Reading Time: 13 minutesAugust 29, 2023

ASTRO-MUSIC COMPOSITION (CHART TO MUSIC)

Part 3 of the article “Astro-Music Composition”. If you have not read the previous parts, then I suggest you read Part 1 & Part 2 first.

IMPLEMENTATION: THE SOLAR SECTOR

“As Above, So Below” ~ Hermes Trismegistus

(The Zodiac Signs are “above” the Planets “below”.)

With modern western music and astrology the 12 Planets + 12 Tones combination can be implemented to create a “Solar Scale“. The idea behind this is that every planet can be represented by a tone. We could give “tone” to the planets based on their rulership, the tone of their domicile. 

RULERSHIP

A planet posited in the sign it rules is said to be in its rulership, domicile, or home. 

Example: The Sun is the ruler of Leo. Leo is presented by the tone of E (and tonality of E Major), thus the Sun is represented by the tone of E (and tonality of E Major) as well.

DETRIMENT

On the contrary, when a planet is in the sign opposite the sign it rules, it is said to be in detriment. The Detriment of planets (being located opposite to the Domicile) in musical theory would represent the Tritone above or below the Tonic (root).

7 CLASSIC PLANETS

According to Wikipedia the bulk of the tradition assigns planetary rulerships according to the ancient Chaldean astronomical order of the planets (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon; the former order of the planets in distance from Earth geocentrically):

PLANET
DOM. SIGN
DOM. TONE	C/D♭(C♯)	G/A♭(G♯)	D/E♭(D♯)	A/B♭(A♯)	E/F	B	G♭(F♯)

What you might have noticed, is that the tones as listed above do follow the Circle of Fifths:

• First signs (starting at Aries): C-G-D-A-E-B
• Second signs (starting at Libra): Gb-Db-Ab-Eb-Bb-F

I do think though that the Thema Mundi (used in Hellenistic astrology that shows the supposed positions of the seven visible planets – including the Sun and Moon – at the beginning of the universe) might “match” better with modern astrological systems.

PLANET
DOM. SIGN
DOM. TONE	C D♭ (C♯)	G ♭ (F♯)	D B	A	E	A♭ (G♯) F	E♭ (D♯) B♭

With the Classical and Traditional rulership it becomes a bit “complicated” to assign tones to the planets. Some planets rule 1 sign, others rule 2 and that would thus mean that some planets are represented by more then one tone. Musically that does not make much sense at all. Nonetheless, if you only use the “Classic” planets, then you have to make some decisions about when you are going to use what tone for each planet that represents 2 tones.

7 CLASSIC + 3 TRADITIONAL PLANETS

2 planets (Venus and Mercury) rule each 2 houses (signs) and thus represent 2 tones, while the other 8 planets only rule one house (sign) and thus represent only 1 tone with this concept version. And because the planets “inherit” the tone of the houses they rule in this concept version, we end up with a problem, what tone represents Venus and Mercury?

• Are we going to use only 10 tones of the 12-Tone Temperament? If so, are 2 of the 4 tones represented by Venus and Mercury permanently going to be “ruled-out”?
• Or are we going to use all 12 tones of the 12-Tone Temperament, but are the 4 tones (represented by Venus and Mercury) going to be selected based on other conditions?

From a musical point of view “ruling-out” 2 tones would limit the options you have melodically and harmonically. It would thus be better if all tones could be used and certain conditions determine how. In a later stage I will try to “work out” the solutions for this “problem” … suggestions are welcome!

With 10 planets the following rulership is usually used:  

PLANET
DOM. SIGN
DOM. TONE	E	A	D B	F♯(G♭) G	C	G♯(A♭)	D♯(E♭)	A♯(B♭)	F	C♯(D♭)
DET. SIGN
DET. TONE	A♯(B♭)	D♯(E♭)	G♯(A♭) F	C C♯(D♭)	F♯(G♭)	D B	A	E	B	G

So, using 10 planets isn’t the optimal method when using 12-TET as standard for your composition.

1 PLANET, 1 RULERSHIP

Perhaps I am “breaking” the astrological rules with the idea of “1 planet, 1 rulership”.

The more “conservative” astrologers reading this might feel a bit confused or perhaps even a tiny bit agitated …

“There you go, another weirdo with his fancy ideas, who does he think he is, Austin Powers?“

No worries! You can just “skip by” this part of this article and pretend you never read it. *wink*

If every planet has one rulership, then everything aligns: 

12 planets = 12 rulerships = 12 tones = 12 Major tonalities, 12 minor tonalites …

PLANET

SIGN

DOM.

E

A

D

F♯ G♭

C

G♯ A♭

D♯ E♭

A♯ B♭

F

C♯ D♭

G

B

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LINKING THE COSMIC EXPANSE & SOLAR SECTOR

INTERVALS

To “connect” both “zones” (Cosmic and Solar) one could use the musical intervals that are between a planet’s domicile (the zodiac sign over which it has rulership) and it’s location at the Natal chart. When the planet is in it’s domicile the Major tonality is represented. 

In the table below the data of the Natal Chart:

PLANET

SIGN

TON.

G

F♯ G♭

Bm

G

A

G

A

G♯m A♭m

Fm

D♯m E♭m

A

G

When calculating this interval only the planet’s domicile is used (it’s primary tonality).
Domicile = root of Major tonality  | Prograde = root of Major tonality | Retrograde = root of Minor tonality.

THE SOLAR SECTOR			THE COSMIC EXPANSE			MUSIC	ASTROLOGY	GEOMETRY
PLANET	DOM.	ROOT	IN SIGN	MOTION	ROOT	INTERVAL	ASPECT	SHAPE
		E			G	Min. 3rd		Square
		A			F♯ / G♭	Maj. 6th		Square
		D			B	Maj. 6th		Square
		F♯ / G♭			G	Min. 2nd		Dodecagr.
		C			A	Maj. 6th		Square
		G♯ / A♭			G	Maj. 7th		Dodecagr.
		D♯ / E♭			A	Tritone		Line
		A♯ / B♭			G♯ / A♭	Min. 7th		Hexagon
		F			F	Uni/Octa
		C♯ / D♭			D♯ / E♭	Maj. 2nd		Hexagon
		G			A	Maj. 2nd		Hexagon
		B			G	Maj. 6th		Square

For the tone frequencies of the tones listed above both methods (12-TET and Microtonal) could be used.

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MAKING YOUR OWN COMPOSITIONS

Now that the Sign and Planet relationships with the tones have been explained, you could start building your own “tone-collection” / tuning system based on your own chart / chart of your choice.

How many planets (7, 10, 12, 12+) and what system you are going to use (12-TET or Microtonal) is up to you. If you are not familiar at all with microtonal music, or if you want to write music that can be preformed with modern Western instruments, then using the 12-TET system would be the best option, specially in combination with 12 Planets. 

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OTHER RELATED BLOG ARTICLES:

THE FUNCTIONS OF THE INTERVALS

Another article I wrote for my blog named “The Functions Of The Intervals” (referred to in this article) describes might be an interesting read as well?

MUSIC & GEOMETRY

If you are interested in more information about the geometry in music then read the article “Music & Geometry“.

THE ASTRONOMICAL ZODIAC SCALE

If you like my article about the Astrological Zodiac & Tonality and you are interested in Micro-tonal music, then you might also like the article “The Astronomical Zodiac Scale (Temperament)“.

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SOURCES / REFERENCES:

• Wikipedia
• www.physicsforums.com
• www.lunarplanner.com

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This is an original concept by Roel Hollander and falls under the following copyright license:

Reading Time: 28 minutesAugust 29, 2023

ASTRO-MUSIC COMPOSITION (CHART TO MUSIC)

Part 2 of the article “Astro-Music Composition”. If you have not read the previous part, then I suggest you read Part 1 first.

THE COSMIC EXPANSE

The most ideal setup is to use the number 12 for all key aspects of this concept: 12 Tones, 12 Signs and 12 Planets.

I am aware that using 12 Planets is a less common practice among astrologers. Many astrologers do on the other hand look at charts to aspects between planets and the Lilith, lunar nodes, zenith & nadir or stars, asteroids, et cetera. Personally I like using planets and dwarf planets rotating the Sun only, with the Moon as only exception on this concept of course. You will also find info in this article about only using 7 or 10 planets.

It’s up to you how many and which “heavenly bodies” you wish to implement in your personal execution of this concept. 

METHOD 1: ZODIAC SIGN BASED – EQUAL TEMPERAMENT

The most common temperament used in western music is the 12-Tone Equal Temperament (12-TET), a division of the octave in equal sized tone spaces, similar to the Tropical Zodiac that divides the Zodiac circle in 12 equal sized sections of 30 degrees.

The number of planets used for this method does not effect the temperament and thus tone frequencies connected to the Zodiac Signs. Just the number of tones “activated” by a planet’s presence in the signs might be less. After all, 7 planets could generate 7 different tones, with 10 planets you could potentially generate 10 different tones and a 12-Planet based astrology system could potentially generate all 12 tones of the 12-Tone Equal Tempered system.

Using more then 12 planets would not per definition generate more unique tones though when 12-TET is used, that would only be the case if microtuning is used! (see Method 2 below).

The “Zodiac Sign Based” method is tone-frequency-wise not as exact as the “Planet Degree Based” method. This method though can be used with all western instruments and most common music genres and is therefor a concept that pretty much anyone with basic astrological and musical knowledge can implement.

IMPLEMENTATION: METHOD 1 – SIGN BASED

TROPICAL ZODIAC	CIRCLE OF FOURTHS
(planets displayed only)	(major tonalities displayed only)

7 CLASSIC + 3 TRADITIONAL + 2 ADDITIONAL PLANETS

PLANET

SIGN

TONE

G

F♯ G♭

Bm

G

A

G

A

G♯m A♭m

Fm

D♯m E♭m

A

G

If we create a scale with the root or “tonic” (first degree) of each represented tonality and start with the tone of the sign that contains the Sun, then we get the following “Natal Cosmic Scales“: 

7 CLASSIC PLANETS

TONICS	G		A		B		F♯/G♭		G
HZ	383.5		430.5		483.3		362.0		767
INTERVAL		½		1		1½		½

7 CLASSIC + 3 TRADITIONAL (=10) PLANETS

TON.

G

G♯/A♭

A

B

D♯/E♭

F

F♯/G♭

G

HZ

383.5

406.3

430.5

483.3

304.4

341.7

362.0

767

INT.

½

½

1

1½

1

½

½

7 CLASSIC + 3 TRADITIONAL + 2 ADDITIONAL (=12) PLANETS

TON.

G

G

G♯/A♭

A

A

B

D♯/E♭

F

F♯/G♭

G

HZ

383.5

406.3

430.5

483.3

304.4

341.7

362.0

767

INT.

½

½

1

1½

1

½

½

If the planets would have been “spread out” over more Signs then with Roel’s chart above, then the number of tones of the scale could increase. And consequently, when the planets are more clustered then as in Roel’s chart, then the number of tones of the scale will decrease.

In Roel’s case we end up with a 4-tone (7 planets) or 7-tone (10 and 12 planets) scale.

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METHOD 2: PLANET DEGREE BASED – MICROTONAL

When you are looking for a more precise “Natal Scale” (like an unique “acoustic fingerprint”), then using the exact degrees of the planets would be your method of choice. 

This means though that we are stepping outside the confined 12-TET system and are going to use micro-tuning. In this case we are going use a system where every degree becomes a tone. Instead of 12 tones per octave, we will now divide the octave into 360 pitch-classes (tones), the so called 360 EDO (Equally Divided Octave) system. EDO is an abbreviation for TET. 360 EDO/TET divides the octave into steps of 3 1/3 (3,333∞) cents. 

! IMPORTANT:

You have to use micro-tonal instruments to work with the “Planet Degree Based” concept. Many (“traditional” Western) instruments will not be able to use this musical interval system / temperament. To implement it with modern software and hardware requires a deeper understanding and experience in working with and composing for micro-tonal instruments. Read the article Instruments & Tuning for more information about the tunability of instruments.

With this method we need to temper (pitch) the 12-TET tone frequencies with the planet degrees. First we decide what Concert Pitch to use. A4=440Hz is the present musical standard, but since we’re micro-tuning and standard 440Hz 12-TET based instruments can no longer be used, we can chose any Concert Pitch we like. For this example I will use C4=256Hz, the “Scientific or Philosophycal Pitch“. The tone frequencies listed below are rounded up at one digit behind the dot for convenience.

TONE	C	C♯ D♭	D	D♯ E♭	E	F	F♯ E♭	G	G♯ A♭	A	A♯ B♭	B
HZ 12-TET	256	271.2	287.4	304.4	322.5	341.7	362.0	383.5	406.3	430.5	456.1	483.3

As mentioned above, 360 EDO divides the octave into steps of 3 1/3 (3.333∞) cents. 1 degree = + 3.333∞ cents. To round the cents off till 3 digits behind the dot is sufficient, the difference between 1 digit and 3 digits behind the dot is but approx. 0.01Hz, a difference that even the best musicians, composers and sound engineers will not notice. Calculation example: The Sun is in Taurus at 19°, Taurus represents G=383.5Hz, thus:

19 x 3.333 = 63.327 cents.
383.5Hz + 63.3 cents = 397.78160939995274Hz

IMPLEMENTATION: METHOD 2 – DEGREE BASED (MICROTONAL)

TROPICAL ZODIAC	CIRCLE OF FOURTHS
(planets displayed only)	(major tonalities displayed only)

7 CLASSIC + 3 TRADITIONAL + 2 ADDITIONAL PLANETS

PLANET
SIGN
DEG.	19°	3°	3°	10°	26°	10°	27°	4°	13°	20°	0°	1°
TONIC	G	F♯ G♭	B	G	A	G	A	G♯ A♭	F	D♯ E♭	A	G
12-TET	383.5	362.0	483.3	383.5	430.5	383.5	430.5	406.3	341.7	304.4	430.5	383.5
+CENT	63.3	9.9	9.9	33.3	86.7	33.3	89.9	13.3	43.3	66.6	0	3.3
NEW HZ	397.8	364.1	486.1	390.9	452.6	390.9	453.4	409.4	350.4	316.3	430.5	384.2

The following microtonal “Cosmic Scales” are formed:

7 CLASSIC PLANETS

TONE	G	G	A	A	B	F♯ G♭
HZ	390.9	397.8	452.6	453.4	486.1	724

You might have noticed that the scale above only contains 6 Tones. This is because 2 planets (Venus and Jupiter) were in the same sign at the same degree, thus generate the same tone. In musical scales it is though not logical to display the exact same tone twice, thus 6 tones instead of 7. Many listeners might not even hear the difference of 0.8Hz between A=452.6Hz and A=453.4Hz unless played simultaneously and even then some people might not be able to differentiate between those two tones. So, in this case we might even end up using a 5-tone scale, using only one of the A’s.

7 CLASSIC + 3 TRADITIONAL PLANETS

TONE	G	G♯ A♭	A	A	B	D♯ E♭	F	F♯ G♭	G	G
HZ	397.8	409.4	452.6	453.4	486.1	632.6	700.8	724	781.8	795.6

Many listeners might not even hear the difference of 0.8Hz between A=452.6Hz and A=453.4Hz unless played simultaneously and even then some people might not be able to differentiate between those two tones. Another thing you might have seen is that the frequencies for D♯/E♭, F and F♯/G♭ have are doubled in frequency. This was done to make sure all tones fall in between the tonic of this scale G=397.8Hz and it’s octave G=795.6.4Hz.

7 CLASSIC + 3 TRADITIONAL + 2 ADDITIONAL (=12) PLANETS

TONE	G	G♯ A♭	A	A	A	B	D♯ E♭	F	F♯ G♭	G	G	G
HZ	397.8	409.4	430.5	452.6	453.4	486.1	632.6	700.8	724	768.4	781.8	795.6

You might have noticed that the scale above only contains 11 Tones. This is because 2 planets (Venus and Jupiter) were in the same sign at the same degree, thus generate the same tone. In musical scales it is though not logical to display the exact same tone twice, thus 11 tones instead of 12. Many listeners might not even hear the difference of 0.8Hz between A=452.6Hz and A=453.4Hz unless played simultaneously and even then some people might not be able to differentiate between those two tones. Another thing you might have seen is that the frequencies for D♯/E♭, F and F♯/G♭ have are doubled in frequency. This was done to make sure all tones fall in between the tonic of this scale G=397.8Hz and it’s octave G=795.6Hz.

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CHORDS (12-TET & MICROTONAL)

Every planetary position represents a tone as well as a chord. As mentioned earlier in this article the prograde (direct) planets represent Major tonalities and chords, the retrograde planets represent minor tonalities and chords. Below an example based on Roel’s Chart:

PLANET
SIGN
ROOT	397.8	364.1	486.1	390.9	452.6	390.9	453.4	409.4	350.4	316.3	430.5	384.2
KEY	G	F♯ G♭	Bm	G	A	G	A	G♯m A♭m	Fm	D♯m E♭m	A	G

The chords as listed above do contain tones though that do not “belong” to Roel’s “Natal Cosmic Scale” that were made through the interpretation of the natal chart.

Take for example the chord of G Major that belongs to Taurus, it contains the following tones: G – B – D. The tones G and B are both “native” to Roel’s “Natal Cosmic Scale” but the tone D is not.

“NATIVE” TONES

If you wish to “build” chords strictly from “native” tones of Roel’s “Natal Cosmic Scale“, then you could combine the root (“tonic”) tones used in the 12-TET or Microtonal “Natal Cosmic Scale”, as found through the position of the planets in the Zodiac sign sections.

EXAMPLE CHORDS “BUILD” WITH “NATIVE” TONES ONLY:

The root tones of the sign section can be 12-TET or micro-tonal, depending on the method you work with. 

CHORD	ROOT TONES OF	SIGN SECTIONS	“ACTIVATED” BY PLANETS
GAug	G+B+E♭	+  +
G7♯5	G+B+D♯ + F	+  +  +
G9♯5	G+B+D♯ + F+A	+  +  +  +
G♯m	G♯ + B + D♯	+  +
G♯m6	G♯ + B + D♯+F	+  +  +
G♯m(M7)	G♯ + B + D♯+G	+  +  +
G♯m13	G♯ + B + D♯ + G♭ + F	+  +  +  +
A♭m	A♭+B +  E♭	+  +
A♭m6	A♭ + B +  E♭ + F	+  +  +
A♭m7	A♭ + B +  E♭ + G♭	+  +  +
A♭m(M7)	A♭ + B + E♭ + G	+  +  +
A♭m13	A♭ + B +  E♭ + G♭+F	+  +  +  +
BAug	B+E♭ + G	+  +
B	B + D♯ + F♯	+  +
B6	B + D♯ + G♭ + A♭	+  +  +
B7♭5	B + D♯ + F + A	+  +  +
B7	B + D♯ + G♭ + A	+  +  +
B7♯5	B + D♯ + G + A	+  +  +
B7/13	B+E♭ + G♭ + A+A♭	+  +  +  +
E♭Aug	E♭+G+B	+  +
F7♭5	F+A+B+E♭	+  +  +
F9♭5	F+A+B+E♭ + G	+  +  +  +

Explanation of the chord names (for the non-musicians/composer among the readers).

When looking at the table above, you might have noticed that all formed chords contain one or more tones related to planet positions in Gemini and Libra.

• F♯ / G♭ – tone of Libra – presented by a (prograde) Moon.
• D♯m / E♭m – (parallel minor) tone of Libra – presented by a (retrograde) Pluto.
• Bm – (parallel minor) tone of Gemini – presented by a (retrograde) Mercury.

I looks like the “vibratory nature” of these tones play a major role in the audible “fingerprint” of this natal horoscope.

NATAL CHORD

When you sound these tones B – D♯ – F♯ together you hear the B Major chord. B Major is the Major tonality of Virgo, that “happens to be” the ascendant sign in Roel’s birth chart.

NATAL TONE(S)

In this natal chart 2 tones are equally often present in the chords: the tones B and D♯ (E♭). They are present in all 22 chords that can be created with Roel’s “Natal Solar Scale”. 

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This is an original concept by Roel Hollander and falls under the following license:

Reading Time: 10 minutesOctober 1, 2016

ASTRO-MUSIC COMPOSITION (CHART TO MUSIC)

FOREWORD

In response to many questions I received via e-mail and Facebook about my article “The Astrological Zodiac & Music Tonality – Tone Zodiac” about the implementation of the Tone-Zodiac I have decided to write this article to present several ideas on this subject. 

I am not an astrologer or astronomer (I am but a musician-composer and sound engineer with a keen interest in this subject). This article is in the first place written for musicians that – like myself – are intriqued by this topic and perhaps for some astrologers it might turn out to be an interesting read as well. 

I do welcome additional info, suggestions and corrections (in case of mistakes made in this article). Thank you! 

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INTRODUCTION (BACKGROUND INFORMATION)

ASTROLOGICAL SYSTEMS AND THE NUMBER OF PLANETS

The planets of our Solar system are key to most astrological systems, but the number of planets “used” differs between Astrological systems.

In “modern” western astrology 10 or more planets are used: the 7 “classic planets” + Uranus, Neptune, Pluto and by some astrologers Ceres, Chiron, Eris, Haumea, and/or Makemake.

In “classic” western astrology 7 “classic planets” (or “Ptolemaic planets”) are used: Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. These planets also represent the 7 days of the week.

Some other astrological systems use different number of planets (in this article we will not go deeper into those systems though):

Chinese astrology works with 5 planets representing the elements: Mercury (water), Venus (metal), Mars (fire), Jupiter (wood) and Saturn (earth).

Hindu astrology works with the 7 “classic planets”: Sun (Surya), Moon (Soma), Mars (Mangala), Mercury (Budha), Jupiter (Brihaspati), Venus (Shukra) and Saturn (Shani) + Rahu and Ketu, a total of 9 planets.  

PLANETS AND MUSICAL INTERVAL SYSTEMS

In modern western music a Musical Interval Systems that contains 12 tones is used, the 12-Tone Equal Temperament. For the explanation of this concept I will use 12 signs, 12 planets and 12 tones, but will provide more information for those who want to use less planets (5, 7, 9).

Below a small list with the number of planets, geometric shapes (polygon and polygram), temperament and scale related / used for the astrological systems referred to in this article:

*These scales with 5, 7 or 9 tones per octave could either use tones from the 12-tone Equal Temperament or be used as a microtonal tuning system.

**The Melodic Minor has when ascending raised 6th and 7th tones but descending these tones are no longer raised. You could say that the scale contains two 6ths and 7ths, raising the total from 7 to 9 different tones.

***Scriabin created two 9-tone scales for his composition Opus-67 (semitone steps: 121211112 and 121121121).

DOCECA (12)	HEPTA (7)	PENTA (5)	NONA / ENNEA (9)

If you like to know more about the relationship between music and geometric shapes, then read the article “Music & Geometry“.

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SYMBOLS

Not all visitors of this blog have experience with astrology, therefore, here first the symbols of the Zodiac signs used in this article:

Aries	Taurus	Gemini	Cancer	Leo	Virgo	Libra	Scorpio	Sagittarius	Capricorn	Aquarius	Pisces

… as well as all the planets used in this article:

Sun	Moon	Mercury	Venus	Mars	Jupiter	Saturn	Uranus	Neptune	Pluto	Ceres	Chiron

If you’re not an astrologer or astronomer and not very familiar with astrology might not recorgnize “Ceres” and “Chiron”. Ceres is a “dwarf-planet” within in the asteroid belt that lies between the orbits of Mars and Jupiter. Chiron (not to be mistaken for Pluto’s moon Charon) is orbiting the Sun between Saturn and Uranus.

For the 12-Tone scale example in this article I chose to use Ceres and Chiron, but feel free to select: Eris, Haumea, and/or Makemake instead for your personal musical scale. 

If you are “in to” microtonal music and do not intend to perform your composition with traditional 12-Tone instruments, you could for example also include Eris, Haumea, and Makemake and create a 15-tone instead of a 12-tone scale and temperament.

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ASTROLOGICAL ASPECTS, SIGN-GROUPS, AND MODES

Astrological aspects do not represent the tones themselves, but the “distances” between tones, in music we use the term intervals for that. Intervals in music have a function and a meaning, (kind of) like aspects have with Astrology. The meaning of the aspects and those of the musical intervals are not all “one-on-one” interchangeable, but could add an extra “layer” to their interpretation. 

Read Roel’s World article “The Function Of The Intervals” to get a broader understanding about the function and meaning of the intervals.

“Opposition“, “Trine” and “Square” are commonly used terms by astrologers to define important relative positions of planets. Every aspect relates to a particular number of degrees. Opposition = 180°, the Trine = 120° and the Square = 90°. 

Kepler is said to have been impressed – as Ptolemy before him – by the fact that these three most powerful aspects are expressed by the same ratios as the three perfect consonances in music. 

ASPECT	DEGREES	RATIO CIRCLE	RATIO INTERVAL
Opposition	180°	360:180 = whole circle to half	2:1 = Octave
Trine	120°	360:240 = whole to greater part	3:2 = Perfect Fifth
Square	90°	360:270 = whole to greater part	4:3 = Perfect Fourth

You can read more about Ptolemy, Kepler and others and their view on the tone-zodiac relationship in the article “The Astrological Zodiac & Musical Tonality“.

POLARITIES	TRIPLICITIES	QUADRUPLICITIES
LINE	TRIGON	QUADRAGON	HEXAGON	DODECAGON	DODECAGRAM	SUPERIMPOSED
Opposition	Trine	Square	Sextile	Semi-Sextile	Quincunx
180°  6{2}	120°  4{3}	90°  3{4}	60°  2{6}	30°  t{6}	150°  t{6/5}={12/5}
TRITONES	MAJOR THIRDS & MINOR SIXTHS	MINOR THIRDS & MAJOR  SIXTHS	MAJOR SECOND & MINOR SEVENTH	PERFECT FIFTHS & PERFECT FOURTHS	MINOR SECOND & MAJOR SEVENTH	ALL ELEVEN INTERVALS IN GEOMETRIC SHAPES TOGETHER.

OTHER ASPECTS

The “Decile” (36°), “Semisquare” (45°), “Quintile” (72°), “Tridecile” (108°), “Sesquiquartile” (135°) and Biquintile (144°) are aspects that can not be used in the “Zodiac Sign Based” concept (due to the 12-Tone Equal Temperamental restrictions), but are possible intervals to be used in the “Planet Degree Based” (microtonal) concept.

MOTION OF PLANETS: PROGRADE (DIRECT) & RETROGRADE

When a planet is retrograde, its energies are turned inward and becomes more subjective.
In music Major tonalities are considered more “extrovert” while minor tonalities are considered more “introvert“.

It seems logical that the apparent retrograde motion of a planet is represented by the minor relative tonality of the Major tonality that represent it’s prograde (direct) motion. 
By Example: Aries is represented by C Major = Prograde (direct) & A minor = Retrograde. 

THE CIRCLE OF FIFTHS

The tone + zodiac-sign relationship as a result of layering the Zodiac circle and the Circle of Fifths is (in my opinion) the perfect combination. 

The Tone / Tonality and Sign combination I use is as follows (Steiner, Von Gleich Tone Zodiac):

RUDOLF STEINER	SIGISMUND VON GLEICH

SIGNS

MAJOR

C

G

D

A

E

B

F♯ G♭

C♯ D♭

G♯ A♭

D♯ E♭

A♯ B♭

F

MINOR

Am

Em

Bm

F♯m G♭m

C♯m D♭m

G♯m A♭m

D♯m E♭m

A♯m B♭m

Fm

Cm

Gm

Dm

Above the Major and minor tonalities that “belong” to each Zodiac sign have been listed. Of every chord the root or “tonic” (first degree) is the most important. 

By example: Taurus represents the tone of G (tonic) and tonalities of G Major and E minor.

! NOTE: Musicians are used to reading the Circle of Fifths clockwise, but because astrological charts are read counterclockwise, I have turned the direction of the tone-circle (next to the birth charts) around for this article. The Circle of Fifths is there for counterclockwise, thus clockwise the Circle of Fourths (the inverse interval of the Fifth).

If you like to use the Chromatic Circle instead, then keep in mind that several of the tone-sign combinations will be different, they swap places. The implementation as described in this article for music composition will still be the same but the data as provided in this article will not match. 

For more information about the history of Tone-Zodiacs and additional information read the article “The Astrological Zodiac & Musical Tonality – Tone Zodiac“

ABOUT THE CHARTS USED IN THIS ARTICLE:

The Zodiac charts used as examples for this article are the charts of myself (Roel). The tones, scales, chords, et cetera you see in this article only apply for my Natal Chart and – unless you were “born under the same stars” – are not “useful” to you musically, except to explain my concept with.

To keep the picture “clean” the Zodiac circles will only display the symbols and degrees of the planets (no nodes, Lilith, et cetera). 

The concept will nonetheless work for you too, you just have to do “the math” yourself, on your own chart. 

The original chart images were created with the free online service 3horoscopes.com (their ‘design’ is a reasonable match with the design of this blog). That site does not have the option to add additional objects to the horoscope (such as Celes and Chiron), if you like to have their positions calculated then visit astro.com and select Celes and Chiron (or any other “object” under “Additional Objects” when you calculate the free chart. 

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THE CONCEPT (ASTRO-MUSIC COMPOSITION)

The idea behind the (musical philosophical) concept explained in this article is to create an “audible fingerprint” based on a horoscope chart. This “fingerprint” can then be used for music composition and production. The chart could be a natal chart, or perhaps if you like to write a special composition for a particular date (like a wedding ceremony).

Key “components” for this concept are: the Zodiac signs, the planets of our Solar system and a musical interval system (+Temperament).

CREATING YOUR OWN TEMPERAMENT

To create your scale / temperament you need to look at the position of the planets. In what Zodiac sign section of the chart we find them? And how do you ‘convert’ position to tone frequency?

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This is an original concept by Roel Hollander and falls under the following copyright license:

Reading Time: 8 minutesJuly 1, 2016

MUSIC COMPOSITION & MATH (NUMBERS/SEQUENCES)

“May not music be described as the mathematics of the sense, mathematics as music of the reason?
The musician feels mathematics, the mathematician thinks music:
music the dream, mathematics the working life.“

~ James Joseph Sylvester

Most people that have visited this blog before have come across various music and math related stuff already, like for example Music & Geometry. In this article I will share some interesting and fun-stuff about music composition and math. Let me start in this article with something I wrote in another article:

MUSIC = MATH 
Music can be explained with math formulas. 

How? 

1. We use ratios – for example 2:1 (Octave) and 3:2 (Perfect 5th) – to “size-up” the intervals between 2 tones (more about that in the article “Music & Geometry” at Roel’s World).
2. A system of combined interval ratios generates a musical Temperament (Roel’s World).
3. With 3 or more tones a geometric relationship can be formed (Roel’s World article: “Music & Geometry“).
4. By using number sequences (consecutive intervals and/or patterns/cycles).

Temperaments and Tuning Systems, Geometry … all cool and so. But what about composing music with Mathematical sequences and patterns?

NUMBER SEQUENCES

Numbers and number sequences can be used in creative manners to compose music:
PI | PHI | FIBONACCI | NUMBER SEQUENCES & PROGRESSIONS | DODECAPHONY | NUMEROLOGY

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PI (π)

The number π (Pi) is a mathematical constant, the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159… Being an irrational number, π cannot be expressed exactly as a fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern). Here you can find the first one million digits. 

There are various musicians and composers that have experimented with using the digits of Pi as melody for their composition. Here’s one of the examples, a implementation by David Macdonald:

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PHI (φ)

Next up is Phi (φ) = 1.61803398874989484820458683436563811772­… Phi is used as a symbol for the golden ratio and on other occasions in math and science.

Phi has been a source of inspiration for some musicians and composers. Here is an example by Michael Blake:

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FIBONACCI SEQUENCE

The Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …) is named after Italian mathematician Leonardo of Pisa, known as Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier as Virahanka numbers in Indian mathematics. Here you can find the first 1000 digits. 

In the example below Radomir Nowotarski has “related” the Fibonacci Sequence to the Lydian Mode (scale) and made the following assignment:

1=C, 2=D, 3=E, 4=F#, 5=G, 6=A, 7=B, 8=C, 9=D, 10=E, 11=F#, 12=G, 13=A et cetera. (see video).

1-8 are the intervals of the Scale (tonic-octave). The following numbers 9, 10, 11 (et cetera) represent intervals greater then the octave and have been added to the table to complete it with all possible intervals related to the scale used. Numbers like 4, 6, 7, 9, 10, 11, 12 (et cetera) are not part of the Fibonacci frequencies and haven’t been used for constructing the melody. This does not mean the tones related to those intervals are not used. “6=A” (not used) as well as “13=A“, as well as for example 34=A, 55=A, while 89=G (et cetera, see video).

This assignment can be applied with any other 7-tone scale (by replacing the 7 tones listed in the first column) or you could use the concept to build a table for a scale with a different number of tones.

At Roels World you can find two more articles about Fibonacci: Fibonacci Temperament and Fibonacci Tones.

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NUMBER SEQUENCES & PROGRESSIONS

There are many more sequences you could use. For example:

Arithmetic progression (a sequence of numbers such that the difference between the consecutive terms is constant, in this example the difference is “+3“: 1, 4, 7, 10, 13, 16, 19, 22, 25, …) 

Geometric progression (a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio, in this example “x3“: 1, 3, 9, 27, 81, 243, …).

Triangular number sequence (counts the objects that can form an equilateral triangle): 
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, …

Square number sequence (the product of some integer with itself. 9 is a square number, since it can be written as “3×3“. – Sequence example: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, …)

Cube number sequence (the cube of a number is its third power: 1³=1, 2³=8, 3³=27, et cetera – the result of the number multiplied by itself twice. It is also the number multiplied by its square. – Sequence example: 1, 8, 27, 64, 125, 216, 343, 512, 729, …)

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There are many more sequences, a complete list of sequences can be found at the “On-Line Encyclopedia of Integer Sequences® (OEIS®)“. This sequence database was begun by Neil J. A. Sloane (henceforth, “NJAS”) in early 1964 when he was a graduate student at Cornell University in Ithaca, NY. He noticed that although several books in the Cornell library contained sequences. In order to keep track of the sequences in these books, NJAS started recording them on file cards.

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Of course instead of using an existing irrational number or known sequence you could also use a “personal” number, like your telephone number or your social security number or the grades on your diploma (or what ever inspires you) to compose a piece of music. 😉

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DODECAPHONY (“Twelve-tone technique” or “twelve-note composition”)

Dodecaphony is a method of musical composition devised by Austrian composer Arnold Schoenberg (1874–1951). The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key.

Now, I could continue writing about it, but instead I’ll post a lovely video about it by Vi Hart. This lovely girl has made many cool and funny math-related videos in a truly original manner (something I highly appreciate and admire in people). She does talk a lot and up-tempo in her videos though, brace yourself! 😉 Hihihi

If you liked what you saw and heard, then you might enjoy many of her other videos as well …

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RETROGRADE, INVERSION AND RETROGRADE-INVERSION

You can allow yourself also some creative liberties and use the sequences also reversed or “retrograde”  [ R ](backward), inversion [ I ] (vertically mirrored) and retrograde-inversion [ IR ] (a combination of both).

Here an examples with a Requiem Canticles by Igor Stravinsky:

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INTERESTING VIDEO ABOUT MUSIC & MATH (SYMMETRY): 

“From Pythagoras’ observations of the fundamental mathematical relationship between vibrating strings and harmony to the digitized musical world we enjoy today, The Majesty of Music and Mathematics with the Santa Fe Symphony and the Santa Fe Institute will explore the remarkable interweaving of the languages of music and mathematics.”

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USING THE NUMEROLOGIC VALUE OF LETTERS TO CREATE A TONE-SEQUENCE

NOTE: Not everyone is equally “interested” in this topic, so I have left it for the end of the article. If this is not “your thing”, then feel free to return to the top (menu) of Roel’s World.

Numerology is any belief in the divine, mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value of the letters in words, names and ideas.

There are various numerology systems which assign numerical value to the letters of an alphabet, including the Abjad numerals in Arabic, the Hebrew numerals, Armenian numerals, Cyrillic numerals, and Greek numerals.

There are also non-alphabetical systems, such as Chinese Numerology where numbers are associated with particular connotations (based on its sound).

Different methods of calculation exist, including Chaldean, Pythagorean, Hebraic, Helyn Hitchcock‘s method, Phonetic, Japanese, Arabic and Indian.

One of the more common assignments is the Pythagorean Method (1-9):

1	2	3	4	5	6	7	8	9
☉	☽	♃		☿	♀		♄	♂
A	B	C	D	E	F	G	H	I
J	K	L	M	N	O	P	Q	R
S	T	U	V	W	X	Y	Z

Another polular assignments is the Chaldean (Indian) Method (1-8):

1	2	3	4	5	6	7	8
☉	☽	♃		☿	♀		♄
A	B	C	D	E	U	O	F
I	K	G	M	H	V	Z	P
J	R	L	T	N	W
Q		S		X
Y

And for the Bulgarian visitors of my blog also the Bulgarian Cyrillic versio:

1	2	3	4	5	6	7	8	9
А	Б	В	Г	Д	Е	Ж	З	И
Й	К	Л	М	Н	О	П	Р	С
Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ
Ь	Ю	Я

Some Numerologers (like Kathleen Roquemore) also add “Master Numbers” to the table:

1	2	3	4	5	6	7	8	9	11	22
A	B	C	D	E	F	G	H	I
J		L	M	N	O	P	Q	R	K
S	T	U		W	X	Y	Z			V

 

THE IMPLEMENTATION

This is an original concept and has not been used/implemented as far as I know. If you can show me a composition made with this concept predating June 1 2016, then I will provide the credits.

As example I will use the name of this blog: Roel’s World for the calculations. For the first row I have used the Pythagorean method, for the second row the Chaldean method.

R	O	E	L	S	(SUM)	W	O	R	L	D	(SUM)
9	6	5	3	1	9+6+5+3+1=24    2+4=6	5	6	9	3	4	5+6+9+3+4=27    2+7=9
2	7	5	3	3	2+7+5+3+3=20    2+0=2	6	7	2	3	4	6+7+2+3+4=22    2+2=4

I will not write about the Numerological interpretation (meaning of the sum), there are enough websites and blogs about that. 

How to relate the tones to numbers related to the numbers they belong with? For this example I will use the scale of C Major, but you could use any scale you with. Let’s “map” the scale.

1	2	3	4	5	6	7	8	9
C	D	E	F	G	A	B	C	D

When using the Pythagorean method the melody would progress as follows:

D – A – G – E – C     G – A – D – E – F

When using the Chaldean method the melody would progress as follows:

D – B – G – E – E     A – B – D – E – F

You could turn these tones also into a chord progression if you like, in the case of the Pythagorean Method the chord progression could be something like:

Dm – Am – G(7) – Em – C     G(7) – Am – Bdim – Dm – Em – F

Another option is to give every word of a lyrics it’s own chord, based on the tones related to the letters of the words. This way you can create a word-compatible chord progression. With words longer then 5 or 6 letters one could devide the tones into two progressive chords or use the additional tones for creating a bass-line and or melody.

ROELS: C Major 6,9 (C-E-G-A-D)     WORLD: D minor 9,11 (D-F-A-E-G)

These are just a few different ideas for implementing this concept. A combination of these concepts might also be an option and perhaps you come up with yet another way to implement it.

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You like to read something about music and Geometry? Then check the article “Music & Geometry“.

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Reading Time: 2 minutesJuly 1, 2016

MUSIC & GEOMETRY (The Sacred Geometry Of Music)

“Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them.”
– Rudolf Steiner

A note to start this article with:

Perfect geometric shapes only occur when using Equal Temperament. Sonically though the intervals of Equal Tempered instruments/music aren’t perfect (accept for the Octave). They are always a bit sharp or flat in comparison with the Harmonic Series (how sound occurs in nature) and Just Intonation.

The most harmonious sounding (Just) intervals (the octave excluded) do NOT create perfect symmetrical geometric shapes!
If you “stack” one or more “type” of Just Intervals you will always end up with a spiral!

In this article all geometrically perfect shapes (trigone, square, pentagon, et cetera) thus relate to 12-Tone Equal Temperament as do any and all perfect geometrical shapes used on this blog as well as on any other blog, website and book available.  

“Music theory has no self-evident foundation in modern mathematics yet the basis of musical sound can be described mathematically (in acoustics) and exhibits “a remarkable array of number properties”. 
In its form, rhythm and metre, the pitches of its notes (intervals) and the tempo of its pulse music can be related to the mathematical measurement of time and frequency, offering ready analogies in geometry.”

Now, of course tones and chords are not the same “things” as for example polygons and polygrams. Units like Hertz and Degrees are not the same, they have their own function and use. But in the math behind many “things” there are formulas and ratios (relationships) that are very similar, if not identical. Would it thus be too ‘far-fetched’ to say that the same “rules” apply for many – if not all – things in the universe?

This article will “zoom-in” into geometry in particular.

Over time this article grew so big that the time it took to load started to have a negative effect SEO-wise. I thus decided to split it up in 4 smaller articles: Intervals & Scales, Harmony, Rhythm and Various.

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