement must come from your ears. The tremolo is right when it is right to your ears, no matter what the tuning app says.
Note: because the deviation in cents does not stay constant the octaves in the offset reeds are not completely dry. You should check that the "wetness" of these octaves is low and consistent as you go through the octaves.

 

[Paul vdV]

First of all you need to ensure that the non-offset reeds are tuned "perfectly" (ideally within 1/2 cent, allowing for more tolerance on very low notes).
You need to ensure that when you play octaves together there is absolutely no beating. Professional tuners not only use a measuring device but also check by ear in the "standard" octave that the quarts and quints have the same slow beating.
For the tremolo you first have to decide how much tremolo you want. All your accordions are probably different. Decades ago the general trend was for more tremolo than nowadays. There is no absolute consensus on how the tremolo changes as you go up the scales. Two extreme approaches are:
1) Keep the number of beats you hear constant. That means the deviation in cents one octave higher is 1/2 of what it was. So if A4 has 10 cents tremolo A5 has 5 cents.
2) Keep the octaves 100% dry in the offset reeds, which means keeping the deviation in cents constant. A5 then has twice as many beats as A4.
Real world tuning sits in between these two extremes. What you do is that when you go up one octave you keep about 2/3 of the deviation in cents. So if A4 has 10 cents tremolo then A5 has around 6.5 cents (and A6 has just over 4 cents). When you go down in frequency you "max out" the deviation in cents. So if A4 has 10 cents tremolo then A3 will not have 3/2 or 15 cents but a bit less.
The table you posted reflects this real world tuning.
What the table does not tell you is that the final judgement must come from your ears. The tremolo is right when it is right to your ears, no matter what the tuning app says.
Note: because the deviation in cents does not stay constant the octaves in the offset reeds are not completely dry. You should check that the "wetness" of these octaves is low and consistent as you go through the octaves.

Thank you for your wisdom, Paul. I appriciate the view that ulimately one's ears have to decide. 

I am triggered by " ... about 2/3 of the deviation in cents." Have to think about that ... The Hohners I measured were surprisingly close.

 

[Glug]

I'm quite interested in how this all works, but I haven't tried tuning anything yet.

Here's the tuning on my 1959 Hohner Lucia IV P

But I'm fairly certain it hasn't been tuned in years.

It is actually around 16.5 cents at A4, but the slope isn't linear.

I measured the tuning after I bought it in a spreadsheet, which generates the graph above.

Now I'm thinking I should add some beat progression curves

 

[Paul vdV]

Thanks for the graph.

Maybe I will put the number of beats in the sheet ...

I have seen the sloped lines. That was one of the reasons I made the Excel sheet. It would be easy to put in a curved line, but when Hohner seems to tune in a linear fashion, I would like to hear arguments why and how this should be ... also the "about 2/3" is still linear ...

Maybe I'll do a search for more graphs like this one and see if a compilation into Excel helps to solve this riddle ...

 

[Glug]

Theres quite a lot in Accordion Revival part 3 (http://accordionrevival.com/ACCORDION_REPAIR_3.php).
He mentions The ins and out of the Accordion by Thierry Benetoux:

Although Mnsr. Benetoux has drawn simple straight lines to represent each of his curves, none of his curves are actually simple straight lines. If you plot them on graph paper with the 41 key scale across the bottom, you can readily see that they all have an inflection point somewhere in the first half of the keyboard, after which the curve rises more steeply.

Then theres a nice graph.

And I did see a discussion about beat progression curves somewhere else that I cant find at the moment.

 

[Paul vdV]

Thanks, I saw that one, too. Don't know why it is so ...

 

[debra]

The 2/3 rule that I roughly use sort-of keeps the middle between keeping beats constant, which sounds too dry in the high notes, and keeping the tremolo in cents constant, which sounds too wet in the high notes. In the end it's all about what your ears tell you is right.

 

[Glug]

The other place I read about tuning was in usenet groups (now google groups) which is all a bit old, but I doubt tuning ideas change that fast.
Theres years of information in there but it takes a lot of searching to find anything usefull.


rec.music.makers.squeezebox: https://groups.google.com/forum/#!forum/rec.music.makers.squeezebox


In particular a post from Mario Bruneau on 2006/06/22, but the links no longer work since hes moved his web site:

Get my MP3 file of my composition la voix des anges (Angels voices) and listen

to the modern french musette tuning I did on my Brandoni PA.

http://www.abcde.net/mariobruneau/voixdesanges.mp3

Then, check the chart I have made to illustrate this tuning in my
Accordion Multimedia Conference.

http://www.abcde.net/mariobruneau/cents3.jpg

You can show this chart to your tuner as well as have him to listen to
my recording of la voix des anges.  Further more, the third middle
reed in an MMM configuration, I tune it to twice the value of the
violins sharp second reed.  Here it is:

M = A440Hz    0 beat/sec      0 cents
M = A441.5Hz  1.5 beat/sec    6 cents sharp   VIOLIN
M = A437Hz    3 beat/sec     12 cents flat    MUSETTE

 

[Glug]

Having reread the Accordion Revival tuning page and looked at the graph a bit closer I tried fitting the Lucia tuning against a linear increase in bps.

Yellow line is 1.7bps at F3 and 7bps at F6 and linear inbetween:

It looks like a close match.

Accordion Revival says an option is a slower rise at the start and faster at the end.

Edit: fixed A3 typo

 

[Glug]

Last post - I'm not trying to take over the thread

I made the spreadsheet do a least squares line fit to the measured beats per second and then generate a bps and cents curve from that:

Yellow is line fit bps, green is line fit cents.

The fit was 1.71 bps at F3 and 7.06 bps at F6, which gives 16.01 cents at A4 which is about "German Musette" tuning.

I'm convinced this works as an explanation of how this was tuned.

 

[Morne]

In terms of tuning beats, Ill try to write some more over the weekend, but for now Ill leave you with this intentionally messy looking chart showing the beats for the sharp reed:


The general idea there is your Hertz/beat curves are based on an exponential formula. This is described in Toni Schwalls books on tuning. The majority of those are from actual instruments, although Ive just identified them with the table name used in the book. Im not sure if they are literally correct for the original instruments, or if Toni tried to fit the best curve through them.

I also tried to plot some of Benetouxs curves based on whats written on Accordion Revival, but I believe I am a bit off there (I need the A4 and A5 beats to calculate these curves, otherwise I need to fiddle around and guess until it gets close).

The black lines represent some research done in Russia in the late 70s. It shows what the researcher (Porvenkov) concluded to be the optimal maximum (wet) and minimum (dry) curves along with what he considered to be the most optimal tuning (for some kind of light pop music). Of course, this is like asking whats the optimal colour?. Anyhow, should you wish to go down that rabbit hole, here is a Google Translated version of it:
https://translate.google.com/translate?sl=auto&tl=en&u=https://poigarmonika.ru/garmon-tehnicheskie-aspekty/26-optimalnyi-rozliv-v-nastroike-yazychkovih.html

The jagged line in there represents a Hohner tuning method. Its a bit unclear in that messy chart, so here it is by itself along with the cents:

The jagged lines are based on a process described by Wolf Linde (at Hohner). Apparently the first version of the repair manual describing this process was published in 1978 (according to Toni Schwalls bibliography, although I have a much more recent copy with two copyright dates of 1999 and 2007). Essentially it involves using a tuner and changing your reference A4 and then tuning the reeds to zero beats. Reference A4 is then changed again and the next octave is tuned to 0 beats. Since that results in some weird jumps in the beats, when you apply the exponential method but using the same A4 and A5 you get the smoothed curve. The rough parameters there are A4 = 4 Hz (15.7 ct) and A5 = 7 Hz (13.7 ct).

As for how long Hohner used that method and whether they used that for all their instruments, I dont know.

---

Professional tuners not only use a measuring device but also check by ear in the standard octave that the quarts and quints have the same slow beating.

I just want to make sure I understand what that achieves. Does that mean that you end up with a noticeable difference compared to equal temperament, or does that refer to the method used to tune equal temperament when you dont have a tuner available? The latter is described in Toni Schwalls book and you end up with something like this



The idea is to set A4 correctly according to a tuning fork (or some other source) and then tuning those intervals (quarts and quints) by counting the beats (produced by the harmonics). At the end you have that one octave thats as close to equal temperament as you can get without using an actual tuner. And then you tune the other octaves to zero beats based on that octave. But I doubt those small differences to ET really make much of a difference. However, if it does, then you could just set a digital tuner to those slightly different values and you should end up with the same results without all the effort of literally counting beats with a stopwatch or metronome.

 

[Glug]

I definitely don't understand that yet, I'm going to have to read it a few more times

I've seen something like the first graph before somewhere.
It's interesting that Toni Schwall says to use exponential curves mostly, but 2 of them do seem to be linear.

And that rusian reference is great, if a little difficult to understand in translation.
As you say "what's the optimal colour" and tastes in musette have changed over the years.
But the "optimal bottling" curve is something I'd like to hear - and looks relatively modern.

 

[debra]

...

---

Professional tuners not only use a measuring device but also check by ear in the "standard" octave that the quarts and quints have the same slow beating.

I just want to make sure I understand what that achieves. Does that mean that you end up with a noticeable difference compared to equal temperament, or does that refer to the method used to tune equal temperament when you don't have a tuner available? The latter is described in Toni Schwall's book and you end up with something like this

The idea is to set A4 correctly according to a tuning fork (or some other source) and then tuning those intervals (quarts and quints) by counting the beats (produced by the harmonics). At the end you have that one octave that's as close to equal temperament as you can get without using an actual tuner. And then you tune the other octaves to zero beats based on that octave. But I doubt those small differences to ET really make much of a difference. However, if it does, then you could just set a digital tuner to those slightly different values and you should end up with the same results without all the effort of literally counting beats with a stopwatch or metronome.

---

This is precisely what I mean and it is how I learned to tune in the Accordion Craft Academy in Castelfidardo. You only need one note and can do all the tuning (equal temperament) just by ear, using quarts and quints. What we didn't do, but piano tuners do, is to also use thirds because they result in a higher number of beats per second and it's easier to judge whether it's the right number. With quarts and quints you aim for about 1 1/2 beats per second. It's true that when you just use an electronic tuner (e.g. a phone app) you achieve the same result and you just need to check what's displayed instead of listen, but in the end what it sounds like is what matters most.

 

[Glug]

Something I found: free software to fit an exponential curve of the form a + b*exp(c*x)

basicTrendLine package: https://github.com/PhDMeiwp/basicTrendline
R Statistical Package: https://www.r-project.org/

Actually quite easy to use, but being a nerd helps

For the Hohner Lucia it gave y = 27.089 - 25.651 exp (-0.0065479 x)
with R squared = 0.9677.

Yep, thats a negative exponent.  The curve is almost exactly the same as the linear fit (R squared 0.96679).

 

[jollyrogeraccordions]

As Paul says... use your ears. It is very easy to get hung up on how many cents for this and that. I've seen a tuner not use a meter at all, but set concert reeds by comparing to a tone generator, and then tune the tremolo entirely by listening to the beats. Meters are very useful, obviously, but your ears are most important.

 

[HiTechBiniou]

Hey I'm back!
I managed to translate my Guide de l'Accordéon to Accordion Guide in English.
Here is the file Glug was referring to.
You can also visit https://accordionguide.info

 

[HiTechBiniou]

Question for you guys.

WHAT IT IS THAT IS "EQUAL" IN THE EQUAL TEMPERAMENT?

 

[Siegmund]

Question for you guys.

WHAT IT IS THAT IS "EQUAL" IN THE EQUAL TEMPERAMENT?

The ratios of the pitches of consecutive notes in the scale, at 2^(1/12) ~ 1.059 : 1.

In just intonation (in C), minor seconds like D-Eb and E-F are wider (16/15 ~ 1.067:1) than augmented unisons like Eb-E (25/24 ~ 1.042:1). F-C-G-D, Db-Ab-Eb-Bb, and A-E-B-F# are chains of perfect 3:2 fifths, but D-A makes your ears hurt (40/27 ~ 1.481:1 instead of 3:2). This sounds really nice as long as you stay in the key of C.

There are many alternatives in between the two. A popular alternative in the 17th century was 'meantone' tuning, which flattened each of C-G, G-D, D-A, and A-E just enough to make E an in-tune major third above C. This works beautifully in most keys with between 2 flats and 3 sharps... but the leap between Eb and G# is the wrong size, and if you play G#-C-Eb or B-Eb-F# you get something much uglier than a Ab major or B major chord is meant to be.

In a nutshell, you have a choice: make one key sound really good and the rest really bad; make half the keys sound OK and half the keys quite bad; or make all the keys equally out of tune.

Doing better requires more than 12 notes per octave. Every now and then I daydream about an accordion that has two banks of reeds about 15 or 20 cents apart... and a special register switch that lets me tell it what key I'm in, so I can play scale steps 1,2,4 and 5 on the sharp bank and 3,6,7 on the flat bank.

 

[debra]

The ratios of the pitches of consecutive notes in the scale, at 2^(1/12) ~ 1.059 : 1.

In just intonation (in C), minor seconds like D-Eb and E-F are wider (16/15 ~ 1.067:1) than augmented unisons like Eb-E (25/24 ~ 1.042:1). F-C-G-D, Db-Ab-Eb-Bb, and A-E-B-F# are chains of perfect 3:2 fifths, but D-A makes your ears hurt (40/27 ~ 1.481:1 instead of 3:2). This sounds really nice as long as you stay in the key of C.

There are many alternatives in between the two. A popular alternative in the 17th century was 'meantone' tuning, which flattened each of C-G, G-D, D-A, and A-E just enough to make E an in-tune major third above C. This works beautifully in most keys with between 2 flats and 3 sharps... but the leap between Eb and G# is the wrong size, and if you play G#-C-Eb or B-Eb-F# you get something much uglier than a Ab major or B major chord is meant to be.

In a nutshell, you have a choice: make one key sound really good and the rest really bad; make half the keys sound OK and half the keys quite bad; or make all the keys equally out of tune.

Doing better requires more than 12 notes per octave. Every now and then I daydream about an accordion that has two banks of reeds about 15 or 20 cents apart... and a special register switch that lets me tell it what key I'm in, so I can play scale steps 1,2,4 and 5 on the sharp bank and 3,6,7 on the flat bank.

Thanks for that clear explanation. Another way to look at it is the following:
An octave higher means frequency x 2. A quint higher means frequency x 3/2. If you go up 12 quints the frequency goes to (3/2)^12 or up by about a factor of 129,75. If you go up by 7 octaves the frequency goes up by a factor of 128. But on an imaginary keyboard you end up with the same key. Obviously 128 < 129.75 and that difference needs to be hidden somewhere. What we do today on an accordion is to make all the quints off by the same amount to keep the octaves exactly x 2. We essentially need to do that as each key can be three different octaves at once (L, M and H register). But on some other instruments a compromise is possible which is called "stretching": quints going up are not off by as much as on the accordion and octaves become just slightly over x 2. Strangely enough our ears (brain actually) more or less expects this. When an accordion and a modern wind instrument (say a saxophone) are tuned the same at some base note (like A4=440Hz) then by the time the wind instrument goes up by 2 octaves you will notice it sounds higher than the accordion going up by 2 octaves. This obviously creates problems for playing together.
Another way to deal with the difference is to start with the first quints C-G-D-A-E-B for instance to be exact and then hide all the problems in the quints B-F#-C#-G#-D#-A#-E#-B# so these quints then sound worse. In the past people have played with which quints to make sound nice and which quints to sound badly, creating instruments that sound better in when playing in some keys and worse in other keys. Baroque compositions played on baroque instruments can only be played in the key they were composed for and sound badly when you transpose them. Music played on a modern "well-tempered" instrument (like the accordion) sounds the same when transposed, except higher or lower.