Washburn 5-Limit Acoustic Gtr

Washburn 5-Limit Acoustic

Remember your first acoustic guitar? The one with which you recorded all your first tapes? You brought it into the music shop and they said it was "not worth saving," it "couldn't be fixed." They were wrong.

My song, Hierophony, heard on Spiral Garden's self-titled debut, interweaves the story of this guitar with other questions of feeling old and new, and the planned obsolescence of devices. (Scroll down to listen!)

As that song says, it was reborn into "The Keys to the Five," meaning 5-limit JI. So, it uses only harmonics/intervals with prime factors of 2, 3, and 5. Therefore, it's not so different from everything we know.
The 5-Limit reveals in nature some common favorite harmonies and progressions in JI, including The Major and Minor Triads, Major-7th Chords, Authentic and Plagal cadences, some Secondaries, some Borrowed Chords, Chromatic Mediants, and more. Tried and True. My old favorite the Augmented-Major-7th

As you can see in the pictures, this guitar contains more than just the obvious frets for 5-Limit. The more microtonal-looking frets involve 25's (5^2). These are the major thirds when the chord root is already a 5. For example, the first fret is 25/24. Hierophony, mentioned above is in E major, but moves to a Chromatic Mediant of G#. The third of that G# chord is B# which is a 25/16 above E. This fret is used to move the B string up from 3/2 (24) up to 25. 25's also give us the fifth of a 5-Limit Augmented chord in the same fashion. For reference, the interval of 25:24 is also the distance between the major and minor thirds in 5-Limit JI: 6/5 to 5/4, 8/5 to 5/3, etc.

The full fret-scale (ratios of the frets starting at 1/1) is: 1/1, 25/24, 16/15, 9/8, 6/5, 5/4, 32/25, 4/3, 45/32, 64/45, 25/16, 8/5, 5/3, 16/9, 15/8, 48/25. Notice this is fully-symmetrical up from 1/1 and down from 2/1.

The 5-Limit is quintuple-edged sword. Its pure and simple major and minor triads sound so sweet and familiar as vertical harmonies. Its horizontal harmonic progressions are so satisfying and time-tested. It launches us from the icy purity of the 3-limit into the vast, warm network of triadic harmony, encompassing not all music, but an incredible percentage of music from the last centuries, spreading geographically of late.

On the other hand, the 5-Limit has it's puzzles, snags, quirks, and thorns, as do all tuning systems. The problem of needing two versions of some common scale pitches is only the beginning. On this guitar, note that there is no 10/9 fret. And since it's a symmetrical fretting, it also doesn't have 9/5. Fine, no problem, we can get to these pitches with tuning choices of the strings. But the more tunings you try, the more trade-offs are necessary.

The very need for two "versions" of a pitch, like 10/9 and 9/8 in the first place is enough for some critics to throw in the towel. I read some guitarists take on it which amounted to "Just Intonation, wouldn't that be nice, unfortunately it doesn't work and is impossible on guitar." While of course they are wholly wrong. What they meant is "It's impossible for me to tune to 5-Limit JI and get all the pitches I could possibly want and all the progressions and chords I'm accustomed to in one tuning." This is a legitimate problem that I've run into as well. However, fortunately for my practices, I don't try to get one guitar to fulfill all my harmonic dreams. Rather, the limitations, as the saying goes, in some cases help me find freedom. Indeed, in each of the three songs featured below, there were chords and progressions that occurred to me along the way, which were not possible in the tuning I needed for other parts of the song, at least not with all voices of the chord occurring on the guitar. I tried many tunings. In some cases these issues were deal-breakers and I moved on to a different tuning to accommodate what I wanted to try. In other cases I found a different type of solution that did work on the tuning.

For me, harmonies, lyrics, melodies, keys, progressions, form, etc. all get intertwined in their needs as these songs slowly grow. The chord progression may think itself complete until the lyrics require a Bridge section, whose progression then might affect the tuning. This webbed pushing and pulling for me is enjoyable. And even though I sometimes doubt it will happen, my goal of finding the "quintessential version" of a song usually happens.

Below are some of the many possible tunings for this guitar, and a few audio examples from some of my songs.

Hierophony

Here is that song, which is about this instrument, and much more...

The guitar tuning is given below. It is an E Major 9 Chord when played open.

This song uses the aforementioned Chromatic Mediants of G# and C# major chords.

As with many of my tuning diagrams and scores you will notice a lot of half-flats. This is because I am using a base frequency of 60Hz (the frequency of A/C current, and thus the electrical hum in the US and many other places in the world). The pitch of 60Hz is B half-flat. You can ignore the half-flats on this chart for a simpler reading of the tuning.

The color coding groups pitches which are on the same 3-Limit "spine" in a lattice. In other words, they have the same basic accidentals (in the HEJI system I use) and are related by perfect fifth.

6b. Washburn Tuning 10 [E-G#-B-F#-B-D#].jpg

A View from the Trees

Here is a song begun in a treehouse and written about my son a few weeks before he was born.

The tuning for this song is given below. It is a G Major 7 (/D) based on the G that is a 5/4 below 60Hz, or an 8/5 above. Therefore 60Hz is the 5th harmonic in this key, whereas it was the 3rd harmonic in Hierophony.

I should mention that I have never used every fret on a guitar in a song before. Rather I usually limit the total pitch-classes ("notes") to much less, usually 12-24, sometimes more, sometimes less. However, I wanted to include the full tuning charts on this page, since they show the many possibilities of the tuning on this instrument.

26. A View...Washburn Tuning (all pitches).jpg

Ok, now that I've said I've never used every fret in a song before, that's probably gonna happen. Stay tuned.

432

The healing powers of the frequency of 432 Hz. Listen to the lyrics and you decide.
This is just a demo, real release to come later on.

69. 432 [3-15-25]Ben Hjertmann

00:00 / 03:19

This song uses the classic "Open-D" tuning known to guitarists, in 5-Limit JI. Again you can ignore the half-flats for simplicity. But notice that the 5th string and the first chord of the song are, indeed, tuned to 432Hz. It relates to both 60Hz and A440Hz.