Neat idea -- what inspired the use of tetrahedral numbers? How do you perform the truncation? Do you use c_n = T_n / 2400, or another method?

dan stearns - drums, 20-tone equal temperament electric guitar

Stearns - 20etexample2

A multicultural journey through the traditional 28 Lunar Mansions.

Systems used are the Chinese (28 Lunar Mansions), the Arabic (28 Manzil), and the Indian (28 Nakshatra). For the video, the cycle of the moon mansions were aligned to begin with Aries (Sidereal).

The 28 Mansions are split into 4 sections (Quadrants) of 7 unique notes. The 7 notes used for each quadrant were derived from a single 28-TET octave arranged into a custom “Cycle of 5ths” (which is actually a “Cycle of 18/29”).

The names for each of the individual mansions can be seen on screen and sourced from:
Chinese: https://en.wikipedia.org/wiki/Twenty-...
Arabic: https://en.wikipedia.org/wiki/Lunar_s...
Indian: https://en.wikipedia.org/wiki/Nakshatra

Composed and Produced by Shawn Michael
© 2022 Ambient Esoterica

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28 Mansions of the Moon

28 Mansions of the Moon in 28-TET

Used To Be

Give It Time

Often the chaos and confusion of life needs to be turned down a few notches. This is an aural demonstration of how it feels to be overwhelmed by everything surrounding us.

https://youtu.be/XcshtIN8Mco

Motifs & Microtonal Demos

AUDITORY PROCESSING CHAOS in 16:9

No Question

Rescoring and rearranging the 3/4 original into 4/4 with additional production.

Music / Lyrics: Mykola Dmytrovych Leontovych / Микола Дмитрович Леонтович
Rearrangement: Shawn Michael for Ambient Esoterica

Shchedryk Lofi in 4/4 | Щедрик | “Carol of the Bells”

LoFi Samhain Seasonal Theme with a Pumpkin Spiced Twist

Mystic LoFi 

Mystic LoFi 🎃 Hallowe'en 🎃

you want a love
someone who really cares 

Piece Of The Pie

Experiments with a 22-note unequal temperament scale.

A tetrahedral number is the sum of a series of triangular numbers in sequence order.

The sum of the first 22 triangular numbers is 2024.

The current Gregorian Calendar year is 2024; the first time since 1771 the year was a tetrahedral number.

About the scale and tuning:
The values between each of the first 23 tetrahedral numbers determine the 22-note tetrahedral scale.

The 23rd tetrahedral number is the point at which the octave repeats.

The first 23 tetrahedral numbers are:
1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300.

This numerical series is then converted into cents and truncated to a single 1200-cent octave while retaining their ratios between each other.

After conversion, the scale becomes:
A(Root)
A(+13)
A(+26)
A(+43)
Bb(-35)
Bb(-9)
Bb(+22)
B(-43)
B(-4) - M2
B(+39)
C(-13)
C(+39)
C#(-4) - M3
D(-43)
D(+22)
Eb(-9)
E(-35)
E(+43)
F(+26)
F#(+13)
G(+4) - m7
Ab(0) - M7
A(Octave)

17 notes to reach the 5th;
and a perfect equal-tempered major 7th!

The major 2nd, major 3rd, and minor 7th;
all within 4/100th of an equal-tempered semitone!

Fun stuff!

If you wish to experiment with this tuning, I have made it available for export from Sevish’s Scale Workshop:
https://sevish.com/scaleworkshop/?n=T...

To nerd out on Tetrahedral Numbers:
https://en.wikipedia.org/wiki/Tetrahe...

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Composed and Produced by Shawn Michael
© 2024 Ambient Esoterica

#microtonal  #drone  #steinberg  #cubase  #nativeinstruments  #kontakt  #lofispace  #raum  #flair  #deelay #maserati  #ozone  #waves  #2024  

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INSTAGRAM ➤  https://www.instagram.com/ambientesoterica/

TWITTER ➤  https://twitter.com/ambientesoteric 

BANDCAMP ➤ https://ambientesoterica.bandcamp.com/

YOUTUBE ➤  https://www.youtube.com/@ambientesoterica 

BLOG ➤ https://www.ambientesoterica.com/

T22 = 2024 Tetrahedral Tuning | Unequal Temperament

Starshai

Ambient Esoterica is an audio/visual project inspired by data sonification, microtonality, mathematics, esoteric correspondence systems, and sacred geometry.

T22 = 2024 Tetrahedral Tuning | Unequal Temperament

Ambient Esoterica

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