modern solfeggio tonality

Inspiration:
“If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.”
– Nikola Tesla

Description:
The numbers 3, 6 and 9 have ancient, numerological application.  For example, 3 can symbolize two opposing extremes with a point of balance in between, and the numbers 6 & 9 govern the I-Ching’s Yin-Yang dynamism, but this is only scratching the surface.  If you wish to take the plunge, consider immersing yourself with this thread on Lo Shu.

One way of incorporating this idea will be the use of specific frequencies that have a ‘digit sum’ of 3, 6 or 9, just like those in ‘solfeggio’:

UT – 396 Hz
RE – 417 Hz
MI – 528 Hz
FA – 639 Hz
SOL – 741 Hz
LA – 852 Hz

Example:
For instance FA = 639:  6 + 3 + 9 = 18, and  1 + 8 = 9.
Therefore the ‘digit sum’ of 639 is 9.

UPDATE!!  There is some confusion online as to what is ancient and what is modern in respect to this system.  What we know for sure is that the ancients did not have any devices for measuring or producing pitches in absolute cycles-per-second values (i.e. they did not have any digital computers).  As such, these pitches are a modern, absolute and experimental translation of this numeric series into Hz or cycles-per-second values and therefore could not have been sonically available to the ancients.  That being said, there are also many traditional musical characteristics that can be found within this system.

Here is a scale created with the following set of 81 Lo-Shu tones within the 729 fabric:

111,123,135,147,159,162,174,186,198
219,222,234,246,258,261,273,285,297
318,321,333,345,357,369,372,384,396
417,429,432,444,456,468,471,483,495
516,528,531,543,555,567,579,582,594
615,627,639,642,654,666,678,681,693
714,726,738,741,753,765,777,789,792
813,825,837,849,852,864,876,888,891
912,924,936,948,951,963,975,987,999

The following audio clip represents my first attempt at composing using only pitches from this scale:

Audio clip: Adobe Flash Player (version 9 or above) is required to play this audio clip. Download the latest version here. You also need to have JavaScript enabled in your browser.

Much of melodic expressionism lies in the ‘notes between the notes’ so-to-speak, and this scale is one specific way of exploring such a practice.  Weighing in at a little over three octaves (111, 222, 444 and 888), its intervals resonate with unique harmonic characteristics unheard in 12-tone equal temperament.  These 81 tones are a ‘geometrically-coherent, crystalline structure’ ripe for harvest.  There is much to explore in composition.

The technical how-to:

This scale was fabricated digitally with the help of the software CSE (Custom Scale Editor) which can be used separately or in conjunction with Scala.  If you’re looking to get involved with MIDI microtunings, I recommend to skip the elaborate process of installing Scala and simply use CSE to save time and potential frustration.  CSE is all you need to create and/or perform custom tonalities.  Its author, Aaron Hunt at H-Pi Instruments was hugely helpful in getting this little experiment off the ground.  To download my template files, click here.