Review after three months

[xjscott]

Well, I read all of Bills papers there, and I know Bill and have followed his excellent work for decades. But that doesn't change what I said.

the entire wicki/hayden layout can be defined by two intervals, the fifth and octave, and that these are the two intervals off of which tuning theory and practice is based

Right, and assumptions about octave equivalence being anything more than an artistic choice are wrong, so the whole thing falls apart. It's a theory based on a limited way of thinking, and a preference, not a law.

[xjscott]

Please consider posting your experience

Hi Ken. Although there's a finite number of reasonable mappings, there's an infinite number of combinations and interactions between these mappings and tuning systems. Given a tuning, many mappings will work well for it and highlight different features of the scale. This has obvious usefulness in performance and composition, as does the ability to pivot onto other mappings in real time while performing.

An interesting discovery is that mappings that seemed like an obviously good theoretical idea often are the least interesting musically, and other non-intuitive mappings often are far more useful and inspiring musically.

Let's take 88 cent equal temperament as an example. 88cET has fantastic subminor thirds (7/6), neutral thirds, supermajor thirds (9/7), fifths and harmonic sevenths (7/4). Thus it's obviously very well suited towards jazz and blues and other idioms that make use of the septimal intervals, and is more useful and interesting than 12 tone equal temperament which has fewer interesting harmonic resources.

In practice, the ability of the standard harmonic table layout when used with 12 equal to play major and minor root position triads with one finger is not really all that useful or interesting. From a playability standpoint, I find that the larger triangles formed by skipping a key and variations of it is a far better geometry to target for interesting base harmonies. This also leave spaces in between for alternate intervals and more things that can be done in intuitive geometrical structures. This all comes out wonderfully in practice. It's essential to actually do rather than talk about this. I could post diagrams all day long and people could talk about math and do analysis, and that would be wonderful for theoretical academic types, and yet actual experience shows it is all utterly useless and is demolished with even five minutes of working with the actual keys on a real instrument. This is why my Axis-64 is the greatest instrument ever! I have access to all these mappings to work with tunings, I can try and hear different ones in an instant (with my custom setup) and discover every day things that would never have been intuited from an analysis that was based on the broken principles and false assumptions of the typical academic paper.

Getting back to 88cET, a great layout is to have neutral thirds vertically, and 88 cent steps along one of the diagonals. Any diagonal works, lower left to upper right is probably the most obvious one, but others work great too and may help break free of acquired patterns once one gets used to the first one.

But that's not the only useful map. Also one can do fifths and sevenths as primary intervals, and even the harmonic table works very well for 88.

Rather than draw diagrams or try to convince any one with silently typewritten words about music (which are intrinsically useless by their very nature), I encourage everyone to get a Axis and start working with it, and the truths of music will reveal themselves to the ear.

[MusicScienceGuy]

The W/H layout is perhaps not perfect as the synoptic tuning articles assert.

For example. there's the problem of how to tune those pesky thirds - if you tune the thirds perfectly. then they don't quite line up with the Fifths: going up 2 perfect fifths (or a tempered fifth either) (then down an octave) just will not put one on the perfect third.

I have not bothered to argue the point. The W/H does allow more choices in tuning, since the sharps are separated from the flats. As more jammers are out, people will investigate the new world and find the useful points.

What I intend to try out One Day Real Soon, is to have the fifths perfectly tuned (about 1.89 semitones above equal temperment) and stretch the octave a bit - like on a piano (say 2-3 semitones). This should sound interesting, and not too awful.

Ken.

[JlMoriart]

Well, I read all of Bills papers there, and I know Bill and have followed his excellent work for decades. But that doesn't change what I said.

Bill's papers there were most for the support of the applicability of the other papers' principles, if you haven't read the others they most support my assertions.

Right, and assumptions about octave equivalence being anything more than an artistic choice are wrong, so the whole thing falls apart. It's a theory based on a limited way of thinking, and a preference, not a law.

The syntonic temperament, and the wicki/hayden layout based off of it, do not assume octave equivalence. If one chooses the octave vector/generator (alpha) to be a value other than 1200 cents and then lets the rest of the layout will still fall into place isomorphically, you even end up with a tuning that is far more consonant with certain timbres who's partials have stretched or shrunk octaves like some percussive instruments, the repeating element in its music being something other than a frequency's powers of two.

Like I said, I am arguing that the wicki/hayden layout is "superior" because the it is the only layout who's valid tuning range covers the entire tuning range of the syntonic temperament; it is the ideal and "true" layout *for the syntonic temperament.* Though not "all important", the syntonic temperament has been the most thoroughly explored temperament in human history, and very nearly the only one.

Given another temperament such as Magic or Hanson, the ideal and "true" layout becomes one who's two vectors that can define the entire layout are those that are the generators for that given temperament.

This of course assumes it is one's desire to have one's skills learned for a given musical interface to apply to the most musical possibilities. If this is not your goal, one could certainly argue the advantages of layouts that not only have very small valid tuning ranges (such as the bosanquet or fokker) but layouts that do not have fingering invariance across any existent temperament at all, like the harmonic table, due to its lack of consistency in vector location and differentiation between enharmonic equivalents' and their harmonic functions.

Also, the relation of the tonal relatedness of two notes as a function of their location in a stack of perfect fifths from a given tonic ties right into the wicki/hayden layout, which defines itself off of the fifth (as the beta generator), so that regardless of the size of your fifth and octave in cents (and therefor regardless of the tuning), all of the most tonally and harmonically related notes to a given tonic fall in a tight block around it. I IV V is right up the middle, then spreading out to the left and right you get pentatonic, diatonic, chromatic, and so on progressing through more and more MOS (moment of symmetry) scales.

Though yet to be fortified by practice, it seems very likely that the tonal relatedness of notes to a given tonic in other temperaments will be related to their location in the stack of that temperament's beta generator, be it the fifth (syntonic), or major/minor third (magic/hanson).

I'd be curious as to how you map your axis to play in 88 equal divisions and how difficult it is to play because, regardless of the benefits for harmonic timbres in just intervals, if it is too hard to play it is useless. Do you even retain isomorphism in mapping the axis to this tuning? Do you have any videos or explanations of how you do it?

Thanks!

John M

[notepool2]

Nice review !

I'm not sure I understand how you play it, but as a guitarist, the layout is nearly perfect for me - it's nearly the same process to learn/apply scales : learn the pattern. The hard things is to use both hand, and learn what polyphony truelly means.

I agree entirely with your point about the octave. For now it's "enough" to compose, but not to play - which was the goal of C-Thru, to play we have the 64 - I hope to get one someday.

No co-incidence that the sonome was invented by a guitarist!

[JlMoriart]

For example. there's the problem of how to tune those pesky thirds - if you tune the thirds perfectly. then they don't quite line up with the Fifths: going up 4 perfect fifths (or a tempered fifth either) (then down an octave) just will not put one on the perfect third.

Real quick correction Ken: tempering the fifth to 696.5, you do get the perfect third, right around where the keyboard would be tuned to 31-edo. In fact, you can end up with every basic just ratio somewhere along the syntonic temperament's tuning range. The minor third you get with a fifth of 694.6 cents and the perfect fifth you get around 702 cents.

John