Harmonic Instrument Design

Well kids, this is all very improving but how about we build a harmonically tuned instrument? First – tuning an electronic keyboard, and then we’ll get into guitars. The offsets I provide could be used for tuning any instrument, really.

electronic Keyboard instrument

The easiest one is a MIDI keyboard instrument – especially if you have the Apple “Logic” software where you can set an offset for each note in the octave. The table below is the collection of frequencies extrapolated from our “magic” Earth tuning. Note: that A is 436.9 Hz (neither 440 Hz, nor 432 Hz), for reasons explained, here.

I use http://www.sengpielaudio.com/calculator-centsratio.htm to calculate the cent offsets from the frequencies

I also use the Oscillator in Apple Logic which confirms the exact frequency being produced for each offset on the piano note.

Here’s the same data, set up like a keyboard, showing just the offsets compared to 440 Hz Equal Temperament tuning:


OK, let’s get into guitars. Unless we’re going to play slide all the time, we need a guitar with the frets in all the right places to hit all the right frequencies – harmonically. (It won’t be able to play in every key because of the lemma – which I’ve discovered is a fractal reflection of your starting frequency in the cycle-of-fifths, here.) Guitars with the kind of fret placement we’re talking about will sound slightly out of tune with equal-temperament instruments like piano and normal guitars.  But it will be acutely in-tune with itself and the frequencies we have identified as being “the still points in the turning universe”.  It will be truly musical, in the deepest possible sense. Ideally, it will hit the frequencies in the table above.

Well, I’ll cut to the chase. Last week, I received this stunning, new, custom guitar from Manton Customs, in Shropshire, UK:

Open Tuning

I played open tuning, e.g. 5-string open-G (GDGBD), or open-D (DADF#AD). I like the big chords and the ability to play melodically against a drone. Here’s a design I developed here – although I haven’t yet actually built it. Cable-ties on a fretless guitar can be a good way to explore these fret placements, I’m told.

True Temperament guitars and necks

One thing you’ll notice about True Temperament fretboards are the “curvy” frets. This is the True Temperament (TT) fretting system (and their instructions on how to tune it). Now, some people say TT is designed to make your guitar more “Equal Temperament” like a piano. But, having seen this video, it looked like it was pretty harmonically aligned, so I went ahead and included it in the design for the Manton guitar.

Amazingly enough, I have found that I am able to almost exactly achieve the “Earth tuning” on this guitar – just by following True Temperament’s standard tuning offsets, with the addition of setting the default A on my tuner to 436.9 Hz, instead of 440 Hz. So, “TT” is actually a harmonic temperament.

I spent some time tuning it up, and at the end, I played along (badly) to this rendition of Beethoven’s Moonlight Sonata (which I have manipulated so every note corresponds to the Earth tuning). The guitar seemed to match the piano pretty well!

Using the True Temperament offsets for the curvy frets, I’ve explored how to achieve the Earth frequencies on the TT guitar, as follows

  • Column-AG are the notes
  • Column-AH are the Earth frequencies we’re trying to achieve on the guitar for each of those notes
  • Column-AK is the calculated Equal Temperament frequencies based on A = 435.7 Hz (an offset I’ve chosen as it seemed to provide the most “hits”)
  • Column-AL is the True-Temperament offsets for each notes, as explained on the TT website.
  • Column-AM is the resulting calculated frequency in Hz once the TT offset (column-AL) has been applied.
  • Column-AN shows the difference in Hertz between the frequency we’re striving for (column-AH) and the frequency we get on the True Temperament guitar (column-AM). I’ve coloured these according to “white” as a perfect hit, green as a near miss, yellow as acceptable, and red as a poor match.

In this way, Bb, D, Eb, and F are “exact”; A, G and Ab are a near miss; C-sharp is OK; and B, E and F-sharp are off. The average difference between the frequencies we’re trying to get and the frequencies we do get is 0.3 Hz (it would take on average more than 3 seconds for you to hear a dissonant “beat” between harmonics).

Regarding the “red” ones: The good news about B is that the “Geo” B is 245.76, and the “magic” B is 242.73 Hz (see the three “Geo”, “Magic”, and “432” columns of this chart) – so with the TT guitar giving 244.39 Hz shown in column-AM above, we’re getting a tempered blend between the two extremes.

Similarly with E: while the Geo E is 327.68 Hz, the “Magic” E is 323.63 Hz, so our True Temperament frequency of 326.26 Hz is a blend of these.

To tune a TT guitar, you need a tuner with which you can off-set the strings or notes by a specific number of cents. There are several tuners which support this:

  • I use the Peterson StroboClip HD, and I’ve created an on-line chromatic tuning configuration called “ERT” which you can use if you have this tuner and have registered it on the Peterson site. This tuning does not take into account the offsets of the True-Temperament guitar. It is basically the offsets to tune any note exactly to the Earth frequency on any instrument. On the TT guitar, it gives the satisfaction of tuning the guitar’s open strings exactly to the Earth frequencies, but you’ll have to bend the fretted notes so they line up across strings.
  • I’ve also created a hybrid Earth/TT tuning on the Peterson site called “ETT” which gives you the offsets from column-M above – that is, the Earth frequencies as offset from standard 440 Equal Temperament, taking into account the recommended offsets for the True-Temperament guitar to match the table above.
  • I’ve also created another tuning on the Peterson site called “JTT“, which is simply each of the 6 to 8 strings on a guitar with the recommended True-Temperament offsets applied. To make this match the chart above you can set your reference frequency for “A” on your StroboClip itself to 436.9 Hz or 435.7 Hz.
  • Other tuners I use include the Sonic Research ST-200 Turbo-Tuner, which comes with the True Temperament offsets pre-programmed. It also supports custom tunings, and I’ve programmed mine with the offsets above.
  • Also, on Android, the StroboPro app supports True Temperament tuning and is both accurate, and a good way to validate your tuning from the other tuners.

Conclusion on the True-Temperament guitar:

It sounds more in-tune than other guitars I’ve tried, and at least some of our Earth frequencies are exact or close to exact. As shown in the video above, if you play a note or a harmonic in place on the neck and then play along to it, those other notes are mostly in tune. It’s also easy to play – with no extra frets to confuse you. To me, it’s worth it to have the satisfaction of being mostly in-tune with the Earth, and it solves the problems of the “gap” intervals which we get on the piano keyboard tunings where everything sounds perfect except for a big gap between two of the third-harmonic notes. The tempered aspect of the TT frets keeps us something which is more harmonic than Equal Temperament

The other beautiful thing about the Manton Matriarch True Temperament guitar is the inclusion of the EverTune bridge: once you figure out how to use this bridge, and you’ve tuned your strings – they will basically stay in-tune regardless of changes of temperature or humidity.

This is actually my 4th TT guitar neck, but now I’ve now figured out how best to tune it, and the EverTune and the impeccable intonation of the Manton guitar means that I can really experience the precision of these tunings on a consistent basis.

G&L Legacy, Reverend Club King 290, Tanglewood parlour guitar – with True Temperament frets

FreeNote Guitar

My earlier attempt was the FreeNote guitar neck – which adds extra frets – so you can play 11th harmonics etc.  I had taken the plunge and purchased the FreeNote 24-Fret Just Intonation Neck and put it on on a Stratocaster body I had bought from Stew-Mac.  It fit perfectly without intercession from a luthier.  

FreeNote 24 fret Just - all frets

The only trouble was, it’s 24 frets per octave.  That’s a lot of frets, and even at the octave and fifth, the frets were so close together that it would require a change to my guitar technique – which wouldn’t be compatible with the “big-chords-and-quick-fills” technique I’ve developed over the years.  It’s enough to keep track of 12 frets per octave – so 24 is a bit much for me!  If you do a bar chord on this guitar, you sort of have to choose notes from the micro-frets next-door for it to sound good.  And I don’t have that kind of precise mind!  So, I tried to simplify by identifying the key frets that I really need.

This required a fair bit of analysis to figure out which frets would yield the frequencies I’m after depending on what note the string was tuned to.  I created the table below, where I put a different starting frequency in the second column for each string, and calculated what frequencies would be produced by the Jon Catler JI neck at each fret, and bolded those that matched the target frequencies we worked out in the first section.

Catler frequencies

In the table, the second column is the note that the string is tuned to.  The fourth row indicates the fret of the FreeNote neck, and the second row indicates the harmonic fraction being generated at that fret.  If the frequency generated at the fret matches one of the frequencies we’ve determined to be “correct”, I’ve indicated the resulting frequency and note in black text; if it’s close, then I’ve indicated that in gray text.  The column on the far right tallies the number of “hits” I get for that string overall.

As you can see, some string did better than others: F, C and B-flat all achieved 7 hits per octave (100%).  Also, some frets had a good cluster of hits on them, while certain frets yielded just one “hit” – so, it seemed to me, those were frets that could be removed. And in fact, the red in the 4th row in the table above indicates those frets which I did actually end up removing; so now the guitar looks like this (presumably – unfortunately, it got stolen!)

FreeNote 24 Fret Just - less frets.jpeg

14 thoughts on “Harmonic Instrument Design

    1. Hi Kite – that’s great. I used to live in Portland. Anyone trying to do this sort of thing is alright with me.


  1. I wonder what your thoughts on the 528hz frequency is and if it somehow fits within your research? I see studies with evidence of significant stress hormone reduction and oxytocin increase as well as testosterone regulation. I have not seen evidence of a greater level of UV light absorption in DNA but it is claimed to benefit healing DNA like this as well. The book of 528 has some interesting claims as well with structured water at 528hz, center of colour/sound spectrum, chlorophyll freq..etc. Instead of using earths relations he uses relations through the the galaxy with planet rotations and such like you do with earths. The Math is far out for my knowledge.


    1. Hi JP – funnily enough, i’m about to re-write my section on the Solfeggio. E.g. 528 may be the sacred number. But the ancient Hebrews didn’t have the second, they had the Helek which is 3.33333 seconds. So 528 / 3.3333 seconds = actually is an octave of 316.8 hz. 31,680 miles is the perimeter around the earth, as well as the circumference around the earth going through the middle of the moon if the moon was resting on the earth. It is therefore related to the 7 to 11 ratio of earth and moon and (22/7), Pi.

      316.8 hz is also the 11th harmonic of our Bb at 7.2 hz – which we know has an electro magnetic interaction with the gravitatational rotation of the earth. I’ll do an analysis of all the solfeggio based on the Helek. I’m just reading Len Horowitz’ book about the solfeggio and he says it’s encoded in the old testament. So heleks make more sense than seconds and Hz. 33 per helek is 9.9 hz.

      This is a frequency i’ve used for my under mattress magnetic resonator thing. Time to dust that baby off too!

      What it looks like is that the solfeggio were referring to vibrations per helek. Plus they are all 11th harmonics of our frequencies. 11 is a sacred number but each of the solfeggio frequencies need to be divided by 3.3333 to convert them into vibrations per second. Basically,
      1. everyone is listening to them wrong at present
      2. They validate again my frequencies because it turns out not only that Mi 528 is an 11 th harmonic of our gravito-magnetic Bb of 7.2 Hz. But also Ut is the 11th harmonic of our F at 10.8 Hz!
      Amazing stuff – that our frequenciea are encoded in the bible!


      1. Wow! This is amazing. I’ve made flutes with solfeggio and played around with numbers but could never find much relation and knew something was missing. This makes sense and gives me chills lol. I’ve seen the research where the 11th harmonic is the key and watched the video under microscope of it imploding cancer and bad cells. Always intrigued me about the 396 and 528 being 5ths even 417 is 128:81 in the Pythagorean temperament. I’ll divide my solfeggio flute design by 3.33 and make a new playable design. I’m stoked to read your update on the page and thank you for taking the time for a lengthy insightful reply! I’m curious what is this magnetic frequency mattress thing you have? I’m curious as I’ve landed in this frequency rabbit hole after many years of pain and disease and perhaps some magnetic frequency thingy could help me out too haha


  2. Cheers JP. I’ve bought the PVC pipe and plan to experiment with flute hole placement soon!
    I’ll publish the Solfeggio update in a few days. Between the decoded solfeggio frequencies (divide by 3.3333 seconds, and then divide by 11 to find the root note each one may be the 11th harmonic of) and the dofferences between the Hz frequencies, you have most of the tones for a harmonic scale based on Bb.

    Here’s a video by the inventor of the EarthPulse magnetic thing i use. Interestingly, i may have been one of the two letters that he mentions about 432 hz. This video is about 9.6 Hz – which is the Eb a 3rd harmonic below our Bb of 7.2 Hz. The 11th harmonic of that Bb is 9.9 Hz, so in manual mode you can set it to 9.9 hz too. I’ll be forwarding the new solfeggio update to him as well! https://youtu.be/8P6WhEbX1uw

    Yes, 417 translates into 363.93 hz which is very close to F# of 364.088 as F#, several 3rd harmonics below that Eb.


  3. Some interesting things coming up now! Just wanted to note maybe you have already the solfeggio 417/3.33 is 125.225 which octaves down to 7.83 hz! The Schumann resonance 🙂 I have a drone flute design that may just be supernatural haha

    Liked by 1 person

    1. Need to get those supernatural flutes out to the people!

      V. Interesting on the schuman, well spotted! although /3.3333333 = 7.8187500078

      I understand from sources the schuman varies, so i don’t get as excited aboit it compared to these frequencies which all tie back to sub-harmonics of 1/86,400 seconds, AKA a day!

      I think the whole Solfeggio is transposed by the 11th harmonic rather than to be taken at face value after the conversion from Heleks – but all insights are good.


      1. Ok I’m losing it over here. I calculated all the solfeggios to hz, their 4ths, 5ths, 11th root, 11th multiple. The numbers showing up are blowing my mind. It’s been over a decade of treasure hunting the rabbit hole of frequency and healing in this reality and there’s so much lining up now it’s wild. I’m sure you’ve been having the same fun over there. Healing frequencies from 432 tuning, 444 tuning, clinical studies of specific hz, my old ohm voice recording, even a random video Robert grant did meditating in the great pyramid I analyzed the audio a couple months back and the multiple hz that peaked in the analysis are also showing up. The hz calculation from 417, 528 and 285 are all there! You’ve either helped me completely lose it or finally find it. Haha incredible
        Thanks I have noted the root of the 11th. I will be experimenting with all different variations. The first will be face value knowing the root Bb and f you had discovered is resonating in space as is but I am making it a drone to be able to play the Root 11th at the same time anyways and may just tweak the fundamental to be 9.9 hz off for that binaural beat. I easily have another douzen flutes to design and experiment with this information.
        Interestingly I’ve made around 30-40 flutes learning the craft and have just setup to begin recording so I can release this magic to the world but now I have some more flutes to make 🙂 because I think this is the potent power here. When I get a nice design tried and true with all this new info I will make you one for helping me along this harmonics of nature journey. If you want to experiment with hike placement and frequency check out website flutopedia. The guided naflutomat has the math built in and you can put in custom hz and modify hike placement and size. It’s how I’ve been able to explore so well with the craft. Cheers 🙂


  4. Perhaps you’ve noted this already but I just realized the ancient Indian mystical popular number 108 when divided by 3.33333333 gives us the C at 518.4 hz that you have discovered in your scale 🙂


    1. Hi JP – yes through the miracle of math, going down a 5th harmonic, and then going up a 3rd harmonic, equates with dividing by 3.333. E.g A can be 108 hz as the 5th harmonic of F at 345.6 Hz, and C as 259.2 Hz is the 3rd harmonic of F.

      25,920 in years is the length of the great year. But 259.2 vibrations per helek (instead of Hz) is 432 Hz. If you look at my “A Day is G” page, i’ve shown the corresponding vibrations per Helek, per second, angles of earth rotation, and duration of time for each “note”.

      This is why the same numbers (eg 108, 72, 54) show up both as Helek frequencies and as Hertz frequencies – but with a different name for the note. I suspect that, being as the sexagesimal (60 based) counting system, and all the ancient metrology of cubits, fathoms, greek feet, egyptian feet and all the rest were worked out during ancient hebrew/babylonian/egyptian times, that the mumbers are best understood musically as vibrations per helek, because they didn’t have seconds. For an amazing investigation of ancient units of measure, and how our same vibrational numbers based on the rotation of the earth were also used to define the units for measuring the distances on the earth, see John Michell’s book, the dimensions of paradise. Also on my to-do list is a write-up of this.
      Sorry I din’t update my Solfeggio page at the weekend – i was finishing decorating my studio. But i will try to during the week. Seems like you’re finding some interesting correlations!. And thanks for the Flutopia links – what a fantastic resource that calculator is!


  5. Hello JP. Sounds like you have done some great work. I have just been chatting with Jules/Phred on email. I am a trainee acupuncturist and flute player from the UK and interested in musical vibration and Qi energy vibration. I understand you make native American flutes…. I’d be very interested to know more. Thanks 🙂


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