Learning to tune ...

[HiTechBiniou]

Answer: the distance between each key, the distance between each 1/2 tone. That's it! All intervals except the unison and octave are OUT OF TUNE.

 

[Gonk]

Here is a useful resource comparing equal temperament (often abbreviated ET or 12-TET for the 12-tone scale) to just temperament.

Scales: Just vs Equal Temperament

"Just intonation" is the result of ensuring the ratios between waves are such that the waves line up without creating extra aural beating. This is achieved by simple ratios like 1:2, 2:3, 3:4, etc. These ratios are sometimes called "perfect" or "just." If you picture two sine waves superimposed, a 1:2 ratio will feature peaks that line up every time the longer wave reaches its period - this is what makes octaves sound so consonant. A 2:3 ratio will feature peaks that line up every other time the longer wave reaches its period. This kind of tuning is only possible with relation to a fixed point - for example, you can achieve a pure fifth between C and G, and a perfect third between C and E, and a perfect fifth between E and B. But then you will not have a perfect third between G and B. This is what makes just intonation sound different in different keys, and is the reason that the keys in modal music have associated "characters" or feelings.

There is another problem that is often misunderstood or misrepresented: even for a diatonic instrument that plays in only one key, perfect just intonation is not possible across multiple octaves. This is due to the fact that the scale of frequencies and their corresponding pitches is not linear but exponential. The difference between the tuning possible by calibrating the fifths perfectly, and that possible when calibrating the octaves, is called the "Pythagorean Comma" - the deviation between 7 octaves and 12 perfect fifths (which "should" theoretically be the same note). One cannot tune all the octaves to 1:2 ratios, and then achieve pure fifths, nor can one tune all the fifths to perfect 2:3 ratios and then get the octaves to match.

Pythagorean comma - Wikipedia

en.wikipedia.org

This is part of what makes tuning a Hard Problem, and one which demands compromises - even for just-tempered instruments! These compromises are sometimes called "compromise tunings," or "well temperaments." They are various approaches to mitigating the damage done by ET. "Well-tempered" does not indicate a single type of temperament; there are many well temperaments. To add to the confusion, the term "well temperament" is sometimes mistakenly used when "equal temperament" is what's meant.

Well temperament - Wikipedia

en.wikipedia.org

In my view, one of the ways the accordion (at least, a wet-tuned one) mitigates or obfuscates these problems is to embrace aural beating. When each note actually plays two pitches, separated by roughly the difference between a just major third and an equal-tempered third (14-15c), there will be an interval that is close to a perfect third in the aural "mix" when one plays the ET third. [Mistakenly wrote "fifth" here earlier, good catch Paul] And even when the just interval is nowhere to be found, the resulting aural beating is masked by the beating of each individual note. That said, a wet-tuned instrument that is tempered to a compromise tuning (such as an Italian organetto) has its own unique character and the pleasure of the consonant 3rds and 5ths can still be felt despite the complexity of the soundwave interactions.

Sorry to stir the mud! I think it's a really interesting subject and one with many approaches.

 

[saundersbp]

Sorry to stir the mud! I think it's a really interesting subject and one with many approaches.

Brilliant post Gonk!
It's actually really important what you say because it makes a huge difference to how 'good' an instrument sounds way beyond whatever is making the sound source or the label on the front of it.
I've seen some masters at work tuning posh pianos and cathedral organs. They explained they tune to their own (closely guarded) "well temperaments" which people casually call 'equal temperament' exactly as you explain. I guess top level accordion tuning must be an equally sophisticated art. I wonder what sort of tuning compromises come into play with accordions with converter basses - I'd need a few years to think that one through! I had thought for a while that these converter instruments sound more 'in tune' when playing freebass than in stradella mode. It might be a trick of the mind, or perhaps there is science involved.

 

[debra]

Brilliant post Gonk!
It's actually really important what you say because it makes a huge difference to how 'good' an instrument sounds way beyond whatever is making the sound source or the label on the front of it.
I've seen some masters at work tuning posh pianos and cathedral organs. They explained they tune to their own (closely guarded) "well temperaments" which people casually call 'equal temperament' exactly as you explain. I guess top level accordion tuning must be an equally sophisticated art. I wonder what sort of tuning compromises come into play with accordions with converter basses - I'd need a few years to think that one through! I had thought for a while that these converter instruments sound more 'in tune' when playing freebass than in stradella mode. It might be a trick of the mind, or perhaps there is science involved.

I believe that the 14 to 15 cents Gonk mentioned is actually too much to just mask the "error" between an equal-tempered fifth and a just fifth. In accordion tuning we learn to tune such that a fifth (quint) beats at about 1.5 times per second. That corresponds to about 6 cents.
My prefered tremolo tuning is 8 cents. It makes intervals sound pretty good for my ears, but opinions may vary.
Regarding the convertor there is an important difference between the quint convertor (and some older chromatic convertor designs that do not use the typical large convertor switch) and a modern chromatic convertor. In a convertor accordion tuning is done (to perfection) for the melody bass. With a modern chromatic convertor this also results in the best tuning for Stradella. However, with a quint convertor the convertor works by operating register sliders that work on reed blocks that have resonance chambers with two holes for each note: one hole is used for melody bass and one for Stradella. When you tune a reed perfectly using the hole for melody bass that reed may be slightly off when using the hole for Stradella. But because Stradella plays chords you don't really notice that little bit out of tune whereas with melody bass you would notice when tuning is slightly off.
There are other things at play I do not fully understand. Some concert players prefer "concert tuning" (2 cents tremolo) over "dry tuning" (0 cents tremolo) and some manufacturers are rumored to tune the bass side of a convertor instrument 2 cents higher than the treble side (so treble=440Hz is combined with bass=440.5Hz). I don't know why that is done.

 

[Dingo40]

A fascinating topic when discussed like it is here, but my head is already spinning .
Don't think I'll be doing any hands on tuning myself soon!
I have noticed, on one of my accordions in particular, a kind of qualitative tonal difference between the lower and the upper treble octaves (although still in tune). It's a bit like having two different instruments on the one keyboard.
I just accept it as a natural state of affairs.

 

[Mr Mark]

Bookmarked this thread for continued returns, lots of interesting information not meant for my head to be absorbed in one go. I've tuned a couple dozen accordions in the last year and can confidently say that in and of itself is an art form. Tuner first and ears get the final say, Seems I like them on the wet side with middle A around 20 cents (mostly compact Hohners with the low G around 28 and the high E around 12). It would be nice to experiment but holy smokes that is a lot of work so I'll stick to the science reading I have found here thank you!

I believe that the 14 to 15 cents Gonk mentioned is actually too much to just mask the "error" between an equal-tempered fifth and a just fifth. In accordion tuning we learn to tune such that a fifth (quint) beats at about 1.5 times per second. That corresponds to about 6 cents.
My prefered tremolo tuning is 8 cents. It makes intervals sound pretty good for my ears, but opinions may vary.
Regarding the convertor there is an important difference between the quint convertor (and some older chromatic convertor designs that do not use the typical large convertor switch) and a modern chromatic convertor. In a convertor accordion tuning is done (to perfection) for the melody bass. With a modern chromatic convertor this also results in the best tuning for Stradella. However, with a quint convertor the convertor works by operating register sliders that work on reed blocks that have resonance chambers with two holes for each note: one hole is used for melody bass and one for Stradella. When you tune a reed perfectly using the hole for melody bass that reed may be slightly off when using the hole for Stradella. But because Stradella plays chords you don't really notice that little bit out of tune whereas with melody bass you would notice when tuning is slightly off.
There are other things at play I do not fully understand. Some concert players prefer "concert tuning" (2 cents tremolo) over "dry tuning" (0 cents tremolo) and some manufacturers are rumored to tune the bass side of a convertor instrument 2 cents higher than the treble side (so treble=440Hz is combined with bass=440.5Hz). I don't know why that is done.

Is this 8 cents on middle A (or C for full size) then 8 cents either way?

I get confused with this statement and am not sure of its meaning in entirety.

 

[debra]

Bookmarked this thread for continued returns, lots of interesting information not meant for my head to be absorbed in one go. I've tuned a couple dozen accordions in the last year and can confidently say that in and of itself is an art form. Tuner first and ears get the final say, Seems I like them on the wet side with middle A around 20 cents (mostly compact Hohners with the low G around 28 and the high E around 12). It would be nice to experiment but holy smokes that is a lot of work so I'll stick to the science reading I have found here thank you!



Is this 8 cents on middle A (or C for full size) then 8 cents either way?

I get confused with this statement and am not sure of its meaning in entirety.

The tuning (like my 8 cents) is for A4 which is the second A on a 41-key PA. When you tune this A4 to a tremolo to a certain tremolo of say X then I go up in tremolo as I go down in frequency, to about 4/3 X for A3 and pretty much constant or going a bit down as notes go even lower. Above A4 the rule is to have the tremolo go down to 2/3 X for A5 and to 4/9 X (2/3*2/3) by A6.
When someone wants a "normal" musette tremolo I use 16 to 18 cents. When someone like a milder tremolo I use 12 cents. I find that 12 cents is a really nice tremolo and 8 cents is as low as I go for a very mild tremolo that is good to represent a flute or a group of violinists.
Hohner has used 18 cents too (but when you get an older instrument tuning goes all over the place as the instrument ages so it can become 20 cents). Amsterdam, Scottish or Irish is more tremolo, like 25 cents, and true Amsterdam tuning requires MMM with -25, 0, +25 and it comes with a promise of headache (but paracetamol not included).

 

[Gonk]

I believe that the 14 to 15 cents Gonk mentioned is actually too much to just mask the "error" between an equal-tempered fifth and a just fifth.

Paul, good catch, I thought "third" and wrote "fifth." I'll fix that. I find the major third to be the most irritating ET interval, especially in high octaves. It tends to be around 14-15c out.