Yes folks, I’ve finally built my first just-intonation guitar – and I’ve provided the instructions so you can do it too! – here
I had seen this before, and it seemed a bit random until I grouped the entries according to the mixolydian harmonic notes which they contain (instead of just listing them with the major and minor flavors of each key next to each other). By doing this, we can contrast the passive, negative outlook for the Minor key against the robust, active expression of the same emotion in the Major key.
I also listed these major/minor groupings in order of musical fifths, starting with the keys related to our “magic” key of B-flat mixolydian, then its fifth – F, then its fifth – C, etc. It’s interesting that Schubart’s findings closely match my own hypnotized synesthesia – with the emotional flavor of the keys getting steadily darker and less pleasant the more harmonically distant from B-flat they become – with the very last key in the cycle (A-flat major) actually described as “the key of the grave”!
Here we go:
Keys based on B-flat mixolydian mode:
- Eb Major (Bb myx – F dor) – the key of love, of devotion, of intimate conversation with God.
- C Minor (Bb myx – F dor) – declaration of love and at the same time the lament of unhappy love. All languishing, longing, sighing of the love-sick soul lies in this key
Keys based on F mixolydian mode:
- Bb Major (F myx – C dor) – Cheerful love, clear conscience, hope aspiration for a better world
- G Minor (F myx – C dor) – discontent, uneasiness, worry about a failed scheme; bad-tempered gnashing of teeth; in a word: resentment and dislike
Keys based on C mixolydian mode:
- F Major (C myx – G dor) – Complaisance & Calm
- D Minor (C myx – G dor) – Melancholy womanliness, the spleen and humours brood
Keys based on G mixolydian mode:
- C Major (G myx – D dor) – Completely Pure. Its character is: innocence, simplicity, naïvety, children’s talk
- A minor (G myx – D dor) – Pious womanliness and tenderness of character
Keys based on D mixolydian mode:
- G Major (D myx – A dor) – Everything rustic, idyllic and lyrical, every calm and satisfied passion, every tender gratitude for true friendship and faithful love,–in a word every gentle and peaceful emotion of the heart is correctly expressed by this key
- E minor (D myx – A dor) – Naïve, womanly innocent declaration of love, lament without grumbling; sighs accompanied by few tears; this key speaks of the imminent hope of resolving in the pure happiness of C major
Keys based on A mixolydian mode:
- D Major (A myx – E dor) – The key of triumph, of Hallelujahs, of war-cries, of victory-rejoicing. Thus, the inviting symphonies, the marches, holiday songs and heaven-rejoicing choruses are set in this key
- B Minor (A myx – E dor) – This is as it were the key of patience, of calm awaiting ones’s fate and of submission to divine dispensation
MY “BAD KEYS”:
Keys based on E mixolydian mode:
- A-Major (E myx – B dor) – This key includes declarations of innocent love, satisfaction with one’s state of affairs; hope of seeing one’s beloved again when parting; youthful cheerfulness and trust in God.
- F# Minor (E myx – B dor) – A gloomy key: it tugs at passion as a dog biting a dress. Resentment and discontent are its language
Keys based on B mixolydian mode:
- E Major (B myx – F# dor) – Noisy shouts of joy, laughing pleasure and not yet complete, full delight lies in E Major
- C# Minor (B myx – F# dor) – Penitential lamentation, intimate conversation with God, the friend and help-meet of life; sighs of disappointed friendship and love lie in its radius
Keys based on F# mixolydian mode:
- B Major (F# myx – C# dor) – Strongly coloured, announcing wild passions, composed from the most glaring colours. Anger, rage, jealousy, fury, despair and every burden of the heart lies in its sphere
- Ab Minor (F# myx – C# dor) – Grumbler, heart squeezed until it suffocates; wailing lament, difficult struggle; in a word, the color of this key is everything struggling with difficulty
Keys based on C# mixolydian mode:
- F# Major (C# myx – G# dor) – Triumph over difficulty, free sigh of relief uttered when hurdles are surmounted; echo of a soul which has fiercely struggled and finally conquered lies in all uses of this key
- D# Minor (C# myx – G# dor) – Feelings of the anxiety of the soul’s deepest distress, of brooding despair, of blackest depresssion, of the most gloomy condition of the soul. Every fear, every hesitation of the shuddering heart, breathes out of horrible D# minor. If ghosts could speak, their speech would approximate this key
Keys based on G# mixolydian mode:
- Db Major (G# myx – D# dor) – A leering key, degenerating into grief and rapture. It cannot laugh, but it can smile; it cannot howl, but it can at least grimace its crying.–Consequently only unusual characters and feelings can be brought out in this key
- Bb minor (G# myx – D# dor) – A quaint creature, often dressed in the garment of night. It is somewhat surly and very seldom takes on a pleasant countenance. Mocking God and the world; discontented with itself and with everything; preparation for suicide sounds in this key
Keys based on Eb mixolydian mode:
- Ab Major (Eb myx – Bb dor) – Key of the grave. Death, grave, putrefaction, judgment, eternity lie in its radius.
- F Minor (Eb myx – Bb dor) – Deep depression, funereal lament, groans of misery and longing for the grave.
Translated by Rita Steblin in A History of Key Characteristics in the 18th and Early 19th Centuries. UMI Research Press (1983). Plagiarised from various
(acknowledged) sources by Paul Guy
Of particular note, in relation to my own synesthesia:
- B-flat mixolydian: I say “soul”/God – he says, “conversation with God”
- F mixolydian: I say heart/body – he says, “aspiration for a better world“
- C-major: I say pure consciousness – he says, “children’s talk“
- G-major: I have always thought of as a key which embodies trees and nature, and he says “rustic”
We do disagree about E-major – but in his day, things were sometimes tuned down a little (A=515 Hz), so his E may be closer to my E-flat. Also, he describes B-minor as “patient”.
But Schubart’s description of B major matches my personal experience with band break-ups catalyzed by songs played in the key of B – “Anger, rage, jealousy, fury, despair and every burden of the heart”. That seems to sum up what I’ve seen when we’ve played songs in that key!
It has been suggested that Schubart’s attribution of emotion to certain keys was due to the slight variances in the intervals between the notes in the temperaments used in his day. The confluence of his findings with mine – based on harmonic, just intonation – and not a “temperament” at all, to me, reinforces the notion that the vibrations themselves carry a certain emotional weight, based on their harmonic association with our magic vibrations of 7.2 Hz for B-flat, and 5.4 Hz for F.
These emotional annotations give us a palette of colour and emotion for pure musical expression according to the vibrations of nature. Although, I’ll stick with my own!
- In the second column, the frequencies in the first column have been divided by 2 a few times to bring them into familiar octaves
- The third column adds up the digits of each frequency, numerologically and reveals that most of them factor to 9
- The fourth column indicates (in red) if these frequencies exactly match the harmonic frequency for that note as we determined from our magic base frequencies of 5.4 Hz and 7.2 Hz – and indicates in black if they are close matches
- The last column highlights in red where Zarlino’s frequencies match the frequency of that note if it is determined via a different harmonic approach than the one we chose
- Being as Zarlino was an intelligent fellow, we’ll keep track of these frequencies in case they are useful when it comes to the practicalities of building a Just Intonation musical instrument
To summarize the findings – of the eight notes that Zarlino lists, A, B, C, C#, D, E, F#, G:
- We exactly match A, B, D, E
- And we exactly match C#, F#, G if we calculate these harmonics still starting from B-flat, but using an alternative harmonic of harmonics
- The only one that’s a miss is C – probably because he perhaps wanted to take the simplistic approach that 1 x 2 = 2, 2 x 2 = 4, 4 x 2 = 8, 8 x 2 = 16, 16 x 2 = 32,
32 x 2 = 64, 64 x 2 = 128, and 128 x 2 = 256. In other words, for this one note, he seems to have determined this note mathematically – (and perhaps this is the correct frequency. We’ll keep that one in our hat, also)
I’m not going to argue with Zarlino on the correct way to determine the harmonic frequencies – what is significant here is that we came up with a bunch of musical frequencies based on a chance encounter with vibration in a Johannesburg hotel room – and those frequencies, one way or another, also match what Zarlino recorded in his book published in 1558.
How is this possible? Well, first of all, Zarlino was the first advocate in Western culture for Just Intonation. Secondly, he must have started with the same frequencies as I did in order to calculate his just, harmonic series; either that, or the frequencies were passed down to him from some earlier culture. I will have to read his book to find out.
Just another confirmation from history that we are on the right track with these frequencies – and good to point out to the internet trolls (professional or otherwise) that you “cannot prove a negative” – as we used to say when I was 8. In other words, you can’t prove that something doesn’t exist. All you can prove is that you haven’t found that evidence of a documentation of A = 432 Hz – but we have! – and it matches and corroborates our findings.
Perhaps when we’re done being confused in this lifetime by the strange harmonic relationships between the orbits of our planets, we go to this place where all the planets’ orbits are in whole number ratios to one another and ring out like one funky piece of music! http://www.system-sounds.com/trappist-sounds/
Here’s a podcast about Glenway Fripp’s discovery of standing waves that seem to miraculously form in certain places when a B-flat note is played, sung or, in this case – whistled: http://atlantic.org/sonic-ids/b-flat
And a snippet more about him from NPR: http://www.npr.org/templates/text/s.php?sId=7442915&m=1
Closer to home, a friend of mine was telling me a few years ago about an experience he had while jamming where a note that the band was playing seemed to just hang above his head – floating there. They all took it in turn to move into that part of the room while playing the note, and they all experienced it, seemingly dwelling above their heads – taking on a life of its own – like some sort of zero-point energy source.
My friend says he has a recording of that, too. It will be interesting if he can dig it out.