(Bear with me, this does have musical significance. I was inspired by that other thread to make a blog post.)

In golf, I often have to walk off the distance between my ball and a known yardage marker. If my ball is 7 paces back from the 150 yard marker, then I am 157 yards away from the hole, and I pull out my 7-iron and whack away...

Since many common definitions of "interval" involve distance, we tend to think that intervals work the same way. But they don't. If you were a small person standing on the 'A' of a piano and walked four paces towards the treble, you would NOT be a 4th away. You'd be a fifth away, on an 'E.'

I was thinking of this because in another thread, the Alfred Dictionary definition of "octave" was reported to be:

"The interval of eight diatonic steps or from one note to it's nearest note of the same name."

I read that a few times and realized that the first part of that definition is wrong. If you, as a small person, started on a 'C' and took 8 paces forward, you'd end up on 'D', not 'C'!

This is because intervals are *ordinal*, not *cardinal* numbers. They do not measure distance, they designate position. We call a 5th a 5th (and not 5) because it is the 5th note of the diatonic scale, not the note that's 5 steps away.

I mention all of this not to nitpick, but because it can make all the difference when you teach intervals to your students. When showing a student the interval of a third, for example, don't use cardinal numbers (don't count the notes 1-2-3), use ordinal numbers. Say "Think of a D Major scale, and show me the 'third' note." The third note of a Major scale is the interval of a major third. I still remember the day I started using "1st, 2nd, 3rd" with my students instead of "1, 2, 3." The world of intervals suddenly made perfect sense, and I learned an important lesson about the power of language in teaching.

On a side note, this also explains why the symbol for 2 octaves above is 15ma. The musical term "15ma" is short for the Italian word "quindecima," which means 15th. We often wonder why it's not "16ma" but if you look at a keyboard and count, you'll discover:

C(1st) D(2nd) E(3rd) F(4th) G(5th) A(6th) B(7th) C(8th) D(9th) E(10th) F(11th) G(12th) A(13th) B(14th) C(15th!!!)

I'll admit to having been too lazy to catch that

I wasn't taught scales as a series of intervals (or, perhaps more accurately, I didn't learn them as a series of intervals) when I was in music lessons so long ago. A real light came on when I first discovered the intervals, rather than the individual notes

When I looked up a definition of octave in the two pre-1930 music dictionaries I have I was surprised to not find the definition that Tim posted in the other thread. One of them was, uh, laughable, and the other said "A series of eight consecutive diatonic tones" or "the interval (1:2) between the first and eighth tone of such a series." But wikipedia, I think, does a good job: "In music, an octave ... is the interval between one musical pitch and another with half or double its frequency."

I was showing a young, quite bright pianist how to play "oom pah" and he asked me if it was always "a fourth" and I had to think a split second before I said "yes" because I always think of it as "1 - 5" - the first and fifth notes of the scale with the second one played lower. But the interval is a fourth.

I often have to write/re-write several times before I say anything coherent, and sometimes I still come up short! But I think taking the time and making the effort to make the kind of distinctions in language that you're talking about, and to be accurate in our speech, is important.

Cathy

Doesn't seem like nit picking to me, but rather a very clear picture of something that seems to have become muddy.

You bring up several really good points and you said it beautifully!

Thank you for being concise

I have no objection to nitpicking when it's done well, as this is. Bravo!

You caught me as well, I carelessly used the word step incorrectly. My apologies.

I applaud you not only using the correct number, 15 vs 16, but the ma ending instead of va. I've noticed 15 instead of 16 has caught on finally, but most continue to end it with va.

Do you have an opinion on correct usage when we mean one or two octaves down? I subscribe to 8va b (basso) and 15ma b, but 8vb and 15vb seem to be more common.

This is actually something that hit me as a student the first time I heard the terms "major third" and "minor third". I went up *two* notes, so where did that *three* come from? I was told that this involves counting all the notes that are involved in a naming process. Bottom line is that what you brought up was indeed an issue for me as a student.

A step is a particular distance from one note to the next note, so an interval. But when people learn it via the piano, I think they tend to identify steps with the piano keys themselves. Is that possible?

I think this is a great example... it's such a minor difference in terminology, but it avoids so much potential misunderstanding. It also has the happy consequence of divorcing the notion of intervals from finger numbers.

Yes, I think it happens quite often. When I'm teaching elementary reading, I say this for 5-finger patterns:

"C, whole step up, whole step up, half step up, whole step up"

In other words, I give students a starting place (the C) and then try to use the word step as a verb instead of a noun, and when I write "WWHWWWH" underneath a scale, I make sure the letters come between the notes, not directly under. (And we mark whole steps with Brackets and half steps with V's.)

Bravo to both of your posts, Kreisler, and particularly this bit! Ah, clarity - I love it!