Ray Tomes wrote:

Joseph wrote: (in reply to David)
>... I take your point about changing modes.

I didn't get this. Could someone explain please.

>I have only ever heard one little piece by Galilei, but that was quite special.

I have never heard such a piece. Where would I find one?

Joseph Milne wrote:

About changing modes, Andy and I may have different answers. As I understand it, changing mode is changing the scale structure and creating a different tonal sense - as in changing from major to minor scales that Andy mentioned. Theoretically there are several ways to do this. One way is simply to change the place of the tonic and modify the new notes with accidentals, as in modulating to the relative harmonic minor. Another is to retain the same tonic but modify all the other notes to obtain a different mode. A third way, which I have explored in composition, is to retain all the notes of the major scale in just tuning, and shift the tonic to one of the Church modes (without any accidentals). Thus C, D, E, F, etc can become the tonal centre of different modes, giving seven modes in the major scale without employing accidentals. Andy can tell you about the Greek modes and how one changes from one to another.

As I mentioned before, this involves keeping the just tuning, including the 40/27 ratio D - A. I say this because there are two possible answers to the problem of tuning. One is to 'correct' the tuning of each chord so that they are in small whole number ratios. This is the usual remedy, easily done by ear with strings or voices. The other, which I find the more interesting, is to retain the tuning of each note to C and 'permit' the strange tunings that occur with certain harmonies. The theoretical reason for this is that the 'centre' of the harmony is the tonic, while 'correcting' the tuning of certain harmonies takes each harmony in isolation from the tonic, and so any modification changes the relation to the 'silent' tonic.

As I mentioned before, I was a member of a string quartet and did a lot of experimentation with tunings. Two of us were very interested in composing in the various Church modes. We always tuned the open strings to just tuning, tuning from C, not A. This means that A is slightly flat and the perfect fifth to E is true in relation to C, not sharp as it usually is in a string quartet. Quartet players get used to E being sharp and are quite happy to play the open E of the violin against the open C of the viola or cello. However, we got completely familiar with the just tuning without any correction.

This means that decisions have to be made about the harmonies of each mode. For example in the mode on D does one employ the chord D-F-A which is not a true minor chord? My answer is no, unless it occurs naturally as a dissonance. This means, in my view and working solely from the sounds themselves, rather than from theory, that there are certain harmonic restraints that belong naturally to each mode - especially if one thinks of harmony polyphonically rather than in terms of block chords or triads. I have no authority from history to back up my belief, only experience in composition in the modes in just tuning. My feeling that my instinct is right is confirmed by the fact that music composed this way sounds dreadful played in tempered tuning, which becomes all discords to my ear! But more significantly, it destroys the sense or 'tonal feel' of the mode.

Each mode (of the Church modes) has a unique quality and lends itself to certain types of music, but this can be discovered only through deep familiarity with the sounds of the modes and the way the tonic of each mode shapes it. From this basis, one can either compose music that belongs to a particular mode and stays in that mode, or one can compose music that moves through several modes but all keeping the identical tuning for each note. The possibilities here are immense. I have composed a lot of music this way without using a single accidental. Once your mind gets into this tuning, accidentals become 'foreign' sounds. Their use can only be to change the pitch of the modes - as when classical composers modulate from one major key to another by introducing a sharp or flat. Some composers say that each major key has a different quality. This is not a 'modal' fact, but is connected (in my view) with some sense of absolute pitch. How that is known is rather mysterious - it may be connected with your idea of the harmony of the universe.

As to the Galilie piece of music, I will have to ask a friend about that, who has it on an old record. It is a little piece for harp. I will get back to you on this. I hope this goes some way to answering your questions - and that it has not been too boring for others on this list. I am afraid that to us votaries of the Muses this is the most fascinating and important thing in the whole world!

Andrew Green wrote:

Regarding changing modes, I think Joseph explained admirably. I will probably add something though.

Vincenzo Galilei was associated with Mei and the Camerata in Florence, engaged in the resurrection of ancient Greek music. He published a number of books (available in a few libraries, and in facsimile), and engaged in arguments over the emerging iniquity of what would become "equal temperament". A couple of bits, in translation, follow:

Music was numbered by the ancients among the arts that are called liberal, that is, worthy of a free man, and among the Greeks its masters and discoverers, like those of almost all the other sciences, were always in great esteem. And by the best legislators it was decreed that it must be taught, not only as a lifelong delight but as useful to virtue, to those who were born to acquire perfection and human happiness, which is the object of the state.

But in the course of time the Greeks lost the art of music and the other sciences as well, along with their dominion. The Romans had a knowledge of music, obtaining it from the Greeks, but they practiced chiefly that part appropriate to the theatres where tragedy and comedy were performed, without much prizing the part which is concerned with speculation; and being continually engaged in wars, they paid little attention even to the former part and thus easily forgot it. Later, after Italy had for a long period suffered great barbarian invasions, the light of every science was extinguished, and as if all men had been overcome by a heavy lethargy of ignorance, they lived without any desire for learning and took as little notice of music as of the Western Indies.........

For all the height of excellence of the practical music of the moderns, there is not heard or seen today the slightest sign of its accomplishing what ancient music accomplished, nor do we read that it accomplished it fifty or a hundred years ago when it was not so common and familiar to men.

Thus neither its novelty nor its excellence has ever had the power, with our modern musicians, of producing any of the virtuous, infinitely beneficial, and comforting effects that ancient music produced. From this it is a necessary conclusion that either music or human nature has changed from its original state.

Vincenzo Galilei: Dialogo della musica antica e della moderna, 1581, from Strunk.

He had two sons. One, Michaelangelo, was a lutenist, and a number of his works are available. The other was Galileo (and the rest is history!).

Vincenzo should not be underestimated. Without him there may have been no Opera!

His published lute music is available, but I'm afraid I don't have much in my collection. (Ray, if you email me I can arrange to let you have material, and at least one recording).

Joseph Milne wrote:

I wonder if you have considered the Vedic description of the four Yugas or ages of the world? They are reckoned in divine years and are multiplied by 360 to obtain the sum of 'human' years.

"Each cosmic age is preceded by a "dawn" (sandhya) and is followed by a "dusk" of equal length (sandhyansha). each of these two periods constitutes one tenth of the respective yuga. The four yugas are (1) Krita- or Satya-Yuga (1,728,000 human years); (2) Treta-Yuga (1,296,000 years); (3) Dvapara-Yuga (864,000 years) (4) Kali-Yuga (432,000 years). The total is 4,320.000 human years (12.000 divine years) equals one maha-yuga, or 'great age.' Two thousand maha-yugas equal one day and one night in the life of Brahma." (Rider Encyclopedia of Eastern Philosophy and Religion)

Ray Tomes wrote:

The Vedic cycles periods are very interesting in relationship to the periods that I calculate by the Harmonics theory. Although the actual periods do not match, the pattern of ratios of 2 and 3 are similar and many of the numbers are my very strong harmonics with two zeros added. For example, 4320, 8640, 12960, 17280 are all strong harmonics, being my 34560 number divided by 8, 4, 8/3 and 2 respectively. Generally the Vedic periods have more ratios of 10 (or 5) than I believe is correct.

About 18 months ago I had some email correspondence with a Hare Krishna chap who was able to answer some of my questions about the subject. My conclusion, as with several other aspects of ancient knowledge, is that originally the basic knowledge appears to be very similar to the Harmonics theory but that with the passage of time some of the meaning has been lost. I suspect that the use of 100 year multiples is a misinterpretation along the way.

This has made me think about the old testament numbers. I have been told that the old testament contains lots of astronomical cycle knowledge but in coded form. For examples the planets are referred to as animals. I believe that Daniel is the main book concerned. Someone who I find generally trustworthy said that there is mention of a 2300 year cycle there which is fascinating, because there is a 2300 year cycle in climate and in astronomy, but the astronomical one depends on knowing about Uranus and Neptune! It takes a large amount of recorded history to discover a 2300 year cycle or some good inspiration. Does anyone know more about biblical codes and such like?

In the last 20 years there have been 2 or 3 different ancient (pre 1500 BC I think) texts from africa and the middle east decoded by someone who realised that they were in fact astronomical calculations. It seems that the method used is more or less equivalent to recognising that the planets move in ellipses and the method allows quite accurate predictions.

To return to Vedic knowledge and the musical relationships mentioned earlier. As well as the octaves (ratios of 2) they had up to eight ratios of 3, three ratios of 5 and one ratio of 7. In the harmonics theory, beginning from the fundamental, after about 19 ratios of 2 there should be eight of 3, three of 5 and one of 7 (although the next ratio of 7 would be nearly due). In other words, Indian music has the ratios in it to cover a range of frequencies of more than a million million times. As human hearing cover a range of about 1000 times (20 to 20,000 Hz) this seems excessive to say the least.

Cynndara Morgan wrote:

I haven't been able to contribute anything to your discussion of tuning because my understanding is so limited compared to yours, but you have been exploring a number of ideas that have just started working on me in the last couple of years. For one thing, Ray and Andy have finally explained why it is that when I am tuning my harp by ear, the damned chords just don't match up -- if I get C, G, and Dm chords perfect off of each other, then the Am and F chords won't fall in, and vice-versa. It's so nice to know that the reason I can't do something is that it really can't be done, not just a tin ear.

But as a magician, I have other questions, and one I have been working on is listening to the effect of rhythms, modes, and pitches through my to analyse the effects of music. This is incredibly complex and effects are far from predictable, but I seem to sense a few things that flew in the face of my conventional music "training", such as it is.

First, of course, with a tempered scale, key changes aren't supposed to affect the music. It should be possible to transpose and play a piece in any key, to fit the instrument (or more often, the voice). But "pitch" has a distinct effect on the emotional/physical perception of music. So transposing *does* affect how the piece is heard. A man's voice and a woman's singing the same piece will arouse different emotions. This seems to be related to perception in the "chakras", but now I hesitate, because some performers and pieces *don't* seem to be rhythmically impacting one of the seven classic chakras, but instead positions between them. Nevertheless the perception has been confirmed by several of my colleagues.

Next, rhythm seems to develop a harmonic with pitch, so that according to tempo and rhythm, a pitch that normally impacts in one zone may be shifted either slightly or even widely, something that again I wonder if it has a harmonic basis. For instance, say, most pieces played on piano seem to affect the third chakra area, and increase the ego-sense/self-esteem. This relationship holds up and down the scale and across keys, relating to the "voice" of the instrument itself. But occasionally, a piano piece in a minor or dissonant mode will defy this rule . . . which I suspect but cannot substantiate might involve the destructive interference in dissonances.

Again, changes in tempo and rhythm can also affect the effect of the basic piano voice, or enhance it. A simple four/four beat in a moderately quick tempo again calls on the third chakra. But slow the beat or syncopate the rhythm, and the interactions become more complex.

One possible channel of interaction between music and human emotion and health could be the "pacing" effect well-known to hypnotists. The heart and breathing are subconsciously reactive to outside rhythms, and the body will attempt to "pace" the rhythms in its environment either exactly or at an achievable harmonic. This means that factory workers work faster when disco music is played over the loudspeakers, and slow music assists relaxation. But it also means that other endocrine reactions will occur in a cascade at the prompting of changes in heartbeat and respiration; these physical reactions are interpreted by the receiver as emotions and feed upon themselves in that sense, especially if there are words to go along with the music.

Volume controls the raw force with which the music and its rhythmic effects impinge on the human system. For this reason, I am appalled at the common tendency in this era of people to listen to rock music at high volumes. Frankly, the cardiovascular system can only tolerate so much jerking from one direction to another at high power before it collapses. However the emotional effects seem to involve generating an artificial sense of excitement and power; clearly a panacea for generalized alienation, sense of powerlessness, and massive boredom. I find it especially interesting that most of this raucous, overplayed music also stimulates the third chakra (4/4 beat, moderately quick tempo, major key, drums overwhelming both voice and guitar) -- again propping up the ego-sense and self-satisfaction.

If my perceptions are correct, it is no wonder that a culture which lives in a constant matrix of such music at continual high volume would develop towards ever-increasing degrees of self-centered individualism.

I'm afraid that I'm wandering all over the field, here, with no data to back me up at all. But I have been interested in the light which your knowledge throws across these murky theories, and would be interested if you have any connections or (sigh) corrections to make with them.

Curt Lang wrote:

I would like to hear more of your subjective thoughts on the physiological and emotional effects of music. They may not be easy to defend but they _are_ interesting. Have you observed other keys and time signatures that touch other chakras?

Ray Tomes wrote:

This is another whole fascinating area. It is, as you say, incredibly complex but there are snippets of information about the effects on the body.

Several years ago I saw a paper on some experiments where people were sat on a chair attached to a machine which could vibrate the chair and person at various frequencies (I suppose that sound could be used directly instead) and they explored the effect of all the low frequency ranges (about 1 to 100 Hz). It listed the frequencies and which parts of the body had what sorts of feelings in them. Many or the responses are emotional as well as physical. Unfortunately, later when I went back to make a copy of the paper it was no longer there.

I suspect that the effects are due to two main factors. One is the size and shape of the various organs and bones in our bodies. This determines the distance that sound must travel in a bone for example and back again and so it will have a series of natural vibration modes just like a string. The other is similar, being natural resonances, but not necessarily sound. Nerve impulses have a very definite speed and so are capable of having resonances also. No doubt there are others.

It follows that because different people have different dimensions and possibly different nerve characteristics that there may be some variations between people in the responses that they get.

Another related research is the subject of ELF waves. ELF stands for Extra Low Frequency and means around 1 to 30 Hz radio waves. As mentioned previously, the earth supports a natural 7.5 Hz standing wave and harmonics of this. Because of the variations in the size of the zone that separates the earth's e/m field from the solar wind (the earth has a sort of bag that sometimes has a cometary type tail) there are variations in the natural frequencies.

I believe that human brain waves are in the ~7.5 Hz range because of the effect of these waves around the earth. Experiments have shown that exposing people to slower or faster e/m fields (say 5 or 10 Hz) does either slow down or speed up their reaction times. In other words our brain clocks itself to the signal.

Exposure to slower or faster ELF waves also produces unpleasant or exciting feelings respectively. I believe that changes in the ELF waves present around the earth are possible the causes of such mass human actions as stock market panics and the like. Maybe this is the mechanism for starting wars also, as it is known that solar activity does affect the ELF waves.

This is confirmed by another research (in Budapest) which found that when 3 Hz ELF waves are strong around the earth the number of accidents that people have is considerably increased. My interpretation is that the old clock is running too slow and we bang into things before we have time to think about changing direction.

With this background I think that it is possible to at least partly understand your other observations.

>First, of course, with a tempered scale, key changes aren't supposed to
>affect the music. It should be possible to transpose and play a piece in
>any key, to fit the instrument (or more often, the voice). But "pitch"
>has a distinct effect on the emotional/physical perception of music.
>So transposing affect how the piece is heard.

This is a generally accepted concept. Each key is supposed to have a particular set of emotional responses associated with it. I can't find my book which lists the traditional associations at present.

To link this to what I said above, it is necessary to recognise that for any given key, especially when chords are played, there is a fundamental frequency which all others are a multiple of. This fundamental is NOT the key note itself, but the 4th note in the scale. Let me explain.

If we are in the key of C then the relative frequencies of the notes are

C   D   E   F   G   A   B   C

24  27  30  32  36  40  45  48

What is the meaning of this fundamental note? It is the time interval over which the sound repeats. So, even though we play C4 G4 E5 G5, the sound is repeating over a time interval that is characteristic of C3 which wasn't even played. In terms of body responses, the C3 resonance will be important. Most of the body responses are in the low range and even below the threshold of hearing. The fundamental frequency is usually below 100 Hz. For example in C, using the notes in the octave from middle C will give a fundamental of 262 Hz / 24 = 10.9 Hz.

So, returning to you observations, the key is very largely determining this "fundamental frequency" and so establishing the body responses. This idea of a fundamental frequency is my own term, but it is probably known to other people also (though I haven't seen references to it anywhere). It is important in my automatic just intonation invention as all the other frequencies are then played as exact multiples of this notes frequency.

>... This seems to be related to perception in
>the "chakras", but now I hesitate, because some performers and pieces
>*don't* seem to be rhythmically impacting one of the seven classic chakras,
>but instead positions between them.

I would very much like to hear from you (and others) what keys or pieces of music affect each chakra. It would lead to some interesting study.

> Nevertheless the perception has been confirmed by
>several of my colleagues. Next, rhythm seems to develop a harmonic with
>pitch, so that according to tempo and rhythm, a pitch that normally impacts
>in one zone may be shifted either slightly or even widely, something that
>again I wonder if it has a harmonic basis.

Yes, this came up briefly before. Rhythm has a rate such as 103 beats per minute which is 1.72 beats per second. Although we cannot hear this frequency, we can work out its key by doubling it repeatedly to get say 440 Hz (1.72, 3.44, 6.88, 13.76, 27.5, 55, 110, 220, 440) which is the key of A. Therefore if a piece is played in A at 103 beats per minute then the rhythm is in tune with the key. The great composers get this right most of the time (I checked them out :-)

Therefore if you switch this piece from A to C to accommodate someone's singing range then you are either out of tune or need to sing it 19% slower (heaven forbid!) to have it be in tune.

> For instance, say, most pieces played on piano seem to
>affect the third chakra area, and increase the ego-sense/self-esteem. This
>relationship holds up and down the scale and across keys, relating to the
>"voice" of the instrument itself.

Ah yes, this is neat! Every different instrument has its own echo cavity. The overtones of all notes are much stronger when they fit evenly into the echo cavity of the instrument and weaker when they fit something and a half times as they then cancel themselves out. I found this out by digitally recording my mouth organ, guitar and piano on a computer and analysing the overtones. The cavity is either the length of the instrument (for mouth organ) or the depth (for the others).

Therefore a piano has a characteristic timbre associated with its physical depth. For a one foot depth you get 550 Hz as sound travels 1100 feet per second there and back.

This is also the reason why many electronic instruments are no good. They make a G by playing a C 50% faster and it has the wrong overtone structure and sounds like a different instrument. It would be possible to do this right in an electronic instrument.

>One possible channel of interaction between music and human emotion and
>health could be the "pacing" effect well-known to hypnotists. The heart
>and breathing are subconsciously reactive to outside rhythms, and the body
>will attempt to "pace" the rhythms in its environment either exactly or at
>an achievable harmonic. ...

Literally, the composer is "playing" the audience. We are his instruments. Apparently there are strong ultra sounds that can cause involuntary responses in people including such things as bowel motions!

>I'm afraid that I'm wandering all over the field, here, with no data to
>back me up at all. But I have been interested in the light which your
>knowledge throws across these murky theories, and would be interested if
>you have any connections or (sigh) corrections to make with them.

I am fascinated by your observations. It is interesting for me to see the relationships between the emotional and intuition side and the scientific side.

R Brzustowicz wrote:

This is curious enough to evoke a take-it-for-what-it's-worth anecdotal account.

Some years ago,a friend of mine was very involved with importing various ch'i kung (or qigong) teachers from the PRC -- though just that fact alone requires an article on the scientific qigong movement to give it a proper socio-religio-political context, and I'm not going to do it.

One of the groups that came through had developed a "qi machine" (or "qigong machine" -- a Faraday cage in which one sat, while connected to a device that read what seemed to be changes in galvanic skin response from one's arms and played them back (a) into the area of the head by means of EMF generated by a metallic mesh embedded in a rather dilapidated hat and (b) via a variable magnetic field generated in a cushion on which one sat.

The idea was that two important regions (and their associated acupuncture points and *their* associated meridians) would be activated, much as is supposed to happen in more traditional qigong meditations and exercises -- and would be shaped by the machine into more salubrious patterns.

At a public presentation, the people who had developed the machine said that the head end of the body was more "yang," and the perineum more "yin", and thus the head got the electricity and the perineum the magnetism. I thought this was a bit reminiscent of 19th century European occultism ("electricity" and "magnetism" were seen as polarities -- a notion that did not occur as far as I know in traditional China, or in Europe prior to the 19th, or maybe late 18th, century -- though I'd have to check Benz and a few other places to make sure), so I asked the rationale.

They supported my suspicions by saying that electricity was yang and magnetism was yin (no pedigree for this notion unfortunately was provided) -- and added that they had tried reversing the two and found that putting the magnetic field near the head could produce short-term memory loss, so they decided it was a bad idea.

I had this filed away in the cross-cultural curiosa gallery of my memory theater until recently, when I came across work involving the use of highly focused magnetic fields as a preferred replacement for electro-convulsive therapy. It is possible to be much more precise in affecting only small parts of the brain, it is possible to reduce the incidence of actual seizures -- and the procedure can cause short- term memory disruption.