Melodica I

This retuned melodica uses an 11-Limit JI scale that repeats at the 3:2 (perfect fifth).

Below I explain the tuning for this melodica and give full instructions on how to retune your own.

Tuning of Melodica I

The above chart shows the tuning of this melodica. The scale is 1/1–33/32–9/8–7/6–5/4–21/16–11/8 | 3/2.

More details below in next section.

3:2 Repeat Ratio: Perfect Fifth Cycle

The scale repeats at the perfect fifth (3:2), rather than the octave. The repeat ratio is the interval at which the scale repeats. Traditionally this is an octave (2:1). We are so accustomed to this repeat ratio that it is not usually questioned. Though I'm not the first of course. This 11-Limit scale allows for some overlap between each cycle, meaning some octaves on the keyboard are octaves (2:1), others are not. Since this is a melodic instrument, these differences do not get exposed in the same way they would in a harmonic (chord-making) instrument. Of course, some scales do not repeat at all, such as my 13-Limit Ombak Raincheck scale.

But why a 3:2 Repeat Ratio?

– To try it!

– There is a somewhat niche history of considering the "Tritave", the 3:1, as a repeat ratio. Check out Elaine Walker, Sevish, and Stephen Weigel's discussion on Now and Xen if you are curious how to pronounce "Tritave". Since the 3:1 is the next raw harmonic after 2:1, there is logic to have a repeating scale at this interval. If you play in parallel "12ths" (3:1), the upper pitch will always be a harmonic of the lower pitch. The Bohlen-Pierce Scale is probably the most famous example, though many others have been devised, including by the artists I just mentioned. So, the 3:2 is a related repeat ratio to the 3:1, cycling at the fifth rather than the twelfth.

– It relates to Extended Lydian (Do-Re-Mi-Fi), Extended Dorian (Do-Re-Me-Fa), Extended Phrygian (Do-Ra-Me-Fa), etc. which repeat at the perfect fifth. I 'invented' these scales in college, assuming others had likely devised similar or identical scales, though they were not widely known. Years later the Lydian version has been renamed by Jacob Collier something like "SuperHyperMegaMeta Lydian" or somesuch. These are 12-Tone Equal-Tempered phenomena which repeat at the 12TET perfect fifth 700 cents, not a perfect 3:2. Still it's related. I found beautiful harmonies this way including the "15th" (Sharp Root) as a high added tone in a Major9,#11 in my college days.

– Locally, wherever you are in the scale, you have intervals neighboring in either direction that are structurally significant, since you've built them into the tuning of the repeating scale. It's only when you leap more than a fifth that you encounter the spiraling effect on non-octave-repetition. Therefore, the melodica being a melodic instrument (though you can play a few pitches at once for a short breath) is well suited to this. It is possible to play with small intervals and move fluidly over the entire range while not noticing that there are differences in the tuning of some (not all) pitches related by octave. This can create a magical effect of unbounded tuning while taking no unusual steps. This could imbue a melody with a logic similar to the plots of dreams, where one event follows another, without being beholden to the original starting place.

Melodica I Tuning Analysis

In the notation above I've given the entire Melodica I scale with HEJI accidentals. The scale could continue above and below the range of this melodica.

I've shown ratios above several fundamentals (G, D, A, E, B) which are all related by 3:2 perfect fifths. This illustrates that one could work in a particular fundamental/key and include several pitches above and below the cycle which starts on that pitch class. Notice how the second cycle begins on D but we can analyze most of the entire scale in D if we choose. Indeed, as with all Just Intonation landscapes, we could analyze each pitch in relation to ANY fundamental or other pitch. I just limited the labels to those with simpler ratios.

Notice the inclusion of 8–9–10–11–12 in the cycle, so that each 'new' 8 is the 'old' 12 moving up the scale. This is an 11-Limit JI version of Extended Lydian (mentioned below as well). Similarly, there is a 7-Limit Extended Dorian of 1/1–9/8–7/6–21/16–3/2 repeating at the 3:2. There are spiraling major and minor pentatonics as well.

One way to describe its composition is 6–7–8–9–10–11–12–14 built on the same series of fundamentals but extended up and down by a fifth which are not fully seen in this range (C, G, D, A, E, B, F#). This accounts for all the pitches present except for the second scale degree which is a 33:32 above the starting pitch of each cycle. These pitches are simply the 11th harmonics of the following cycle (up a 3:2) moved down an octave. So, if we wanted to build the entire scale in this method we would simply need to move it up an octave (12–14–16... instead of 6–7–8...) and put the 11 below. So, the entire generating scale could be seen as 11–12–14–16–18–20–22–(24). This pivoting on 11 suggests an interesting mode that deserves exploration.

How to Retune a Melodica

This was my first metal reed retuning, and I learned a lot. The reeds are in the free reed family along with harmonica, accordion, concertina and harmoniums/pump organs. See my Orcoa and Padre instruments for more. The reeds are fixed at one side and work by interrupting the airflow as they vibrate back and forth over the opening.

To raise the pitch you want to allow them to vibrate faster, thus interrupting the airflow more often and creating a higher frequency. Therefore to tune them higher you want to remove material (metal in this case) on the vibrating end to give them less mass so they can vibrate faster.

To lower the pitch you want them to vibrate slower, creating a lower frequency. This is more difficult as any barber can attest. We can't glue on metal dust. Actually maybe you can, but I'll let you try that. So instead we want to remove material on the fixed end thus making their relative mass larger on the vibrating end compared to the fixed end. This does work, but does not change the pitch quite as much as removing from the vibrating end.

Keep in mind, there is only so much you can remove. One of the amazing things about metal free reeds is that they may keep their tuning for decades (or longer?). However, since the material is limited, it is likely you are committing the instrument to a final tuning for its lifespan using this method. Small tweaks can always be made, but it's best to have solid plan for your tuning in advance.

Be careful. These delicate reeds are only a few centimeters long and quite thin. I first took to them with a nail file and whoops, that took too much material off. This is not the case with thicker reeds like those on my Padre pump organ. But with melodica and harmonica reeds, they are so tiny that a few passes may change the pitch by a quite a bit. The higher (smaller) reeds are even more sensitive to this process.

Instead of a file, use light/medium (400-120 grit) sandpaper and hold a piece of thick paper under the reed. Lightly remove a bit of material at a time and then check the tuning. Repeat this process until in-tune. Be careful to follow the direction of the reed with the sandpaper (lengthwise) rather than side-to-side. Do not remove material from the sides of the reeds because it may not allow them to interrupt the airflow properly.

When choosing a tuning, err on the side of less alteration from its standard tuning. I would suggest designing a tuning that pushes each reed no further than a quartertone (half of a semitone/half-step) and if possible, raise more pitches than you lower, for the reasons given above. You can make revolutionary tunings that are wildly different than standard 12-Tone Equal Temperament while only moving each note a bit.

Another fantastic element of tuning these instruments is how accurate you can get the tuning: down to a few cents or less margin of error. However, it is one of the most time-intensive tuning processes because you need to reassemble the instrument each time you remove material in order to check tuning. Sure, you can flick the reed and get a rough idea of its pitch, but to really tell if it's in-tune, you need to put the casing back on and blow air through it. This means it can take quite a long time to tune.

Personally, I find the slow, meditative tuning process enjoyable. I hope you will too.

These instruments are inexpensive (especially used) and almost free to retune, all you need is a bit of sandpaper, some patience, and an idea of how you want to tune it. Have fun!