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In the following video, Jordan Rudess from Dream Theater is reviewing the Axis-64 by C-thru-music. It's a keyboard/MIDI controller that uses a geometric harmonic table rather than a traditional keyboard.

@ ~3:40

He mentions that John Petrucci will write very pattern-based things on guitar that he then has to move to piano, "which is not pattern-based." I understand that the piano uses different fingerings for different scales, but I still see it very geometrically when I play. Then again, I was mostly self-taught and my first instrument was guitar. Do certain instruments or teaching traditions lend themselves to pattern and non-pattern based musical thinking? Or is there some other factor here that I'm missing?

Edit: The Axis-64's harmonic table for reference Harmonic Table

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I believe that when J. Rudess is referring to "pattern based" he is talking about describing musical phrases as a series of relative intervals, and then repeating those series of intervals from different starting pitches.

On a guitar this is straight forward to do by moving up and down the neck: play a particular passage, and then play the same arrangement of string/finger combinations again, but (for example) two frets further up the neck. The geometry of how/where the fingers are moving (relative to one another) is exactly the same, and the relative intervals between the notes is exactly the same. This is the defining feature of an "isometric keyboard" -- two keys with the same physical separation, produce two notes with the same intervallic separation.

In this sense the guitar is isomorphic in terms of moving up/down the neck, at least when no open strings are used. If it weren't for the major 3rd between the G and B strings, it would also be isomorphic to changes from string to string, which is why some people have tried "all fourths tuning" -- to make changes from one string to another the same pitch interval, for every string.

The Axis keyboard is explicitly designed to have the feature that no matter where you move around its surface, a given pitch interval always has the same spatial separation. This makes pattern based music, as defined above, more obvious.

Piano keyboards are not isomorphic in that as you change scales/keys, sometimes a given interval is between two white keys, and sometimes it is between a black and an white key (or the other combinations). The different physical offset of the black and white keys means you can't use the exact same physical fingering patterns to make the same intervals.

Some instruments that use isomorphic keyboard, and thus are likely to be suitable to this kind of pattern based music include

  • Essentially any grid-based MIDI controller (not just the Axis) could be made to be isometric, by appropriately assigning notes to keys -- but this Axis keyboard is explicitly designed with this in mind.

  • The Janko keyboard was an attempt to make an isomorphic piano that never took off,

  • More recently, there was failed effort to produce a new type of electronic instrument called thummer (or jammer) that never took off, but still has some DIY interest, and the dualo seems to be the most recent iteration of this idea

  • Some concertinas (Wicki-Hayden) and accordions (chromatic button accordions) use an isometric keyboard layout,

  • The harpejji is an isomorphic tapping instrument

One feature of pattern based playing (as defined above) is that for most phrases, and most shift intervals, you can easily get to distant (in terms of circle of fifths) keys, or imply chords that live in those distant keys. So this kind of approach is found in more artsy and conceptual music (in rock terms, progressive) and rarely used in more folk/traditional music (except for the truck driver key change).

  • There's the proper music term for "transposing a phrase, keeping the intervals exactly the same", but I can't remember what it is. Something like chromatic alteration maybe? – Dave Mar 19 '15 at 16:12
  • Is it term out of 12-tone technique? Or maybe a more classical form of embellishment? – Dan D Mar 19 '15 at 16:21
  • @DanDavis early classical, not 12 tone, sometimes a phrase/motif is repeated, transposed, but diatonically (Cmaj example: {c e g} => {d f a}) other times it is transposed chromatically (e.g. {c e g}=>{d f# a}) there's a term that distinguishes between these two. – Dave Mar 19 '15 at 16:27
  • The first one could be scalar or modal. If not, I don't believe I'm familiar with the term. – Dan D Mar 19 '15 at 16:32
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I assume he partly means that it's not Isomorphic (http://en.wikipedia.org/wiki/Isomorphic_keyboard). The guitar is not fully isomorphic either when tuned in a standard way due to the G-B interval being different to all the others, though you can use a different tuning with consistent string intervals.

I also think he may be noticing that the Axis and guitar are both two-dimensional, so that a 2-D pattern can appear, whereas the piano is basically linear, so patterns on the piano can't so easily be seen in terms of geometric shapes.

I'm not sure "pattern-based" is a suitably precise bit of vocabulary to use - the whole field of music theory is about finding patterns in music. You could argue that the piano is more pattern-based than the guitar as the piano is arranged around a particular pattern - that of the diatonic scale.

  • I had specifically taken "pattern-based" to mean geometric, but didn't specify that because I wasn't sure that that was Judess's intention. I'm almost sure he meant physical patterns, though, not conceptual ones. The Isomorphic idea makes a lot of sense judging by the emphasis that he puts on being able to move these patterns around. Dream Theater does this quite a bit with their riffs. – Dan D Mar 19 '15 at 15:59

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