Conversion to 5-Limit Just Intonation

I created the following tuning for Hierophony, as mentioned above, but it is flexible enough to play many basic songs, even simple songs in many genres.  Both 12-Tone Equal Temperament (12TET, 12EDO) and Just Intonation use harmonies/chords that contain common tones.  Keep in mind that Just Intonation is a vast cosmos of harmony, so you may read one thing about it which is true and another that conflicts and is yet also true since it is not one tuning system, but rather an enormous category of tuning systems.  In this case, the 5-Limit Just Intonation that I'm using involves many familiar harmonies, so much so that the chords would be labelled with traditional roman numerals.

However, in Just Intonation, as we expand the web/lattice of pitches, and add more an more chords, we end up requiring more and more pitches, especially what we might call "different versions of the same note."  These multiple versions of a note are separated by commas, very small intervals.   One has the option of limiting their pitch set or scale to only 5, 7, 12, 30 or any number of pitches, or not limiting at all.  In my own work, their are songs that use 12 pitches, or 8, or dozens, even hundreds, depending on the context.  In the case we are considering with this autoharp, the amount of pitches needn't be limited to 12, per se, but it is necessary to keep the common tones as the "same version of a note."

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I began with the existing chords that were standard on this model of Autoharp.  I may have asked the question, "Is it possible to play all of these chords in 5-Limit Just Intonation?"  The answer is "Not Quite."  Furthermore, I believe that the Major-7th chord is more natural in 5-Limit music than the Dominant-7th chord that populates the traditional model.  There are Dominant-7th chords in 5-Limit, say 36:45:54:64, using 16/9 as the m7, but they are not as relevant or simple as the beautiful 8:10:12:15 Major-7th. 

 

Keys, Chords and Felts for Hjertmann 5-Limit Autoharp
 

I set out to find a 'felting' and tuning that allowed the following:
– Major-7ths replacing the Dominant-7ths

– Common tones shared between chords using the "same versions" of pitches

– As few changes other felt pad changes as possible

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Below you will see the 'Key/Felt Map' of the entire instrument.  It shows the tuning of the strings horizontally across the top and the chord labels on the left. 

 

Note that this is a transposing instrument.  It's keys are labelled in C Major with related chromatic chords, but the sounding pitches/chords (shown in HEJI, colored boxes) are about 150 cents lower.  As I've mentioned elsewhere on my site, I use 60Hz (B 1/2-Flat) for all of my Spiral Garden songs, and many other works.  This allows the transposed part for the autoharp player to read easily in the key of C, while sounding in B 1/2-Flat with the rest of the band.  The other reason for the transposition is that this instrument can be tuned up to C major and used to perform other music, keeping the 5-Limit tuning and design.  (You could tune it back to 12EDO, as well of course)

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The horizontal lines on the chart show felts that mute the strings labelled above when pressed down by the key (labelled on the left).  The 0's refer to the open strings which are not muted by that key, and thus are part of the chord.