## Musical Half and Whole Steps with Respect to Frequency (Hz) [10 points!]?

Question by Sketchy Skeptic: Musical Half and Whole Steps with Respect to Frequency (Hz) [10 points!]?
I’m somewhat new to music theory and would like to truly understand it, not just memorize, so I can use it properly. I’m looking for a little more of an explanation that “because that’s the way Western music is”.

I would like to know why in a major scale we call E->F a half step and B->C a half step. An octave is a doubling of the frequency of a note, and I assume the notes A->G are spaced by some relationship of frequency (I would appreciate this relationship if you know). What I really want to know is, does this relationship of frequency actually change between E->F relative to D->E (i.e. is the expected jump in frequency between notes halved or something?) and if so, why does it sound good (do they sound like a half an interval the trained ear?), and why would they bother giving them major letter names- just laziness when making major scales?

I know that’s a lot of questions, but if you can answer them, you will have probably changed my entire outlook on music. Thanks in advance!
Cheers!

I don’t know music theory either, but I do know that Hz increases exponentially. Therefore, the jump from F3 to G3 is not as big number-wise as the jump from F4 to G4.

If you graph (easiest with a graphing calculator) the function y equals 2 to the x power,or y=2^x, you’ll notice that the interval from x=1 to x=2 is not as big as the jump from x=2 to x=3, which is not as big as the jump from x=3 to x=4, etc.
Here’s a picture of the function y=2^x http://hotmath.com/images/gt/lessons/genericalg1/exponential_graph.gif

I think you may get more (and better, and more useful) responses if you ask again somewhere else entirely (not Y! Answers). Good luck, and sorry if I couldn’t help

## Musical Half and Whole Steps with Respect to Frequency (Hz) [10 points!]?

Question by Sketchy Skeptic: Musical Half and Whole Steps with Respect to Frequency (Hz) [10 points!]?
I’m somewhat new to music theory and would like to truly understand it, not just memorize, so I can use it properly. I’m looking for a little more of an explanation that “because that’s the way Western music is”.

I would like to know why in a major scale we call E->F a half step and B->C a half step. An octave is a doubling of the frequency of a note, and I assume the notes A->G are spaced by some relationship of frequency (I would appreciate this relationship if you know). What I really want to know is, does this relationship of frequency actually change between E->F relative to D->E (i.e. is the expected jump in frequency between notes halved or something?) and if so, why does it sound good (do they sound like a half an interval the trained ear?), and why would they bother giving them major letter names- just laziness when making major scales?

I know that’s a lot of questions, but if you can answer them, you will have probably changed my entire outlook on music. Thanks in advance!
Cheers!

I’ll just answer one, see if you can figure out the rest.
One octave=doubling of frequency
There are 12 notes in one octave (never mind what they are called, 12 is the relevant number).

Each note differs from the previous ( and consequently the next one) by the 12th root of 2 which is about 1.0596. So the frequency of D is 1.0596x frequency of the (preceding) C and so on.

Note that this spacing makes the notes belong to a geometric, rather than arithmetic, progression.

Now, let’s introduce the notes’ names: A, B, C etc. We stop at G: that is seven names and we have 12 notes, so we add # (or ♭if you go backward … :-)) to each name. Problem: we now have 14 names for 12 notes! 2 have to go and you know which ones went.

Now,why 12 notes, why flats and sharps and so on: search the net, it is a long story. You may want to read why Bach composed the Preludes for the Well Tempered Clavier.

## Five Basic Steps For Building Model Railroads

Selecting the hobby of building model railroads is one of the better choices that anyone can make for use of their time. Make no mistake about it, this is not a hobby that is only for the retired with plenty of time on their hands. In fact, model railroading has risen over the years to such a high level of popularity, that people from all walks of life, gender and age, have and are committing themselves to this amazing hobby.

Not only does this hobby provide it’s participants with an outlet to demonstrate their creative talents, it can potentially let you immerse yourself in a past era, rich with historical fact. Model railroading is a hobby that can also bring families together, with each member sharing in the planning and building of their model railroad layouts. With all of the various aspects involved in becoming a model railroader, time becomes something that most enthusiast tend to lose track of while working with this unique hobby, and considering all of the difficult challenges that we face in our day to day life, the therapeutic value this hobby offers is indispensable.

]]>

In starting out with model railroading, it is best as it is with any new venture to outline what it’s basic requirements are, and the following steps should help you:

1. The first and most important issue to consider the finances you have available to commit to this venture. Model railroading is not without it’s expense, and can become rather pricey. The good news is that you can begin very modestly and at any level, and gradually add to your train collection and layout as you can afford to.

2. After determining what your initial start up costs will be, the next step is to decide on what scale and gauge you’d like to use. If your new to building model railroads, the question of scale and gauge can be made a little easier by simply knowing exactly what these two terms mean.

Scale: The easiest way to describe scale is the comparable difference in size of the model train in relationship to the corresponding full size prototype. For example, the HO model train is 1/60th the size of it’s real life counterpart.

Gauge: Simply put, gauge is the distance or measurement between the two outside rails of track when referring to model trains. The measurement is taken from the center of the two outside rails when dealing with toy model trains.

3. The next step in the process is to actually choose which model scale train you’ll be adding to your railroad, and you have several to choose from. Your choice will involve the consideration of a number of factors, most of which are related to budget and the amount of space you have available for your layout.

4. Now it’s time to decide on the theme of your railroad, and this will require a little research. You may want to build a contemporary setting or you may decide to reach back in time and choose a historically rich era in railroading.

5. With all of the previously described choices made, the next step is to begin building your model railroad, and this will include constructing your bench work, dealing with all of the electrical aspects related to running your railroad, and finally the creation of your scenery.