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[Jono]

Yes, fair enough. For what it's worth, I play two fixed pitch instruments, melodeon and piano, and I feel that this imperfection is part of their charm, but that's just me. As we know maths isn't precise either, when you get down to it. God is an interesting person, if you believe in that sort of thing, which I do.

[Owen Woods]

Yes, fair enough. For what it's worth, I play two fixed pitch instruments, melodeon and piano, and I feel that this imperfection is part of their charm, but that's just me. As we know maths isn't precise either, when you get down to it. God is an interesting person, if you believe in that sort of thing, which I do.

Eh?

[pikey]

Ref cellos and violins. I reckon thats why you're taught not to play using open strings, so you can adjust the tone to be in tune using your fingers.

Sadly it doesn't work like that on melodeon. At least tremolo tuned reeds hide the dischordance 

[Jono]

I'm not talking about the maths of music, if that's the cause of your query. I'm talking about complex maths, which mathematicians have written about so that non mathematicians like me can understand them. Mathematicians once thought that all mathematical proofs were solid and definite. But they're finding out more and more that maths is actually more of a human language than anything else. Mathematical proofs can come down to a sort of faith, because ultimately they are impossible for a human to prove. It's a philosophical point, or a theological one.

Regarding Pikey's post, I like tremolo on the melodeon. Lots of string players use open strings by the way, both solo and as part of an ensemble. Open strings often sound great, depending on the passage being played.

Talking of equal and just temperament, on an instrument that plays in one, or at most only a few related keys, you could get it retuned to suit your taste.

[Jono]

Ah, but that's a play on words. "Proof" is what the mathematicians call it, whether provable or not by their own admission. I'm only quoting them. It has theological or perhaps philosophical implications only in the context of my original post. It was not given as a general statement with which to attempt to prove any point for or against the existence of God, if that's what you mean. Only to hint at or suggest that music, as I see it, is something God has given us, taken by me on faith of course, and open to rejection by others who may see it differently. From my point of view I'm suggesting that music might be something rather more broad and interesting than we have sometimes given it credit for. I was not implying or stating any mystery or indeterminacy regarding the mathematics of temperament, which is straightforward.

[Jono]

Oh well, please forgive me for being incoherent in this one instance. I should have written that mathematicians are finding that their propositions are not really provable.

[Owen Woods]

Ref cellos and violins. I reckon thats why you're taught not to play using open strings, so you can adjust the tone to be in tune using your fingers.

Sadly it doesn't work like that on melodeon. At least tremolo tuned reeds hide the dischordance 

Open strings sound different from non-open strings (something to do with end conditions I think), which is why you're not supposed to use them so much in classical music. In folk music that difference is exploited. The times when a string quartet might have problems include points where the cello or viola play their lowest note and the violin plays say a high G-E double stop. In that scenario they have to (I think) use the E open string.

I'm not talking about the maths of music, if that's the cause of your query. I'm talking about complex maths, which mathematicians have written about so that non mathematicians like me can understand them. Mathematicians once thought that all mathematical proofs were solid and definite. But they're finding out more and more that maths is actually more of a human language than anything else. Mathematical proofs can come down to a sort of faith, because ultimately they are impossible for a human to prove. It's a philosophical point, or a theological one.

Ah right. Well I'm an Engineer, so in my world, Maths is as solid as things can be.

[rees]

I believe in Theo. Logical really. 

[Theo]

I believe in me too.

[Andy Simpson]

I don't believe in Theo anymore. I even used to go to the post office with my melodeon to send it off to "Newcastle" to be tuned but I never actually saw him. I think my Mum or Dad actually used to work on them and Theo was made up to make it seem more magical.

[pikey]

I'm amazed that no-one has commented on my odd temperament yet. 

[Jono]

aradru, why do you put my quote in your post? I'm responding to the original poster, whose blog article mentions the existence of God. I don't think any of this is absurd, as you say, and I'm not trying to argue for God's existence here, using an "anomaly" as you put  it. I was defending my earlier post, in the quote that you have selected. If you're uncomfortable at the God topic being raised, have a go at ukebert. He actually asked for our responses, you know. I'm the one who is on topic. So there.

[Theo]

Getting back to the original topic ...

The best definition of tuning that I've encountered is: tuning is a matter of agreement between musicians.

So whatever tuning system you adopt, it should be a result of listening to the people you make music with.

[DaveCottrell]

Agreement amongst musicians is tuning

Temperament is "agreement" between the notes of a chord on one instrument.

For monotonic instruments, temperament is only an issue if it is impossible to match another instrument at the same time.  Issues of temperament mainly arose as keyboard instruments and players developed in capability.

Kind of like the God issue.  Faith is a personal thing and, like the conflict between what a note is and what you think it should sound like in its surroundings,  only creates discord when the note is played with another.  Any argument to the contrary is, by definition, a proof of this point.

[Nick Collis Bird]

Oh well, please forgive me for being incoherent in this one instance. I should have written that mathematicians are finding that their propositions are not really provable.

Fermatt's theorem is worth a read.
 As for the blog, I am enlightened and gob smacked all at the same time.
Pi seems to have been proved also.
 So here we go ( Sorry Theo )
There was once an Indian chief , he had three wives, his favourite wife slept on a Hippotomus skin, and the less favourite wives slept on rabbit and pig which weren't  worth as much. They all slept together in the tepee.
So it was said  wait for it-----:-
The squaw on the Hippotomus  was equal to the sum of the other two squaws on the opposite hides.
I'm off!

[pikey]

 

Owen's article is brilliantly written and understandable (well, most of it!).  I hope someone recognises his talent and gives him a job.

Nick - I prefer Beermats theorem: I drink, therefore I am.   

 

[Owen Woods]

The best definition of tuning that I've encountered is: tuning is a matter of agreement between musicians.

So whatever tuning system you adopt, it should be a result of listening to the people you make music with.

Nicely put!

Just for the record, my argument about God in that post was not the most serious thing that I have ever written.

[Pete Dunk]

Just for the record, my argument about God in that post was not the most serious thing that I have ever written

Thank Fred for that! 

[Pete Dunk]

The dyslexic insomniac: He's awake all night wondering if there is a DOG.

I work here. Dyslexics I can cope with, no problem! 

Curiously enough the kids are endlessly fascinated by my melodeons and always find them to be fun and instinctive to play but I can't get one to take it up properly, not 'cool' enough apparently. 

[Chris Brimley]

No one yet seems to have discussed the extent to which tuning differences are noticeable, but isn't this an important issue?

Let's say that two pure notes of nearly the same frequency are playing simultaneously - what difference in frequencies would a listener notice?  I'd suggest that maybe less than say around 5 seconds would be noticeable as a pulse or beat.  So for A at 440Hz, a 5 second beat would equate to a frequency difference of 0.2Hz, or 0.045%.  I would expect that the beat frequency that's noticeable might well vary with frequency - the 'swell' effect seems to be more discernible at mid to low frequencies, I don't know why.  But let's take that figure, and compare tuning techniques.  If you tune all four strings on a violin on the basis of the 3/2 harmonics rule, you would expect that compared with an ET spot-on bottom G string at 392Hz, the top E would be 392x(1.5**3), or 1323Hz.  ET would suggest 1318.51Hz, a difference of 0.34%.  That's over 7 times the noticeable difference! 

And just for one string tuned 3/2 harmonically, D would work out at 588Hz, whereas ET suggests 587.33, a difference of .114%, over twice the noticeable difference.

Immediate moral - all stringed instrument players need to get themselves electronic tuners!

I've sort of known all this for a long time, but I confess that I thought the main problem was guitar manufacturing inaccuracies, old strings, or a poor ear.  Now I realise how much improvement you can get from always using a tuner.

So the next question with boxes for me is this - what are the likely discord issues with say a two-row (dry-tuned) quint box, theoretically?  I've always thought Hohner factory-tuned the A chord horribly sharp on their pokerworks, but now I'm not so sure - is there a good reason they do it that way?