music theroy question - should be easy

[req 5,000+ posts]

how do ya calculate a half step (octave) up or down? im getting mixed results, and i thought id ask to make sure im doing this right.

thanks.

Click to read more...

 

[JimJ 5,000+ posts]

http://www.midicode.com/tunings/acoustics.shtml

Have fun.

 

[JimJ 5,000+ posts]

And it's "theory"...still haven't learned from your question on enclosure alignments, have we?

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[req 5,000+ posts]

yea yea. lol, i am dislexic sometimes //content.invisioncic.com/y282845/emoticons/tongue.gif.6130eb82179565f6db8d26d6001dcd24.gif

thanks for the link though jack.

 

[monte_carlo97 10+ year member]

mind giving the rest of us a quick rundown on what you are trying to do?

 

[req 5,000+ posts]

um. im trying to find what a half octave of a certain frequency is //content.invisioncic.com/y282845/emoticons/tongue.gif.6130eb82179565f6db8d26d6001dcd24.gif

1.7 The 3rd Harmonic and the Interval of a Fifth
The relationship of a frequency, F, and its double, 2F, is an octave, 4F a further octave and so on. But what of a frequency three times that of the fundamental, 3F? This is about an octave and a half above the fundamental and is the interval known to musicians as a twelfth, or one octave plus a fifth (because it is that many steps in the conventional musical scale). This interval is the second most important interval after the octave.

The interval of a twelfth is represented by the ratio 3 / 1. To obtain the interval of a fifth we must reduce this by an octave, 1 / 2, so the interval of a fifth is represented by the ratio 3 / 2, three times the fundamental but transposed down an octave. A fifth is the interval which exists between the 2nd and 3rd harmonics of an harmonic series.

so a 3\1 fraction = .33 repeating. so say i want to do one half step down from 60hz.

60 x .33 = 19.8

60 - 19.8 = 40.2hz

so 40.2hz would be one half step (half octave?) down from 60?

is this right?

 

[monte_carlo97 10+ year member]

and how is finding that valuable. Just trying to learn something new today.

 

[req 5,000+ posts]

um. its related to a certain SPL application a friend of mine is doing. 60hz is pulled from my ***.

basically, i read a few places that tuning a SPL box to a half octave below the cars resonant frequency is a good place to start - rather than guessing. so im trying to learn how the hell music theORists calculate half octaves. thats all.

 

[monte_carlo97 10+ year member]

why not just get ahold of an RTA and go that route. More acurate.

 

[req 5,000+ posts]

what? how would an RTA aid me in finding half step\octave below the peak? i could try to find the peak (or near it) with the RTA - it will NOT give me specific numbers like 64hz, because its only 1\3 octave - and will not show every frequency, and it does not list the decible level (sadly - or id use it for a makeshift SPL mic //content.invisioncic.com/y282845/emoticons/tongue.gif.6130eb82179565f6db8d26d6001dcd24.gif )

 

[squeak9798 5,000+ posts]

so a 3\1 fraction = .33 repeating. so say i want to do one half step down from 60hz.

Well, to start with; the fraction 3/1 = 3, not .33

2nd, That scale was for increasing in frequency. You are wanting to decrease in frequency by one-half octave; not increase.

So, if an octave higher is represented as 2/1, then an octave lower would be the reciprocal of that, or 1/2. Now, you are wanting to find 1/2 of that 1/2; or more easily, 1/4. So, you could take that 60hz and subtract 1/4, or (more quickly) mulitply it by 3/4.

So, one octave lower than 60hz is 45hz. To verify this; one octave lower from 60hz is 30hz. The middle point between those is 45hz.

Correct me if I'm wrong, but that's just using logic.

 

[Acidburn 5,000+ posts]

^^thats what i thought

45Hz

 

[RandyJ 10+ year member]

Well, to start with; the fraction 3/1 = 3, not .33
2nd, That scale was for increasing in frequency. You are wanting to decrease in frequency by one-half octave; not increase.

So, if an octave higher is represented as 2/1, then an octave lower would be the reciprocal of that, or 1/2. Now, you are wanting to find 1/2 of that 1/2; or more easily, 1/4. So, you could take that 60hz and subtract 1/4, or (more quickly) mulitply it by 3/4.

So, one octave lower than 60hz is 45hz. To verify this; one octave lower from 60hz is 30hz. The middle point between those is 45hz.

Correct me if I'm wrong, but that's just using logic.

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I read Req's reply and it was drivin me crazy. I didnt know wether or not I had forgotten everything I learned in Physics and Calc or if he was just wrong.

 

[RandyJ 10+ year member]

Just one more example.

An octave down is, as mentioned, 1/2 the origional F. So an octave down of 4F would be 2F, and up would be 8F. So use simple math to find the answer.

Take 500Hz.

Divide by 2 for 250Hz.

500-250=250

Divide 250 by 2 for 125

250Hz + 125Hz = 375Hz.

This leaves you with 125Hz above 1/2F and 125 below 1F. The half step will always have the same value above AND below 1/2F and 1F, therefor being 3/4F //content.invisioncic.com/y282845/emoticons/wink.gif.608e3ea05f1a9f98611af0861652f8fb.gif.

 

[req 5,000+ posts]

at first i was doing the 1\4 thing, because that was logic. but somewhere i read that it was some kind of weird graph chart logrythm thing and it wasnt just a quarter less //content.invisioncic.com/y282845/emoticons/tongue.gif.6130eb82179565f6db8d26d6001dcd24.gif

45hz was my first guess - thanks though. im not that big of a math person.