Q. Is there a program (or is it possible to make a program) in which you type in a frequency (say, 440 Hz for A) and it will be played for you. And then if you typed 450 (not an actual note) it would still play the exact sound (a slightly sharp A). I'm trying to see how it would sound if instead of musical octaves being separated into 8 equal parts when creating a major scale (as in, containing 8 distinct pitches/notes), octaves had some other number of separated parts (pitches/notes). Are major scales even divided equally? Are all the frequencies between the notes in a major scale the same interval?
A. Hi!
First off a program to explore frequencies :
http://pages.globetrotter.net/roule/sa/accord.htm
Is a Java program that allows you explore frequency online.
Otherwise you could use a sound editing suite. I have MAGIX MP3 maker and I can create an MP3 by adding add simple frequencies, together. like 1 second of 440Hz, 1 sec of 500Hz, etc.,
Your question about major scales is more complicated. How to divide the octave into parts to make a scale is a question that has been debated for 2000 years! Pythagoros, the famous triangle man, was one of the first people to start on it,
A major scale is not evenly divided.
Imagine a piano keyboard. As we play up a C major scale, we will just use the white keys. So from C to D skips a black key. So that interval is a Tone. From D to E skips D#, so that interval is a tone. Then from E to F, there is no black key, so that is only a semitone.
So the way a major scale is divided is T-T-sT-T-T-T-sT
If you now play it and listen carefully, you will hear that the major scale is not equal divided. It is just that we are so conditioned to listening to music in the major key that we just don't hear it, unless we listen carefully.
Now, next, what frequencies will you need to put into your tone generator to generate a major scale.
So if A is at 440Hz
A the octave above is twice the frequency = 880Hz
(This is always the case you always go up an octave by doubling the frequency)
Now the 'modern' way of dividing this frequency range is called equal temperament. It is called equal temperament because every semitone is the exact same ratio of frequencies. Knowing this we can mathematically work out exactly what the frequencies need to.
There are 12 semitone steps in an octave. An octave doubles the frequency, so the ratio between a frequency of a note and that of the semitone above needs to be the 12 root of 2! (1.0535)
So we can write out the frequency for an a major scale, using equal temperament.
NoteIntervalFrequency
A440.0Hz
BT493.9Hz
C#T554.4Hz
DST587.3Hz
ET659.3Hz
F#T740.0Hz
G#T830.6Hz
A'ST880.0Hz
Equal temperament is very useful, because it means that a piano can be a transposing instrument, that means you can play any key signature equally on it. And the chords you make on it will sound equally good in any key.
There is a disadvantage though. There are some particular ratios of frequencies that sound very good together, there are very pure harmonies.
For example a pure fifth, the interval between A and E for example, if it was tuned exactly would have the exact geometric ratio of 3:2 or a ratio of 1.5.
So if we tuned our piano this way to give this very pretty 5th, E should be 440*1.5 = 660Hz. But our equal system has put it at 659.3. Very close but not a perfect interval. The fourth is even worse. That is why some people say the equal temperament is equally out of tune :)
You look up more on temperament on sites like :
http://www.terryblackburn.us/music/temperament/stoess.htm
Hope this has been some help. But the subject you are just entering is quite complicated, but fascinating.
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Title : Where can I find a program that will reproduce any sound frequency?
Description : Q. Is there a program (or is it possible to make a program) in which you type in a frequency (say, 440 Hz for A) and it will be played for ...