What is the formula for finding a note that is a certain interval below a given note?

Question

When given the note ‘F’ and asked to write a minor sixth below it. What is the formula for finding that note?

Answer 1

Thank you again to Guitarpicker. It's a pleasure to be on the same board as him. I am not going to give you a bunch of fancy formulas. they are out there, but they are inevitably a bit confusing. I am going to tell you to learn a bunch of songs.

First of all, Whatever you do going up, is the opposite going down. the musical scale is built that way. A perfect fourth up, is a perfect fifth down. (Always count the note you start on as ONE by the way. The biggest mistake people make when they start out doing this stuff is to ignore the note they start with. That's just like ignoring your date when you come to pick him or her up. Either one is a disaster waiting to happen.)

Let's prove it Going up? C - D - E - F ( 1 - 2 - 3 - 4 )
Going Down! C - B - A - G - F ( 1 - 2 - 3 - 4 - 5 )

Now let's do all of the intervals:

Going up Going Down
Prime - Octave
Minor Second - Major Seventh
Major Second - Dominant Seventh
Minor Third - Major Sixth
Major Third - Minor Sixth
Perfect Fourth - Perfect Fifth
Augmented 4th - Diminished Fifth
Perfect Fifth - Perfect Fourth
Minor sixth - Major Third
Major Sixth - Minor Third
Dominant Seventh - Major Second
Major Seventh - Minor Second
Octave - Prime

Works perfectly except that some of the names don't quite match up. the Dominant seventh is also a minor seventh. An augmented fourth and a diminished fifth are also known as the Tritone, one of the most interesting intervals in Harmony. I'll have to write about that some other time

The best way to remember these intervals, is to remember a song that they go well with

Minor second - Jaws

Major Second - Do - Re - Mi from the Sound of Music
( Do, a deer, a female deer, Re, a drop of golden sun)

Minor third - The middle of Somewhere over the Rainbow
(Someday I'll Wish upon a star)

Major Third - If I Loved You (From South Pacific)

Perfect Fourth - Here Comes the Bride

Tritone (Augmented fourth or Diminished Fifth) Maria from west Side Story

Perfect Fifth - Bagpipes (the drone behind the music)
Or Star Wars (Or Saints if you use the first four notes)

Minor Sixth - theme from Love Story
(Where do I begin)

Major Sixth - Hi Lilly, Hi Lily, Hi lo
(The song of love is a sad song)

Dominant seventh - There's a Place For Us - From West Side Story

Major Seventh - a bit of a stretch, but Bali Hi - from South Pacific
(You have to ignore that it goes to the octave first, and then down to the Major Seventh. You also have to ignore that the whole thing is pitched on the fifth and not the octave, but I honestly don't know of a better example)
C3 - C4 B3

So, the easy way to find any note is to take the smaller interval and reverse the tonality

You are given the note F and asked to write a minor sixth below it.
Minor six down, is major third up!
Down - F - E - D - C - Bb - A (I am using the small b as a flat sign)
Up - - - F - G - A

You are given the note F and asked to write a major sixth below it
Major sixth down is minor third up
Down - F - E - D - C - Bb - Ab
Up - - - F - G - Ab

It takes a little bit of practice, but it is an excellent way of checking your work and once you internalize it, you never forget it because it just makes sense.
If you work with is and are still having trouble, send me a quick e-mail and I will send you an entire chart. Shouldn't take more than a half hour to work out.

I stuck some links below because it really doesn't matter how you learn this or if my method is the best or not. what really matters is that you learn it, and that you find the method that is best for you. These each have something going for them, and I went to the sites to get the http addresses instead of just making a list of links. That way I know that each of these sites are active as of the day I posted them. Hope this helps.

Answer 2

People will give you formulas that ask you to count half steps, etc. What you need to know is that second, thirds, sixths, and seventh can be major or minor ( also, augmented or diminished). Unison, fourths, fifths, and octaves are PERFECT intervals - neither major nor minor (but they can also be made augmented and diminished).

Let's just stick to major and minor for now. Working UP may be easier for you at first. If the interval is a SECOND, it's either a 1/2 step - minor second - or a whole step - major second. A third is either a step and a half (C-D-E flat) or two steps (C-D-E). A sixth - same deal. Either a fifth plus a HALF step - minor sixth; or a fifth plus a WHOLE step - major sixth. Sevenths - either a half-step short of an octave (or two steps more than a fifth) - major seventh. A FULL step short of an octave, or a step and a half above a fifth - a minor seventh.

OK - intervals BELOW a note. As another poster said, all the colors invert - C up to D - major; C DOWN to b - minor. Again, once you take out the perfect or pure intervals, there are only four left to deal with - second, thirds, sixths, and sevenths.

Answer 3

For a minor sixth below, you count down eight half-steps.

The only "formula" for determining distances is simply counting the half-steps. Minor second is one half-step, major second is two, minor third is three, major third is four, etc. After a short while, you'll be able to immediately know where any given interval is in relation to a note.

Answer 4

You have some great questions. In your e-mail I referred you to Cconsaul whose expertise should answer both your questions.

For once I am stymied on giving an accurate answer.

Conversely, to obtain a minor sixth from a minor seventh we would lower (flatten) the dominant seventh note 1/2 step. The basic formula is 1 1/2 + 2 + 1

Answer 5

The rule of 9:

M up + m down = 9

m down + M up = 9

examples:

minor 6th up is the same as Major 3rd down
Major 7th up is the same as minor 2nd down

Answer 6

1

Answer 7

Remember a certain song for each interval. Nursery rhymes are pretty easy to remember for that. (interval between the first 2 notes)

Answer 8

You listen.....