Reading music in the higher frets

I have seen classical guitar written with the 8va- - - - - - - - - - symbol, so I assume it is the same.

I have to work on the upper fret. I get lost still :roll:

It's the same. 8ve lets you write one octave lower, so the "standard" range - the range all full size guitars can play - would only need one ledger line (the highest standard note is 19th fret B). Many steel string acoustics have 20 frets, which would need 2 ledger lines, and a 24 fret neck would need 3.

There's also a 15ve notation, which means you'd play 2 octaves above the notation. I suppose you could use that... it would put the extreme notes in the staff... but I've never seen it used for guitar.

it's not '16ve' = 2 x 8ve? or is this somehow related to 8va and 15ma?

It's 15ve, not 16ve for the same reason that compound intervals are the simple interval plus 7 which puts it an octave higher.
So an octave increased by an octave is 8+7 = 15, or a unison increased by 2 octaves is 1 + 7 + 7 = 15

thanks, Fretsource. I see now that it's based on convention, but not consistent logic: it's a mixed units "calculation": symbolic for the first octave ("8ve") and interval (7 western major scale steps) for the next octave.

The logic is the same, Greg. It's 8ve because it encompasses eight letter names, eg C-D-E-F-G-A-B-C. But two octaves is 15 letter names (because you wouldn't play the C twice!)

Thanks guys, appreciate all the input on clarification. I noticed that it's only with written music and not tab books though.

I now understand the convention, Tom. and it's self consistent within the musical paradigm and definitions. but I'm trained in engineering/math, where the logic would not count the first C for additive math, as the interval from C to C is 0. it would only be a 1 for geometric (harmonic) purposes, as those are multiplicative. this aspect of musical notation has always bothered me.

Ah, but music is geometric, Greg!

Music is composed of sound and silence. That gives us a 3D system (because both frequency and duration depend on a third dimension, time), and we're trying to take a 2D measurement - the comparison of one musical event to another, measuring the difference in frequency.

Intervals are the comparison of two musical events, either of which can be sound or silence. So let's think of silence as zero, and sounds as some non-zero number. Interval calculation is actually multiplicative: take event A x event B, and you have the result... the interval value of any sound combined with silence is zero.

If we compare two non-null events, we run into the problem that pitch values are logarithmic. The distance from C to c is only half the frequency distance from c to c', but our musical analysis says both intervals are the same. And the distance from C-E is identical to the distance from D-F#. Measuring relative distance requires placing the "one" of our logarithmic scale on the lower frequency.

This doesn't solve all the problems of tonal music measurement, because intervals in tonal music are not physically equidistant. But that's really a problem of resolution.

Using a science analogy, we could look at the night sky and see two stars. We can't tell how far apart they are - we can only measure the angle between them. We can't actually measure the distance from star A to star B; we can only say that star A looks closer to star B than star C does - the opposite might actually be true. On this first pass, the astronomers have arbitrarily said "this is where we start", and given angle zero to that position; they then measure the angle to the next star, and get a result - they confirm that star B has a smaller angle to A than star C does.

Musically, we pick the lower sound and give logarithmic unit one to whatever pitch label we're using - we may say the musical starting point is C. We get a rough guess of where the second musical star is, and we call it E. Now we can say we're looking at two pitches that are a third apart; this is an approximation. It doesn't really describe the sounds, but it tells us they look closer together than pitches labeled C and F. Just like with astronomy, this might be wrong - C-E# is actually a bigger distance than C-Fbb.

Astronomers can then wait six months and look again, using parallax to sharpen their measurement. If the stars are near enough to us, they can give a better answer to the question: how far apart are they? They haven't actually given the answer, because their measurement tools aren't precise enough... but now they've got better resolution. They now know an approximate distance.

We sharpen our interval measurement by adding a quality refinement. Our second pass may label the higher pitch Eb (minor third), E (major third) or E# (augmented third).

Neither the astronomers nor the music theorists have given an exact answer, because the measurements are relative and subject to other factors. They've got things that muddy the waters (red shift, gravitational lensing, whatever). So do we - our major third isn't the same as Bach's, because of changes in temperament.

When you get right down to it, all measurements are approximations, whether we're dealing with music or engineering. In fact, in some ways musical measurement makes more sense than math concepts like angle measurement - we always deal with absolute values: since unit 1 is always assigned to the lower pitch, we can't diminish a unison; C-Cb is always identical to Cb-C. Astronomers may use -1 or +1 as an angle measurement, while music theorists always start from the left end :)

Cool explanation Noteboat. Thanks!

And you have all of this in your book Noteboat? If so, I definitely need to buy it now. :D Another thought, didn't you mention sometime back that you have another edition coming out?

Is there an emoticon for "Over my head?" :lol:

That was a great explanation and something I didn't even begin to think about.

Tom -- of course the frequencies of the notes are geometrically related, or close enough. (I won't argue the accuracy and precision point.)

so I was thinking about the log representation model/argument on and off today, wondering why it still bothers me. (also noticing your edits -- esp where you dumped the log(1) = 0 part :wink: ). turns out, it bothers me for the same reason that using 8 tone scale interval names (e.g, 3rds, 6ths) bothers me: while the 1:8:15 octave representation is valid as a scaled log representation of relative freq ratios for those octave intervals, other compared intervals that look like they should have the same freq ratios do not because they do not encompass the same number of semitones, due of course to the half steps B-C and E-F. but if the entire log representation were based on chromatic scale, this problem does not occur. the "octave" representation of 1:12:23 in semitones would result and lesser intervals would be consistent. but the notation is the notation.

so anyway -- thanks for the discussion.

Well, you're right about that Greg. Diatonic scales don't have equidistant notes, but they've been around for a long time (Bob Fink has a theory that it dates to Neanderthal times - some European musicologists believe him, most in the US don't)

We didn't start stepping away from the diatonic scale until about the 9th century. In Arabia, they solved the problem of more notes mathematically, ending up with a 25 part octave division (revised to 24 a century or so later); in Europe we basically ignored the notation issue for 300 years or so, then started tinkering with flats and sharps.

It doesn't start to get really messy from a notation standpoint until the late 1800s. By 1920, there's lots of music being written that could benefit from a different system, and many have been proposed - in the mid 1980s the Music Notation Modernization Society was formed (now the Music Notation Project)... they've collected more than 500 proposals.

Theorists are still grappling with the math aspects of our irregular scale. Allen Forte's set theory approach has a lot of traction with many theorists, but universal changes are really, really slow - remember the metric conversion project in the US in the 1970s? The only thing I've seen change since then is the size of liquor and pop bottles!

I think the next big breakthrough won't come from theorists. It'll come from some future composer who uses an elegant system in his or her own works, which makes sense to others. Stravinsky made major changes to the way orchestral scores are noted, and a lot of modern composers are following his lead - but the average Joe/Jane never stands behind the podium. The last huge changes to music notation (sharp signs, modern key signatures) came because Josquin des Pres did things that made sense to all the other composers, and the huge changes before that (the staff, clefs) came from a couple guys who worked out better systems that made sense. Someone someday will come up with that 'aha' method, and when that happens I think it'll spread pretty quickly.

And fibaz, none of this is in my book. The interval numbering system is, but it's really just a basic text, without a lot of historical context. The next edition is still pending at the moment, because I've been so busy with the new music school - we just completed construction for an expansion (a week ago today, in fact), and it's keeping my days pretty full.