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 on one of my favorite forums, Alfred’s “Essential Dictionary of Music” was reported to have defined octave as:
“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!!!)
This is great – I have had many students who were confused about the naming of intervals. I think that thinking of it as coming from the tonic, as you say, is the key. In addition, thinking of it “from the tonic” will come in handy when students are learning about key signatures and chords/Roman numerals later on. =]
(p.s. – is it okay if I link to your post in my blog?)
Hello Joy – yes, feel free to link the post anywhere you’d like! Thanks!