Ben Hjertmann
Music Composition, Teaching, Recording, Instrument Building
HP43 (#1): Full 43-Tone Partch Tuning
After making Jeffrey Gavett's Partch Adapted Guitar I, to perform Harry Partch's Barstow, December, 1942, and new works by myself and others. HP43 (#1) is a custom fretted Yamaha classical guitar designed to perform the complete 43-tone Just Intonation system developed by Harry Partch. The instrument’s fretboard has a new custom fret layout that contains all 43 pitches of the scale across three octaves. Every fret position was calculated directly from the frequency ratios of Partch’s system, allowing performers to navigate the full tonal vocabulary of 43-tone Just Intonation on a standard tuned guitar.
The Goals of this Instrument
This guitar was designed to include all three of the following:
1) Standard tuning 3-Lim, either EADGBE or down a whole step to DGCFAD to align with Partch's G.
2) All Partch 43, 3 full octaves E-E (D-D if tuning down to Partch G).
3) All standard open chords and many but not all other chord shapes.
I am really excited about this standard tuning thing, especially for people who are both guitarists and theorists. You and I being composers and singers and more don't necessarily need standard tuning but for classical guitarists let's say, it sure is useful to already have everything mapped the same.
I may make others that are 2 of the 3 bullet points above, or even just one, all are interesting to me. This is obv a lot of frets/notes. There is a way to get all HP43 with less frets and sacrifice open chord shapes. But imagine playing a guitar that sounds in G, has a boatload of frets and can make a C chord shape but *whoops* one of the strings doesn't have the fret you need. That's one reason I like this.
However, another very useful and more obvious thing to do would be to keep the standard tuning and HP43 as a basis, but not try to get every pitch in every octave. That would work great. but this is nice because I can play the full utonal and otonal hexatonic scales in the full range.
I do respect and appreciate the difference between tiny frets where you rock the same finger over them to tune vs. beefier frets that you can play normally. These are very different, and the music written for them should be too.
Standard Tuning in 3-Limit JI
The open strings are tuned in a 3-Limit JI standard tuning: EADGBE, but tuned down a whole step to match Partch's home 1/1 of G. So the sounding pitches of the open atrings are DACFAD. For ease of the player and discussion of the instrument, I will mostly reference the transposed/written tuning of EADGBE. A player can also tune it that way and have all of Partch's 43 tone system in A instead of G if desired.
The 3-Limit adjustment from 12edo is slight.
The A (or sounding G if tuning down to Partch) string is tuned to A440 (+/- 0 cents, or down to G), the E strings are +2 cents, the A string +4 cents, the C string -2 cents, and the F string is -4 cents. This creates a fully integrated 3-limit Just Intonation framework while preserving much of the physical logic and playability of the standard guitar.
Complete Harry Partch 43-Tone Scale
HP43 (#1) is a custom-refretted Yamaha classical guitar designed to perform the complete 43-tone Just Intonation system developed by Harry Partch. The instrument’s fretboard has a new custom fret layout that contains all 43 pitches of the scale across three octaves. Every fret position was calculated directly from the frequency ratios of Partch’s system, allowing performers to navigate the full tonal vocabulary of 43-tone Just Intonation on a standard tuned guitar.
Fret System
Unlike conventional guitars, whose fret positions are derived from equal temperament, the HP43’s fret locations are calculated directly from whole-number frequency ratios. The result is an instrument capable of producing acoustically pure intervals throughout the 43-tone system. Players can move seamlessly between familiar harmonic structures and the rich microtonal resources of Just Intonation without abandoning established guitar technique.
The HP43 was conceived as both a performance instrument and a practical bridge between conventional guitar playing and the expansive harmonic world explored by Harry Partch. By combining a familiar six-string format with access to all 43 tones of the scale, the instrument offers performers a direct and intuitive path into one of the most comprehensive Just Intonation systems ever developed.
Open and Familiar Chord Shapes
Because the instrument retains a familiar intervallic layout, many conventional guitar shapes remain recognizable. Major chords, minor chords, dominant sevenths, major sevenths, minor sevenths, suspended chords, diminished chords, augmented chords, and extended harmonies can all be performed using fingerings closely related to those used on a standard guitar. At the same time, the expanded fret system allows access to the numerous additional intervals and harmonic relationships found within Partch’s 43-tone scale.
One essential design element is that each Otontality (rooted on each Udentity 1/1,3,5,7,9,11) are located where the 1/X is on the fretboard. So, if you want to play an Otonal 8-16/11 (no 13 of course) you go to the 16//11 location (fret 6.5) and there are all the pitches you need within reach. Many are located elsewhere too. This element is
