What is it that musical notes have in common with each other?
ie a in 1 octave sounds very much related to a 1 octave higher.
why do scales sound ‘right’ etc?
Is it a property of the human ear? Or some larger concept of sound?
What is it that musical notes have in common with each other?
ie a in 1 octave sounds very much related to a 1 octave higher.
why do scales sound ‘right’ etc?
Is it a property of the human ear? Or some larger concept of sound?
The current standard for the note A above middle C on the piano is 440 cycles per second. An octave below that is 220. More knowledgable people will be in shortly to explain about well tempered claviers and so forth, but yes, there is a mathematical basis to tuning.
Our musical scale is based on tones that sound pleasing to us. This citation of from Physics, Hausman and Slack. *"The characteristics of the ear impose certain physical restrictions on the frequencies of the sounds to be combined to secure harmonious effects. … the ear recognizes two sounds to have the same tonal interval as two others, if the frequency ratios, rather than the frequency differences, are the same for the two pairs.
…
Experience shows that tones having frequency ratios of 2 to 1, 3 to 2, 4 to 3, 5 to 3, 5 to 4, and 6 to 5 produce consonance; musical scales are based upon these ratios. The scales are formed by using three consonant combinations called triads, each of which is a chord formed of three tones. In such a chord, the octave of a tone may accompany or replace the fundamental without altering the nature of the chord.*
So sounds that are based on combinations of tones, having the specified ratios, within an interval between two tones related by a frequency ratio of 2 to 1 sound consonant and not dissonant to us.
I think the book might put it a little too strongly when they say “the characteristics of the ear impose certain physical restrictions” on harmony. Oriental music sounds dissonant to me but seems to please them.
To clarify a bit on octaves, they’re the 2:1 ratio mentioned above. If you take a string of a given length, and halve that length, you’ll get a note one octave above the starting (full length of string) note. Halve it again (1/4 of the origninal length) and you get a note another octave higher. Halve it again (1/8 the original), the next octave.
The string length in the above example is proportional to the frequency of vibration. Thus we have an A note at 55 hz, 110 hz, 220 hz, 440 hz, 880 hz, etc. The same principle is true for any note, although the particular numbers will of course be different. Take any given frequency, or any given string length, and either double it or halve it and the result is one octave from where you started (either up or down depending on which way you went).
An important factor of the octave, in particular, is that it is the first interval in the harmonic series. I’ll explain:
A note as played on an instrument is not made of just one pure tone. It consists of many different tones of various amplitude. When you hear a violin play a G, you are hearing a combination of various pure tones in the harmonic sequence. The harmonics are “stacked” above the base tone in the following intervals:
Octave, Perfect 5th, Perfect 4th, Major 3rd, Minor 3rd, etc.
Any of the above intervals sound natural to the listener because the upper note is, in a sense, already sounding as part of the harmonic series of the lower note. Dig?