### NATURAL PURE TUNING

Natural Pure Tuning consists of the Pitch Reference Frequency and of
pure intervals, whose frequency ratios are the quotients of natural
numbers. All is based on the natural overtone series. Natural
Pure Tuning begins with 1 Hz and includes 432 HZ as well as 256 and 440
HZ.

The Natural Pure Tuning System consists of

Pitch Reference
Frequencies

and

Intervals in Just Intonation

whose frequency ratios are the

quotients
of
natural numbers.

Just intonation or pure intonation is any
musical tuning in which the frequencies of notes are related by ratios
of natural numbers.

Any interval tuned in this way is called
a pure or just interval.

Scientific Tuning builds on **
Scientific Pitch
(Verdi Tuning)**

which is based on middle C (C4) = 256
Hz.

256 divided by 2 = 128

divided by 2 = 64

divided
by 2 = 32

divided by 2 = 16

divided by 2 = 8

divided by
2 = 4

divided by 2 = 2

divided by 2 = 1 Hz (1 cycle per second)

**1 Hz is the basic reference frequency of Natural Pure Tuning
System.**

256 Hz is the eighth octave of 1 Hz.An octave
means the doubling of an frequency.

Row of octaves:

0-1-2-4-8-16-32-64-128-256-512-1024-2048-4096-8192-16384-32768
.........

The Pitch Reference Frequencies are always

odd numbers,
integral
numbers,
natural numbers

and bear reference to the traditonal 12 keynotes of western scales.

The second reference frequency could be 2 Hz.

Because 2 Hz belongs to the octavation of 1 Hz,

3 Hz is the next reference frequency for a pure scale.

4 Hz belongs to the octavation of 1 Hz. Next is 5 Hz and so on.....

1 |
3 |
5 |
7 |
9 |
11 |
13 |
15 |
17 |
19 |
27 |
45 |

C |
G |
E |
Bb |
D |
F |
Ab |
B |
Db |
Eb |
A |
Gb |

##### Various builds of just intonation

Cosmo Welfare uses Zarlino by default

### Reference Frequencies

Natural Rure Tuning builds on scientific pitch, first proposed in 1713
by Joseph Sauveur. It is an absolute concert pitch standard which is
based on middle C (C4) being set to 256 Hz rather than 261.62 Hz as
in the common A440 pitch standard. I have expanded scientific pitch
to the Scientific tuning system.

### Keynote

C is a symbol, which stands for the first note of a musical scale.
C has no information about the real pitch. The frequenz of C is the
important thing. We say: C has a frequency reference of 1 HZ. That is
precise! The Concert pitch (A4) is 426,67 Hz. Another example: A is
the first note. A has a frequency reference of 27 HZ. The Concert pitch
(A4) is 432 Hz.

### Concert pitch

Concert pitch refers to the pitch reference to which a group of musical
instruments are tuned for a performance. Concert pitch may vary from
ensemble to ensemble, and has varied widely over musical history. In
Scientific Tuning the concert pitch varies according to the
reference frequency.

#### Why does Just Intonation sound so good?

Source

There are several reasons for this. First
of all our auditory systems find it easier to process simple harmonic
information than complex harmonic information. Just Intonation intervals are much
easier for our ears to "digest". For example, a pure major
third has the two tones in the ratio of 4:5, whereas a major third in
12 Tone Equal Temperament has them in a ratio which is approximately
504:635.

Our brains tell us that the first interval
is more consonant, simply because it requires less effort to process
than the second one. Of course, in the real world, things are rarely
absolutely perfect and two tones in the ratio of 40001:50001 will be
heard as "near enough" to 4:5.

However, the further an interval strays
from a nice simple ratio, the harsher it will tend to sound. Intervals
that do not form perfect small number ratios with each other produce
beats.

#### Wikipedia

Scientific Pitch
Octave
Hertz
Scale
Just Intonation
Interval
Chromatic
Natural Number
Odd Number
Integer
Number
Overtone