A bunch of different tunings that make traditional scales like Hirajoshi pop, plus some tunings that didn’t work, too — a summary of Western hobbyist Budjarn Lambeth’s tuning misadventures
If you’ve ever played around with Japanese scales — Hirajoshi, Akebono, Kokin-Joshi, Min’yo — you probably discovered them by default in standard Western tuning: twelve equal notes per octave, each semitone an identical 100 cents apart. It works fine. But did you know that this tuning system, called 12-tone equal temperament (12-TET), was basically imposed on Japanese music relatively recently, and that the notes in those scales may actually sing differently under other tuning systems?
A xenharmonic wiki contributor named Budjarn Lambeth has been experimenting with exactly this, and their write-up is a fascinating rabbit hole for any musician curious about how tuning affects feel. This article walks through their findings — what worked beautifully, what fell flat, and why — with some historical context along the way.
First: How were Japanese scales actually tuned before 12-TET?
Before we dive into Budjarn’s experiments, let’s clear up a common misconception: Japanese traditional music was not always tuned the way you hear it today.
The 13-string koto, the fretless shamisen, and the bamboo shakuhachi flute were all instruments capable of flexible, expressive intonation. Strings could be bent, lip pressure on a flute could alter pitch, and the movable bridges of the koto meant each performance could be tuned by ear according to natural, resonant intervals. Fretted instruments were not part of the core classical tradition — which meant performers weren’t locked into fixed pitches the way a piano is.
Historically, Japanese court music (gagaku) drew on a Chinese-influenced 12-pitch system derived from stacking pure perfect fifths — essentially Pythagorean tuning, the same ancient system used in medieval Europe. The famous scales of the Edo period, including the koto tunings like Hirajoshi (also called Kata-Kumoi), emerged from indigenous Japanese tonal sensibilities that evolved during Japan’s period of deliberate isolation. These scales weren’t designed around equal temperament — they predate it in Japan by centuries.
12-TET effectively arrived with the Meiji period in the late 1800s, when Western music was adopted and promoted aggressively as part of Japan’s modernisation. Traditional Japanese music was actually suppressed during this era; Western theory was taught in schools while traditional forms were pushed to the margins. The pitch compromises of 12-TET — which deliberately tunes every interval slightly “wrong” so that every key sounds equally okay — were not native to the tradition. One shakuhachi scholar, Justin Senryū, notes that 12-TET is “definitively out of tune” for the characteristic meri (lowered) notes of traditional shakuhachi music, which sit roughly 25 cents flatter than the nearest 12-TET pitch.
So when you play a Hirajoshi scale on a standard-tuned piano or a digital synth set to 12-TET, you’re already using a foreign tuning system. The question is: is there a better one?
What is a tuning system, really? (A quick explainer for the uninitiated)
If you know what cents and intervals are, feel free to skip this section.
A “tuning system” or “temperament” is simply the set of precise pitch relationships you use when dividing the octave. The octave itself (a 2:1 frequency ratio) is the one constant that almost every culture agrees on. But how you divide it up — how you space the notes in between — is where tuning theory gets interesting.
In 12-TET, you divide the octave into exactly 12 equal parts, each 100 cents wide (a cent is one hundredth of a semitone, a tiny unit of measurement used in tuning). The great advantage is uniformity: every key sounds the same, and you can play in any key without retuning.
The disadvantage is that those 12 equal steps are mathematical compromises. A pure perfect fifth (the interval from C to G, say), derived from nature’s own harmonic series, is about 702 cents. In 12-TET it’s 700 cents — close, but not quite. A pure major third is about 386 cents; in 12-TET it’s 400 cents, noticeably wider. To your ears, pure intervals have a smooth, resonant quality. Tempered ones can have a subtle beating or tension.
Different tuning systems make different trade-offs. Some push the fifths wider or narrower than 12-TET. Some aren’t based on equal division at all. Budjarn’s experiments cover several of these alternatives applied specifically to Japanese pentatonic scales.
The scales in question
Budjarn’s experiments cover eleven Japanese pentatonic scales, all of which are five-note scales built from a small set of interval patterns. The most important ones to know are:
Hirajoshi (also called Kata-Kumoi): This is the scale most people think of when they hear “Japanese music.” It has a distinctive minor-second-heavy sound. In 12-TET the notes are spaced (in semitones from the root): 2, 1, 4, 1, 4. Its haunting character comes from those close minor-second steps sitting beside wide gaps.
Akebono I and II: Relatives of Hirajoshi, used in folk and koto music. “Akebono” means “dawn” in Japanese.
Kokin-Joshi: Another koto-derived scale, with a slightly different flavour.
Min’yo (also called the minor pentatonic): Probably already familiar to you — it’s the “blues scale” basis used worldwide. In Japan it’s called Min’yo and is used in folk music.
Iwato: A more unusual scale, very dark and sparse-sounding, named after a cave in Japanese mythology.
There are also rotations of these scales — starting the same pattern from a different note — that produce different emotional colours while using the same underlying pitches.
The tunings Budjarn loved
Meantone temperaments (especially 55-EDO and 43-EDO)
Meantone temperament is the family of tunings that dominated European music from roughly the 1500s to the 1700s — the era of Renaissance and Baroque keyboard music, before 12-TET won out. The defining feature of meantone is that the fifth is tuned slightly flatter than the pure 702 cents, in order to make the major third (four fifths stacked up) land close to the pure, resonant 386 cents rather than the 400-cent third of 12-TET.
There’s a whole family of meantone tunings depending on exactly how much you flatten the fifth. The famous quarter-comma meantone (used on historical harpsichords) flattens the fifth to about 697 cents and produces an exquisitely pure major third. Other variants include 1/5-comma, 1/6-comma, and so on.
What Budjarn found — and this is the surprising finding at the heart of their write-up — is that these Renaissance-era European tunings actually sound wonderful with Japanese pentatonic scales. Their top picks are:
- 55-EDO (~1/6-comma meantone): Divides the octave into 55 equal steps. The fifth is about 698 cents. Budjarn calls this one of the best-sounding overall.
- 2/11-comma meantone: A specific “comma fraction” meantone sitting between quarter-comma and 1/5-comma.
- 98-EDO and 43-EDO (~1/5-comma meantone): Also top-tier picks.
What’s EDO? EDO stands for Equal Division of the Octave. 12-EDO is what you know as standard tuning. 55-EDO has 55 equally spaced notes per octave. You don’t have to use all 55 — you just pick five of them for your pentatonic scale, but they happen to fall in the sweet spots that meantone theory predicts.
Why do meantone tunings work so well here? Budjarn doesn’t spell out a full theoretical explanation, but the intuition isn’t hard to find. Hirajoshi and its relatives are built from perfect fifths and minor thirds — the exact intervals that meantone is designed to optimise. When you tune those intervals smoothly and purely, the scales ring with a clarity that 12-TET’s compromises slightly muddy.
Budjarn also notes that for all these meantone tunings, their favourite tonic pitch is somewhere between 100 and 120 Hz (that’s around G#/Ab through Bb, a register that’s quite low for a melody instrument), and their favourite timbre is a koto-like “piano” aperiodic sound with a percussive envelope and moderate reverb.
Other good-but-not-top-tier meantone options include anything with a fifth between 697 and 701 cents — which covers 74-EDO, 43-EDO, 67-EDO, 79-EDO, 91-EDO, and even 12-EDO itself (which lives right at the top of this range). Yes, 12-TET counts as a meantone tuning; it’s just not the best one.
Undecental and Leapday tunings (70-EDO, 99-EDO, 29-EDO)
These are more exotic. Leapday is a temperament where the fifth is tuned sharper than pure (about 704 cents), the opposite direction from meantone. This gives a completely different harmonic character. Where meantone emphasises the “5-limit” world of pure thirds, leapday emphasises the 7-, 11-, and 13-limit — higher harmonics that produce unusual, otherworldly consonances.
Budjarn found that leapday tunings close to 29-EDO also work beautifully, but for a different reason than meantone: instead of functioning as 5-limit scales (scales built from pure thirds and fifths), they’re interpreted as no-5s 13-limit scales — meaning the pure major third disappears from the picture entirely, and instead the scales resonate through a web of higher harmonic relationships involving the 7th, 11th, and 13th harmonics. The result apparently has no “wolf intervals” (those clashing, out-of-tune moments that plague some tunings when the circle of fifths doesn’t close neatly).
Similarly, undecental tunings — centred around the 11th harmonic — apply this approach, giving the scales a more complex, floating harmonic character.
Over-2 Primodality (Just Intonation)
Primodality is a Just Intonation approach developed by composer Zhea Erose. “Just Intonation” (JI) means using exact integer frequency ratios rather than equal temperament approximations — the mathematical ideals that the harmonic series itself suggests.
“Over-2” primodality means taking the tonic as the 2nd harmonic (i.e., treating the octave itself as the anchor) and building the scale from ratios based on small multiples of 2. In practice this means notes like 34/32, 36/32, 38/32, 40/32, 43/32, 48/32, 51/32, 54/32, 57/32 — fractions whose denominators are all powers of 2, creating a particular blended “gestalt” quality.
Budjarn lists specific Over-2 JI tunings for all eleven scales, and this represents the most harmonically pure version of the experiment — no equal divisions, just raw ratios.
The tunings Budjarn didn’t like — and why
This section is just as valuable as the successes, because the reasoning is instructive.
Pythagorean tuning and similar systems (schismic, garibaldi, 53-EDO, 41-EDO, 65-EDO): These use pure or near-pure fifths of ~702 cents, which produces very accurate fifths but wide, harsh major thirds (~408 cents). Budjarn found these suffered from too many “wolf intervals between intervals” — that is, the intervals in the scale interacted badly with each other. This parallels the historical critique of Pythagorean tuning for polyphonic music: it’s great for fifths and fourths, ugly for thirds.
It’s ironic that Pythagorean tuning was the dominant European system before meantone, and also arguably the closest historical parallel to ancient Japanese court tuning (derived from stacked fifths). Yet for these specific scales, Budjarn finds it doesn’t sound good.
Flat meantone tunings (31-EDO, quarter-comma, 50-EDO, 1/3-comma): Here the fifth is narrowed more aggressively, below about 696 cents. The problem is that some of the tritone intervals (augmented fourths / diminished fifths) end up slightly sharper than the pure 10/7 ratio (~617 cents), and to Budjarn’s ears those tritones sound “unbearably bitter.” This is a subjective call — many people love 31-EDO for its warm, mellow quality — but for the specific emotional character of Japanese pentatonics, those sharp tritones clash with the scales’ aesthetic.
Standard 5-limit Just Intonation: This is the most “obvious” approach — tune every interval as a simple fraction, keep everything in the 5-limit (ratios involving only 2, 3, and 5). The result has too many wolf intervals: places where intervals that should sound consistent instead clash, because pure JI doesn’t close into a tidy octave without compromises.
Leapday tunings close to 46-EDO: The 10/7 tritone gets too sharp again, producing the same bitterness as the flat meantone tunings, but from the opposite direction on the tuning spectrum.
Comparing all this to historical Japanese tuning
So how do these experimental findings relate to how Japanese music was actually tuned before 12-TET arrived?
The honest answer is: we don’t know precisely. Pre-modern Japanese instruments like the koto and shamisen were tuned by ear to resonant, natural-sounding intervals — which in practice approximates Just Intonation in whatever form the performer’s ear found pleasing. There were no strict theoretical prescriptions equivalent to European meantone theory. The flexibility was built in; the shamisen’s fretless neck and the koto’s movable bridges meant pitch was always somewhat performer-dependent.
What we can say is:
- Pythagorean tuning (the theoretical basis of ancient East Asian court music) would have been the formal theoretical framework, but in practice the fretless/unfretted instruments drifted toward whatever sounded natural — often closer to 5-limit JI for individual intervals.
- 12-TET was not native to the tradition. It arrived with Meiji-era Westernisation, and scholars of traditional Japanese music consider it a poor fit, especially for the characteristic subtle lowerings and inflections that define the style.
- Budjarn’s meantone findings are interesting precisely because meantone — while a European invention — produces the major thirds and minor thirds that sound the smoothest to ears trained on harmonic resonance. The instruments used by Edo-period performers would naturally have gravitated toward those resonant intervals when tuning by ear, even without any theoretical framework. So meantone might capture something real about what these scales were “meant” to sound like, even though it was never used in Japan explicitly.
- Primodal JI is perhaps the most theoretically honest approach: use exact ratios, let the scale breathe with pure intervals, and accept that you’re not trying to approximate some Western equal-tempered standard.
- The microtonal tradition is real: Traditional Japanese music genuinely employed microtones — pitches between the 12-TET notes — as expressive tools. The “meri” (lowered) notes of shakuhachi are one example; the string-bending of the koto is another. So the xenharmonic exploration Budjarn is doing has some genuine cultural resonance, even if the specific tuning systems chosen are Western in origin.
How to try this yourself
If you want to experiment with these tunings, a free piece of software called Scale Workshop (available at scaleworkshop.plainsound.org) lets you build and play scales in any tuning system, including all the EDOs and JI ratios mentioned here. Budjarn specifically mentions the Scale Workshop “piano” aperiodic timbre with a percussive (medium) envelope and moderate reverb as their preferred sound — they describe it as reminiscent of a koto.
For a starting point, try 55-EDO with the Hirajoshi scale at degree positions 9, 14, 32, 37, 55 (those are the five notes out of 55, returning to the octave at step 55). Play the root around 110 Hz (A2 or nearby) for the effect Budjarn prefers. Then compare the same scale in 12-TET and notice the difference in how the intervals lock into each other.
If you want to go deeper into xenharmonic theory, the Xenharmonic Wiki is an extraordinary community resource. Relevant articles include:
Budjarn’s original page (with the full tables of scale degrees for every tuning) is at: https://en.xen.wiki/w/User:BudjarnLambeth/Some_tunings_for_Japanese_scales
A quick summary for the busy musician
If you want the take-home list, here it is:
Try these (Budjarn’s favourites): 55-EDO, 43-EDO, 98-EDO, and 2/11-comma meantone. More broadly, any meantone with a fifth between 697 and 701 cents works well — that includes 74, 67, 79, and 91-EDO. For something more exotic, try 29-EDO (leapday family) or Over-2 Just Intonation.
Avoid these: Quarter-comma meantone (too flat), 31-EDO (too flat), Pythagorean / 53-EDO (too many wolves), standard 5-limit JI (wolf problems), and leapday tunings near 46-EDO (too sharp tritones).
Even 12-TET is technically a meantone tuning, just not the best one for this job — it lands at the sharp end of the acceptable range, where the fifths are almost Pythagorean, and the scales work but don’t sing as richly as they could.
These are one person’s subjective findings, and Budjarn is explicit about that: the write-up is framed as personal opinion throughout. But they’re an unusually thoughtful set of opinions, backed up by a huge amount of listening across a wide range of tuning systems. For any musician who loves Japanese scales and wonders if there might be a richer, more resonant way to tune them — this is an excellent place to start.
Sources: Budjarn Lambeth’s Xenharmonic Wiki page “Some tunings for Japanese scales” (last edited November 2025); Xenharmonic Wiki articles on Meantone, Leapday, and Primodality; Britannica on Japanese music and koto tuning; Justin Senryū’s analysis of shakuhachi temperament and traditional scale tuning (senryushakuhachi.com).
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