A Solution from Equal Temperament

The experience of the fifth as spiritual experience was the first to be lost to humanity.
Modern man does not have the experience of the fifth that still existed, let us say, four to five hundred years before our era. At that time the human being truly felt in the experience of the fifth, “I stand within the spiritual world.”

He required no instrument in order to produce outwardly the interval of a fifth. Because he still possessed imaginative consciousness, he felt that the fifth, which he himself had produced, took its course in the divine realm. Man still had imaginations, still had imaginations in the musical element.
There was still an objectivity, a musical objectivity, in the experience of the fifth.
Man lost this earlier than the objective experience of the fourth –Rudolph Steiner.

Article 2008-2020@Brian T Collins

There are many questions that need to be answered for the discerning musician that has been trained under the de facto music concert pitch standard of A=440 Hz Equal Temperament and consequently feels the wonderful difference of A=432 Hz/C=256 Hz in different intonations but are still held to “A=440 Hz E.T. performance peer pressure”.

In January of 2008, I gave a lecture at the “Toronto Dowsers” regular monthly meeting that I aptly named; “432 The Harmonic of Light” The meeting was sold out as there was a general interest on the topic of 432 Hz.

In that meeting I described several different perceptions on the relationships between light, sound, electro-magnetisim and DNA and it was an intense question filled night with not only demonstration on a piano but also showing live cymatics of a vibrational plate that I had built for just for the occasion. The problem was, I created more questions than I could answer in the time allowed. People would not let me finish the lecture despite the host insisting that I stop due to the allotted time running out.

One of those questions was from a man selling “new age”  sound healing music  his argument for not using A=432 Hz as a legitimate tuning system was that equal temperament used in 440 Hz would not work at 432 Hz and that the latter only works for Pythagorean tuning which although natural, is quite dissonant due to the Pythagorean comma. There is no legitimate evidence that Pythagoras used any tonal reference as an absolute as central pitch.

He stated the age old repeated dogma that equal temperament was the excuse for musicians to unify a standard of concert pitch so they could all be in tune with; this point of belief is certainly valid as a half truth.
From the start it was a one sided argument as this half truth is often used to close minds into a fallacious absolute instead of taking up the stance of logical debate over the issue of intonation and tuning in music; and can another system actually be more sonorous or resonant in the sensation of tone in consciousness than the arbitrary international standard compromise of A=440 Hz ET that has enjoyed de facto standard status since 1953.
I tried to explain about equal temperament, just, true and werckmeister tunings and the reason why temperaments are locked [due to fourier transform and the logarithmic spiral]  due to the tempering, but I ended up causing instant confusion to the rest of the crowd who had no primer in even the most basic rudiments of musical theory or basic physics, but then when I decided to let the audience hear the difference that was when the excitement began.
Although I could not tune the acoustic piano on the spot I had prepared two recordings, one done in A=440 Hz and one done with A=432 Hz. The results was not one of theoretical or mathematical recognition but instead one of the sensation of “feeling” in audiences sub conscious validated by their physical reactions of surprise and excitement. What needed to be stated her was I only prepared a retuning done from equal temperament to stretch tuning in A=432 Hz,  Not the acoustic tuning of Twelve Fifths at 256 Hz/432 Hz and the results with a room full of sensitive dowsers was still incredible.

For most people and even some musicians, they have never heard of Equal Temperament A=440Hz however they listen to most music in the western world using that arbitrary standard of intonation of harmony in tuning.

What is Equal Temperament?

Simply put in non musical non scientific terms, it is a slightly closed sensation of frequency used for music that was introduced a long time ago and due to it’s arbitrary compromise on the sensation of resonance it may possibly induce a dampened perception of the sensation of tone upon the listener. When I mean tone, I am referring to what musicians call harmonic intervals, or spacing of time between musical notes called oscillations.

According to textbook definitions of Equal Temperament Lets examine what “The Oxford Concise Dictionary of Music” says: “Adjustment in tuning (i.e. ‘tempering’) of mus. intervals away from ‘natural’ scale so that such pairs of notes as B♯ and C, or C♯ and D♭, are combined instead of being treated individually. This leaves neither note accurate but sufficiently so for the ear to accept it. In kbd. instr. this avoids unmanageable number of finger‐keys. The pf., organ, and other fixed‐pitch modern instr., are tuned to equal temperament, in which each semitone is made an equal interval, making it easy to play in any key and to modulate.
Before equal temperament (which was introduced for pfs. in Eng. in 1846 and for organs a little later), the commonest system was mean‐tone temperament, which left certain keys tolerable, others less so, and some unusable. The untempered scale is known as just intonation. Instr. such as the vn. family can have no system of temperament, the player determining the pitch and checking it by ear. Some 20th‐cent. composers have restored 12‐note scale to just intonation. Others have used microtonal scales in just relationship. Still more have used ‘prepared’ instr. producing unexpected pitches, or elec. systems, or computers.”

Perfect textbook example of why tempering came into play into the sensation of western music, but should this be just accepted without question or logical debate?

In a Research Paper Presented to Dr. David Ward-Steinman by Momilani Ramstrum It clearly states; and I quote directly from that paper: “Temperament has been called “controlled mistuning” and is used to compensate for the acoustic phenomena that all perfect fifths and perfect octaves in all keys can not exist at the same time…” “Closed system: A system in which you end up where you began.
For example, in equal temperament at an octave you end up at the same note. All tempered systems create a closed system…” “Equal temperament is an “acoustical compromise… designed to satisfy as completely as possible three incompatible requirements- true intonation, complete freedom of modulation and convenience in practical use in keyed instruments.- and that it sacrifices the first of these to the second and third.
In the ancient diatonic scale, the scalar steps are uneven, which promotes tonality. In the equal tempered scale, there are no beginnings and endings and no tonality. Modern music “promotes neutrality of key centers and abstract harmony. Equal temperament is the only completely atonal temperament that has existed in history…” “Resistance to equal temperament was not dead until 1885…” Research Paper Here: THE DEVELOPMENT OF WESTERN TUNING SYSTEMS

When examining that paper we conclude that music tuning and intonation of harmony is not an absolute and that like the tide, tunings and perceptions on the sensation of tone has risen and fallen throughout history. The danger we face in the modern compromise of 440Hz Equal temperament is that ET is an absolute for all musical tuning. Although Equal temperament works well for entertainment and commercial broadcasting,
This is certainly not the case with dynamic changes inherent in organic life. No system of tuning is absolute. Lets examine the human voice. When a singer sings a note they usually sing one tone or tonic.
( Tuvian chanters are an exception ) When two singers sing they sing in harmony which according to music theory should create a consonant interval, in other words two notes that sound pleasing to the ear according to the 1/3/5/7/9/11 intervals.
Add a third singer in harmony and you sense the emotional colour of sound in the form of a major or minor triad. Major sounding happy and Minor sounding sad. Each successive singer added can alter the colour of music in the form of church modes sounding bright to dark. Add fourteen four part chords and you have a soup base of colour and emotion in music that is dominant in jazz theory today.

To achieve melodic harmony requires that each singer learns the harmonic space or consonance between the notes by using a system of consonant harmonic intervals such as a solfeggio scale. (Do re me fah so la te do) In order for a solfeggio to be consonant sounding it MUST derive from ONE center of concert pitch only and must sound pleasing to the ears of the listener in terms of the intervals of 1/3/5/7/9/11.

Although today we use a compromise of equal temperament in instruments such as the piano, the human voice wants to expressively spiral or expand out of equal temperament due to the natural organic quality of being human rather than a theory. This is why choirs and string quartets sound fuller and resonant than fretted instruments or pianos tuned to equal temperament.
The human organic sensation wants to expand or contract the intonation due to the dynamic expressive “feeling of” from one moment to the next. This very action in symphonic orchestration can be expressed through the harmony of leading notes and was mentioned by Pablo Cassels (1876-1973) in what he coined “expressive intonation,” which is the emotional action of having a leading note say from C# to D slightly higher than equal temperament as the C# leads expressively upwards into D. Likewise the Harmonic series demands that this expressive action is better served as the leading note C# rising into a slightly flattened D resolve.
This very Concept between the two is why an orchestra has an almost natural chorus like organic quality to` the sound of the harmony, as a body of people in harmony it never truly sits absolutely in the singular artificial compression of equal temperament.

The current system we have today of equal temperament came from a compromise between three systems of musical philosophy, namely the mathematic system, the harmonic overtone / undertone series and the geometric system, the latter largely derived from mystery schools. Trouble arose in the arguments of philosophy when mathematics, harmonic ratios and geometry were introduced as it was found that there was an increasing resonant tonal logarithmic spiral by natural design and when natural intervals were stacked up 12 steps the 5th overshot consonant division of the octaves and created what we know as the pythagorean comma, a very dissonant sounding interval of a ratio of 23.46 cents overshoot which almost sounded like half a semitone out. Yuck!

This wolf tone as it is nicknamed is very displeasing to the ear so the compromise was to close the expansion of spiral resonance into a closed circle known today as the cycle of 5ths. Each 5th was slightly rounded down or tempered and although the average untrained or academic ear cannot tell the difference until demonstrated in using A posteriori participation, the subconscious feels foggy, dulled or dampened under it’s influence, hence from a metaphysical philosophical perception; the tesseracted closed Cube of perception within the Sphere.

The Solution from Equal Temperament

The Maria Renold system of twelve true fifths allows for a maximum amount of natural intervals which creates a higher sonerous oscillation field of resonance. This tuning naturally balances out the luciferic rise in brightness in the upper register between 440hz and 449Hz of music and the decending lower realms of arhimanic selfish tones below 427Hz, leaving 432Hz as the great balancing christ force in the consciousness of humanity according to Rudolph Steiner. This is of course a metaphysical description and not a science descriptor.

Although I will not give the exact procedure of tuning the 5ths out of respect for the systems creator I will however list the approximate values needed for this tuning. This tuning solves the issues of equal temperament and frees the sensations of tone and spirit to new heights of oscillation.

Note & Hertz Values A0 =215.6Hz Bb0=228.6Hz B0 =242.5Hz C1 =256.0Hz** C#1=271.5Hz D1=287.8Hz D#1=305.2Hz E1 =323.7Hz F1 =341.7Hz F#1=362.4Hz*** G1 =384.3Hz G#1=407.4Hz A1 =432.0Hz**** Bb1=458.2Hz B1 =485.9Hz C2 =512.9Hz

**** A=432Hz tuning fork *** gelis=362.4Hz tuning fork ** C=256Hz tuning fork

This is a basic guideline for 12 true 5ths tuning and the tuner must rely on the ear to make this system work as using electronic tuners will lead to flaws in the tuning due to the natural fifths and augmented 4th. Each instrument according to their manufacture is unique and must be tuned by ear. What is also important to point out is that this is a geometric formed scale of mean tone and true tone intervals.

An incredible sensation of tone results from this tuning if tuned to C=256Hz A=432Hz, which seems to emanate from all around the instrument but caution is advised DO NOT USE it at 440Hz-449Hz as such tunings can negatively influence human beings according to Maria Renold and Rudolph Steiner.

Graham H Jackson’s views on 12 true 5ths tuning opened my eyes to this new wonderful 432Hz sensation of freeing oneself from equal temperament.

Here is what Graham has to say from his website: “For the “twelve true-5ths tuning”: you first set C at 256 Hz. Then you tune the 7 “white keys” by the circle of 5ths, using however natural 5ths. Then you divide the octave at C exactly in half (which can be done handily with a special tuning fork), and tune the 5 “black keys” by natural 5ths to that F#.

You end up with two series of natural 5ths–one of 7 notes and one of 5 notes, linked by an “unnatural” interval of an augmented 4th (which is actually the same augmented 4th found in the equal-tempered system).

Why I like the tuning

My own piano (on which the recording Graham made) has been tuned this way for about 20 years. My first reaction after playing on it, was how clear and resonant it sounded. The notes seemed to float free in the room, whereas when I play a piano with equal-tempered tuning, the notes tend to feel glued to the keys, relatively speaking. My next reaction, after playing on it for half an hour, was that I somehow felt healthier.

After these years, my impressions, although less noticeable, have not changed. Certainly the tuning does not harm the music. Bach, Mozart, Chopin, not to mention my music, just sound even better.”

Please visit Grahams website HERE and don’t forget to get his wonderful book about 432Hz/256Hz Called “The Spiritual Basis of Musical Harmony.