[Desecrated]

https://home.comcast.net/~davejanelle/music.htm

Some cool graphs.

[TheHandOfStone]

This is fascinating. I remember reading about the 19-note-per-octave idea a while ago, but never understood why anyone would want to try it.

[Desecrated]

Originally Posted by TheHandOfStone

This is fascinating. I remember reading about the 19-note-per-octave idea a while ago, but never understood why anyone would want to try it.

People want more notes to write their music.
Also other ethnic groups uses 19 tones, like some Arabic and Indian styles.
The guys over at the fretless forum use 19TET pretty often.

[All_¥our_Bass]

In 19 notes per octave tempering, the thirds are closer to the natural overtones than in 12.

[Drew]

One way of judging the worthiness of a well-spaced scale is seeing how close it comes to other simple ratios. A given note and its octave have frequencies in a 2:1 ratio. So - perhaps it would be nice if other notes had frequency ratios of 3:2 or 4:3 as well. Two notes with simple frequency ratios tend to sound pleasing when played together.

That's a very big assumption right there, and it's really at that point that his argument falls apart.

Why 3:2 or 4:3? Why indeed? Why not 5:2 or 6:5? It's a totally arbitrary choice, and one that dictates his eventual conclusion - 12 is the first number that all 2, 3, and 4 all factor evenly into. If you asked the retorical question, "wouldn't it be nice if 5:2 or 6:5 were even, as well?" then the same math would eventually dictate 30 notes per octave as the cleanest approach.

I would counter-argue that a 12-note octave is dictated not by "note ratios" but by the pitches that naturally occur in the harmonic series.

[JBroll]

I can see the fact that 12 is only relatively prime to 1, 5, 7, and 11 being interesting and useful. That is basically why we can play successive major seconds, minor and major thirds, and tritones to get part of the scale. If we had an 11 or 13 note scale (11 and 13 are both primes) any given interval repeated over and over would eventually hit every note... I've been thinking about 13-note scales and trying to figure out what notes should go everywhere, and while I'm still tinkering with tone generators it is fun having a B#.

There's really no usefulness I can see behind that same ratio statement... but Drew, where are you going with the harmonic series? The nodes of the harmonics of a given string will be tied to the harmonic series, but anyone who tunes by harmonics and fretted notes can easily attest to the fretted notes not quite being where the harmonics are all the time (I'm looking at you, 19th fret...) and I didn't think they followed any pattern at all.

Jeff

[Drew]

I could be wrong, dude, but up to a certain point at least the harmonic series spells out most of the intervals of the major scale...

Either way, the dude's analysis is totally a product of his assumptions.