Relativity & Sound: Exploring Musical Octaves

[Lear]

Hello! I am new and posting my first post on these forums... so I hope I have posted in the right place for my question.

I should say first that I am not a Physicist, I am a Mathematician. So please keep answers as easy to understand as you can.
I also apologize for the fact that my question will take us into the realms of music theory which many of you will not (nor could you be expected to) understand.

I hope you understand the fact that the musical octave does not fit without certain notes being tuned slightly off? I now remember reading somewhere that Einstein had shown that it was only in our space-time continuum that the octave does not fit (and it is only my guess-work that has linked this with relativity).

Is this indeed correct? and if so, could someone explain how it works please?
I would also be interested to know if there would be any way of finding (even a mathematical basis of) a space-time continuum in which the octave does fit without some notes needing to be tuned off.

Hope you understand what I am on about, and I apologize for my lack of knowledge about physics.

Lear.

 

[matheinste]

Hello! I am new and posting my first post on these forums... so I hope I have posted in the right place for my question.


I hope you understand the fact that the musical octave does not fit without certain notes being tuned slightly off? I now remember reading somewhere that Einstein had shown that it was only in our space-time continuum that the octave does not fit (and it is only my guess-work that has linked this with relativity).


Lear.

The accoustic spectrum being (we assume) continuous), any interval can be divided up as we wish. I assume that the the divisions of an octave have a precise mathematical definition giving each note a specific frequency. I think it is the case that there are various methods of tuning within the octave resulting in some notes not having exactly the frequency required by the mathematical definition. The various tunings or divisions are probably a matter of human and cultural preference and practicality.

I don't think the spacetime continuum has any specific or special relevance to the subject.

Matheinste.

 

[Al68]

I hope you understand the fact that the musical octave does not fit without certain notes being tuned slightly off? I now remember reading somewhere that Einstein had shown that it was only in our space-time continuum that the octave does not fit (and it is only my guess-work that has linked this with relativity).

The specific method for individual note spacing varies greatly between different systems.

In the most common (western) tuning system, 12 tone equal temperament, the frequency ratio between adjacent notes is exactly the twelfth root of two for each pair of adjacent notes. And the notes fit perfectly in the octave, the frequency ratio between any note and the same note an octave lower is exactly 2.

That's just a human convention, and there are many others, but what do you mean by "octave does not fit" and "tuned slightly off"?

 

[pervect]

This doesn't have anything to do with the space-time continuum...

The modern "even tempered scale" divides an octave, which is a 2:1 ratio in frequencies, into 12 intervals. The ratio of frequencies in an interval is a constant. Given that there are 12 "intervals" in an octave, with each interval with a constant ratio, I think you can see that this ratio is 2^(1/12)?Unfortunately, this makes certain chords sound funny, unless you detune them slightly, by making one of the notes higher or lower so that the ratio comes out right, which is what you're talking about.

Take an example from http://en.wikipedia.org/wiki/Equal_temperament

Consider an interval of 5 of these evenly spaced intervals between an octave. Perfectly tuned using the even tempered scale, that gives frequency a relationship of 1.3348, approximately. But this interval sounds better when the ratio is 4:3, which is 1.333333 exactly.

See for instance http://en.wikipedia.org/wiki/Equal_temperament

This gives the equal tempered intervals, and the "just intervals" that they approximate. The example I used is called a perfect fourth.

 

[seb7]

Harmonics of notes are more musically natural. That is, note frequencies which fit well with other note frequencies, like halves, quarters, thirds. But the way we have dividing the octave into 12 notes is actually slightly out of tune to this.

Apparently violinist will often attempt to play closer to the more natural notes.

As with space-time continuum. Well if time was running at a difference pace, then the frequency of notes would be different. How strings vibrate depends on the types of materials used, the material within the space its vibrating in and its tension. So I suppose sound is time-space dependant, but fitting to an octave is just simple maths.

 

[S.Vasojevic]

I have heard from respected piano tuner and builder, that in fact when tuning a piano they purposely of-tune some notes, just slightly, and that is considered as coloring. That is the reason why pianists have favorite tuners, and why pianos are still tuned by ear, not with electronic device. Nothing to do with physics, though.

 

[Ich]

They tune an octave > 2/1, to make the harmonics match better. Because the strings have a finite diameter and are a bit rigid, the second harmonic is not at double frequency, but a bit higher.