19-tone music?

[TellyKNeasuss]

A friend who's a violinist said that one of the orchestras that she's in is going to play a "19-tone piece" at their next concert. Can anyone explain what 19-tone music is to a layman?

 

[Gazpacho]

If you look at a piano keyboard, you will see that the same layout of 12 keys (black and white) repeats across the keyboard. The interval of 12 keys is an octave, and each octave starts at a vibration frequency twice that of the octave below it. Within each octave, there is a continous range of frequencies, but only 12 of them are available on the piano. Most western music (and international music influenced by it) is written for this 12-tone scale.

Many instruments are fixed to one scale by design, but strings are not. It is possible to play music in which 19 tones are available per octave. The aesthetic benefit is that chords are closer to "perfect" harmony, in the sense that the ratios between the frequencies of the notes are closer to ratios of small integers.

 

[Bikewer]

There are a wide variety of such tuning schemes. For a while, a company was selling guitars with replaceable fretboards set up for various alternate scalar systems.

 

[calebprime]

there are a limited number of equal-tempered scales of some number of notes per "octave" or 2/1 ratio, that have good 3/2 ratios, that is, approximately C-G, or a "5th".

they are:

5 notes per octave
7
12
17
19
31, etc.

step-size is around 63 cents, or around 3/4 of a typical 12-tone "half-step."

referring to the (dependable) table in Partch's Genesis of a Music:

the "5th" C-G Do So is 694.7 cents, or around 7 cents flat from 702 cents, an ideal 3:2 "fifth". not bad, not great.

a big advantage of 19-tone is improved "thirds" --ratios including 5's, like 5/4 and 6/5. These are approximated more accurately than in 12-tone equal temperament. (Which orchestras only sort-of play in anyway...)

and also, a completely different geography, and logic of pitch-relation, although a composer can just sort of adapt what she hears to the new system, and not worry about the "logic" too much.

computers, synthesizers, have really helped people explore these new tunings...

More on 19-tone if anyone wishes...

Hard for an orchestra to do!

eta: wiki looks good here. http://en.wikipedia.org/wiki/19_equal_temperament

 

[calebprime]

oops, make that around 2/3rds of a half-step.

doesn't matter--when you play this stuff, you wouldn't think in those terms...