(please read previous posts for continuity)
I've found it useful to use the numbers of the Planetary Squares to invoke the Planetary virtues, while using the primary numbers to induce states of mind that are harmonious with Number. For instance, the sum of the Saturnian square is 45; I would use the mudra for 45 to summon the Virtue of Saturn, but would use the mudra for the number 2 to enter into a trance that allows for communion with that number, also assigned to Saturn. Use the primary numbers to alter personal state of mind, and the sum of the Planetary Square to engage the macrocosmic force related to the Planet.
The sums for the Planetary Squares are as follows:
To form the mudras for each Planet, build the number one section at a time; for Venus, first you would perform the mudra for 1000, then for 200, then 20, then 5. The final mudra is held for as long as you wish the Virtue to be invoked. For example, if you were to invoke Venus, and use her song to fill an area with her virue in order to distract wild animals from attacking you, you would perform the Mudra and Song, make your petition/statement of intent after completing the song, and would hold the mudra for as long as you wished the effect to last. In this Arithmatic magic, the mudra is the material basis which holds the concentrated virtue in place; when it is released, so is the virtue, to dissipate back into the Azoth.
The Scales of the Planets
Agrippa in his Three Books of Occult Philosophy gives us yet more insight, sharing with us the scales that are harmonious with the Planets, which we might use to fill an area with their virtue and presence. In Chapter XXVI, Agrippa notes that tone goes a far measure toward matching the nature of the Planets; for instance, he says that "Saturn hath sad, hoarse, heavy and slow words, and sounds, as it were pressed to the center; but Mars rough, sharp, threatening great and wrathful words.." In crafting the Songs of the Planets, the tone and nature of the song is of more import than the notes used, or even the scale. It stands to reason, though, that combining the correct tone with the correct scale would be even more useful, and in my experience it is.
To Sol is attributed the Dorian mode, ( E F G A B C D E)
To Mars goes the Phrygian mode, (C Db Eb F G Ab Bb C)
To Jupiter the Lydian mode, (C D# E F G A# B C)
To Saturn the Mixolydian mode, (C D E F G A Bb C)
To Mercury the Hypophrygian mode, (G F E D C B A G)
To Venus the Hypolydian mode, (F E D C B A G F)
To Luna the Hypodorian mode, (E D C B A G F E)
To the Stars, the Hypomixolydian mode. (D E F G A B C D)
A better way to understand how this works for those without much musical training is to think of the modes as a series of rising or descending movements in pitch, with each mode being a certain pattern of movements. It gives each mode a mathematical and musical proportion, which is worth studying in it's own right. Where T is a whole tone, and S is a semi-tone, and TS is a whole tone and a half, the modes look like this:
Mercury/Hypophrygian (descending): T-T-S-T-T-S-T-T
Venus/Hypolydian (descending): S-T-T-S-T-T-T
Luna/Hypodorian (descending): T-T-S-T-T-T-S
The Fixed Stars/Hypomixolydian: T-S-T-T-T-S-T
In order to use these proportions to create our songs for the Planets, we need only refer to our sources for incantations (Picatrix, Three Books) and take from either the Orphic Hymns, the Songs of Circe (which we have from Giordano Bruno) or the incantations of the Picatrix to sing the virtue of the Planet while making the appropriate Mudra. Another powerful part of using the mudra in this instance is that it makes the entire business a magical act; we may read the incantations of hymns at any point, but we only Sing them while making their sign when we are doing the Work.
I prefer to use the Orphic Hymns, as given below; the Hymns are sung with each sentence being dedicated to a Note; they are between a song and a chant, similar to the way the famed Gregorian monks intoned their hymns. It makes sense that the Hymns would be sung, and this is the most straightforward and efficacious method I know of. The bold letter is the note with which the verse following it is sung. It's the proportions that make the Songs align with a Planet; it matters not which note you end on, so much as that the proportion between notes in the scale has been acknowledged. You may choose yourself whether to sing a repeated tone at the same octave as the one already sung or at a new octave; again, it's the proportion that is important in the pattern sung, and i would recommend not jumping octaves, but keeping with the pattern of steps given in the scales themselves.
The Hymn to the Sun
E With matchless sight illumines all the sky. Native, unwearied in diffusing light, And to all eyes the object of delight:
F Lord of the Seasons, beaming ight from far, Sonorous, dancing in thy four-yok'd car.
G With thy right hand the source of morning light, and with they left the father of the night.
A Agile and vig'rous, venerable Sun, Fiery and bright around the heavn's you run,
B Foe to the wicked, but the good man's guide, O'er all his steps propituous you preside.
C With various sounding golden lyre 'tis thine to fill the world with harmony divine.
D Father of ages, guide of prosp'rous deeds, The worlds commander, borne by lucid steeds.
E Immortal Jove, Flute-playing, bearing light, Source of existence, pure fiery bright;
F Bearer of fruit, almighty lord of years, agile and warm, whome ev'ry power revers.
G Bright eye, that round the world incessant flies, Doom'd with fair fulgid rays to set and rise;
A Dispensing justice, lover of the stream, the worlds great master, and o'er all surpreme.
B Faithful defender, and the eye of the right, of steeds the ruler , and of life the light;
C With sounding whip four fiery steeds you guide, when in the glittering car of day you ride,
D Propitious on these mystic labours shine, and bless thy supplicants with life divine.
The Hymn to the Moon (the notes are descending, as they are for Mercury and Venus)
E Hear, Goddess queen, diffusing silver light, Bull horn'd and wand'ring thro' the gloom of Night.
D With stars surrounded, and with circuit wide, Night's torch extending, through the heav'ns you ride:
C Female and male, with silv'ry rays you shine, and now full orb'd, now tending to decline.
B Mother of ages, fruit-producing Moon, whose amber orb makes Night's reflected noon;
A Lover of horses, splendid queen of night, all-seeing pow'r, bedeck'd with starry light,
G Lover of vigilance, the foe of strife, in peace rejoicing, and a prudent life.
F Fair lamp of Night, its ornament and friend, Who give'st to Nature's works their destin'd end.
E Queen of the stars, all-wise Diana, hail! Deck'd with a graceful robe and ample veil.
D Come, blessed Goddess, prudent, starry, bright, come, moony-lamp, with chaste and splendid light,
C Shine on these sacred rites with prosp'rous rays, and pleas'd accept thy supplicants' mystic praise.
The Hymn to Mars
C Magnanimous, uncounquer'd, boistrous Mars, in darts rejoicing and bloody wars
Db Fierce and untam'd, whose mighty pow'r can make, the strongest walls from their foundations shake.
Eb Mortal destroying King, defil'd with gore, Pleas'd with war's dreadful, tumultuous roar;
F Thee, human blood, and swords, and spears delight, and the dire ruin of mad savage fight.
G Stay, furious contests, and avenging strife, whose works with woe, embitter human life;
Ab To lovely Venus, and to Bacchus yield, to Ceres give weapons of the field;
Bb Encourage peace, to gentle works inclin'd, and give abundance with benignant mind.
The Hymn to Mercury
G Hermes, draw near, and to my pray'r incline, Angel of Jove, and Maia's son divine;
F Prefect of contest, ruler of mankind, with heart almighty, and a prudent mind.
E Celestial messenger of various skill, whose pow'rful arts could watchful Argus kill.
D With winged feet 'tis thine thro' air to course, O friend of man, and prophet of discourse;
C Great life-supporter, to rejoice is thine, In arts gymnastic, and in fraud divine.
B With pow'r endu'd all language to explain, of care the loos'ner, and the source of gain.
A Whose hand contains of blameless peace the rod, Corucian, blessed, profitable God.
G Of various speech, whose aid in works we find, and in necessities to mortals kind.
F Dire weapon of the tongue, which men revere, Be present, Hermes, and thy supplicant hear;
E Assist my works, conlude my life with peace, Give graceful speech, and memory's increase.
The Hymn to Jupiter
C O Jove, much honoured, Jove supremely great, to thee our holy rites we consecrate,
D# Our pray'rs and expiations, king divine, For all things to produce with ease thro' mind is thine.
E Hence mother Earth, and mountains swelling high, proceed from thee, the deep and all within the sky.
F Saturnian king, descending from above, magnanimous, commanding, sceptered Jove;
G All-parent, principle and end of all, whose pow'r almighty shakes this earthly ball;
A# Ev'n Nature trembles at thy mighty nod, Loud-sounding, arm'd with light'ning, thund'ring God.
B Source of abundance, purifying king, O various form'd, from which all natures spring;
C Propitious hear my pray'r, give blameless health, with peace divine, and necessary wealth.
The Hymn to Venus
F Heav'nly, illustrious, laughter-loving quenn, sea-born, night loving, of an awful mien,
E Crafty, from whom necessity first came, producing, nightly, all-connecting dame;
D Tis thine the world with harmony to join, For all things spring from thee, O pow'r divine.
C The triple Fates are rul'd by thy decree, and all productions yield alike to thee,
B Whate'er the the heav'ns, encircling all contain, Earth fruit producing, and the stormy main,
A Thy sway confesses, and obeys thy nod, awful attendant of the brumal God:
G Goddess of marriage, charming to the sight, Mother of loves, whom banquetings delight;
F Source of persuasion, secret, fav'ring queen, Illustrious born, apparent and unseen:
E Spousal, lupercal, and to men inclined, Prolific, most-desir'd, life-giving, kind;
D Great sceptre-bearer of the Gods, tis thine, Mortals in necessary bands to join;
C And ev'ry tribe of savage monsters dire, in magic-chains to bind, through mad desire.
B Come, Cyprus-born, and to my pray'r incline, Whether exalted in the heav'ns you shine,
A Or pleas'd in Syria's temple to preside, Or o'er th' Egyptian plains thy car to guide,
G Fashion'd of gold, and near its sacred flood, Fertile and fam'd to fix thy blest abode,
F Or if rejoicing in the azure shores, near where the sea with foaming billows roars,
E The circling choirs of mortals, thy delight, or beauteous nymphs, with eyes cerulean bright,
D Pleas'd by the dusty banks renown'd of old, to drive thy rapid, two-yok'd car of gold;
C Or if in Cyprus with thy mother fair, where married females praise thee ev'ry year,
B And beateous virgins in the chorus join, Adonis pure to sing and thee divine;
A Come, all attractive to my pray'r inclin'd, for thee I call with holy, reverent mind.
The Hymn to Saturn
C Etherial Father, mighty Titan, hear, great fire of Gods and men, whom all revere;
D Endu'd with various council, pure and strong, to whom perfection and decrease belong.
E Consum'd by thee all forms that hourly die, by thee restor'd, their former place supply;
F The world immense in everlasting chains, strong and ineffable thy pow'r contains;
G Father of vast eternity, divine, O mighty Saturn, various speech is thine;
A Blossom of Earth and of the starry skies, Husband of Rhea, and Prometheus wife.
Bb Obstetric Nature, venerable root, from which the various forms of being shoot;
C No parts peculiar can they pow'r enclose, diffus'd thro' all, from which the world arose,
D O, best of beings, of a subtle mind, propitious hear to holy pray'rs inclin'd;
E The sacred rites benevolent attend, and grant a blameless life, a blessed end.
This method is very, very simple, but it preserves the proportions in the numeric patterns and works well. Using either an instrument, or an app for a smartphone, the arithmancer can play the tone for the line and then incant it, doing so for each line until the incantation is complete. Eventually it will be memorized, of course, and then more lovely. The way the notes are sung should be tuned by the nature of the planet; intone Saturn as a melancholy dirge, Venus in a sensuous manner, etc.
If desired, the arithmancer could certainly sing multiple lines of the hymn at one tone in order to end on the Tonic; I personally enjoy the small bit of variety changing tones each line allows us. I think it is important to avoid making over-complicated songs here; these are holy hymns, magical devices that create audible proportion, and not melodic pop fair.
We are also given modes to work the elements and humors with--the Phrygian to Choler and Fire, the Lydian to blood and Air, the Dorian to Water and Plegm, the Mixolydian to melancholy and Earth. I use Eliphas Levi's hymns to the Elements to build songs for working with them. They can be used to alter mood, to adjust the humours of the body. There are many applications.
With just this much, we can create powerful incantatory song, in combination with mudra and arithmatic technique to divine connection through number and invoke the Virtues of the heavens into our spheres and environments.
Use the above patterns to create tonal chants for the Elements on your own.
OK! No more posts for a while, I promise! I totally understand if you have to tl;dr on all this, but there are some useful bits in there. Hope you are all well.