Perfect Pentatonic

I've been studying the basic math behind music theory, especially Pythagorean Temperament vs Equal Temperament, and the relationship it has with base Hertz frequencies. I find it fascinating. Today our tuning standard is 'A 440Hz'. That means that on any modern piano/keyboard, the A key that follows 'middle C' vibrates at 440Hz. Since 440 is evenly divisible by 8, this is ideal for the western "Octive" model of harmonic resonance. However, in the past, composers like Bach, Mozart, and Beethoven where known to use A 432Hz, and as far back as the Middle Ages, A 415Hz was in use.

This means the classical masterpieces that you hear recreated today did not sound the same when they were first composed. The chords ring clearer today due to Equal Temperament coupled with the A 440Hz standard, but the mood shift caused by the tuning imperfections and dissonance is long dead. Just think about that the next time you hear a timeless classical masterpiece.

Why am I saying this? To inspire the mind of readers in the same way this knowledge inspired me.

I have a programmable chromatic tuning app on my phone: Pitchlab. It allows you to adjust the Hertz standard you want and select one of the many Temperaments. The ancient civilizations largely used Pythagorean Temperament. It won't work on modern guitars unless you adjust the fretboard.

So I decided to make my own Pentatonic Scale composed of 5 equidistant whole tones per resonance point (pentive).

To achieve this, used A 420Hz as my standard. Why?Because 420 is evenly divisible by 5 (pentive for resonance), 7, 6, 2, and 3.

To distinguish this scale from standard pentatonic scales, my tones are: V, W, X, Y, & Z.

So V = 420Hz.

420÷5=84 Hz whole intervals

V=420Hz
+84Hz
W=504Hz
+84Hz
X=588Hz
+84Hz
Y=672Hz
+84Hz
Z=756Hz
+84Hz
Pentive Resonance
V=840Hz

From this point, I divided each value by 2 repeatedly until the values where low enough to tune my guitar.

Tuning:

String 1=X 294Hz
String 2=V 210Hz
String 3=Y 168Hz
String 4=W 126Hz
String 5=Z 94.5Hz
String 6=W 63Hz

Now I just have to figure out how to remove my frets.

Playing it is pretty easy. Every 3.5 or so fret spaces is whole step and whole tone (unlike standard tuning). The sound is a bit exotic; a little bluesy, mildly ancient and moderately alien...but the frets are still getting in the way.

I call it the perfect petatonic becaues each whole step yields a wholetone.

Next project is the perfect heptatonic.

a reply to: BELIEVERpriest

Hi
I like Pitchlab, it's very useful.
You seem to know a lot about scales.
In the paid version of pitchlab you get a better view on the spectral analyzer and also split screen...

Do you play electric guitar?
Cheers

a reply to: arit_

I got the free app, but thats good to know. Thanks

Actually, I know very little about scales. I know how the Diatonic (ABCDEFG) and the Chromatic Halfstep scales work, but everything I posted here, I learned via google within the last 72 hours. I'm an obsessive researcher.

In fact, I wanted to create my own "perfect" scale for the sake of simplicity. If you look at the modern Diatonic scale, the tones B-C, and E-F are only a half step away. That's diffcult for me to remember on guitar. So in reality, the heptadic-diatonic scale is really an expanded Pentatonic Scale.

Yeah, I play electric and acoustic. Got almost all of Metallica's old tab memorized.

In the ancient days, music theory was for genius'. Today, with the knowledge of Hertz frequencies, we can mathematically reverse engineer music and create our own systems in a matter of minutes. There's a strange beauty to it.

a reply to: BELIEVERpriest

Deep music theory is not something that can be replicated yet by computers. However the elementary stuff like scales and tunings certainly can be. I only know this because in Grad School I hung around a number of Music Theorists Ph.D. candidates. It is a whole other world when you get to that level.

Another common tuning method is to go with A=432Hz, or Verdi tuning for even temperament. I like it, since it moves the music to the deeper, notes which tends to give the music a bit more of a fuller sound.

a reply to: AntigravityField

I agree, and I'm by no means any sort of music theorist, but by creating a scale and tuning of your own, its like staring from a clean slate. The rules are yours to discover.

I just pried off my acoustic frets with pocket knife (didn't even need to remove the strings). The lines are still there if I want to use the Equal Temperament, but now I'm free to discover my new scale. So exciting.

a reply to: BELIEVERpriest

Removing frets can be a pain in the butt, here's a video to help you..
(hang about, cant find the one, give me a minute)
(sorry, still cant find the one I was after - but to help save on chipping the fretboard this is a helpful hint/tool. I'd think about making something similar myself, only because Stewart MacDonald stuff if incredibly expensive.
But I'm guessing that since you're making a new fret positioned scale, you will be replacing the whole fret board anyway?)


Also, so others can get a better understanding of what you are saying in your op, here's a video which explains it and has some interesting scale divisions.

What an ironic name for a title

a reply to: BELIEVERpriest

what is all this doing to your chord shapes?
how are you making adjustments?

I play a standup fretless 5 string bass....the micro-tonal subtly adds another dimension to music. I don't read music or tablature so I don't know what you are talking about but it sounds interesting.

a reply to: BELIEVERpriest

Been on tour worldwide years ago and remember tuning our stage baby grand pianos to standard A 440....unless we went around Australia and other S.Hemisphere countries...where the standard A was slightly off, and not 440....but several semitones sharper or flater. Guitars and horns (Bb)....would have to adjust tuning accordingly.

Thought it a bit odd then...thanks for the thread. I've studied and taught theory since 1970.

Blessings.....MS

originally posted by: TinySickTears
a reply to: BELIEVERpriest

what is all this doing to your chord shapes?
how are you making adjustments?

Well my new tuning doesnt fit the fretting, so I removed the frets. The Chord arrangement is similar, but you can hear differences. Im going to buy some red dot stickers to mark all the new wholestepps.

a reply to: BELIEVERpriest

Hello

Regarding "Got almost all of Metallica's old tab memorized. "



PLEASE ADVICE

Need advice on something weird.

I am practicing like crazy the solo of "Am I evil".


I have the speed on my left hand already....
But the picking mechanincs are confusing me.

If I pick with the pick at 0 degrees to string I get a good soound but can't get the speed.
If I pick at 70deg pick to string I have the speed but no sound comes out at all.

I cna only achieve 100% speed at 70 deg angle.

What am I doing wrong?

SEEN FROM above like place guitar flat on floor and look at it

0deg: Sounds good, slow.

---------------------------------------------------------- string _ pick



70 deg: Fast, no sound.

---------------------------------------------------------- string \ pick


Cheers

originally posted by: BELIEVERpriest

originally posted by: TinySickTears
a reply to: BELIEVERpriest

what is all this doing to your chord shapes?
how are you making adjustments?

Well my new tuning doesnt fit the fretting, so I removed the frets. The Chord arrangement is similar, but you can hear differences. Im going to buy some red dot stickers to mark all the new wholestepps.

thats cool
i wonder if you picked up a fretless like the vigier would it sound cool with your tuning?

a reply to: TinySickTears

Well I removed the frets but the grooves are still there, so I can more or less move from semitone to quartertone by approximation. It sounds pretty wicked, like a mix of middle eastern and gothic. Thats the best I can describe it.

a reply to: arit_

I always had trouble with their solos. Maintaining the speed on the higher strings is my problem. I'm best at the thrashy stuff like the opening to MASTER OF PUPPETS.

I usually alt-pick and sweep at 70ish degrees sweeping down and mirror tilt coming back up.

^

Try moving up higher on the bridge to give the notes a more fluid ring.

a reply to: BELIEVERpriest
Dang believer, pulling the frets out? Now that's commitment. Not sure if your genius or have way to much time on your hands. Any hoot....keep it up )