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Tunings that use the “penchromatic” octave: IMPORTANT UPDATE

Posted: Sat Sep 16, 2017 3:02 pm
by IaNerd
NAME: This topic will not be about one tuning, but rather a new category of tunings which will share the “penchromatic” octave.

Various researchers have concluded that Western music heavily favors some keys over others. I could cite some of that research here, but like Jack Hammer, I don’t wanna.

Most Western songs are in these keys: G major, C major, D major, A major, A minor, E minor and B minor. To play in C major and A minor, one need not use any accidentals. To play in G major and E minor, one needs the F#. To play in D major and B minor, one needs the F# and the C#.

By extending this logic, we can see F# is, relatively speaking, the most useful accidental note in Western music, followed by C#. G# is next, and in last place are D# and A#.

Stay with me … this is going somewhere ….

We often think about harps in terms of being either “diatonic” or “slide chromatic”. Some non-sliding harps can be played in a fully chromatic way, but doing so typically requires the mastering of difficult bends and overblows. Many slide harps can be played fully chromatically with much greater ease, but the mechanics of the slider and the valves have their downsides.

Recently I began to ponder non-sliding harmonicas which are PURPOSEFULLY, NEARLY chromatic. Going by the research results described above, it seemed like we could omit one or two of the least useful accidentals and end up with a “diatonic” harp which can be played NEARLY chromatically. I looked for a tuning which met the following parameters:

A. No slider required.
B. All the notes of a chosen diatonic scale playable without bends.
C. No accidentals among the non-bending notes.
D. Only accidentals among the draw-bend notes.
E. The draw-bend notes need not cover all five accidentals.
F. The included draw-bend accidental notes will be those which are RELATIVELY the most useful in Western music.

WHEN/HOW: September of 2017. I have not yet have any made.


Once discovered, the solution proved to be a very simple one. The blow layer consists of the Dm7 chord, repeated to the left and right as needed. The draw layer consists of the Em7 chord, repeated to the left and right as needed. The omitted accidental will be G#/Ab. (I tried to get rid of the even less useful D# and A#, but couldn't make that work.)

As stated above, this will be a whole new CATEGORY of tunings that contain one or more of the penchromatic octaves. I will diagram a 10-hole harp as the first example of this model, based on the key of C major.

The blue line in the diagram shows one of four possible pathways to play the Cmaj diatonic scale for two octaves up and down the harp. The notes highlighted in bright blue are those of the minor hexatonic blues scale in G.


Re: Tunings that use the “penchromatic” octave

Posted: Sun Sep 17, 2017 5:07 pm
by IaNerd
I just noticed that I've made this SAME (although transposed) "penchromatic" octave before.

In another topic on this forum (see "Quasi-Circular (Modded Major Cross)"), channels 6-10 shows this same diatonic octave with the characteristic repeated supertonic note.

I arrived at this same octave through two different lines of inquiry: a case of convergent evolution. Mind blown.

Re: Tunings that use the “penchromatic” octave

Posted: Wed Sep 27, 2017 5:50 pm
by IaNerd
Some of my cousins to the south might say, "Well, butter my butt and call me a biscuit!"

In several topics on this forum I have used what I call the "penchromatic" octave. I actually arrived at this delightful octave at least twice, through different lines of inquiry. I am particularly proud of the analysis in this topic (above).

Recently another forum member--I'll call him Lark Lossinn--kindly informed me that he achieved penchromaticity some years ago. I have no reason to doubt this. Like pi and phi and e, something as cool as this octave is likely to turn up in many places by independent means.

Well, this morning when I reviewed Brendan Power's "Power Bender" tuning in my topic called "Diagrams of well-known tunings", I found the penchromatic octave right there in his channels 4-8. Then, looking back at my topic called "Richter-Penchromatic tuning for 10-hole 'diatonic' harp", I realized that my tuning there was identical to Power Bender EXCEPT FOR channels 9 and 10.

So I tip my hat to "Lark Lossinn", Brendan, and everyone else who has "discovered" or used the penchromatic octave. As I said at the beginning of this topic, I encourage folks to think of this not as "a" tuning but as a versatile modular component of myriad tunings.