Ordinarily seven steps, phases, periods or levels in a complete cycle, gamut or process. This makes sense when considering so many things are not "things" but processes or cycles of evolution. Processes and cycles can be divided into seven steps or phases each having its own peculiar characteristics - especially in relation to each other. Music is a good example where there are seven main tones to an octave - the eighth step is to the next octave. Each tone interval is unique in its qualities when related to the other tone intervals.
I believe the number seven got much support from the fact that white unseen light refracts/differentiates into seven colors. The same phenomenon occurs with music where a fundamental differentiates into the seven diatonic notes of the natural scale. Seven is contained in and is born from the One Undifferentiated Whole. Same for three. 1 -> 3 -> 7 then on into smaller divisions represented in music by intervals of less than a whole step. [Dale Pond, 12/4/20]
Dr. H. Spencer Lewis wrote considerably concerning the seven stages, steps or periods of universal cycles.
Reich looked at cycles as having four main steps or phases.
Ancient and sacred texts are filled with references to seven.
Between the high silence of these intense vibrations, and the low silence of oscillating pendulums and revolving planets, God has constituted an audible sphere of vibrations, in which is placed a definite limit of systematic sounds; seven octaves are carried like a measuring line round twelve fifths; and motion and rest unite in placing a horizon for the musical world, and music comes [Scientific Basis and Build of Music, page 39]
that Nature has done so.1 And in every new key into which we modulate Nature performs the same operation, till in the course of the twelve scales she has cut every greater note into two, and made the notes of the scale into twelve instead of seven. These we, as a matter of convenience, call semitones; though they are really as much tones as are the small intervals which Nature gave us in the genesis of the first scale between B-C and E-F. She only repeats the operation for every new key which she had performed at the very first. It is a new key, indeed, but exactly like the first. The 5 and 9 commas interval between E and G becomes a 9 and 5 comma interval; and this Nature does by the rule which rests in the ear, and is uttered in the obedient voice, and not by any mathematical authority from without. She cuts the 9-comma step F to G into two, and leaving 5 commas as the last interval of the new key of G, precisely as she had made 5 commas between B and C as the last interval of the key of C, she adds the other 4 commas to the 5-comma step E to F, which makes this second-last step a 9-comma step, precisely as she had made it in the key of C.2 [Scientific Basis and Build of Music, page 48]
dividing itself by 2 or 3 or 5, etc., up through the whole geometrical series of numbers, not keeping fixed at one thing; but while the whole length is vibrating the fundamental partial, it keeps shifting the still nodes along its length, and sometimes longer and sometimes shorter segments are sounding the other partials which clothe the chief sound. It has been commonly said that "a musical sound is composed of three sounds," for every ear is capable of hearing these three, and with a little attention a few more than these; but many will be startled when told that there are twenty-five sounds in that sound. Eighteen of them are simply the octaves of the other seven, all of these seven except one having one or more octaves in the sound. Four of the seven also are very feeble, the one which has no octave being the feeblest of all. Two of the other three are so distinctly audible along with the chief partial that they gave rise to the saying we have quoted about a musical sound being composed of three sounds.1 If the three most pronounced partials were equally developed in one sound, it could not be called one sound - it would decidedly be a chord; and when in the system they do become developed, they form a chord; but in the one sound they, the partials, having fewer and fewer octaves to strengthen them, fade away in the perspective of sound. The sharp seventh, which in the developed system has only one place, not coming into existence until the sixth octave of the genesis, is by far the feeblest of all the partials, and Nature did well to appoint it so. These harmonics are also sometimes called "overtones," because they are higher than the fundamental one, which is the sound among the sounds, as the Bible is the book among books. [Scientific Basis and Build of Music, page 59]
Seven Chords in Diatonic Chord The number of Diatonic Chords. In the major there are three simple chords, two compound chords, and two double compound, seven in all - subdominant, tonic, dominant, subdominant sixth, subdominant fourth, dominant seventh, and dominant ninth. In the minor there are the same number and order, making fourteen. It is not normal to the tonic chord to compound, but it may, in exceptional instances; the major tonic may, in a certain cadence, assume the top of the minor subdominant; and the minor tonic may assume, in a cognate case, the root of the major dominant.1 [Scientific Basis and Build of Music, page 70]
the excess of the vibrations of the one note over the other makes one or more sounds which are called "grave harmonics;" e.g., in the interval of the fifth, in the ratio of 2:3, the excess of 3 over 2 is 1, so the grave harmonic is an octave below the lowest of the two notes, that is, the ratio of 1:2. This reinforces the lowest note, 2, and gives it a solid effect. In this way the octave is incorporated into the fifth, and unity with variety is combined with the law of continuity at the very threshold of harmony. In 32 of the 42 intervals the grave harmonics are notes which belong to the natural scale. In the 10 remaining intervals which have not the exact number of vibrations found anywhere in the natural scale, 6 of them are from the number 7, thus - 7, 7, 7, 21, 21, 35; the remaining 4 are from 11, 13, 13, and 19. [Scientific Basis and Build of Music, page 77]
The simple natural scale is the fifth; the compound natural scale is the octave; the harmony scale, or chord-scale, is the three fifths; the great genetic scale is six octaves; for, like the six creation days, it takes the six octaves to give birth to the elements of which the wondrous structure of our music is built up; the birthplace of B, the seventh of the octave scale, is the sixth octave of the great genetic scale. The area of the twelve major and twelve minor scales is twelve fifths or seven octaves, the twelfth fifth being a comma and the apotome minor in advance of the seventh octave. This is a quantity so small that it can be ignored in real music; and the two notes, say E# and F, joined to close the circle of this horizon of our music world. E# is the top of the twelfth fifth, and F is the top of the seventh octave; and they are practically, though not exactly mathematically, the same note. Illustrations of this will be found among the plates of this work. [Scientific Basis and Build of Music, page 79]
The difference between B# and C♮ is the apotome minor - a very small difference - and this can only occur in the mathematical scales. In tempered scales, such as are played on the piano, one key serves equally well for both. Although seven sharps may be employed, seven black keys are necessary. As F# and G♭ have the same relation to each other as B# and C♮, and as B# does not require a black key but is found on a white one, so all the semitonic necessities for twelve tempered scales are fully supplied by 5 black keys, since the white keys are as much semitonic as the black ones. [Scientific Basis and Build of Music, page 80]
Seven notes in the Octave are required for the major scale, e.g., the scale of C. All the notes of the relative minor A are the same as those of the scale of C major, with exception of D, its fourth in its Octave scale, and the root of its subdominant in its chord-scale; thus, one note, a comma lower for the D, gives the scale of A minor. [Scientific Basis and Build of Music, page 88]
notes each; that is, 24 new notes, which, with the seven original major notes and the one different minor note, make 32 in all; and 32 notes in the Octave are all that belong to 13 major and 13 minor mathematical scales.1 [Scientific Basis and Build of Music, page 89]
Three times three are nine this would give nine notes; but as the top of the first chord serves for the root of the second one, and the top of the second for the root of the third, in this way these three chords of three notes each are formed from seven different notes. [Scientific Basis and Build of Music, page 96]
together on radial lines from the center they appear grouped in various chords and combinations, dropping out and coming in in such succession as to constitute what Ramsay, whose genius was given to set this thus before us, calls "Nature's Grand Fugue." Beginning at F in the center at the top, and moving either to the right or to the left, after a run of 7 notes we have 4 consecutive Octaves, and then comes the Minor fifth, A-E, followed by the Major fifth, G-D; and this by another Major fifth, F-C; the combinations keep changing till at the quarter of the circle we come to F, A, C, E, G, a combination of the subdominant and tonic Major; and after another varied series of combinations we have at the half of the circle the elements of 2 minor chords, D, F, A and A, C, E, and one Major chord, C, E, G; at the third quarter we have a repetition of the first quarter group; and the various chords and combinations dropping out and coming in, fugue-like; finally we return to where we began, and end with the three-times-three chord, in which the whole 25 notes are struck together, and make that wondrous and restful close of this strange Fugue. No one can hear the thrice-threefold chord of this close and ever forget it; it is "the lost chord" found; and leads the saintly heart away to the Three in One who is the Lord of Hosts; Maker of Heaven and Earth, and all the host of them. [Scientific Basis and Build of Music, page 103]
save the octave, and made them into one, so that in its proximate meetings during its period it seems composed of the ratio 2:3 twelve times, and 3:4 seven times; twelve times 2 and seven times 3 are 45; twelve times 3 and seven times 4 are 64. This long period of 45 to 64 by its proximate meetings divided itself into 19 short periods, and oscillates between the ratios of 2:3 and 3:4 without ever being exactly the one or the other; the difference being always a very small ratio, and the excess of the one being always the deficiency of the other. This fifth, B to F, has been misnamed an "imperfect fifth." When these two notes in the ratio of 45:64 are heard together, the oscillating proximately within it of the two simple ratios gives this fifth a trembling mysterious sound. [Scientific Basis and Build of Music,page 106]
There are seven differential and eleven proximate periods all differing in their degrees of complexity according to the individual character of the ratio; and they illustrate to the eye what is the effect in the ear of the same ratios in the rapid region of the elastic vibrations which cause the musical sounds. [Scientific Basis and Build of Music,page 106]
This plate is a representation of the area of a scale; the major scale, when viewed with the large hemisphere, lowest; the minor when viewed the reverse way. It is here pictorially shown that major and minor does not mean larger and smaller, for both modes occupy the same area, and have in their structure the same intervals, though standing in a different order. It is this difference in structural arrangement of the intervals which characterizes the one as masculine and the other as feminine, which are much preferable to the major and minor as distinctive names for the two modes. Each scale, in both its modes, has three Fifths - subdominant, tonic, and dominant. The middle fifth is the tonic, and its lowest note the key-note of the scale, or of any composition written in this scale. The 53 commas of the Octave are variously allotted in its seven notes - 3 of them have 9 commas, 2 have 8, and 2 have 5. The area of the scale, however, has much more than the octave; it is two octaves, all save the minor third D-F, and has 93 commas. This is the area alike of masculine and feminine modes. The two modes are here shown as directly related, as we might figuratively say, in their marriage relation. The law of Duality, which always emerges when the two modes are seen in their relationship, is here illustrated, and the dual notes are indicated by oblique lines across the pairs. [Scientific Basis and Build of Music, page 106]
When Leonhard Euler, the distinguished mathematician of the eighteenth century, wrote his essay on a New Theory of Music, Fuss remarks - "It has no great success, as it contained too much geometry for musicians, and too much music for geometers." There was a reason which Fuss was not seemingly able to observe, namely, that while it had hold of some very precious musical truth it also put forth some error, and error is always a hindrance to true progress. Euler did good service, however. In his letters to a German Princess on his theory of music he showed the true use of the mathematical primes 2, 3, and 5, but debarred the use of 7, saying, "Were we to introduce the number 7, the tones of an octave would be increased." It was wise in the great mathematician to hold his hand from adding other notes. It is always dangerous to offer strange fire on the altar. He very clearly set forth that while 2 has an unlimited use in producing Octaves, 3 must be limited to its use 3 times in producing Fifths. This was right, for in producing a fourth Fifth it is not a Fifth for the scale. But Euler erred in attempting to generate the semitonic scale of 12 notes by the use of the power of 5 a second time on the original materials. It produces F# right enough; for D27 by 5 gives 135, which is the number for F#. D27 is the note by which F# is produced, because D is right for this process in its unaltered condition. But when Euler proceeds further to use the prime 5 on the middles, A, E, and B, and F#, in their original and unaltered state, he quite errs, and produces all the sharpened notes too low. C# for the key of D is not got by applying 5 to A40, as it is in its birthplace; A40 has already been altered for the key of G by a comma, and is A40 1/2 before it is used for producing its third; it is A40 1/2 that, multiplied by 5, gives C#202 1/2, not C200, as Euler makes C#. Things are in the same condition with E before G# is wanted for the key of A. G# is found by 5 applied to E; not E in its original and unaltered state, E30; but as already raised a comma for the key of D, E30 3/8; so G# is not 300, as Euler has it, but 303 3/4. Euler next, by the same erroneous methods, proceeds to generate D# from B45, its birthplace number; but before D# is wanted for the key of E, B has been raised a comma, and is no longer B45, but B45 9/16, and this multiplied by 5 gives D#227 13/16, not D225, as Euler gives it. The last semitone which he generates to complete his 12 semitones is B♭; that is A#, properly speaking, for this series, and he generates it from F#135; but this already altered note, before A# is wanted for the key of B, has been again raised a comma [Scientific Basis and Build of Music, page 107]
It is very interesting to observe how the number seven, which is excluded from the genesis of the system of vibration, comes into view after the genesis is completed, not only in the seven seconds of the melodic scale, but also in the seven of each of the intervals. As there are seven days in the week, though the seventh was only after the genesis of creation was finished, so there are six intervals, but seven of each, as we have seen; and in each 7-fold group three magnitudes determined by the three genetic magnitudes of the seconds. There is much symbolic meaning in all this. Any of the intervals may be used in melody; in harmony also, either in simple or compound chords, they all have the honor of fulfilling a part; and even those, such as seconds and sevenths, which are less honorable in themselves, have great honor in compound chords, such as dominant sevenths and compound tonics, which fulfill exceedingly interesting functions in the society of chords. [Scientific Basis and Build of Music, page 110]
with her irrevocable proportions to measure his scales for him. The stars at the C of the first scale and at the B# of the last show the coincidence of 12 fifths and 7 octaves. The number of B# is 3113 467/512; C24 multiplied 7 times by 2 brings us to the number 3072; these two notes in the tempered system are made one, and the unbroken horizon of the musical world of twelve twofold keys is created. The very small difference between these two pitches is so distributed in the 12 tempered scales that no single key of the 12 has much to bear in the loss of perfect intonation. [Scientific Basis and Build of Music, page 118]
The scheme endeavours to prove that the development of harmonies of sound and of colours is regulated by the law of Evolution as gained from the Scriptures
—Youthful impressions regarding my great-uncle Dr. Darwin's views
—My cousin Charles Darwin's views touched upon
—The scheme involves the belief that life developing from the Almighty is the general key to disentangle the intricacies of the Natural Sciences
—A remark of Sir John Lubbock's quoted
—The development of Numbers, the stream of Time, the Sevens of Creation, &c., may eventually be proved to proceed by the same laws, . . . . . . . 9 [Harmonies of Tones and Colours, Table of Contents1 - Harmonies]
The eighteen tones of keyed instruments veering round and in musical clef below, the twelve seen that develope major keys
—The seven colours answer to the seven white notes
—The use of the two chasms, the key-note C and its root F rising from them
—A major key-note complete in itself, embracing the eighteen tones
—In the whole process of harmony there is limit, every key-note having its point of rest, and yet it is illimitable, . . . . . . . 22 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]
The key-note C sounding from within itself its six tones to and fro in trinities, the tones written as notes in musical clef
—The trinities hereafter termed primaries and secondaries
—The seven of each of the twelve key notes developing their tones
—The order in which the tones meet, avoiding consecutive fifths
—Dissonance is not opposition or separation
—The use of the chasms and double tones is seen
—The isolated fourths sound the twelve notes
—Each double tone developes only one perfect major harmony, with the exception of F#-G♭; F# as the key-tone sounds F♮ as E#, and G♭ as the key-tone sounds B♮ as C♭
—The primaries of the twelve key-notes are shown to sound the same tones as the secondaries of each third harmony below, but in a different order
—All harmonies are linked into each other, . 23 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]
The twelve major scales
—The term key-note employed in the ordinary sense of the musician
—The twelve key-notes, with the six notes of each as they veer round in trinities, are written in musical clef, and the scales added
—The reversal of the four and three of the key-note and its trinities in the seven of its scale
—The twelve keys follow each other seven times through seven octaves linked into the lower and higher series
—The modulating of scales, the eleventh notes rising to higher keys, . . . . . . 26 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]
—The fourteen roots of the chords of the twelve major keys
—A threefold major chord examined, fourfold with its octave
—The seven of each key seen to have two chords and its scale one chord, thirty-six in all, forty-eight with octaves
—The chords of the twelve keys as they follow in order are written in musical clef
—Colours seen to agree, . . . 27 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]
The twelve keys, their trinities, scales, and chords, rising seven times through seven octaves, each thirteenth note octave of the previous twelve and first of the rising twelve
—Descending, ascending reversed
—The Pendulograph alluded to, . . . 28 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]
The difference in the development of a major and a minor harmony
—The twelve developing keys mingled
—D♭ shown to be an imperfect minor harmony
—E♭ taking B♮ as C♭ to be the same as D#
—The intermediate tones of the seven white notes are coloured, showing gradual modulation
—As in the diagram of the majors, the secondaries are written in musical clef below the primaries, each minor primary sounding the secondaries of the third harmony below, but in a different order, and one tone rising higher, . . . . . 34 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]
The twelve major and the twelve minor keys written in musical clef
—First, the twelve major keys rising mingled as they develope seven times through seven octaves
—Second, one series of the twelve meeting by fifths, keys not mingled
—Third, the twelve minor keys mingled
—Fourth, the twelve minor key-notes and their trinities, the keys meeting by fifths in the line above the keys of the ascending scales, and in the line below the keys of the descending scales, 42 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]
If health is still granted to me, and if an interest is created on the subject of these pages, I shall endeavour to explain by what means I gained the laws here described, and to enter upon the development of numbers as showing the stream of time ever falling into infinity, and gliding onwards; also the sevens in creation, with several other branches of the subject which are here untouched, or but briefly alluded to. It is my earnest desire that all may be closely examined. Indifference will grieve me, but even severe criticism will afford me pleasure, as proving that the subject is considered worthy of investigation. [Harmonies of Tones and Colours, Introduction2 - Harmonies, page 10]
In the diagrams the circles are not drawn as interlacing into each other, from the difficulty of representing them accurately as rising spirally in geometric progression. If we endeavour to realise the development of harmonies, both in geometric order, and at the same time advancing and retiring, as in musical clef, we must imagine a musician having the physical power of striking all the notes on a circular keyed instrument of seven octaves, linked to a lower series of seven octaves, and a corresponding series of seven higher. But in fact the depth of the lower series, and the height of the higher, are alike unfathomable to our present powers. C, the first note of the seven octaves, sounds the four lowest tones, F, G, A, B of the lower series; and B, the last and highest note of the seven octaves, sounds in its harmony C♮ and D# of the higher series of sevens. [Harmonies of Tones and Colours, The Method of Development or Creation of Harmonies3, page 17]
Throughout the scheme seven tones and seven colours develope in every harmony. In the relationship between tones and colours the seven may be con- [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies2, page 19]
A key-note developing its harmony may be compared to a seed striking its root downwards, and rising upwards. On striking a note, it sounds from within itself, in a rapid and subdued manner, the six kindred tones necessary to its harmony, and all which do not belong to that individual harmony are kept under; thus all harmonies are in sevens. Each seven forms an ascending and descending series; the ear is aware of the tones, but not of the order in which they rise. [Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]
DIAGRAM III.—MAJOR KEY-NOTES DEVELOPING BY SEVENS. "Creation is the realization of Divine Thought."::
Harmonies of Tones and Colours, Diagram III - The Major Keynotes Developing by Sevens, page 25a]
THE first circle on this diagram represents seven major key-notes, beginning with C on the third space in the treble clef, and sounding as their roots the seven last key-notes which have developed. The second is a continuation of the first circle. The seven previously developed key-notes are now the roots of seven higher key-notes. The intermediate notes are not coloured, but may be seen to be complementary pairs. [Harmonies of Tones and Colours, Diagram III - The Major Keynotes Developing by Sevens, page 25a]
The second circle is a continuation of the first, shewing the 7 previously developed Key-notes are the roots of the 7 higher Key-notes. [Harmonies of Tones and Colours, The First Circle are 7 Keynotes, page 25c]
The Sevens of the Key-notes and their scales, the latter written also as they pair by fifths. [Harmonies of Tones and Colours, The Sevens of the Keynotes, page 25e]
The twelve key-notes, with the six notes of each as they veer round in trinities, are again written in musical clef, and the scales added. The key-note leads the scale, and, after striking the two next highest notes of the seven of the harmony, goes forward, with its four lowest, an octave higher. The seven of each harmony have been traced as the three lowest, thus meeting the three highest in three pairs, the fourth note being isolated. Notwithstanding the curious reversal of the three and four of the scale, the three lowest pair with the three highest, and the fourth with its octave. The four pairs are written at the end of each line, and it will be seen how exactly they all agree in their mode of development. Keys with sharps and keys with flats are all mingled in twelve successive notes. If we strike the twelve scales ascending as they follow each other, each thirteenth note being octave of the first note of the twelve that have developed, and first of the rising series, the seventh time the scales gradually rise into the higher series of seven octaves beyond the power of the instrument. Descending is ascending reversed. After the seven and octave of a scale have been sounded ascending, the ear seems to lead to the descending; but ten notes of any scale may be struck without the necessity of modulation; at the seventh note we find that the eleventh note in the progression of harmonics rises to meet the seventh. For instance, B, the seventh note in the scale of C, must have F#. This point will be fully entered into when examining the meeting of fifths. To trace the scale of C veering round as an example for all, we may begin with C in Diagram II., and go forward with F, G, A, and B an octave higher. If the twelve scales were traced veering round, they would be found to correspond with the twelve as written in musical clef. [Harmonies of Tones and Colours, Diagram IV - The Development of the Twelve Major Scales, page 26a]
ON a keyed instrument only twelve are major key-notes, but as the double tones C#-D♭ and F#-G♭ are roots, there are fourteen different chords. The fourteen that are roots are written in musical clef. As an example of the major chords in the different keys, we may examine those in the key of C. A major fifth includes five out of the seven of its key; with the third or central note it is the threefold chord, or fourfold when the octave note is added. Including the silent key-notes, a threefold chord embraces eight, or, counting the double tones, not including E#, eleven. The first and second chords of the seven of the harmony are perfect major chords in the key of C; the central note of the third chord, being #C-♭D, is a discord. The first pair of fifths in the scale, with its central note, is a chord of the key; if we include the octave, the last pair of fifths, with its central note, is the same chord an octave higher than the lowest chord of the seven. Of the chords written in musical clef of the twelve keys, the octave chord is only written to C, the seven of each having two chords and the scale one, thirty-six in all, or forty-eight if the octave chords are added. Notice how the chords of each seven and the chord of its scale are altered. [Harmonies of Tones and Colours, Diagram V - The Chords of the Twelve Major Keys, page 27a]
THE twelve keys have been traced following each other seven times through seven octaves, the keys mingled, the thirteenth note being the octave, and becoming first of each rising twelve. Thus developing, the seven notes of each eighth key were complementary pairs, with the seven notes of each eighth key below, and one series of the twelve keys may be traced, all meeting in succession, not mingled. When the notes not required for each of the twelve thus meeting are kept under, the eighths of the twelve all meet by fifths, and as before, in succession, each key increases by one sharp, the keys with flats following, each decreasing by one flat; after this, the octave of the first C would follow and begin a higher series. It is most interesting to trace the fourths, no longer isolated, but meeting each other, having risen through the progression of the keys to higher harmonies. In the seven of C, B is the isolated fourth, meeting F#, the isolated fourth in the key of G, and so on. Each ascending key-note becomes the root of the fifth key-note higher; thus C becomes the root of G, &c. [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys1, page 29]
The following table shows the regularity of each seven of the twelve key-notes ascending by fifths, and the use of the two poles is again seen. The key-notes and their trinities are closely linked into each other, the three highest notes of the lower fifth key becoming the three lowest of the higher fifth key, and the four lowest becoming the four highest in an octave higher. The twelve keys, rising in each note a tone higher and descending a tone lower, cause the meetings by fifths. Having examined the table, we may strike the keys by fifths as written in the musical clef, beginning with the lowest C in [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys1, page 29]
In the development of the key-notes, the sharp or flat is written to each note, but not to the keys. The reversal of the three and four notes of each seven of the twelve key-notes and their trinities meeting by fifths having been traced, we will now examine the twelve scales meeting by fifths, and the results arising from the reversal of the three and four notes of each fifth lower scale in the fifth higher. Take as an example the scale of C: C D E F G A B, and that of G: G A B C D E F#. The four lowest notes of the seven of C are the four highest, an octave higher, in G; F, the central and isolated note of the seven of C, having risen a tone higher than the octave in the scale of G. The twelve scales thus modulate into each other by fifths, which sound the same harmonies as the key-notes and their trinities. Refer to the twelve scales written in musical clef ascending by fifths, and strike them, beginning at the lowest C in the bass clef; this scale sounds no intermediate tones, but these must be struck as required for all the scales to run on in fifths. After striking the seven notes of C, if we fall back three, and repeat them with the next four notes of the seven; or strike the seven and octave of C, and fall back four, repeating them and striking the next four, the four last notes of each scale will be found to be always in the harmony of the four first of the fifth higher scale. When the twelve scales ascending have been thus gained, as we trace them also on the table, they may be struck descending by following them as written in musical clef upwards, and [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys2, page 30]
The keys of C and G meeting are coloured, and show the beautiful results of colours arising from gradual progression when meeting by fifths. Each key-note and its trinities have been traced as complete in itself, and all knit into each other, the seven of each rising a tone and developing seven times through seven octaves, the keys mingled. The twelve scales have been traced, developing seven times through seven octaves, all knit into each other and into the key-notes and their trinities. The chords have also been traced, each complete in itself, and all knit into each other and into the key-notes, trinities, and scales. And lastly, one series of the twelve keys, no longer mingled, but modulating into each other, have been traced, closely linked into each other by fifths through seven octaves, three keys always meeting. Mark the number of notes thus linked together, and endeavour to imagine this number of tones meeting from the various notes. [Harmonies of Tones and Colours, The Twelve Scales Meeting by Fifths, page 31a]
Round the circle the eighteen tones of keyed instruments are shown; the twelve developing perfect minor keys are written thus
, the seven white-keyed notes are coloured, the intermediate tones left uncoloured. [Harmonies of Tones and Colours, Diagram VIII - On the Development of the Twelve Minor Harmonies, page 32]
Below the circular diagram are seen in musical clef the twelve minor key-notes, as gained from the majors. There is only one meeting of the same note in the seven of every major harmony. All the twelve follow the same plan; the lowest note of the seven of C is F, the highest note of the seven is E. The lowest tone sounded by E and the highest tone sounded by F is the same, A—leading the ear from C to its relative minor A. [Harmonies of Tones and Colours, The Minor Harmonies, page 33a]
AS an example of the twenty-four, compare A major, developing, in Diagram II., with A minor, Diagram IX., taking the notes in the order which they sound in trinities. The three notes of the primaries sounded by A minor are, first, the same root as the major; the two next are the fourth and seventh higher notes (in the major, the fifth and sixth); the secondaries only vary by the sixth and seventh notes being a tone lower than in their relative major. Observe the order in which the pairs unite; the fourth in depth, sounded seventh, isolated. A and its root do not rise from the chasms. The fundamental key-note C was seen not to be interfered with, neither is the fundamental minor key-note A; G# on the one side, and B♭ on the other, being the key-notes. The seven of each minor harmony embrace only seventeen tones. C major and A minor are the only two keys which sound the seven white notes of keyed instruments. The minor scale and chords of A are not included in this remark. [Harmonies of Tones and Colours, Diagram IX - The Minor Keynote A and Its Six Notes, page 34a]
IN the first circle are represented seven minor key-notes, beginning with A on the second space in the treble clef, their roots being the seven last key-notes that have developed. [Harmonies of Tones and Colours, Diagram X - Minor Keynotes Developing by Sevens, page 35a]
The second circle is a continuation of the first; the seven previously developed key-notes become, as before, the roots of seven higher. The uncoloured intermediate notes are in the same way complementary pairs. [Harmonies of Tones and Colours, Diagram X - Minor Keynotes Developing by Sevens, page 35a]
The second circle is a continuation of the first, shewing the 7 previously developed Key-notes are the roots of the 7 higher Key-notes. [Harmonies of Tones and Colours, First Circle are 7 Minor Keynotes, page 35c]
BEGINNING with the lowest A in the bass clef, let us strike the trinities, scale, and chords, carrying each key-note a fifth higher, counting the seven belonging to its harmony. If the silent notes are included, each fifth is the eighth meeting. [Harmonies of Tones and Colours, Diagram XIV - The Modulating Gamut of the Twelve Minor Keys by Fifths1, page 39]
Let us first examine the meeting of the key-notes and their trinities in musical clef; the isolated fourths rising through the progression of the twelve now meet, seven and seven pairing. We must notice how closely they are linked into each other, the three highest notes of the lower seven being the three lowest of the higher seven an octave higher, and the four lowest becoming the four highest an octave higher; we descend by following the keys as written in musical clef upwards. [Harmonies of Tones and Colours, Diagram XIV - The Modulating Gamut of the Twelve Minor Keys by Fifths1, page 39]
Fourthly, we have one series of the seven of each of the twelve minor keys meeting by fifths through seven octaves. The keys of the twelve ascending scales are written in musical clef above the former, and the keys of the descending scales below. The ascending scales sound the fifth higher harmonies than the key-notes and their trinities, and the lower scales the fifth harmony lower than the key-notes and their trinities. The three series follow out their keys in three successive series, and all meet by fifths. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]
The 7 of the 12 Minor Keys as they rise mingled, and the 13th octave. [Harmonies of Tones and Colours, The 12 Major Keys as They Rise, page 42c]
The Key of each 7 meeting by fifths, unmingled. [Harmonies of Tones and Colours, The 12 Major Keys as They Rise, page 42c]
DIAGRAM XVI.—The seven of each harmony, with its scale—The pairs of the trinities and scales. Harmonies of Tones and Colours, Additional Diagrams, page 57]
Manly Palmer Hall
"Man must overcome the seven planets and transmute them into soul powers. Their negative forces are the seven deadly sins, which are overcome by a symbolic struggle with demons and dragons and, in turn, are transmuted into the seven cardinal virtues. This is the key to alchemy, for from the seven base metals, first spiritualized and then brought together as a secret compound, is produced the Philosopher's Stone, the purified soul." [Manly Palmer Hall]
DANCE OF THE SEVEN VEILS
"The seven spheres attached to the seven planets symbolize seven principles, seven different states of matter and spirit, seven different worlds which each man and each humanity must pass through in their evolution across a solar system." -- The Wisdom of Egypt
7 Daughters of Atlas
7 Stages of Alchemy - Calcination, Dissolution, Separation, Conjunction, Fermentation, Distillation, Coagulation.
7 Hermetic principles - Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause and Effect, Gender.
7 Notes of the musical scale.
7 Systems of Symbolism - numbers, geometrical figures, letters, words, magic, alchemy, astrology.
7 Rays of Light - Red, Orange, Yellow, Green, Blue, Purple, Violet.
7 Planets of Antiquity - Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn.
7 Churches of Asia Minor
7 Personality Types - Lunar, Mercurial, Venusian, Solar, Martial, Jovial, Saturnine.
7 Days of Week - Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.
7 Arch Angels - Michael, Gabriel, Raphael, Uriel, Chamuel, Jophiel, and Zadkiel.
7 Metals of Antiquity - Lead, Tin, Iron, Copper, Mercury, Silver, Gold.
7 Chakras - Muladhara, Svadhisthana, Manipura, Anahata, Vishuddha, Ajna, Sahasrara.
7 Emotive Spheres of Kabbalah
7 Root Races, each with 7 sub-races
7 Days of Creation
7 Virtues - Faith, Hope, Charity, Fortitude, Justice, Prudence, Temperance.
7 Vices - Pride, Envy, Anger, Sloth/dejection, Avarice, Gluttony, Lust.
7 Stages of Man - the infant, the school-boy, the lover, the soldier, the judge, the elderly man, the senile one.
7 Liberal Arts - grammar, rhetoric, logic, arithmetic, music, geometry, and astronomy - the first three in the Trivium, the latter four in the Quadrivium.
7 Wonders of the Ancient World - Pyramids of Egypt, Hanging Gardens of Babylon, Statue of Zeus at Olympia, Temple of Artemis at Ephesus, Mausoleum of King Mausolus at Halicarnassus, Colossus of Rhodes, Pharos Lighthouse at Alexandria.
7 Headed Hydra
7 Headed Lion
7 Headed Dragon
7 Headed Serpent
7 Seas - Arctic, Antarctic, North and South Pacific, North and South Atlantic and the Indian Ocean.
7 Continents - North America, South America, Africa, Europe, Asia, Australia and Antarctica.
7 Seven Sisters of the Pleiades star system.
7 Parts to the embryo - Amnion, Chorionic Villi, Spinal Cord, Heart, Brain, Umbilical Cord, Yolk Sac.
7 Parts of the body - Head, Thorax, Abdomen, Two Arms, Two Legs.
7 Major Organs - Brain, Heart, Lungs, Stomach, Intestines, Liver, and Pancreas.
7 Glands - Pineal, Pituitary, Thyroid, Thymus, Adrenal, Lyden and Gonad.
7 Divisions to the brain - Cerebrum, Cerebellum, Pons Varolii, Medulla Oblongatta, Corpus Callosum, Spinal Cord, Meninges.
7 Parts to the inner ear - Vestibule, Auditory Canal, Tympanic Membrane, Ossicles, Semi-circular Canal, Cochlea, Membranous Labyrinth.
7 Parts to the retina - Cornea, Aqueous Humor, Lens, Vitreous Humor, Retina, Sclera, Iris.
7 Cavities to the heart - Right and Left Ventricle, Right and Left Atrium, Tricuspid Valve, Mitral Valve, Septum.
7 Body systems - Muscular, Skeletal, Nervous, Digestive, Respiratory, Excretory, Circulatory.
7 Bodily functions - Respiration, Circulation, Assimilation, Excretion, Reproduction, Sensation, Reaction.
7 Levels in the Periodic Table of the Elements.
...and, of course, the 7 Dwarfs.
“The Principles of Truth are Seven; he who knows these, understandingly, possesses the Magic Key before whose touch all the Doors of the Temple fly open.” –The Kybalion
"And God created seven Heavens and seven Earths, and through them all, descends His Command." - scriptural translation
7.16 - Seventh
Diagram III - The Major Keynotes Developing by Sevens
Diagram X - Minor Keynotes Developing by Sevens
Law of Correspondence
law of seven
seven enshrouding veils of Sais
seven major keynotes
seven major keys
seven of each harmony
seven of the harmony
seven white notes
Table of Correspondences
Table of Glands and Correspondences
THE SEVEN FORMS OF SUBSTANCE
The Seven of each Harmony with its Scale
The Seven of Each Harmony
The Sevens of the Keynotes
The Twelve Keys Rising Seven Times
top of the seventh octave
Twenty-seven depolar triple groupings