Music theory - what is it?

[Mario]

Not quite - the overtones correspond to the harmonics, with the exception of the fundamental.
The nth overtone is the n+1 th harmonic.

Clearly, room for improvement on my part!

Maybe, I should quietly continue with my studies (currently STILL Grade 5), and see where that leads us.

Again, Dave, thanks again.

Mario

[PHS]

Music Theory is the thing you do on a Sunday night when you have a tutorial first thing Monday morning!

[Dave2002]

Music Theory is the thing you do on a Sunday night when you have a tutorial first thing Monday morning!

Doesn't that depend on what you are supposed to be studying?

More on harmonics - for physics enthusiasts - here - https://www.physicsclassroom.com/cla...-and-Harmonics

[Eine Alpensinfonie]

[Serial_Apologist]

Is that a take-off?

[cloughie]

Is that a take-off?

Which notation did Holst prefer?

[Serial_Apologist]

Which notation did Holst prefer?

Sans Scrit?

[ardcarp]

thirds on a piano are a bit of a compromise. They are not really the natural third you get in the harmonic series

...which is why Britten's Serenade for Tenor, Horn and Strings is so magical. Britten instructs the horn player to use only natural harmonics. Thus the major third (which is two-octves-and-a-third above its fundamental) is so deliciously 'flat' to our equally tempered ears.

[Ein Heldenleben]

...which is why Britten's Serenade for Tenor, Horn and Strings is so magical. Britten instructs the horn player to use only natural harmonics. Thus the major third (which is two-octves-and-a-third above its fundamental) is so deliciously 'flat' to our equally tempered ears.

Yes a wonderful sound . Like the natural trumpet in RVW’s 5th . But isn’t it really the piano third that’s sharp!

[ardcarp]

Yes indeed, but we are all so used to it. J.S. Bach is said to have instructed the organ-builder Silbermann 'to sharpen all the thirds', by which he meant widen all the thirds. If organs are tuned to some of the 'historic temperaments' (e.g. Werckmeister III) some of the thirds are quite close to natural thirds, but only when playing in the simpler keys of C, G, D, F and so on. Playing in D flat major would produce some howling intervals. Bach had not quite 'discovered' Equal Temperament...as is sometimes claimed for Das wohltemperierte Klavier... but he had come close to a tuning system in which all the major and minor keys sounded reasonable.

Afterthought: This thread is now discussing the word theory in its truest sense. Historically, Pythagoras, Tartini, Vallotti and English polymath Thomas Young all had their pet theories about tuning. Probably lots of other people too. A fascinating subject, but nothing to do with Music Theory as we learned it, i.e. the nuts and bolts of writing and reading music.

[Bryn]

. . . Bach had not quite 'discovered' Equal Temperament...as is sometimes claimed for Das wohltemperierte Klavier, but he had come close to a tuning system in which all the major and minor keys sounded reasonable.

So, are you a fan of the Bradley Lehman interpretation (or perhaps, http://www.bjarne.altervista.org/music/temperament.html

[ardcarp]

So, are you a fan of the Bradley Lehman interpretation

Sorry, Bryn, that's a new one on me....and I couldn't get your link to work. Tell us more.

[Bryn]

Sorry, Bryn, that's a new one on me....and I couldn't get your link to work. Tell us more.

Basically, Bradley Lehman came to the conclusion that the squiggly design that adorns Book 1 of The Well-Tempered Clavier was a codification of his intended 'well-temperament'. Perhaps the Youtube offering below might help:

There was a typo in the previous link. It should have read http://www.bjarne.altervista.org/music/temperament.html

And http://www.larips.com/

[Dave2002]

Yes a wonderful sound . Like the natural trumpet in RVW’s 5th . But isn’t it really the piano third that’s sharp!

From the figure in https://en.wikipedia.org/wiki/Harmonic_series_(music) previously referred to, the third will be 14 cents flatter compared with the equivalent note in equal temperament tuning. However the diminished fifth would be 49 cents flatter compared with its equivalent note in 12TET. One semitone in 12TET is 100 cents using modern parlance, so the diminished fifth is almost half a semitone flatter, while the third is about a sixth of a semitone flatter.

To say that the piano third is sharp depends on how one views the tuning systems. The starting point for most tuning systems seems to be based on octaves and fifths. One might imagine that a sequence of fifths would eventually lead back to a whole number of octaves, but in fact it doesn't.

C - G - D - A - E - B - Fsharp - Csharp - G sharp - Dsharp - Asharp - Esharp (F) - C looks as though it might work with a gap of 7 octaves, but the frequency ratio would then be 2^7 = 128:1 with perfect octave tuning, while it would be (3:2)^12 with perfect fifth tuning, which evaluates to approx 129.75:1. If the notes are tuned so that the fifths are good, then the octaves will be slightly wider - the higher note in each octave will be slightly sharp, while if the notes are tuned so that the octaves are good, then the fifths will be slightly narrower - i.e. the upper note of each interval will be slightly flat.

Similarly if the thirds are tuned based on fifths, then the ratio will be 1.5^4:1 =5.0625:1 and "normalising" down 2 octaves gives 1.265625:1 - a slight discrepancy compared with the "correct" ratio of 1.25:1 for an equal temperament system. There are always going to be errors based on static tuning systems. Nowadays the use of Equal Temperament tries to spread the errors out evenly over all the keys, so that actually none of them are perfect, but none is significantly worse than the others.

Players of some wind and string instruments can dynamically alter the pitch of each note, and thus play closer to an ideal tuning system - if one can decide what that might be.

Other factors might also influence whether one thinks that notes are flat or sharp in a particular scale form, and I believe that there are slight differences in perception between intervals low in the range, and intervals much higher up.

There have been attempts to devise dynamic tuning systems for instruments based on keyboards and fixed keys, though they don't appear to have been widely adopted or successful.

[Bryn]

I will just add that Richard Egarr's recording of the 48 used Bradley Lehman's tuning: