(13th December, 2022: Please note I’ve changed some of the pictures and tuning files since I published them, having found some errors – so you may want to download again if you downloaded them before today.)
Hiya – I’ve been asked to provide some project files with the tunings defined in them so that, if you have Apple Logic, you can open them up and play around on the Steinway – or the instrument of your choice, and try these tunings.
These are the same ones, in sequence, as you’ll find here.
And I’ve done some little visuals to show from which “column” of the harmonics the notes come from. What I mean by “column” is how I illustrated the harmonics generation here – so that:
- The left column are all 3rd harmonics of a Day.
- The middle column are all 5th harmonics of the frequencies in the first column (and this is the column where I had experienced the sub-harmonic Bb and F notes creating the strange non-stirring effect as explained here: www.harmonicsOfNature.com )
- The right-column are the 5th harmonics of those middle, “phenomenal” frequencies, and this is where A = 432 Hz
The point here is that we know certain things for sure….
- A day is 86,400 seconds – so that is the “clock” of the Earth, and it happens to be a G which octaves up to 388.36148148 rec Hz
- Bb is 7.2 Hz, because that’s the way I detected it
- Eb is 9.6 Hz, a 3rd harmonic below that Bb, and also corresponding to one beat per “Helek” which was the ancient Babylonian measure of time, equal to 3.3333 recurring of today’s “seconds” and also the time it takes the Earth to rotate 1/72nd of a degree. Also, a peak in the Earth’s electro-magnetic field.
- F is 5.4 and 10.8 Hz, which I also detected (see the home page) and it’s a 3rd harmonic above the Bb
- C is 8.1 Hz, or 259.2 Hz. I didn’t detect this one, it’s a 3rd harmonic above the F, but it’s interesting that the number of its frequency in Hz is the same as the Great Year (25,920 years, which is what it takes for the Earth’s precession of the equinoxes to go through all 12 signs of the zodiac (360 degrees) and start again.
Basically, all the other frequencies are up for grabs – and the tunings I’ve provided below are different permutations of the different versions of notes from each of the columns to make it work.
There are some handy things, for example:
- The “Earth/Geo” G in the first column at 388.36 Hz is almost the same as the middle column G of 388.8 Hz. So notes nearby in the “chain” to these notes are going to sound fine together
- The same is true of E as 323.63 Hz and 324 Hz
- And also B at 485.45 Hz and 486 Hz
There are certain conditions I’ve followed, primarily that the 3rd and 5th harmonics are the primary medium for propagating the harmonics.
Some might say, “ah, what about the 7th harmonic, or the 11th harmonic” etc. But the fact that I measured the Bb and F frequencies, and then it turned out they (in the 2nd column) were exactly a 5th harmonic related to the harmonics of a Day (1st column) seems strong proof the way the Earth is spinning and creating harmonic frequencies is certainly using the prominent and strong 3rd and 5th harmonics.
My point is, what I’ve been trying to do is create harmonic musical scales based on the facts above which both sound good, and feel therapeutic. So, here they are.
Click on each of the images – and it will prompt you to download a Zip file of the Logic Pro project for the frequencies which are bolded in black text in the pictures:
You can try other combinations of frequencies. Tips:
- Where you go right to left, that’s a 5th harmonic or what is known in music as “a major third” interval – it’s what you need for making major chords that are exactly in-tune!
- Where you go bottom-up, that’s a 3rd harmonic or what is known in music as “a perfect fifth” and it’s what you need to complete the major chord above. e.g., G across to B, and G up to D gives you a major G chord.
- Minor chords have a flattened “5th harmonic” (or “minor third”) and you’ll find these by going from a note up-one and then one to the left. So, G 384 Hz, up one and to the left is Bb 460.8. Combine that with D 288 and you have a perfectly sonorous minor chord
Let me know if you encounter any technical problems. Or just have questions about the choice of frequencies in these “harmonic scales”.
An interesting thing occurs with this #4, by the way. Take a look at the diagram for it, above:
- When you play an Eb (307.2 Hz) and a D (288 Hz) together, you get a difference of 9.6 Hz, which is essentially a binaural Eb again
- When you play an A (432 Hz) and a B-flat (460.8 Hz) together, you get a difference-note of 14.4 Hz which again is a low, binaural Bb
So, I did that for therapeutic purposes.
Similarly, tuning #1 enables an E of 327.68 Hz to be played with an Ab of 409.6 Hz. At the sub-audio level these frequencies are 0.05 Hz and 0.04 Hz. Someone I met the other day had intuited these numbers as being the foundation for getting into the Gamma state. So, this tuning may do just that for you.
Also with this tuning, the apparent discord (because all of these harmonic tunings have one) is between the E and the B. The E at 327.68 Hz is hoping for a “perfect” 3rd harmonic B of 491.5199999981 Hz. But what it gets in this tuning is a B of 485.451851851 Hz. So, what’s the difference between these two Bs? 6.0681481463 Hz. Which octaves up to 388.36148 Hz = the G for a day. So the lemma is a fraction of a day. So, an E major chord at 327.68 against a B of 485.4518518518 is ringing out a fractal day!
And an E minor chord incorporates that same G anyway! So, just go with the apparent discord! Its how the gamma brain and the world work together, perhaps!
For tunings # “2 and 5” and # 6, the lemma is from the C of 259.2 to the G. It wants a perfect 3rd harmonic of 388.8 Hz, but what it gets in this tuning is a G of 384 Hz. 388.8 – 384 = 4.8 Hz. 4.8 Hz is a low octave of our Eb (9.6 Hz) – which has been measured to be an electro-magnetic peak in the Earth’s resonance and corresponds to an ancient Helek, the time it takes the world to rotate 1/72nd of a degree. So, this tuning will emphasise that frequency as a fractal gap for you.
For tuning # 3, the gap is from A to E. A at 436.9066666 rec Hz wants a perfect 3rd harmonic to E at 327.68 Hz. Instead it gets an E of 323.6345679 Hz. The difference between these two Es is: 4.0454321 Hz. This octaves up to 258.9076544 Hz which is close to our C of 259.2 Hz but no cigar. So, this to me indicates that tuning #3 is not quite the cosmic answer that the others are.
Tuning # 4 goes from G of 388.36148148 to a D of 288 Hz, when the perfect 3rd harmonic D would be 291.27111. The difference between these two Ds is 3.271111 Hz. Which octaves up to 418.702222 rec Hz which again isn’t one of our frequencies. So, perhaps tuning # 4 is also not quite the answer.
So, it looks to me like tunings: 1, 2/5, 6 are the keepers.
Transposition – and other Technicalities
Meanwhile, you’ll notice also in some I’ve altered the Transposition. Putting Eb where F usually goes for this #4 tuning puts all the most sonorous note combinations on the white notes. That said, the black notes when this is done also sound good.
To access the tuning adjustment on a Mac, do Option-P, or from the menu: File – Project Settings – Tuning. It looks like this. You can see I’m using the “User” setting, instead of Equal Tempered. In this case, the offsets I’ve entered in cents are in relation to 440 Hz.
To see the Oscillator at work, to tell you what frequencies you’re playing, click on the “Test Osc” track towards the bottom and then in the “Inspector” window on the left, click in the middle of the blue-button called Test Oscillator and up it will pop. Then, so long as you have “R” for Record on both the “Test Piano” (or whatever instrument you’re playing) and the “Test Osc” track, then you’ll see it moving around to tell you the frequency – it will even do this if you’ve muted it, as I have in the screen-shot below: