Music theory - what is it?

[Dave2002]

I broached this point in #14 - that perhaps a confusion lay in attributing different meanings to the word.

Indeed - and as you now realise I followed this up resulting in msg 29.

English is such an elaborate language!

[rauschwerk]

When I took O level music 60 years ago I was taught that in 4 part harmony it was wrong to double the third in a chord. I don't remember any reason being given. Does anyone here know of one?

When I play chordal piano parts (eg in Tango arrangements) I always alter seventh chords to avoid doubled thirds. Is that because my ears have been conditioned over the years, or because there is a fundamental acoustic problem with doubling the third? All explanations gratefully received.

[Bryn]

When I took O level music 60 years ago I was taught that in 4 part harmony it was wrong to double the third in a chord. I don't remember any reason being given. Does anyone here know of one?

When I play chordal piano parts (eg in Tango arrangements) I always alter seventh chords to avoid doubled thirds. Is that because my ears have been conditioned over the years, or because there is a fundamental acoustic problem with doubling the third? All explanations gratefully received.

See, for instance, http://musictheoryteacher.com/pb/wp_..._915ce38c.html

[Ein Heldenleben]

When I took O level music 60 years ago I was taught that in 4 part harmony it was wrong to double the third in a chord. I don't remember any reason being given. Does anyone here know of one?

When I play chordal piano parts (eg in Tango arrangements) I always alter seventh chords to avoid doubled thirds. Is that because my ears have been conditioned over the years, or because there is a fundamental acoustic problem with doubling the third? All explanations gratefully received.

The explanation given by my O level music teacher was that doubled thirds when sung sound too rich. This only applies to four part choral music . It’s not quite so clear cut with piano music - there are plenty of examples of third doubling in piano music. However it’s interesting how the more fastidious composers tend to avoid them - for example Chopin . As you say a lot of jazz piano voicing (esp Bill Evans who was classically trained ) avoids it. Oscar Peterson doesn’t so much but then I find his chord voicing too thick ( i.e very difficult to play )

[Ein Heldenleben]

See, for instance, http://musictheoryteacher.com/pb/wp_..._915ce38c.html

Good summary that. Good to know there’s a bit of “science” behind the rule ....

[Mario]

When I took O level music 60 years ago I was taught that in 4 part harmony it was wrong to double the third in a chord. I don't remember any reason being given. Does anyone here know of one?

Well now rauschwerk, you've laid bare here a continual problem for me, for I too would love to know why (maybe this is why I'm currently finding cadences so difficult to master?).

Good summary that. Good to know there’s a bit of “science” behind the rule ....

I would agree that that is a good summary (if only I knew what an overtone is ).

Mario

[Mario]

The definition given for an overtone is

“a musical tone which is a part of the harmonic series above a fundamental note, and may be heard with it”,

and

“a component of any oscillation whose frequency is an integral multiple of the fundamental frequency.”

Nope, none the wiser.

Mario

[Serial_Apologist]

maybe this is why I'm currently finding cadences so difficult to master?.

Mario

Elisabeth Lutyens found that the best way was not to bother to master them, and ended up finding another way entirely that pretty well dispensed with cadences altogether.

[rauschwerk]

See, for instance, http://musictheoryteacher.com/pb/wp_..._915ce38c.html

Thanks Bryn.

If I play a D7 chord with f# in the lh and C-D-F# in the rh it always sounds bad to me. If I alter the rh F# to A it's fine to my ears. Why? This can't be a a matter of voice-leading. The best acoustic explanation I can come up with is that both F sharps form tritones (always a rough interval) with the C in the middle. With the A at the top there is only one tritone.

[Ein Heldenleben]

Thanks Bryn.

If I play a D7 chord with f# in the lh and C-D-F# in the rh it always sounds bad to me. If I alter the rh F# to A it's fine to my ears. Why? This can't be a a matter of voice-leading. The best acoustic explanation I can come up with is that both F sharps form tritones (always a rough interval) with the C in the middle. With the A at the top there is only one tritone.

I think it’s because thirds on a piano are a bit of a compromise. They are not really the natural third you get in the harmonic series but a compromise to make “well tempering” work . Just play an octave and a third (a tenth ) even after the piano has been tuned - it doesn’t sound right - slide both notes down a semitone - it sounds wrong. It sounds even worse if you double the third up.
The solution is take up singing or a stringed instrument.,..

[vinteuil]

I think it’s because thirds on a piano are a bit of a compromise. / ... /
The solution is take up singing or a stringed instrument.,..

... or a narpsichord (appropriately tempered, natch)


.

[Ein Heldenleben]

... or a narpsichord (appropriately tempered, natch)


.

Yep then you can tune it every day ... the classic lockdown project

[Dave2002]

The definition given for an overtone is

“a musical tone which is a part of the harmonic series above a fundamental note, and may be heard with it”,

and

“a component of any oscillation whose frequency is an integral multiple of the fundamental frequency.”

Nope, none the wiser.

Mario

Most instrument sounds have a characteristic timbre. This arises because there is a set of frequencies constituting the sound. The lowest frequency its the fundamental. This is called the first harmonic. The next tone in most sounds is the second harmonic - which is also called the first overtone. This has a frequency twice that of the fundamental, so it's an octave above.
The third harmonic - also called the second overtone - has a frequency three times that of the fundamental. This is an octave plus a fifth above the fundamental.
The fourth harmonic - called the third overtone - has a frequency four times the fundamental, so it's two octaves up.
The fifth harmonic - called the fourth overtone - has a frequency five times the fundamental, so it's two octaves and a third up etc.

Thus the basic relationships, octaves, fifths and thirds tend to sound harmonious when mixed with the fundamental - though that also means that some instruments may tend to merge together in parts of their ranges.

[Mario]

Most instrument sounds have a characteristic timbre. This arises because there is a set of frequencies constituting the sound. The lowest frequency its the fundamental. This is called the first harmonic. The next tone in most sounds is the second harmonic - which is also called the first overtone. This has a frequency twice that of the fundamental, so it's an octave above.
The third harmonic - also called the second overtone - has a frequency three times that of the fundamental. This is an octave plus a fifth above the fundamental.
The fourth harmonic - called the third overtone - has a frequency four times the fundamental, so it's two octaves up.
The fifth harmonic - called the fourth overtone - has a frequency five times the fundamental, so it's two octaves and a third up etc.

Thus the basic relationships, octaves, fifths and thirds tend to sound harmonious when mixed with the fundamental - though that also means that some instruments may tend to merge together in parts of their ranges.

Very impressive indeed Dave – very many thanks.

Sorry, I haven’t yet learnt all this (I didn’t know overtones were synonymous with harmonics).

Your explanation is crystal clear.

I had learnt something about harmonics on the violin, when I first got to know Tchaik's VC, and got to wonder what those diamond shaped notes were - these are the harmonics correct?

Thanks again,

Mario

[Dave2002]

Very impressive indeed Dave – very many thanks.

Sorry, I haven’t yet learnt all this (I didn’t know overtones were synonymous with harmonics).

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

On a violin the harmonics are produced - I think - firstly by placing a finger lightly about half way up a string - to get the 2nd harmonic = the 1st overtone.
The 3rd harmonic is produced by placing a finger lightly 3/4 of the way up (or 1/4 of the way up) - but the technical details of that I'll leave to string players.

Essentially the string tone is produced, but the fundamental is suppressed, or the 1st and 2nd harmonics are suppressed etc.

As I recall this Youtube video gives a good explanation of how to do harmonics on a violin - https://www.youtube.com/watch?v=HBBZzLNKgPg

What is also quite interesting, if you want to look into this further, is that the notes of (say) a C major scale are not all harmonics (or harmonically related to) of a string tuned to C.
There are discrepancies. For example G would correspond to the 3rd, 6th or 12th harmonic of such a vibrating string.

E would correspond to the 5th, 10th or 20th harmonic.

On the other hand A would correspond roughly to the 27th harmonic.

See this from the page on harmonics here - https://en.wikipedia.org/wiki/Harmonic_series_(music)

Bear in mind though that the higher harmonics of an instrument are generally - though not always - quieter than the fundamental, and they tend to contribute to the timbre of the instrument rather than affect the tuning.
Instruments like the clarinet tend to have only odd harmonics, while flutes have very few harmonics and they are mostly even multiples of the fundamental frequency.
There do have to be some interesting harmonics though, as otherwise all instruments would sound like pure tone generators.

The harmonics of instruments do depend on how the sounds are produced. Vibrating strings and vibrating columns of air tend to have similar harmonics based on simple multiples of the fundamental frequency, but vibrating membranes - as in drums have different relationships between the fundamental the harmonics.

Combining instruments will lead to a complex mixture of tones. Also, just to make things more fun, if two pure tones at different frequencies are played together and then "transmitted" through a non-linear system, difference tones - beats - will be perceived.
These beat tones are usually lower in pitch than the original tones, and may - or may not - be harmonically related. Perhaps the most obvious example of this is if a note and the pure fifth above are sounded together. Normally this should not produce beats, unless there is non linearity present, but it there is non-linearity the effect will be to produce a beat tone an octave below the lower of the two tones.

Perhaps these are not so obvious in many recordings, but sometimes live performances sound very different I think because of such effects - particularly with choirs. You have to remember that the mechanisms of the ear do not always function as a purely linear system, and the environment isn't also guaranteed to behave like a perfectly linear system.