The Perfect Third Discovery. 

Brian Godden's Perfect Third system has been called 'The DNA code of musical sound and the octave'. 
A full understanding of the interval called The Perfect Third,  will light the way to understanding and singing the 22 Shrutis of the Ten Thats of India

The Physics of Ecstasy Copyright 1987 -2005 Copyright All rights reserved. 

Below is an article about learning how to accurately tune and sing the 22 Shrutis of the Ten Thats of Indian classical music, and deal with some of the conflicting issues of melody and harmony.

The Perfect Third is the major third Interval in the pure tuning Octave, (The Shruti is named GA in Indian Music). It is also called the Just Intonation Third, or Pure Tuning Third. 

Please note: The 22 Shrutis contain intervals not found in the Just Intonation 22 Note Octave.  Conversely, the 22 note Just Intonation octave contains intervals not used in the Indian 22 Shrutis. However, the 66 Shrutis does contain all 22 of the Just Intonation Intervals. To avoid confusion I will refer only to the 66 Pure Tuning intervals.

The Perfect Third discovery concerns a new way of understanding the intervals and tunings of musical cultures around the world. This has been a hotly debated topic amongst musicians and mathematicians for thousands of years. This new discovery has remained hidden - in plain view. It seems the scholars had not looked in this direction, and they missed the significance of the most important clue - The Perfect Third.

The geometric nature of the Fundamental Laws Of Vibration And Resonance are reflected in all forms of harmony. Architecture, mathematics, atomic structure, painting, dance, spiral galaxies, and double helix pent angular spiraling DNA, etc.  When this multi-dimensional geometric structure is shown through music and sound, the immutable structure of the octave of 66 pure tuning intervals is the result. There are over 700 intervals which can be positioned in the octave, from these come the 66 pure tuning microtones.  From these 66 pure tuning intervals come the 22 main tones, the 12 note chromatic scale, and the eight note scales of Indian music called The Ten Thats. The 22 Shrutis are the source intervals for the Ten Thats.  The Ten Thats  are 10 X 7 note scales, containing the root - SA, and the  fifth - PA. Other musical systems such as the Chinese spiraling 5ths, or the Persian septimal intervals, can augment the Shrutis, but the 22 Shrutis are the immutable foundation of the Ten Thats. The 66 note pure tuning octave is used in all musical cultures on every continent.

It is universally agreed that there are mystical and spiritual forces found in the music of all cultures. This is especially true of those who draw from the immutable 22 shrutis pure tuning octave of Hindustani and Carnatic classical music scales of India,  American Indian chants, Middle-Eastern music, African folk music, Australian Aboriginal songs, Vedic chants, church hymns, and temple incantations, and so forth. 

Our Perfect Third system has revealed a set of previously undiscovered formulas that make the exact location of each of the 22 Shrutis absolutely clear and sing-able.  This is accomplished without the use or of, or need for, any electronic tuning devices, or any other tuning tools, other than a two note drone. We can teach you how to use the 22 Shrutis in whatever form of music you like.  To the best of my knowledge these hidden formulas were not uncovered earlier as few scholars had a thorough knowledge of both the East and West music systems. They appear to have overlooked the harmonic implications of The Perfect Third.

For the past 200 years the ears, minds, and hearts of Westerners have been saturated with the Equal Temperament  scale (hereafter referred to as: ET) of 12 equally spaced out-of-tune tones on a reducing ratio. ( = 1.05946 See the chart below.)  Westerners have been subliminally programmed (mapped) to accept these 12 out-of-tune ET intervals, as averaging replacements for the 22 Shrutis. Westerners are so totally conditioned by modulating tonal centers, within the ET 12 note intervals, that they hear the ET scale as in tune. When westerners are first exposed to the 22 Shrutis, they hear most of the Shrutis as out of tune, or "weird in-between notes". 

To understand the Shrutis you must learn to identify with the Tonic. To identify with a tamboura tuned to the tonic (SA), and the fifth (PA), requires the listener to be in a peaceful state of listening. This frame of mind is like being in church, or participating in a chant at a temple. Once the listener is hearing the drones clearly they will be able to tune in to a performance of raga, and feel the unique character and power of each of the Shrutis.

A pure tuning perfect third has a ratio: 5:4 = 1.25/1.   Whereas, an ET third is 1.25992/1 (13.686 cents sharp of the perfect third). The ET third has no relevant harmonic or fractional relationship to the tonic.  For that matter, none of intervals of the ET 12 note octave have any true harmonic relationship to the tonic, or to each other.  Some ET intervals are very close to pure tuning intervals, such as fourths and fifths.  However, pure tuning thirds, sixths, and sevenths, are roughly a quartertone flatter than ET, and the pure tuning flatted 2nd interval is a quartertone sharper than ET. (See the charts below.)
 

Pure Tuning 12 note octave

Western Classical music and modern popular music forms have evolved around the 12 tone ET scale, so have the modern instruments like piano, harmonium, and Church organs - They are strictly 12 tone ET instruments. 12 tone ET fretted instruments like guitars, mandolins, and banjos, can be tuned modally, and the strings can be bent or pulled to sweeten the 12 ET tones. Wind instruments like the clarinet, flute, trumpet, and saxophone can stretch some intervals to cross over between traditions. A violin can play Indian classical 22 shruti music beautifully without the need for any modification. All Western fretless bowed instruments are capable of crossing over between systems.

Indian instruments such as: sitar, sarod, sarangi, esraj, surburhar, sursringar, vitchitra veena, rudra veena, Saraswati veena, are drone based instruments, and most have a set of sympathetic strings. None of these instruments function well in a modulating situation. In fact they are considerably limited in what they can do.  Without a shruti/drone based music, they are fish out of water. They can play simple music 1,4,5, chords in the key of C, or A minor, and sound very nice, but the Shrutis are obscured by any modulation. The sitarist could play rag Bhupali (Pentatonic major scale) and stay away from the chicaris (drone strings) during the 5 chord. But it is always a disappointing compromise. A sitarist can move his frets into 12 tone ET positions, but they really sound bad - no Shrutis at all. Without the pure tuning intervals, there can be no Pure Tuning Sympathetic Harmonic Cascade.

I have played professionally in Indian/Western fusion ensembles on guitar, jawari bass, bass fiddle, sitar, and on sarod.  I had the honor of being:  guitarist, bassist, chordal composer/arranger, didjeridu player, and Jawariwalla,  on 2 CDs with Ustad Ali Akbar Khan;  Journey, and Garden Of Dreams. These were both successful albums, and AAK's compositions are truly wonderful. But he, and I felt that the raga weakened every time the ensemble accompanies him. I used a stretched ET tuning for the guitar, and voiced all chords to avoid the ET third wherever possible.  I still perform the music from these two recordings in a band with Ali Akbar's Khan's son Sri Alam Khan.

This chart shows the 12 Equal Temperament intervals C to High C, contrasted with 12 closest Shrutis of the 22 the Pure Tuning Intervals.

Note	Equal Temperament note names and formulas	12 tone (ET) Equal Temper Ratios	ET Cents	Pure Tuning Shruti Name	Pure Tuning Ratios & Fractions 12 of 22  tones  (Closest to ET)	Pure Tuning Cents of 12 closest tones
C	Tonic	1.00000	0000	SA	1.0000	0000
Db	Minor Second  1	1.05946	100	re	1.0666 = 16/15	111.308
D	Major Second 2	1.12246	200	RE	1.125   = 9/8	203.910
Eb	Minor Third     3	1.18921	300	ga	1.2      = 6/5	315.641
E	Major Third     4	1.25992	400	GA	1.25     = 5/4	386.314
F	Fourth             5	1.33483	500	ma	1.333    = 4/3	498.043
F#	Aug. fourth      6	1.41421	600	MA	1.406  =  45/32	590.224
G	Fifth                7	1.49831	700	PA	1.5       = 3/2	701.995
Ab	Minor Sixth     8	1.58740	800	dha	1.6       = 8/5	813.686
A	Major Sixth     9	1.68179	900	DHA	1.666    = 5/3	884.357
Bb	Minor Seventh 10	1.78180	1000	ni	1.8       = 9/5	1017.596
B	Major Seventh 11	1.88975	1100	NI	1.875    = 15/8	1088.269
C	Octave           12	2.00000	1200	SA	2.0000	1200

When in performance skilled western musicians can stretch-tune their instruments and bend the intervals of the ET 12 note scale to include some of the 22 Shrutis, and septimal intervals.  An Opera singer uses a wide vibrato which allows the singer to feel for inner harmonic resonance's, and slide through septimal intervals, while following the modulating tonal center. The same applies to orchestral violinists, gospel singers, wailing Jazz saxophonists, or string-bending blues guitar players. A lot of septimal intervals are used in conjunction with the ET intervals, and this has it's roots in the African based form we now call the Blues.  

I have to say a little more about the septimal intervals. The septimal series of intervals are on a different orbital plane around the tonic and do not relate to the 22 Shrutis. The septimal intervals do not harmonize with SA and PA, or the Ten Thats. They are akin in many ways to the ET temperament. With drones of Sa and PA sounding, only harmonically related intervals are obvious. With non drone-based modulating tonal center music, ET and septimal tones can dominate, and the shrutis will function only as secondary sweetening intervals.

Septimal intervals are the galvanic juice of the Blues. Blues, jazz, and gospel singers wail on the septimal intervals before sliding to the pure third or sevenths.  They work the flat fifth (4th Septimal or tritone, which the European churches often called the "Devil's Interval", as it's intrinsic sentiment is doubt) before sliding to the pure fifth. These septimal intervals are everywhere, but they are like ghosts. We cant sing them accurately by pitching from a drone. The most obvious septimal intervals are the major sixth/minor seventh (6th septimal), and the minor third/major third (2nd septimal).  Afghani rebob, kemanche, oud, and Indonesian gamelan, all use septimal intervals as main tones in some pieces. The Mbira (sometimes called African thumb piano) were often tuned to the septimal intervals, mainly because the clanging nature of the individual tines, contained a noticeable septimal series, and the makers built those intervals into the tuning. Jet engines and vacuum cleaners, often have screeching septimal resonance. Septimal harmonic cascades can show up as unwanted whistling resonance when a tamboura or sitar bridge (jawari) needs reshaping by a Jawariwalla. 

In India is said that the septimal series of intervals form a realm of harmony that is only understood by the Angels and Gods, and they are incomprehensible on the material level. There are 6 main septimal intervals in an octave. Some fall close to Just intervals, and ET intervals, and are obscured by the more dominant adjacent notes - "as the sun hides the moon during the day". However, the 2nd, 6th, and to a lesser extent the 4th septimal intervals, are some distance away from competing Just or ET intervals, and they occupy areas of the octave with less harmonic congestion. The septimal series is in it's element when used with the ET scale. Septimal intervals are common to most Middle-Eastern/African/ music forms, but septimal intervals are not used as main tones in the Ten Thats, or Indian Ragas. During a classical raga performance, the septimal intervals are used by employing Undulin, (slow vibrato) which adds the sentiment of mystery, trepidation, and wonder to the main tones of a raga.

Indian music raga melodies are always moving. Ragas create their distinctive moods by contrasting pure tuning harmonic cascades against the drones. The performer is constantly sliding and ornamenting the melody with deliberate undulation, while nudging the harmonically related 66 microtones of the pure tuning octave.  While sliding, they will pass through the septimal series. however the overpowering dominance of the drone, and the 22/66 Shruti harmonic cascades overshadow the septimal intervals, but the sibilance added by these intervals form an important part of the subliminal ambience. 

Western entertainment/art forms of music are in a different category than pure devotional forms. Some forms such as Disco, Rave parties, and the newer forms, Scratch and Mix, ( in Australia these events are called Doof) employ fast rhythmic bass beats (around 120-140 bpm) which mimic the heart rate of a human body in an excited state. This state of excitement generates mental and emotional entraining, as the heart tries to match the pulsing throb of loud music at that critical tempo. These dance events can go on for days at a time resulting in mass trance states of euphoria.

Jazz and modern fusion forms of western music combine improvisational flights of the imagination, gymnastic melodic invention, telepathic communications between the players, extreme tonal center modulations, all of which combined with fast tempos create a sense of wonder and amazement.

All forms of music are a spiritual practice. Some forms such as Dhrupad (yogic Indian classical music) are primarily focused on the spiritual aspect. Entertainment/art forms combine entertainment and spiritual functions. In all musical forms the communications between performers and listeners opens the flow from the material, mental, and spiritual levels. All music can unlock higher levels of functioning and bring about an ecstatic state of inspiration and exaltation. (This is the basic premise of my book -The Physics Of Ecstasy - Copyright 1987) All forms of music depend on the underlying axiom that - Sound Is God.

Western Music, from Bach and Beethoven, Bebop and The Beatles, continues to reveal the wonderful constantly evolving world of ET 12 tone harmony. These beautiful accomplishments and many thousands of musical masterpieces, would not have been possible without the ET 12 tone system.

The entire field of harmonic tonal center modulation was dismissed by the Indian classical music world, because modulating the tonal center will negate the affect of the drone, and prevent the Shrutis from opening.  

To the purely Classical Indian musician or scholar, Indian classical music is a Devotional Yoga. These scholars feel that the Western ET scale is very sour and repugnant. They contend that the ET scale of 12 out-of-tune averaging tones has turned it's back on the 22 Shrutis, which are revered as spiritual sources of great loving power. They contend that each of the 22 Shrutis must be approached with respect, dignity and love. The harmonium was banned on All India Radio until recently, because of the 12 tone ET tuning. The scholars contend that using and hearing the 12 ET intervals will sour your musical ear, and confuse your spirit. As a result Western 12 note ET music is generally dismissed as impure, insensitive, and even an unhealthy musical form. That's tough talk, but that is the situation from the Indian yogic musicians point of view. 

The Indian popular music culture has incorporated ET 12 tone music. ET has taken root in the film industry, and has become a major presence on popular radio. Western style orchestras, rock ensembles, digital keyboards, and synthesizer work stations, are now standard fare in Bollywood (the largest film industry on the planet). 

The devotional forms like Classical Indian Dhrupad start with, and develop inner peace and tranquility, because each performance of a raga is a love song presented with a garland of Shrutis to God.  When western ET-saturated listeners first hear an Indian music devotional raga, with it's non-modulating, unornamented, 22 shruti, drone-based melodies, they become impatient. They have not learned how to identify with the drone. Their programmed expectations combined with lack of familiarity with the 22 note octave obscure the subtlety of what is happening.  They find it too boring and out of tune to hold their attention.  After the 22 note sensitivities are re-awakened, that boredom of old turns to love of the Shrutis, and consequently the ragas. This is what happened to me.

Prior to the 1960s, Western musical scholars generally dismissed the classical music of India, as a purely melodic drone-based folk music. Over the past 400 years, the evolutionary leaps made in the field of ET 12 tone Western harmony has created a sense of Western musical superiority. Of course in the East the feeling is reversed.  All other non-ET forms were viewed as simplistic and un-evolved. 

When compared to the complicated issues of Western harmony, pure melodic forms  such as Indian classical music are harmonically simple.  Western music can be considered melodically simple due to substituting an arbitrary ET 12 note octave which negates the complexity and purity of the 22/66 note shrutis. 

Until recently, not many classical Indian musicians understood the field of Western harmony, and most have probably not been exposed to the non-tempered/stretched ET western forms, such as:  the blues, old time modal fiddle and fretless banjo, pure tuning jigs and reels, Uilleann and Scottish bagpipes, Hawaiian lap steel guitar, barbershop quartets, to mention a only a few forms. These forms are all tuning to a mix of ET and pure tuning intervals. They all draw from the pure tuning Shrutis, however they only use the simpler intervals.  Pentatonic blues and country scales are a blend of ET and pure tuning intervals, depending on the song. The power of the pure forms such as the blues,  bend the intervals to locate the hidden perfect third and septimal pathways, while trying to avoid the sour ET tempered third, sixth, and seventh.

To Great Masters of Western music bending or sweetening the intervals becomes an intuitive process.  Great Western musical maestros such as: Ray Charles, Ray Brown, Yehudi Menuhin, Pablo Casals, Billy Holiday, Nat King Cole, Charlie Parker, Miles Davis, Louis Armstrong, Django Reinhardt, B B King, Lowell George (a few personal favorites), transcend the limitations of the ET tuning revealing to the listener the depth of their heart and soul by blending the pure tuning, septimal, and the ET intervals. 

Due to ET indoctrination, Westerners have a particularly difficult time finding the correct Shrutis for Indian ragas, and the TEN THATS. Westerners can study raga for many years and remain confused about which note belongs to which THAT, or raga.  The Perfect Third discovery will make that information available to all beginners. You can begin to sing or play these powerful THATS immediately. To fully understand the Perfect Third study will takes a little vocal practice and patience. Once the student grasps the physics of The Perfect Third,  and they can correctly locate and sing the 22 Shrutis, the power and purity of these tunings will be immediately clear. 

The Intervals of the Ten Thats of Indian Classical Indian Music 
Note:  -  means Flat,  and  #  means Sharp

A definition of a THAT is: a seven note octave containing the root (SA) and fifth (PA). There is no debate about the intervals of the TEN THATS (see the chart above), however, there is still plenty of room for debate about the correct Shrutis used for ragas.  There is some debate about which of the 22 shrutis are found in each THAT. In my opinion, that mystery has been solved with this discovery.  It is known to the scholars of India that there are at least 75,000 ragas, with new ones being composed constantly. The TEN THATS are a way of organizing the basic 22 Shruti source intervals for raga. The Shrutis used in ragas vary according to the region of India; Gharana (school), or family lineage. 

Ragas from different regions of India use the same name, but use completely different Shrutis. This is a natural process of cultural modification. The ragas are embellished and modified through successive generations over hundreds of years. Ragas may combine THATS: ascending in one, and descending in another. Or they may use the first tetra chord: SRGm, (C,D,E,F,) from one THAT, and MdnS (F#, Ab, Bb, C) the second tetra chord from another. The variability of raga intonation does not alter the immutability of the 22 Shrutis.

The Perfect Third music training is centered around a process of Re-Mapping. New formulas, and vocal tuning techniques are used to refine the musical ear, and to awaken sleepy or dormant 22 Shruti geometrically sensitive recognition pathways within the brain. The multi-dimensional geometry of the landscape of sound is a resonant microcosm of the same geometric principles that govern all things vibratory. The harmonious nature of the hidden relationships within the 22 Shrutis resonate sympathetically in the DNA within every cell of the body, and within the bodies of all who are listening. 

Above I have outlined as I see it, some of the issues that have isolated these two wonderful musical traditions from each other. We do not understand each other's musical traditions well enough. This mutual disdain has limited productive connections between these musical camps. It has also blinded both sides to the underlying significance of The Perfect Third. 

Our understanding of the octave needs to be re-examined, and we need to let some light in. With this new knowledge of the physics of the octave, and knowing for sure how to sing and play these 22 Shrutis correctly, I believe we are poised on a new musical frontier. I believe that this new patent pending discovery will change forever the way we tune to the octave. 

As well as these systems of music and ear training we will be teaching: World Music Repair, Music as Yoga, The Physics of Ecstasy, many other musical products and inventions from the studios of Brian Godden and his sons Amber, and Kalyan. 
Hear a sample of Brian Godden's  Guitar Jawari Harp

If you are interested, contact us via This link 

brian.godden@bigpond.com

Stay tuned, Brian Godden.
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