whatz music in terms of vibrations? 1

[kashyap]

well we all know that noise is "unwanted/unpleasent" vibrations.But, this is almost a laymans answer.
I would like to know what vibrations constitute the "basic notes"? and what makes it pleasent to ears? Further how is that the music revolves around the 7 basic notes?
as a professional vibration specialist.

regards,
kashyap

 

[IRstuff]

Notes are by convention and the 7 notes you refer to are actually 12 if you include the black keys on the piano. This particular scale is the equally tempered(?), while there are at least 4 or 5 other commonly recognized scales.

 

[electricpete]

The harmonic series consists of musically recognizeable intervals. For example if is your fundamental, the harmonics will be as follows:
C = 1X
C' = 2X
G' =3X
C''=4X
E''=5X
G''=6X
Bbb''=7x (sort of).
C'''=8x
D'''=9/8
From the above it may be deduced that
- an octave corresponds to a factor of 2 change in frequency.
- a fifth corresponds to a factor of 3/2 change
- a fourth corresponds to a factor of 4/3 change
- a major third corresponds to a factor of 5/4 change
- a minor third corresponds to a factor of 6/5 change
- a major second would be a fifth minus a fourth or 3/2 divided by 4/3 gives 9/8.
- a minor second could also be computed as a fourth over a major third or 4/3 divided by 5/4 gives 16/15. You could also compute it as a minor third minus major 2nd or 6/5 divided by 9/8 gives 48/45=16/15

I think there becomes a problem if you try to use these ratio's to construct a chromatic scale... the ratio's don't work out precisely and not every minor 2nd is evenly spaced. There arises a new mathematical definition of the minor 2nd as the twelfth root of 2 (an irrational number). Then any interval can be computed from that by taking the twelfth root of 2 and raising it to a power corresponding to the number of minor 2nds (half-steps) in the interval. For example a minor 3rd would be twelfth root of 2 to the third. I think it comes out pretty close (but not exact) to the rational number described above.

So the music intervals that we recognize are the ones whose frequencies differ by rational numbers (integer ratios of frequencies).

A major chord could be 1X, 1.25X, 1.5X.
A minor chord could be 1X, 1.2X, 1.5X.

There's a lot more that can be said both on the music side and the math side. What are you interested in.

 

[butelja]

Middle C on a piano is 263 Hz. Each whole octave doubles in frequency.

 

[electricpete]

two corrections:
1 - the intro should read: "If C[/] is your fundamental..."
2 - D''' should be 9x.

By the way, a prime superscript is my notation for one octave higher.

 

[electricpete]

I remember that "A" is 440hz. I see the ratio between my number for A and someone else's number for C is 1.667=5/3. That doesn't quite match the ratio's I have above (should be a minor third different = 6/5).

I'm not sure what the explanation for this apparent contradiction is.

 

[electricpete]

No contradiction... I was just thinking a little slow.

The A is above the C, not vice versa. The interval of interest is therefore a major 6th. That is an octave minus a minor third or 2/1 divicided by 6/5 = 10/6 = 1.667.

 

[MikeyP]

For equal temperament (not sure of spelling!), multiplying by the fundamental frequency of a note by the 12th root of 2 (2^(1/12) in Excel notation) gives a note 1 semitone higher (dividing gives 1 semitone lower). So if A is 440 Hz, middle C is 261.63 Hz.

M