G’day. A quick post to discuss different scales. As we’ve seen at “A Day is G!“, our Planet creates a matrix of electro-magnetic harmonics related to its rate of spin. And each harmonic generates other harmonics, providing a vast network of frequencies from which we can construct musical scales. Just to recap:
- The left-hand column starts with the frequency of a Day, and its 3rd harmonics
- The middle column are 5th harmonics of this, and this is where the Bb and F frequencies I discoverd are, as well as the Eb frequency based on the ancient Hebrew measure of time, the Helek
- The right-hand column are 5th harmonics of the middle-column, and it is here that A is 432 Hz – and other frequencies which can be found on some more advanced tuning-forks used by energy healers these days. It’s also where Zarlino constructed his scale.
I have found that there are certain ways to combine these frequencies which yield pleasing major and minor chords and a scale which is overall harmonious. Below is the shape of the basic traversal I have landed on:
P-Shape
I call this “P-shape” because in the diagram above, the configuration of the selected notes in the scale looks like the letter P.
Basically:
- Start with your root frequency, E from the middle column in the example below.
- Now, go up go up 4 third-harmonics from there (e.g. E to B, B to F#, F# to C#), then for four more third-harmonics (Ab, Eb, Bb, F) also “turn right” to include their 5th harmonics, as shown above
As shown by the green and red arrows, you get major chords, e.g. for Ab, Eb, Bb; and minor chords, e.g. C, G, D.
- A major chord is built from the one above it, and the one to the right of it. For example, start with a note in the left column (e.g., Ab), and follow the green arrow to go directly to the right to pick up the “major-third” interval (5th harmonic, e.g., C) and then go directly up from that first note to pick up the “perfect fifth” interval (3rd harmonic, e.g., Eb)
- To build a minor chord, start with a note in the right column (e.g. C), and follow the red arrow to go diagonally up and to the left to pick up the “minor third” interval (e.g., Eb), and then go directly north from the first note to get the “perfect fifth” (3rd harmonic, e.g., G)
The goal for me, when designing a scale, is to get the maximum number of major and minor chord combinations.
And there would be more options if we weren’t limited by most keyboards to 12 notes per scale. e.g., if we could have C as both 259.2 Hz and 256 Hz then we could have a scale with both a pure F-major chord, and a pure Ab major chord.
And below, for that same “P-shape” traversal, are the intervals in red for all of the notes in the scale in relation to that root frequency.
These harmonic intervals, or fractions can be used in tuning software like Entonal, which require a harmonic fraction to programme the scale.
If you are using software like Entonal to modify your tuning for plugins like Kontakt and Heat Up 3, then Entonal can be given these fractions in the scala tuning file, like this;
“backwards L-shape”
Another traversal approach I have found is the “Backwards L-Shape” approach, which seems to be what the Venetian music-theorist Giosoffo Zarlino used for his scale in the 16th century, which we had discussed here. In my view, this is the best sounding scale.
The illustration above shows not just the interval shape which Zarlino writes about in his theories of harmonics, but the actual frequencies in our “right hand column” – that is the frequencies that are 5th harmonics of 5th harmonics of the vibration of a Day (the frequencty in the lower-left corner, 388.3614148recurring vibrations per second..
Have a look here for more which I have researched about Zarlino and a piece I played using his frequencies
Here is the scale interval file for this approach:
In the “backwards L-shape” traversal, there are “8 notes in a row” coming from the right-hand “column” (e.g. C, G, D, A, E, B, F#, C#), and these are augmented by four 5th-harmonics below them (Ab, Eb, Bb, F).
Interesting: You may have noticed that there is not much difference in the actual frequencies for E, B, F# and C# taken from the middle “column” versus coming from the right-hand column. For example, E is 323.63 Hz in the middle column, and E is 324 Hz from the right-hand column. These are so close that it means we have the flexibility to construct the scale either using the Zarlino “8 in a row” approach, or my “L-shaped” approach without changing the audible result much.
Other Keys
OK, so the examples above both yielded similar scales supporting Bb and Eb major. But what if you want to play music in a different key, such as D-major. Well, using the traversals above, D at 288Hz in the right-hand column doesn’t have a 5th harmonic to the right of it – so it’s not going to sound good when played with the F# (5th harmonic) from this traversal. So, in that case, you can have a few other tunings which will take care of these other keys.
In each case, use the the first light-blue note in the traversal as your root frequency, and use the intervals from that to construct the harmonic scale from it. e.g. in the C or F major traversal below, the root note of the harmonic traversal is F#, shown in light blue. Here we go:
D or G Major is more of a Zarlino/Straight-8 traversal:
So is E and A major:
You could construct a matrix with more than 3 columns. Ibrahim Karim, founder of BioGeometry, and his team have mapped out the 7 planes of nature – Physical, Vitality, Emotional, Mental, Spiritual 1, Spiritual 2, Spiritual 3. And it is conceivable that our three columns above corresond to these. So, if you go up high enough, you can play your music in the frequency of God! I’m working up to that!
!
Universal Zarlino
12
!
135/128
9/8
1215/1024
5/4
10935/8192
45/32
3/2
405/256
27/16
3645/2048
15/8
2/1And here are some Entonal xml “tuning” files you can import:
And .scl tuning files you can use in Logic Pro, as advised here: