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Pythagorean stuff

Bobby G

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Ok, I haven't studied it formally, but I know bits'n'pieces e.g. 1:2 is an octave, 2:3 a fifth, etc, and I can see how the notes were arrived at, how we have the 12 chromatic notes in our music, a bit of how harmony works (and would understand more if I studied it). All this is scientifically proveable undeniable incontrovertible fact. It's all based on mathematics, therefore you can't get away from the idea that mathematics is central to music. Rational.

Many musicians play by ear (or from written music) and are quite able to function within their chosen field with very little awareness of Pythagorus's work. We are all working off his developments in some way, but there are those who don't know or don't care about such things.

Some, when improvising employ pitch-bending, glissandi, and vibrato as part of their technique, mainly for emotional impact - every note exactly on-pitch would make most jazz, blues, and rock music far less interesting, engaging, 'human' and have far less 'feel'. In fact I would contend that most people, a lot of the time, are deliberately playing slightly 'out of tune', especially on a sax which has intonation that is easy to manipulate. Without knowing it, they are messing with Pythagorus, not consciously as most have no idea of his contribution, but they are somehow going against the mathematics, stretching and bending it for their own need to express themselves. Not to mention the tensions and releases and ensuing emotional responses created by varying rhythmic changes, playing faster, slower, behind/in front of the beat etc., again going beyond the pure maths of music. The one word that sums all this up is interpretation. Scientifically proveable or explainable? Mystical.

Language - we all use it, most of us can read it, most of us can write it many of us do this without any real notion of how the language developed, where words originated, or all the rules of grammar, clauses, sentence construction etc. but does that stop us from communicating with each other?

Discuss. Or not. I'm getting back on my fence now.

Cheers, Bob
 
Heheh... nice one Bob. Just did a quick check and apparently 99.99% of musos have never heard of Pythagorus, some remember him vaguely from 7th form maths (Pythagorian Theorem) and most of the rest of us wanna know if he's the new coach of Panathinaikos?

The other 0.01% (rounded up) are probably part time music historians?! (Oh, and Martin)

Gee, I always thought that music was about playing it how you heard it. I never realised that some folk felt the need to read up centuries of history to understand what they were playing now. I mean, I know WYnton Marsalis is right behind going back to the roots of jazz, but I don't thing he meant that far back!

Simon
 
I don't have a problem with the centuries of music history per se, facts are facts are facts, it's the human mind's quest for knowledge after all that is at the heart of so much. Pythagorus and so many others have been crucial for increasing the sum of human knowledge and understanding (which are two separate and distinct things really).

I just wonder how much knowledge John Lee Hooker, Louis Armstrong, Duke Ellington, Thelonious Monk, Jimi Hendrix, John Lennon, Bob Dylan, Bix Beiderbecke, George Gershwin etc etc etc had of these earlier developments, how much they needed, and how much they would have wanted. A lot of people just want to communicate feelings, hopefully share them through their music, that's all. Maybe trying to make the personal universal.

Some genuine questions for Pythagorus, who I realise can't speak for himself;

How would you have interpreted the slide guitar or trombone in terms of your mathematical principles of music?

Is the concept of lyrics, i.e. songs rather than pure music, recognised in your principles?

Was your drunk-curing hypo-melody/thingy rhythm (sorry can't find it) a repeatable, quantifiable experiment, or just something that worked randomly, once? If the latter, in what way is this any more than an anecdotal, and therefore not scientifically valid, incident? (As it happens, LSD was for a while a 'cure' for alcoholism, with a success rate of 50%. What happened to the other 50% I do not know)

Does your work take into account the human responses to similar melodies, scales etc usind different tones or timbres?

What was your horn, man? 😉

Cheers, Bob
 
Pythagoras not only invented the scientific method,he killed it off too.!
He was himself something of a mystic...
The point about it is,that there are sound physical mreasons for the phenomena we understand as music.
The word rational,by the way,stems directly from the Pythagorian obsession with describing everything in terms of ratios.

Had I not been infected by the music bug,I would probably have done science (physics) but I was and everything went Bohemian.
So when I finally heard about the harmonics /Py thing at music college (en passant) I was blown away.

At last a good reason for the harmony we had to do at O level etc.

Yes.it is little known,to the extent that a university Maths lecturer who asked me for lessons at a gig.didn't even know about it.
He had to check it before he believed me,but was also blown away.
 
a sliding guitar?

X:Y
is a ratio of a note, X2:Y2 is the ratio of the semi-tone below
as X tends to X-X2, Y tends to Y-Y2.

One of these values would be decreasing and the other increasing.

as one value tends to infinity the other tends towards 0.

I wonder if my maths is any good? Martin.

Music is about expression. in some cases this may be Simon's 'play it as you hear it' in others it could be play it as it's exactly as it's written. In many cases it's play what's written and interpret stylistically.

This I believe needs a knowledge of theory and aural skills equally.

If you are going to compose, I think you also needs both these aspects.

I believe that aural skills and theory go hand in hand. Neither are maximised without each other.
 
Ah, but not all music is 'composed' as such. Some is improvised, some is handed down through the generations, some is played from memory, some is arrived at through jamming and then formalising a tune, structure etc without a note ever being, or ever needing to be, written.

Cheers, Bob
 
Indeed,but maths is the language of the universe.
The shells of snails spiral a la Fibonaci series.
Golden ratios.
Harmonics.

I just wish my maths was really up to it....

The sliding is just a decoration thing,perhaps,or a nod to natural tuning,like the blue third.
A tempered maj 3rd is way high compared to a natural one...
 
Okay, Mr. Science, answer me this:

Why is it better (more pleasing to the ear, or possibly less noticable) to play slightly sharp than it is to play slightly flat?
 
Lee wrote:
Okay, Mr. Science, answer me this:

Why is it better (more pleasing to the ear, or possibly less noticable) to play slightly sharp than it is to play slightly flat?

Just a non-scientific guess, but flatness implies just that - flatness, can't be bothered etc, and sharpness implies just that - sharpness, on-the-ball etc, so your response will be of a similar nature.


No doubt there is a mathematically correct (formulaic) explanation too, taking into account many different factors, but that's what I've come up with, and as I don't think you can quantify emotions it'll have to do 😛

Cheers, Bob
 
Lee wrote:
Okay, Mr. Science, answer me this:

Why is it better (more pleasing to the ear, or possibly less noticable) to play slightly sharp than it is to play slightly flat?


FWIW, I just read a comment from Paul Bley to the effect that the history of western music for the past couple hundred years could be summed up as the gradual acceptance of dissonance. Jazz being a case in point.

Why "slightly flat" equates to dissonance is another issue, probably a blend of psychoacoustics and temperment. Everything for the past several hundred yrs has been built to re-inforce the emotional overtones associated with sharp or upward moving and flat.

At the same time, forces are in play that make dissonance more acceptable as a norm (it's always been there, it was just used sparingly).
 
Someone said "mathematics is the language of the universe"

It seems to be a way of codifying what you can see in front of you and hypothesising rules to explain the way it behaves. As for explaining what it is? Matter of taste I guess. Western music seems to be moving towards the acceptance of dissonance.

From what I've read and heard (taking Chinese Opera as a case in point. I tried, I really did), Eastern music got there a loooong time ago.

🙂
 
I think if you look at a split key keyboard, (cropped up in another thread somewhere) Many of the split keys raise the note, instead of lowering it.

So if you are slightly sharp you are closer to the 'real' pitch than being slightly flat.

Just a guess mind you.
 
"Real" doesn't necessarily mean right, though. I think it's just one of those things 😉 Psychoacoustics, I like that word.

Is Chinese music dissonant? Without having studied it deeply, other musics seem to be not so much 'dissonant' as tonally and timbrally very different to what our Western ears have become accustomed to. I have to say, though, that having grown up musically in the sixties and seventies when in some circles what was considered 'dissonant' was constantly changing, my ears are quite accustomed to what some people like my parents used to describe as, and I quote, 'that's not music, it's just a bloody noise' 😛

I seem to remember someone in a thread somewhere saying that at one time a dominant seventh (like G B D F) was considered dissonant.

Are there other musics which function on other scales or intervals different from our friend Pythagorus's twelve semitones to an octave? Or are other musics still using the twelve semitones with unusual (to our ears) rhythmic variations?

Cheers, Bob
 
tris wrote:
Arrr not this again!

I'm really disappointed in you Tris - I went all through this thread to pick up the, erm, thread, expecting embellishment, discussion and discourse on the points already made, argument, counter-argument and a general moving on, and I get a lousy four words, and one of those isn't English.

I hope your back gets better very soon.

Cheers, Bob
 

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