Isomorphism

I wanted to shine some light on a concept employed in some musical instruments that is a great compositional tool.

The concept is isomorphism and the corresponding isomorphic instruments, that is, instruments that play with the same fingering in every key. This is attained by representing pitch in two dimensions as opposed to one like on a piano or clav. The best example out there is the Thummer which I really recommend you check out, specifically the "easier to learn" section of this website:

.: | Thumtronics - The new shape of music | :.

See how now all musical ideas like scales and chords can now viewed merely as combinations of intervals, which is what they really are, as opposed to certain combinations of deviations from our "all important" C major scale? Now that all keys are treated equal once one learns a musical idea, whether it be a mode, chord voicing, or melody, one now knows it in every key. This leads to new compositional tendencies and also allows you to modulate freely without having to dread playing in Gb, even if that is where your composition is leading you.

This theory of isomorphism has been around for a long time but never caught on because it was so hard to produce and lug around acoustic pianos with alternate layouts. Nowadays with technology it IS possible to create portable instruments with alternate layouts and these types of instruments are getting a lot more attention.

And need I mention that beyond composition, these instruments are GREAT for performance? Ergonomically they are easier to play without any sacrifice while offering new access to different musical ideas and possibilities.

Hope this gets some people interested :)

John M

Personally... that feels kinda dirty to me... Playing with fire type stuff. I mean, I don't have THAT much of a problem with it... but I feel like different keys are MEANT to be played differently. Like, how we have that whole thread on the usage of keys and how pointless it was to label them, but we also discovered that each key has a SLIGHTLY different feel. I would never want to take that away from the performer. It just wouldn't be the same. It's like when I accompany someone for an audition, I ALWAYS transpose by sight rather than letting my keyboard do it for me... I just feel wrong not doing it in the key that is being played.

Just me, I guess. lol.

I dunno.

The samples sound cheap; it looks to me like a MIDI accordion. And Isomorphism has been on string instruments for a while...

Personally... that feels kinda dirty to me... Playing with fire type stuff. I mean, I don't have THAT much of a problem with it... but I feel like different keys are MEANT to be played differently. Like, how we have that whole thread on the usage of keys and how pointless it was to label them, but we also discovered that each key has a SLIGHTLY different feel. I would never want to take that away from the performer. It just wouldn't be the same. It's like when I accompany someone for an audition, I ALWAYS transpose by sight rather than letting my keyboard do it for me... I just feel wrong not doing it in the key that is being played.

Just me, I guess. lol.

If you are talking about the thread on "how to use each key", I have responded to that but will put a similar response here as well.

If you are talking about "key color", or the different "sound" or "charactor" of every key, then all that is is an artifact of approxamating meantone tunings to one dimensional instruments such as the piano. Because tuning theory is TWO dimensional, when one attempts to apply them to a one dimensional pitch axis (piano) one is forced to approximate some of the pitches, giving some of the keys imperfect intervals, and giving every key a different amount of imperfection. That's all it was, different imperfections among keys that we could pick out and eventually recognize per key. This is not applicable in the least today when using 12 tone equal temperament, where this imperfection is spread across all keys so that none are terrible but none are perfect, and all are equal. In this case, or in an instrument with a two dimensional representation of pitch where you can play in all keys with the perfect intervals like the aformentioned thummer, all keys are the same.

There is obviously slight difference in pitch between keys, but 1. most people without perfect or relative pitch can hardly tell the difference and 2. people with perfect pitch can tell, but don't actually get different feelings or moods from different keys.

ALL KEYS ARE THE SAME.

If you are not talking about key color, then the only possible difference in feels among keys that you could be referring to comes from the ergonomics of your instrument. Pianists may play in F# and think anger or annoyance because it is harder to play and/or read in that key. This will likely even change ones compositional style per key, but will not effect anyones interpretation of the piece audibly, as long as you don't tell them what key it is in.

Once again, in 12-TET or other meantone tunings displayed on a two dimensional pitch axis:

ALL KEYS ARE THE SAME.

And, given that all keys are the same, an isomorphic instrument is ideal for learning to play as well as performing.

So, in spite of what almost any pianist will tell you, isomorphism is not cheating, or playing with fire, or "dirty". It is taking music theory and instead of convoluting it by displaying it as one "all important" C major scale and then displaying all other keys as deviations therefrom, it is displaying all keys as equal, which they are, and allowing music to be accessible to more than the elite few that are actually willing to put up with convolution of the piano and/or our notation system.

This is no dig on pianists. Congratulations to those that were able to overcome the immense ergonomic barriers of the instrument so that they could adequately express themselves.

It is a dig on the piano, which is unneccessarily difficult to learn because it displays all keys unequally, requires all keys to be learned and played differently with different fingerings, and requires a mindset to be developed where all keys are different and where they are all just deviations from our C major scale, even though there is no difference between F# and C.

I'm not saying that the piano isn't an ok compositional tool, because you will write very different things playing a piano than you would on the thummer or other 2-D instruments. But it is, no question, more limiting physically and mentally.

When you say you transpose by sight, do you mean you are unwilling to electronically transpose your keyboard because it sounds different, or you are unwilling to move your hands to a different key, because it feels wrong to play differently?

I dunno.

The samples sound cheap; it looks to me like a MIDI accordion. And Isomorphism has been on string instruments for a while...

Well the samples of this thing are as good as you let them be, depending on your sound bank, and considering they are electronic, they sound pretty darn good to me.

Regarding isomorphism on string instruments, they are close but not completely isomorphic. Because one attempts to rely on open strings for playing harmonies, or chords on a guitar, the possibilities for voicings are limited and are played differently per key. They have higher expressive potential, but are limited in that way.