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Music
and mathematics |
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A
musical scale is a discrete set of
pitches used in making or describing music.
Typically a scale has an interval of repetition, which
is normally the
octave. Because we are often interested in the
relations or
ratios between the pitches (known as
intervals) rather than the precise pitches
themselves in describing a scale, it is usual to refer
all the scale pitches in terms of their ratio from a
particular pitch, which is given the value of one (often
written 1/1 when discussing
just intonation.) The most important scale in
the Western tradition is the
diatonic scale, but the scales used and proposed in
various historical eras and parts of the world have been
many and varied. Scales may broadly be classed as scales
of
just intonation,
tempered scales, and practice-based scales. |
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Music Theory
analyzes the elements of music –
rhythm,
harmony (harmonic function),
melody,
structure,
Form, and
texture. |
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The elements of a melody are composed of
pitch, duration, and
timbre created with respect to
scales or
modes. |
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Rhythm is the
arrangement of sounds in
time.
Meter animates time in regular pulse groupings,
called
measures or bars. The
time signature or meter signature specifies how many
beats are in a measure.
Syncopated rhythms are rhythms that accent
unexpected parts of the beat. Playing simultaneous
rhythms in more than one time signature is called
polymeter. See also
polyrhythm. |
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Harmony is the
study of vertical sonorities in music. The vertical
relationship between pitches is referred to as an
interval between the two pitches. These intervals
are often combined into larger structures called
chords. |
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Musical texture
is the overall sound of a piece of music commonly
described according to the number of and relationship
between parts or lines of music:
monophony,
heterophony,
polyphony,
homophony, or
monody. |
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Mozart_effect
suggests that
classical music increases brain activity more
positively than other kinds of music |
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some composers have incorporated the
Golden ratio and
Fibonacci numbers into their work. |
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Fibonacci_number
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The
golden ratio
(phi),
also written τ (tau),
is defined as the ratio that results when a line is
divided so that the whole line has the same ratio to the
larger segment as the larger segment has to the smaller
segment. |
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chromatic scale
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perfect fifths, |
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Pythagorean comma. |
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12 perfect fifths
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53 equal temperament
or
Holdrian comma. |
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Pythagorean tuning |
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Schumann resonance (SR) |
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Link List |
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432 & Lightspeed |
Slowing the speed of light @ washington
Post.com |
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Frequency to Musical Note Converter
Tuning from 440 to 432 Hz is 32 cents flat. |
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Universal
Dance:432 @ akasha.de |
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Schumann Resonance, Human Chakra, Music and Healing |
music revolution @ schiller
institute.org |
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The three fundamental elements
of music are rhythm, melody, and harmony.
The sun, planets and moon stand in the same frequency
ratio as the notes on our most harmonic scale. Harmonics beautify music
and nature for the beholder.
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Music Harmony & Rhythm |
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Rhythm is likely the most fundamental aspect of
music, because percussion instruments were likely in use long before
stringed instruments. Tribal groups dancing to music made only with
percussion instruments is an ancient human practice, which reportedly
continues today. Rhythm recalls the heartbeat which we first heard in
the womb and beats naturally at 72 bpm.
Entrainment is about the tendencies
of the universe to share rhythm, to vibrate in harmony. This principle,
found in many sciences, of the tendency for two oscillating bodies to
lock into phase so that they vibrate in harmony is particularly poignant
in music. Through entrainment music has the potential to (1) resonate
with the listener’s feelings, (2) transform negativity into positivity,
and (3) promote a state of liveliness or serenity. Certain sounds, in
specific sequence can help bring the listener from one place to another.
Melody is about the changes and patterns found in
the foreground of music
For the music to
sound consonant (in tune) the different notes being sounded
simultaneously need to be related in a way which is pleasing to the ear.
Tuning based on a series of twelve notes in perfect fifths has played an
important part in world musical traditions.
The difference in frequency between two pitches is
an octave,
a note and another note with twice its frequency form an octave.
Octaves are
perceived as a consonance in every musical culture.
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Music &
432 |
- 432 times 432 =
186624
the classic speed of light is 186400
miles/second, a difference of .001201.
- E=mc2
---Einstein's famous equation of energy and matter - - where
E= energy, m = matter, and c = the universal constant speed
of light.
 The
speed of light in 1983 was generally accepted to be 186,291
miles per second in a vacuum so 432 as the square root of the
speed of light should only experience the usual suspects as
skeptics. This number converted by the pyramid inch is 186,496.
( 186,291 [accepted speed of light in a vacuum per 1983
agreement] x 1.0011)
The distance
from the center of the earth to the average
height of the atmosphere. This value is
given as 4320 arc-minutes, which
harmonically can be reduce down to 432
the fundamental vibration for the sixth node
in the octave
A line
showing the speed of light on a scale model
of Earth and the Moon, about 1.2 seconds.
The archaic Egyptian
instruments that have been unearthed, so far, are largely tuned
to 432 hz. In ancient Greece (the school book original place for
music) their instruments were predominantly tuned at 432 hz.
Within the archaic Greek Eleusenian Mysteries, Orpheus is the
god of music, death and rebirth, and was the keeper of the
Ambrosia and the music of transformation (his instruments were
tuned at 432 hz). |
Pythagorean tuning
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| Pythagorean tuning
is a system of
musical tuning in which the
frequency relationships of all
intervals are based on the ratio
3:2. Its use has been documented as long ago as 3500 B.C. in
Babylonian texts[1].
It is the oldest way of tuning the 12-note
chromatic scale and, as such, it is the basis for many other
methods of tuning
Pythagorean tuning is tuning based only on the
perfect consonances, the (perfect) octave, perfect fifth, and
perfect fourth. Thus the major third is considered not a third
but a ditone, literally "two tones", and is 81:64 = (9:8)²,
rather than the independent and harmonic just 5:4, directly
below. A whole tone is a secondary interval, being derived from
two perfect fifths, (3:2)²/2 = 9:8.
In equal temperament, and most other modern
tunings of the chromatic scale, pairs of
enharmonic notes such as E flat and D sharp are thought of
as being the same note — however, as the above table indicates,
in Pythagorean tuning, they theoretically have different ratios,
and are at a different frequency. This discrepancy, of about
23.5 cents, or one quarter of a semitone, is known as a
Pythagorean comma. |
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Pythagorean comma |
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In Western music, 12 perfect
fifths and seven octaves are treated as the same interval |
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In
music,
when ascending from an initial (low) pitch by a cycle of
justly tuned
perfect fifths (ratio 3:2), leapfrogging twelve times, one
eventually reaches a pitch approximately seven whole
octaves above the starting pitch. If this pitch is then
lowered precisely seven octaves, it will be discovered that the
resulting pitch is 23.46
cents (a very small amount) higher than the initial pitch.
This
microtonal
interval
is called a Pythagorean comma, and
sometimes called a ditonic comma.
Put more succinctly, twelve perfect fifths are
not exactly equal to seven perfect octaves, and the Pythagorean
comma is the amount of the discrepancy. |
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| The
Schiller Institute in Milan Italy on April 9, 1988 launched a
campaign to lower the international standard musical pitch to
middle-C=256 cycles per second (A=432 cycles per second), in
order to preserve the human voice and to return the performance
of Classical music to that of the classical composers' poetic
intentions. Bach's 440
hz only touches 8, leaving out an entire section of the complete
musical resonance of the universe, which thus remains untouched
and unintegrated within the 440 hz music of today
By
detuning the note 'a' to 432 (harmonic of 54, 108 & 25920 / 60)
then the frequency of 'D' becomes 144 hz (144000
cycles per second) Using 432hz as frequency allows for
all the wavelengths to harmonize easily with each other. |
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"An original new connection of geometry, astronomy and sacred
sites to music theory. The international standard of tuning is
440 Hz = the note "A". set in stone by J.S. Bach when the
correction to 432 is made, the others notes of the entire octave
display a multitude of Gematrian ancient sacred numbers that are
astoundingly relative to astronomy, sacred geometry, The Bible
and other mysterious literary works such as the Bhagavad-gita
and exact longitude and latitudes and hundreds of pyramids and
other sacred sites. |
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Reasons to change the standard of tuning from 440 to 432
- Harmonically aligns to astronomical time
count of Precession of the equinoxes, 432 X 60 = 25920
- The original Stradivarius violin was
designed to be tuned to 432, it is the most precise
instrument ever constructed by humans.
- 432 is found at countless ancient sacred
sites
- over 2,000 signatures on a petition to
the Italian government to change the standard to 432 due to
the registers ripping many opera singers voices in 440
- The most important of all is when the
correction to 432 is made, the others notes of the entire
octave display a multitude of Gematrian ancient sacred
numbers that are astoundingly relative to astronomy, sacred
geometry, The Bible and other mysterious literary works such
as the Bhagavad-gita and exact longitude and latitudes and
hundreds of pyramids and other sacred sites.
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The Scale Of Time by James Paul Furia
James Furia is much quoted on the internet for his case to make the centering note “A” at 432 cps,
rather than the standard pitch 440. He traces the reasons for
the harmonic lapse in judgement to defining the basic
notes as only 7 instead of 12. |
| Harmonics & the
speed of light
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Bruce Cathie has
been writing books on anti-gravity and light harmonics for more
than 30 years. He believes that the
universe is based on harmonic series such as 72, 144, 432. And
144 (a "C" tone in hertz) is a perfect harmonic of the speed of
light, which is 144,000 nautical miles (144,000 minutes of arc
per Earth grid second) in the vacuum of space. Each of these
harmonics are literally a mirror, or a cascade of mirrors within
mirrors, that 8 hz can look into. For example 144 is 18 x 8 hz,
and 72 is 9 x 8 hz. The way that light travels in space is thus
a 144 decimal harmonic (144:144,000),
"Cathic found that the fundamental harmonic
of light in geometric terms has an angular velocity of 144,000
minutes of arc per grid second. The reciprocal harmonic of light
or 1/144,000 repeating .69444. This harmonic refers to the
negative reciprocal light, which in theory forms the basic
building block of the antiuniverse of light or negative
reality."
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Heartbeat of the Planet:
the Schumann resonance
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The Schumann resonance (SR) is a
set of spectrum peaks in the
extremely low frequency (ELF) portion of the
Earth's
electromagnetic field spectrum. Schumann resonances are
global electromagnetic
resonances, excited by
lightning discharges in the cavity formed by the
Earth
surface and the
ionosphere.
Lightning discharges are considered as the primary natural
source of Schumann resonances. Lightning channels behave like a
huge antenna which radiates
electromagnetic energy as impulsive signals at frequencies
below about 100 kHz
[15]. These signals are very weak, but the
earth-ionosphere
waveguide behaves like a
resonator at ELF frequencies and amplifies the spectral
signals from
lightning at the
resonance frequencies
[15].In an ideal cavity, the
resonant frequency of the n-th
mode fn is
determined by the
Earth radius a and the
speed of light c
[6].
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In physics, resonance is the tendency of a system to
oscillate at maximum amplitude at a certain frequency. This
frequency is known as the system's resonance frequency (or
resonant frequency). When damping is small, the resonance
frequency is approximately equal to the natural frequency of the
system, which is the frequency of free vibrations.
Acoustic resonance is the tendency of an acoustic system to
absorb more energy when the frequency of its oscillations
matches the system's natural frequency of vibration (its
resonance frequency) than it does at other frequencies.
A resonant object will probably have more than one resonance
frequency, especially at harmonics of the strongest resonance.
It will easily vibrate at those frequencies, and vibrate less
strongly at other frequencies. It will "pick out" its resonance
frequency from a complex excitation, such as an impulse or a
wideband noise excitation. In effect, it is filtering out all
frequencies other than its resonance.
Acoustic resonance is an important consideration for
instrument builders, as most acoustic instruments use
resonators, such as the strings and body of a violin, the length
of tube in a flute, and the shape of a drum membrane.
The Base
Chakra corresponding to the note C is the 33rd octave
of the first Schumann Resonance. Middle
C on the musical scale has a frequency of 261.63 Hz.
If we divide this frequency by 7.83 Hz. (Schumann
Resonance) the result is 33, the 33rd. octave. |
| Rhythms
on Song Trellis
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It's characteristic that ensemble rhythms
from African traditions
 play patterns against one another that
pulse at different speeds. Many of these have 4 or 5 parts that
interlock in fascinating ways. One part will present an idea
that a different part will answer.As
you listen, play them loudly enough so that you can hear the
parts clearly. Each part leaves space or plays in a different
range to allow its companions to be heard. |
songtrellis.com/rhythmpage
Music and Musical Know-how For You
a framework that supports the growth
of songs and new music, a trellis for song. |
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Poetry
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| "Much in the poetic works
structure brings closer together this kind of art with music. A
distinct rhythm, regular alternation of stressed and unstressed
syllables, ordered dimensionality of poems, their emotional
saturation make poetry by the native sister of the musical
pieces. Each verse has its musical form, its rhythm and melody.
It is possible to expect, that in the poem constitution some
features of the musical pieces, a regularity of musical harmony,
and consequently, the golden proportion will be revealed
themselves." |
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goldenmuseum.com
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"A human being is part of the whole called by us universe, a
part limited in time and space. We experience ourselves, our
thoughts and feelings as something separate from the rest. A
kind of optical delusion of consciousness. This delusion is a
kind of prison for us, restricting us to our personal desires
and to affection for a few persons nearest to us. Our task must
be to free ourselves from the prison by widening our circle of
compassion to embrace all living creatures and the whole of
nature in its beauty. The true value of a human being is
determined by the measure and the sense in which they have
obtained liberation from the self. We shall require a
substantially new manner of thinking if humanity is to survive."
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---Albert Einstein, 1954 |
| Music is a universal language
tying human emotions to the declarations of
truth for the soul's benefit. At its best as a rigorous
production of beauty, the listener is moved by the inner
workings of the listener's own creative mind.
With few exceptions, humans love to listen to music. Nearly
everyone has musical aspirations. If you can't sing, you
probably wish that you could.
There exists an intimate
connection between the planets, vibrations and musical beats,
sounds and colors which reach as far as microcosmic vibratory
qualities of a single cell.
When musical instruments are
again tuned at 432
cycles per second harmonics are produced. This will be healthy
for the body as well as the planet. |
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432 on YouTube
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Harmony is the goal
of the Universe |
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A certain constant
harmonic electron wave of sound is Mozart Effect and is known to raise
IQs. |
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8 hz is in the Fibonacci number series that
nature utilizes to duplicate itself (1, 1:1, 2, 2:1, 3, 3:1, 5,
5:3, 8) into petals, or seeds. 16 such steps renders our 144
beats per minute, whereby PHI and Fibonacci cross into
symbiosis. Since 144 is 89 x PHI (1.618), the Golden Mean
proportion of mirror-into-mirror, pentagon into the next
pentagon within the first pentagon's pentagram etc. |
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23.5 cents, or one quarter of a semitone, is
known as a
Pythagorean comma. |
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The angle of the earth at 23 also |
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golden mean PHI triangles. Triangles whose sides
slant at 72°, and whose base is 36° (half of 72) |
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One zodiacal great year = 30 x 72 years =2160 |
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Our planet beats at 8 cycles per second (8 hz,
fundamental Schumann resonance), Multiplications of 8 cycles
gives one the significant 432 (54 x 8, and 3 x 72).
The universe is based on harmonic series such as
72, 144, 432. And 144 (a "C" tone in hertz) is a perfect
harmonic of the speed of light, which is 144,000 nautical miles
(144,000 minutes of arc per Earth grid second) in the vacuum of
space.
Each of these harmonics are literally a
mirror, or a cascade of mirrors within mirrors, that 8 hz can
look into. For example 144 is 18 x 8 hz, and 72 is 9 x 8 hz.
Mankind, in a non-shamanic state, does not
hear 8 cycles. But one can make audible its harmonics, such as
72 hz (9 x 8 hz), 144 hz (18 x 8 hz) and 432 hz. |
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"If you listen to Hendrix
recordings, a lot of them are tuned a shade flat - not Eb, but
just a little South of E (live ones as well as studio ones).
On his studio recordings he would spend hours tuning up,
supposedly to get the right 'vibe' from his amplifier -
microtuning to get the best combination of overtones, harmonics.
Of course just because the record is mastered to be a few
degrees below A440 doesn't mean that was the original recording
pitch, but the idea that Jimi was tuning into the natural
frequency of the universe is kind of appealing to me
---floopy
on the forum @talkbass.com |
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Our planet beats at 8 cycles per second (8 hz,
fundamental Schumann resonance), |
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light travels about a foot (just
under a third of a meter) in a nanosecond
[a billionth of a second ]
fast enough to circle the
Earth seven times in one second. |
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