Music theory - what is it?

[Bryn]

Here's an even more relevant Bradley Lehman Youtube offering:

There are a good few more out there.

[Dave2002]

Let's remember also that many musicians around Bach's time would have tuned their own keyboard instruments. They may have been more sensitive to slight changes in pitch - or alternatively more tolerant!

Your post 60 seems to have an incomplete sentence.

[Bryn]

Let's remember also that many musicians around Bach's time would have tuned their own keyboard instruments. They may have been more sensitive to slight changes in pitch - or alternatively more tolerant!

Your post 60 seems to have an incomplete sentence.

More a case of finger slip. Now corrected.

[Ein Heldenleben]

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.

Thanks Dave - I was sort of joking! Sharp or flat depends on your point of view and what musical effect you are trying to achieve . Heifetz when playing Gershwin used to flatten his tuning in the most delicious way. So do jazz musicians (except pianists obvs ) . Those South African township Choirs have a way of internally tuning and singing a diatonic scale that’s different from the a church choir singing with an organ but beautiful in its own way . We need not to obsess about ‘correct’ tuning and indeed rampant diatonicism. Though without well tempering we would have to kiss goodbye to a lot of very good music ...

[Dave2002]

Thanks Dave - I was sort of joking! Sharp or flat depends on your point of view and what musical effect you are trying to achieve . Heifetz when playing Gershwin used to flatten his tuning in the most delicious way. So do jazz musicians (except pianists obvs ) . Those South African township Choirs have a way of internally tuning and singing a diatonic scale that’s different from the a church choir singing with an organ but beautiful in its own way . We need not to obsess about ‘correct’ tuning and indeed rampant diatonicism. Though without well tempering we would have to kiss goodbye to a lot of very good music ...

Joking or not, I found it quite interesting, and learnt something by checking. If you ever listen to some performances of music by Harry Partch where almost "perfect" tuning is used, the results are interesting - in a way - but also so smooth that they are dull. Also note that it makes virtually no difference whether the played note has a clash with its 10th harmonic - as almost all harmonics above (say) the 6th (better make it 20th?) are so much quieter on many instruments, and in many cases inaudible anyway.

[Ein Heldenleben]

Joking or not, I found it quite interesting, and learnt something by checking. If you ever listen to some performances of music by Harry Partch where almost "perfect" tuning is used, the results are interesting - in a way - but also so smooth that they are dull. Also note that it makes virtually no difference whether the played note has a clash with its 10th harmonic - as almost all harmonics above (say) the 6th (better make it 20th?) are so much quieter on many instruments, and in many cases inaudible anyway.

Will do .It always struck me as an interesting project for a digital piano keyboard company to offer a range of tuning options....

[Dave2002]

Will do .It always struck me as an interesting project for a digital piano keyboard company to offer a range of tuning options....

Actually if you look at the specs and or user manual for some of the digital piano keyboards they already have several.

[Richard Barrett]

Will do .It always struck me as an interesting project for a digital piano keyboard company to offer a range of tuning options....

That was already the case with one of the very first commercially available digital keyboards, the Yamaha DX7, which came out in 1983.

[Bryn]

https://johnmcwhorter.substack.com/p/is-music-theory-really-sowhite

[Bryn]

I have just been alerted to this YouTube item: