It may be ironic having samples of a great symphony orchestra and playing them with the x2 in frequency for octaves rule used by the cheapest instruments.
x2 in frequency are octaves in frequency but not in pitch.
Our brain cares by definition on pitch (the subjective impression).
For example a good octave of 440Hz is not 880Hz but slightly higher. A double octave of 440Hz is even more than x4 as the effect increases non linearly.
A good real symphony orchestra does this by the collective brain of all people involved. Each musician including the conductor do their best to get the harmony to be harmony to their and our
brain.
It is very complicated as by S. S. Stevens experiments we know that pitch depends not only on frequency but on intensity too.
Another advantage of a good symphony orchestra is that good musician's intonation is according to the key a musical piece is written. Again they try to get the best aesthetic acoustic result and tune their notes in real time.
For example the sound has to fit the overtones of the bass notes. These notes are written by the composer in the score, real instruments play them having real non exact x2, 3, 4 overtones as they sound better. The other instrument's notes have to be tuned in real time to this, or intonated. It seems better that they coincide or are intonated as close to beatless.
No beats means exactly two equal frequencies. This can never be achieved in practice exactly. And it is better this way as it gives a fuller sound. But they have to be close enough.
So the bass overtones with the fundamental notes and overtones of other instruments have to coincide as much as possible for every chord. In fact for every instant in time as much as possible.
Does a good orchestra attempts as a total brain to eliminate as much beats?
Making the whole as pleasing as possible to their and the listener's brain?
Abba for example must have done this. They were using a monophonic miniMoog synthesizer.
And because it could play one note only at a time they had to overdub each note or melodic line separately. This gave them more control from the cheap all octaves x2 in frequency. For example for a high part they could increase the master tuning knob. Some synthesizers and the miniMoog may be one have the facility to adjust very large intervals, 5th octave for example so that they sound correct to our brain.
Other examples may be Vangelis or Air using different instruments and tuning them by ear. For example a Solina string ensemble part playing high notes can be increased in frequency by the master tuning knob so that it sounds correct to brain.
Or a Korg analog bass part may be further lowered in frequency from "equal temperament" by the master tuning knob so that it again sounds correct to our brain on the context of the other musical notes present.
A bender wheel or a tuning knob can help intonate correctly to our brain. We may use the bender knob for example on Garageband increasing the high notes and decreasing the low ones to make them sound correct to our brain.
A good electric guitarist is bending notes by his hand, ear and brain perception.
An interesting experiment may be to measure the frequency of a Pink Floyd guitar solo at a very high note.
A suitable example may be Comfortably Numb at the end of the piece. This masterpiece is written in B minor. So the first bass note is a low B.
And we have at the solo a very high B. It would be an interesting exercise to find out how the beautifully sounding high pitch B is deviated from integer multiples in frequency from the low B for the millions of listener's brain pleasure.
References:
Musical Acoustics - Donald Hall
Sound and Hearing - S.S. Stevens and also Hearing its Phychology - S.S.Stevens, director of phycho physics Laboratory, Harvard
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