# Music and IQ

Chazzz chazz469 at hotmail.com
Wed Sep 27 17:54:25 EST 2000

```>The harmonic series is very straightforward.  I didn't
>matrices (but they teach those at high school these days
>too <g>.)

It is straightforward, the relationships between the tones are simple
ratios.  Example:
Pretty much anything above 13 becomes microtones....
13  ee-flat
12  dd
11  cc-sharp
10  cc
9    b
8    b-flat
7    a                (440 Hz)
6    g
5    e                <----- your basic harmonic series
4    c                <----- (middle c)
3    G
2    C
1    CC

CC:C = 1:2 (an octave has a ratio of 1:2); C:G = 2:3 (P5=2:3);
G:c=3:4(P4=3:4); c:e=4:5(M3=4:5); e:g=5:6(m3=5:6); etc.....
And you derive the other intervals from their first occurrence, e.g. M6=5:3.

All of this might seem somewhat arbitrary, and I guess it is, but what it
refers to are the frequencies of the notes.  Given that a (#7) is 440 Hertz,
you can derive the frequencies of each of the other notes using these ratios
from the harmonic series.

Like this:
Pretty much anything above 13 becomes microtones....
13  ee-flat         (817 Hz)
12  dd              (755 Hz)
11  cc-sharp     (692 Hz)
10  cc               (628 Hz)
9    b                (565 Hz)
8    b-flat          (503 Hz)
7    a                (440 Hz)
6    g                (377 Hz)
5    e                (314 Hz)<----- your basic harmonic series
4    c                (251 Hz)<----- (middle c)
3    G               (188 Hz)
2    C               (125 Hz)
1    CC            (62.5 Hz)

So you say..."How is this important?"  Well, it's absolutely vital in
Oriental Indian music and other microtonal systems, jazz, alternate tunings,
tone color...the list goes on.  For example, when I was in college, my Band
Director would purposely tune the band either sharp or flat, based on the
music that we were playing  and the venue in which we were playing.  Tuning
the ensemble just a smidge flat (say A @ 437 Hz instead of @ 440 Hz) would
give it a very dark, murky sound and tuning it sharp (say 443 Hz) would give
the ensemble a very bright and colorful sound.

>>...
>> and matrices, and Boulez took it to extremes with his Structures, where
>> EVERY aspect of the piece(s) were determined with matrices.

>The harmonic series is very straightforward.  I didn't know about the
>matrices (but they teach those at high school these days too <g>.)

Ever studied the music of Pierre Boulez?  Or the later determinate works of
Shoenberg?  Musical Matrices are very different than the ones that Calculus
uses.

```