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THE ASTRONOMICAL (CONSTELLATIONAL) ZODIAC SCALE

The “Astronomical Zodiac Scale” (musical temperament) is a creation by Roel Hollander.

Feel free to use it for your musical compositions or quote from it for own work, but please, do place a reference to this article when you do (see licence at the bottom of this page).


13

The Zodiac represents the constellations that the Sun passes through in its apparent path across Earth’s sky. Because the Sun (and the planets) are all on about the same plane in the Solar System, they pass through the same constellations. While traditionally the zodiac is considered to have 12 constellations, technically the Sun passes through 13 at present time. 

The reason that there are now 13 constellations the Sun passes through according to various sources is that the axis of the Earth has changed over the millennia. What is important to understand, is that the The zodiac is a belt of space which extends either side of the ecliptic. All the observable planetary activity in our solar system takes place within this narrow celestial belt. Due to a “wobble” of the Earth (one full turn with the “Great Year“) Ophiuchus isn’t always in between Earth and the Sun. As a result of this “wobble” the direction of north has changed with respect to the sky. Vega was the North Star (Pole Star) several thousand years ago, and will become it again in about 13,000 years, according to NASA. Today, the North Star is Polaris.

IMPORTANT: The tropical and sidereal zodiac (and the division of the ecliptic into a number of “signs” named after constellations) is based on the path of the Sun when it’s in between Earth and the Zodiac Constellations, as well as in the case of Tropical Astrology the 4 seasons on Earth (with the Equinoxes and the line of the Solstices forming a cross) while the sidereal system defines the signs based on the fixed stars. The 12 signs used in tropical and sidereal astrology are the so called “Sun signs”, Ophiuchus (the 13th) is not.

13 CONSTELLATIONAL vs 12 ASTROLOGICAL (TROPIC/SIDEREAL) ZODIAC SIGNS
Sky-Map-Zones

The Astrological or Tropical (aligns with the equinoxes and the solstices) / Sidereal (alignes with the constellations) Zodiac divides the year into 12 Equal periods (this correlates with the 12-Tone Equal Temperament).

The Astronomical or Constellational Zodiac depicts the number of days of the Earth’s orbit when the Sun is between Earth and any one of the zodiacal constellations. The Astronomical Zodiac counts 13 constellations, the 13th is named “Ophiuchus

Since each constellation is of different size, and because the ecliptic (the sun’s path) passes through larger or smaller portions of each constellation and the speed of the Earth around the Sun varies along its orbit, the Sun is between the Earth and each zodiacal constellation for varying periods.

Varying (unequal) periods = unequal sectors = unequal interval size!

Another example of the difference between the mapping of the Tropical Zodiac and the actual time that the Sun travels through the Constellations can be seen on the image on the right I found on the internet.

astrological-astronomical-m

The red dashed line shows the path of the Sun (the Ecliptic) crossing the Constellations.

NOTE: In the image on the right the Sun moves from right to left! The “time-line” in this image starts at the Spring Equinox with Aries (Astrology) and Pisces (Astronomically) and ends after the Winter with Pisces (Astrology) and Aquarius (Astronomy).


ROEL’S WORLD IMPLEMENTATION:

For the length of the days per sign I have used calculations made by Juan Anthony Revilla with data from an article by Pierre Bacchus in “L’Astronomie” June 1979, pp.297-99. 

The exact number of days per Zodiac sign could differ a bit (that depends on the source used and the “type” of year you use for your calculations). A 24-hour difference will effect the exact outcome, but I estimate those differences to be up to approx. 1 day per sign. The frequencies thus mentioned in this article are therefor an approximation of the tone frequencies and might differ up to 1Hz. 

To calculate tone-span in cents per Zodiac signs, you have to divide 1200 cents (the distance between a Tonic and the Octave) by the number of days per year and multiply that with the number of days as was calculated. Now, I could use the round number of 365 days for it, but I have decided to use the Anomalistic Year for my calculations.

The Anomalistic year is the time taken for the Earth to complete one revolution with respect to its Apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the Perihelion, where the Earth is closest to the Sun (January 3 in 2011), and the Aphelion, where the Earth is farthest from the Sun (July 4 in 2011). The Anomalistic year is usually defined as the time between Perihelion passages. Its average duration is 365.259636 days (365 d 6 h 13 min 52.6 s) at the epoch J2011.0).

1200 (cents) : 365.259636 (days of the Anomalistic year) = 3.285334271 cents per day (24 hours).

You could also use the Sidereal or Tropical years. In comparison:

  • 1200 (cents) : 365.25636 (days of the Sidereal year) = 3.285363737 cents per day (24 hours).
  • 1200 (cents) : 365.24219 (days of the Tropical year) = 3.285491197 cents per day (24 hours).

Sign

Constellation

Date Span

Days

Tone-span (cents)

 

Aries

Aries

19 Apr – 13 May25.4883.710317225 

Taurus

Taurus

14 May – 20 Jun38.31125.861155922 

Gemini

Gemini

21 Jun – 20 Jul29.2095.931760713 

Cancer

Cancer

21 Jul – 10 Aug20.9668.86060632 

Leo

Leo

11 Aug – 15 Sep37.05121.721634741 

Virgo

Virgo

17 Sep – 30 Oct44.51146.230228402 

Libra

Libra

31 Oct – 22 Nov23.1075.89122166 

Scorpio

Scorpio

23 Nov – 29 Nov6.5221.420379447 = 81.574849949

Ophiuchus

Ophiuchus

30 Nov – 17 Dec18.3160.154470502

Sagittarius

Sagittarius

18 Dec – 19 Jan32.55106.937630521 

Capricornus

Capricorn

20 Jan – 15 Feb27.4490.149572396 

Aquarius

Aquarius

16 Feb – 11 Mar24.0679.04514256 

Pisces

Pisces

12 Mar – 18 Apr37.51123.232888505  

This is how the division of the circles look like with 13 & 12 signs::

⇣ 13 SIGNS                   THE ASTRONOMICAL TONE ZODIAC                    12 SIGNS ⇣


Because we use a 12-tone scale in Western music, the 13th sign (Ophiuchus) and Scorpio (who in the Astronomical Zodiac only has span of 7 days) will be “merged“.

The interval created by just Scorpio alone would be too small (approximately 23 cents) to be of use anyway, while combined with Ophiuchus we end up with a interval of approximately 82 cents, in between a “Hard Semitone” and a “Septimal chromatic semitone“.

I have chosen to start with C4=256Hz (the “Scientific Pitch“) for this temperament, but you are naturally free to use another pitch for C4 to start with. When you add the results from the tables above (combined with the Circle Of Fifth based Tone Zodiac”) to the chromatic scale, we get the following result:

SignConstellationToneCents To Next ToneFrequency (Hz)
Aries AriesC 256256
    83.710317225  
 Scorpio Ophiuchus Scorpio & OphiuchusC/D 268.6825093184329269
    81.574849949  
Gemini GeminiD 281.6457007820792282
    95.931760713  
Capricornus CapricornD♯/E♭ 297.69285251441477298
    90.149572396  
Leo LeoE 313.60514470726037314
    121.721634741  
Pisces PiscesF 336.44808806172546336
    123.232888505  
Libra LibraF♯/G♭ 361.2701348994703361
    75.89122166  
Taurus TaurusG 377.45919239188333377
    125.861155922  
Sagittarius SagittariusG♯/A♭ 405.92268794831494406
    106.937630521  
Cancer CancerA 431.7869586242998432
    68.86060632  
Aquarius AquariusA♯/B♭ 449.30761351210754449
    79.04514256  
Virgo VirgoB 470.29775997051314470
   146.230228402  

THE ASTRONOMICAL (SIDEREAL) ZODIAC SCALE:
SIGN Aries ScorpioGeminiCapricornusLeo PiscesLibraTaurusSagittariusCancerAquariusVirgoAries
TONECD♭DE♭EFF♯/G♭GA♭AB♭BC
HZ256269282298314336361377406432449470 512

IMPORTANT NOTE: Now, it seems fair to warn those who have no “experience” with micro-tonal music that the temperament created with this concept might sound “strange” to your ears! 

This temperament might not work well in all tonalities or for music with complex harmonic structures. The implementation of this temperament works best for Ambient music and for music with “meditative” purposes. 

In case you are fairly new to musical tuning systems and temperaments, perhaps you should read this short explanation first.

WHAT DOES THE ASTRONOMICAL ZODIAC SCALE SOUND LIKE?

Image used for the article banner and Soundcloud player by: whybecausescience.com

Implementation (with Scala) and music by Derrick Scott van Heerden.

Tuning files (256/432Hz): .scl file (Scala) | .tun file
Tuning files (440Hz): .scl file (Scala) | .tun file


THIS TEMPERAMENT & 432HZ

Those of you who are interested in 432-Tuning might have already noticed that we find A4 rounded-up at 432Hz (431.7869586242998Hz). Just to place this number in perspective:

24 hours = 3.285334271 cents, 1 hour = 0,136888928 cents, one minute = 0,002281482 cents. 432Hz – 431.7869586242998Hz = 0,213041376 cents. 

This means we speak about a difference of:

1 hour and 33,3 minutes (0.02%) between 431.786… and 432Hz.

A4=432Hz and C4=256Hz are though the only two tone-frequencies that the Astronomical Zodiac Scale has in common with the standard 432-Tuning (Pythagorean Temperament). With [email protected] there are two other tones that are not too far off F♯/G♭ (363.3Hz) and G♯/A♭ (407.7Hz). 

In other words, this is a unique temperament, an other “cosmic connection” to 432Hz then what you have seen and heard so far.


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

Creative Commons License