How musical frequencies in Western culture have changed.

 

The system of musical pitches we have in the West have been in place for nearly 300 years. But what is the tempered scale, how have the changes occurred, and what are the ramifications for balancing on our planet and the solar system?

 

 

 To understand, we need to look at other rhythms on our planet.

 The woman's menstrual cycle and the moon's phases are inextricably linked.

 In his book The Lunar Effect, Arnold L. Lieber MD says that celestial bodies, but specifically the moon, affect every aspect of human life, including the menstrual cycle. He quotes Walter and Abraham Manager: "Examining existing studies, they found that on the average, the human menstrual cycle is not approximately the same length as the lunar month - it is exactly the same length: twenty-nine and a half days." (1959)

 Research by Winnifrid D. Cutler, Ph. D: "In a selected population of 312 women, prospective menses records were maintained during the autumn of 1977. Women whose menstrual cycle duration approaches the cycle duration of the earth's moon (29.5 days) tend to ovulate in the dark phase of the lunar period. The dark phase encompasses the half-cycle of the month from last quarter, through new moon, to first quarter. Women showing irregular menses also tended to ovulate during the dark phase of the lunar period."

 Medical Astrologer Marcia Starck: "A woman's blood and hormonal cycle follows the ebb and flow of the moon; from new moon to full moon, oestrogen increases leading to ovulation, or maximum fertility, at full moon. From full moon to new moon, the waning half of the cycle, progesterone predominates. Traditionally, women used to start bleeding right before the new moon, in the dark of the moon. In modern times, women begin their menstruation during different phases of the moon. Their bodies are out of sync with the moon and their spirits have forgotten the meaning of Grandmother Moon. One way to get back in harmony with the moon is by performing ceremonies and rituals at different times during the moon cycle and also by honouring the time of menstruation. When a woman begins her monthly bleeding, she has a very special vibration. The blood flow is cleansing as the old uterine lining is sloughed off, one monthly reproductive cycle is ended. At menstruation, women have the chance to rid themselves of all old thoughts, habits, desires, and be receptive to new visions and inspirations for the next cycle. This is the dark moon phase. If a woman continues her normal routine at menstruation, then she loses a uniquely female opportunity for introspection. She also finds she gets more tired, irritable, and upset because her physical rhythm has slowed down. She needs rest, more time for meditation, and less time doing housework, cooking, working in the outside world, and taking care of children. In many Native American tribes and other tribal cultures, there is a separate moon lodge to which all women go. Since most women menstruated at the same time (have you noticed women who live together bleed together) during the dark of the moon, the grandmothers and fathers took care of the children. Food was left outside the lodge several times a day. Women during menstruation were/are considered to hold a certain power and not allowed to mingle with the rest of the tribe. Many tribes have taboos against these women, believing that their power would interfere with the hunt or take away the power of the medicine bundles. This is also why women are not allowed in sweat lodges and must stand outside the circles in other ceremonies when they are in their moon time. We know now that women were also segregated because of fear of the immense power which enabled them to bleed each month and never die -the greatest of all the Mysteries- while a male warrior might succumb quickly after losing so much."

Joachim-Ernst Berendt describes 'measured' and 'lived' time: 

 "The ancient Greeks must have been 'unconsciously conscious' of the difference between measured and lived time. They had two gods of time: Chronos and Kairos. Chronos, the archfather, was the god of absolute, 'eternal' time. For Kairos, however, the younger son of Zeus, time simply meant the favourable moment, the 'right time.' Penelope Shuttle and Peter Redgrove have shown that Kairos has a more female approach to time, while Chronos has more male elements. They found the male element to be rigid, proud of its 'objective' measurement of time, and the female element to be relative, 'waxing or waning,' just as women are subject to natural cycles: 'In the female consciousness, time is subject to the Kairos and less to the Chronos of the male consciousness, although both can be experienced by the same person.'

 The 'most lived' of all times is the female cycle. The woman lives it each month. More than anything else, this cycle is her 'inner clock.' In fact, certain scholars are of the opinion that primeval man first experienced time through the female cycle. That was the actual primal meter - and there we have it: the Greek word metra originally meant 'uterus.' Mater (mother) is related to metre. Almost all words expressing 'measure' come from this root: menstruation, immense, dimension, meter, diameter, parameter, thermometer, meteor. In Sanskrit, matri is the mother and matra is the measure. The 'germ cell' for all these different words is in metra, the uterus. By coming forth from the uterus, man emerges from measure to become mater-ial!"

Frequencies exist in the human body:

  • General Body Frequency - 7.8 Hz
  •  Atoms and Molecules - 10 Hz
  • Heart-Aorta System - 7 Hz
  • Brain - 4000 Hz
  • Circumference of Skull - 2250 Hz
  • Body Length - 375 Hz
  • Trunk and Head - 750 Hz
  • Heart - 2000 Hz

 How many days are there in a year? Not 365, since we add on another day some years (97 in every 400 years). Rather like other planetary phenomena, we tend to conceptualise and correct Nature's rhythms. 

 In the West, we use the Gregorian Calendar. Introduced by Pope Gregory XIII in 1582, it replaced the Julian Calendar. We've moved from 365.25 days per year to 365.2425! This solar calendar is, of course, based on 12 months - a Yang energy.

 To balance this, let's look at a Yin counterpart. The Hebrew Calendar is based on three astrological considerations; the daily rotation of the earth (a day is sunset to sunset), the moon's revolution around the earth (29.5 days) and the earth's revolution around the sun (365.25 days = 12.4 lunar months). Each month begins on the new moon. There are 12 or 13 months in the year, corresponding to the 12.4 month solar cycle.

 In his book 2012 - The Year of the Mayan Prophecy, Daniel Pinchbeck makes comparison between the solar and lunar calendars. He quotes the fairy tale The Sleeping Beauty, where the uninvited 13th wise woman curses the court and princess, sending them into a long sleep. Robin Heath says: "The two numbers twelve and thirteen, juxtaposed whenever our culture seeks to identify a superhero figure such as Jesus, King Arthur or the Mayan Kukulcan, point to a cultural legacy which appears to be calendraic in origin, naturally fundamental to the immutable numbers of sun and moon." Pinchbeck concludes: "The archetypal pattern reveals an enigmatic thirteenth saviour figure, always with twelve knights, disciples or kings, and always sacrificed to be then resurrected in order to save the culture."

Every musical note has a fundamental frequency, but also a series of overtones ie higher sounds called upper partials, making up the harmonic series of that fundamental. This applies equally to the human voice and musical instruments, although timbre of instruments will determine the structure of that harmonic series. If the fundamental note sung is C, then the first harmonic will be eight notes higher, called the octave (to work out the interval or distance in pitch between the two sounds, count up including both the start and ending notes eg C-D-E-F-G-A-B-C). The second harmonic will be the G above. The series progresses upwards: C, E, G, Bb and C; each successive harmonic becoming closer to the previous note.

The Greek mathematician, philosopher and musician Pythagoras (c. 570-475 BC) used numeric ratios to describe musical intervals and ultimately to define everything that we experience, including our solar system. Pythagoras found that by vibrating a string (he played the lyre) he sounded a particular note. Dividing the string in half produces the octave higher, a ratio of 2:1. Below is a table of intervals with their ratios. 

 

INTERVAL

RATIO

Unison

1:1

Octave [8ve]

2:1

Perfect 5th

3:2

Perfect 4th

4:3

Major 3rd

4:5

Minor 6th

5:8

Minor 3rd

6:5

Major 6th

5:3

Major 2nd

8:9

Minor 7th

4:7

Major 7th

8:15

Minor 2nd

15:16

Tritone

32:45

 

  

     

 

 

 

 

 

 

 

 

 

 

 

Pythagoras was particularly interested in the intervals of octave, fourth and fifth. A succession of fifths, with its pure ratio of 3:2 is known as Pythagorean Intonation. It is the Golden Proportion in Sacred Geometry and a Yang energy. The fourth represents the Pythagorean Triangle, being a Yin energy. The octave has been described as being complete, togetherness. To Pythagoras and his followers, all of this was connected to the frequencies of the planets - the Music of the Spheres or Musica Universalis. As we progress through the sequence of fifths, however: C-G-D-A-E-B-F#-C#-G#-D#-A#-E#-B#.........the final note on our well-tempered keyboard would be enharmonically the same as C, but under this pure system of frequencies, B# is about a quarter-tone higher than C; an effect called the Pythagorean Comma.

 A few notes on the interval of the Perfect Fifth........this drone has played a role in various cultures:

  • Chinese philosopher Lao Tzu referred to the fifth as the sound of universal harmony, balancing Yin and Yang.
  • Used in India to create the sound through which Shiva calls Shakti to the Dance of Life; all music begins and ends with this interval.
  •  Apollo, the Greek god of music and healing, sounded the fifth on his lyre, calling dolphins to Delphi, where they channelled messages to the oracles.
  • Called anak by the Egyptians, the combination of even and odd (two and three) represents the unity of heaven and earth.

 The fifth can benefit us by helping mobility of the joints and relieving depression. 

 Music before 1500 was constructed in modes, which did not rely on pitch eg the Dorian mode is uplifting; the Phrygian appears timeless. Our modern scale was not fully developed until the baroque era. St Gregory the Great (540-604) introduced the monophobic plainsong Gregorian Chant, as Pope Gregory I (590-604). Around 895, a treatise called Musica Enchiriadis demonstrates the first use of Organum, whereby a second voice would sing a fourth or fifth below the plainchant melody. These are the intervals that Pythagoras felt were healing, being the balance of female and male energies. The German composer, poet, abbess and mystic Hildegard of Bingen (1098-1179) wrote monophobic liturgical music, much of it constructed along the lines of Sacred Geometry.

 Developing Pythagoras' idea of Musica Universalis, musicologist Joscelyn Godwin says: "The celestial harmony of the solar system...is of a scope and harmonic complexity that no single approach can exhaust. The nearest one can come to understanding it as a whole is to consider some great musical work and think of the variety of analytical approaches that could be made to it, none of them embracing anything like the whole." 

 German astronomer Johannes Kepler (1571-1630) discovered laws governing planetary motion. Based on the time taken for each planet to orbit the sun, Kepler published his findings in Harmonices Mundi (1619). He said: "The heavenly motions...are nothing but a continuous song for several voices, perceived not by the ear but by the intellect, a figured music which sets landmarks in the immeasurable flow of time." Kepler's three laws are as follows:

  • The orbits of the planets are ellipses, with the sun at one focus of the ellipse.
  • A line joining a planet and the sun sweeps out equal areas in equal intervals of time, as the planet travels around the ellipse. 
  • The squares of the periods of the planets are proportional to the cubes of their semi-major axes. 

 A table of Kepler's planetary ratios can be found below. 

 

PLANET

RATIO OF INTERVAL

MUSIC INTERVAL

PITCH NAME

TIME TAKEN

Saturn

4:5

Maj 3rd

G-B-G

29.5 yrs

Jupiter

5:6

Min 3rd

B-D-B

11.9 yrs

Mars

2:3

Perf 5th

F-C-F

687.5 days

Earth

15:16

Maj 2nd

G-A-G

365.25 days

Venus

24:25

Unison

E-E-E

224.7 days

Mercury

5:12

Maj 10th

C-E-C

88 days

Moon

3:4

Perf 4th

G-C-G

28 days

  

  During the previous generation, Italian musician Vincenzo Galilei (1520-1591), the father of astronomer Galileo, researched intervals and their ratios. It had always been thought that 2:1 was the ratio of tension of strings of the same length tuned an octave apart. By hanging weights from the strings, Galilei proved that the ratio of tensions is 4:1. However, in his treatise Dialogo di Vincentio Galilei...della musica antica, et della moderna (1581), he advocates equal temperament, as well as writing ricercars and dance suites in every tonality of the chromatic scale. He was preceded in this by works of Francesco Spinacino (1507) and Giacomo Gorzanis (1567).

 So now we understand that equal temperament is an equal division of each interval of the chromatic scale (C-C#-D-D#-E-F-F#-G-G#-A-Bb-B-C). As piano tuner Anita Sullivan says, "The pure octave ratio 2:1 can be maintained up and down the scale, with twelve notes in between all evenly spaced like blackbirds (on telegraph wires)." Under this system, fourths and fifths are less than perfect, but intervals like the major third (used as part of the triad in classical Western harmony) is less dissonant, as it is wider.

 Along the road to equal temperament as we know today, there were many developments. The German music theorist, organist and composer Andreas Werckmeister (1645-1706) invented four systems of tuning:

  • Werckmeister I - mainly perfect fifths, but some fifths are flattened (C-G, G-D, D-A, B-F#) to make chromatic playing easier.
  • Werckmeister II - C-G, D-A, E-B, F#-C# and Bb-F are narrowed; G#-D# and Eb-Bb are widened. Other fifths are pure. This was designed for more diatonic music. 
  • Werckmeister III - D-A, A-E, F#-C#, C#-G# and F-C are narrowed; G#-D# is widened. Other fifths are pure. This tuning is closer to equal temperament than the first two.
  • Werckmeister IV - this so-called Septanarius tuning is based on the division of the monochord. Its tuning is more rational than the other three.

 Despite inventing these different temperaments, Werckmeister felt that the new counterpoint of the baroque era was connected to planetary motion, so endorsing the findings of Kepler a generation earlier.

 There were others experimenting with temperaments: Francesco Antonio Vallotti (1697-1780) and Johann Georg Neidhardt (1685-1735), but in 1722 was written a composition that would change the face of Western music.

 In that year, the German composer Johann Sebastian Bach (1685-1750) wrote the first of two volumes for keyboard collectively known as the '48' (BWV 846-893) - each book containing a prelude and fugue in every key. Bach writes on the title page: "The Well-Tempered Clavier, or Preludes and Fugues through all the tones and semitones, for the use and profit of musical young people desirous of learning, as well as for the pastime of those already skilled in this study, drawn up and written by Johann Sebastian Bach." The second book was composed in 1742.

 There is an assumption that Bach wrote the '48' with equal temperament in mind, but we cannot be sure that he didn't adopt one of the tuning systems described above. There is a German phrase for equal temperament: gleichschwebende temperatur, which Bach did not use. What we do know, however, is that Bach tuned his own harpsichords and clavichords, and he said to his pupil Johann Philipp Kirnberger (1721-1783) that all major thirds are to be sharpened. 

 Kirnberger devised three tuning systems of his own:

  • Kirnberger I is similar to Pythagorean tuning.
  • Kirnberger II keeps mainly perfect fifths, but splits the 'wolf' interval between two fifths. This also leaves two wide thirds.
  • Kirnberger III - the 'wolf' interval is split now between four fifths.

 Later, the English scientist Thomas Young (1773-1829) aimed to "Make the harmony most perfect in those keys which are the most frequently used." This involved six pure fourths, causing six flat fifths and wider thirds.

 If you are interested in reading my History of Music, let me know. It's free when sent via email. 

 Back to planetary frequencies........in 1978, Swiss mathematician and musicologist Hans Cousto invented the term The Cosmic Octave. He re-discovered a basic system of measurement in which it is possible to tranpose the movements of the planets into audible rhythms, musical notes and colour. It is the universal harmonic relationship between all things, based on sacred geometry from music, astronomy, meteorology and microbiology. The frequencies of planetary gongs are based on his discoveries; please see the chart on my Gong Baths page for more information.

 Do frequencies of equal temperament have a harmful effect? It depends on whether one is regarding the music as an art form, or to aid therapeutic progress. As an art in the Western world, music has the power to inspire us at a deep level indeed, working on the physical, mental, emotional and spiritual bodies. I've had wonderful mystical experiences when conducting my orchestras in great works. On the other hand, we have learnt from Pythagoras, Kepler et al that frequencies are specific to the balance of our health, the wider implications being with the solar system eg the moon frequency will help balance our sacral chakra; the sun our solar plexus. At a time when there are so many changes, including the re-alignment of the planets, we need as much help as we can get. Without vibration, we would not exist, so let us join with the American sound healer Jonathan Goldman in stating that 'frequency + intent = healing.' We have so many tools at our disposal to help us: toning, overtoning, mantras, gongs, bowls, drums, flutes, conch, tingshas and tuning forks etc.

 Let us Resound together!