An interview with Copilot about instruments with inharmonic partials (overtones) - useful for anyone wanting to understand timbre
Which musical instruments have inharmonic partials? For each of those instruments, which ones have stretched partials (ie further apart than the harmonic series), which ones have compressed partials (ie closer together than the harmonic series), and are there any that deviate completely from the shape of the harmonic series and have some totally different set of partials altogether?
Musical instruments are far more diverse in their overtone structures than most people realize. Many do not follow the harmonic series exactly, and some deviate so strongly that their partials form an entirely different pattern. Let’s map out the landscape in a clean, structured way.
🎼 Instruments With Inharmonic Partials
Below is a categorized overview of instruments whose partials deviate from the harmonic series, along with whether their partials are stretched, compressed, or non‑harmonic in a completely different pattern.
🥁 Percussion (Membranes, Bars, Plates)
These are the champions of inharmonicity.
1. Timpani
Partials: Weakly inharmonic but tuned to approximate harmonicity
Pattern: The lowest modes are near 1:2:3:4 but not exact
Type: Slightly compressed (partials lie a bit below harmonic positions)
2. Snare Drum / Tom / Bass Drum
Partials: Strongly inharmonic
Pattern: Membrane modes follow Bessel-function roots (e.g., 1.59, 2.14, 2.30, 2.65…)
Type: Neither stretched nor compressed — they follow a completely different mathematical pattern
3. Steelpan
Partials: Tuned by hammering to approximate harmonicity
Type: Slightly compressed, but varies by note and maker
4. Glockenspiel, Xylophone, Marimba
Partials: Inharmonic due to bar stiffness
Pattern: First few partials often around 1:3.9:9.6… (varies by bar shape)
Type: Strongly stretched (partials lie above harmonic positions)
5. Vibraphone
Partials: Similar to marimba but tuned to be closer to harmonic
Type: Mildly stretched
6. Cymbals, Gongs, Tam-tams
Partials: Wildly inharmonic
Pattern: No harmonic structure at all; chaotic plate modes
Type: Completely non-harmonic — no meaningful “stretched/compressed” comparison
🎹 Pianos
Partials: Inharmonic due to string stiffness
Pattern: Partial frequencies follow approximately
where is the inharmonicity coefficient
Type: Stretched — higher partials are increasingly sharp
Consequence: Piano tunings use “stretch tuning” to compensate
🎻 Bowed Strings (Violin, Viola, Cello, Bass)
Partials: Nearly harmonic, but with slight inharmonicity from stiffness
Type: Very slightly stretched
Notes:
Higher strings (e.g., violin E string) show more stretching
Lower strings (e.g., bass) are closer to ideal harmonicity
🎸 Plucked Strings (Guitar, Harp, Banjo, etc.)
Partials: Slightly inharmonic
Type: Mildly stretched
Special cases:
Banjo has more inharmonicity due to membrane coupling
Electric guitar pickups emphasize certain partials, making inharmonicity more audible
🎷 Wind Instruments
Most wind instruments are very close to harmonic, but there are exceptions.
1. Brass (Trumpet, Trombone, Tuba, Horn)
Partials: Nearly harmonic, but bell flare causes:
Lower partials: compressed (slightly flat)
Higher partials: stretched (slightly sharp)
Type: Mixed — but overall slightly stretched
2. Woodwinds
Flute: Almost perfectly harmonic
Clarinet: Odd harmonics dominate; slight inharmonicity from tone holes
Oboe/Bassoon: Slightly inharmonic due to conical bore imperfections
Type: Generally very close to harmonic, with tiny deviations
🎤 Human Voice
Partials: Nearly harmonic
Type: Slightly stretched at high intensities due to vocal fold tension
Special case: Some vocal techniques (e.g., throat singing) introduce non-harmonic components
🧭 Summary Table
| Instrument Type | Harmonic? | Stretched? | Compressed? | Completely Non-Harmonic? |
|---|---|---|---|---|
| Piano | No | Yes | No | No |
| Violin/Cello | Almost | Slightly | No | No |
| Guitar/Harp | Almost | Slightly | No | No |
| Brass | Almost | Slightly (upper) | Slightly (lower) | No |
| Woodwinds | Nearly | Very slight | Very slight | No |
| Timpani | Approximate | No | Slightly | No |
| Xylophone/Marimba | No | Yes | No | No |
| Cymbals/Gongs | No | No | No | Yes |
| Drums (membranes) | No | No | No | Yes |
🎯 Final Thoughts
So to answer your last question directly:
Yes — many instruments deviate completely from the harmonic series.
These include:
Cymbals
Gongs
Tam-tams
Snare/tom/bass drums
Any vibrating plate or membrane
Their partials follow entirely different mathematical families (Bessel modes, plate modes) and cannot be described as stretched or compressed versions of the harmonic series.
If you want, I can also map out why stiffness causes stretching, or show graphs of partial patterns for different instruments.
Gamelan acoustics are one of those topics where the deeper you look, the more fascinating (and less “Western‑instrument‑like”) things become. Indonesian instrument makers have been shaping inharmonic spectra for centuries, and modern acousticians have spent a surprising amount of time trying to measure and understand them.
Below is a clear, structured picture of what we know.
🎶 Overview: Gamelan Partials Are DeliberatelyInharmonic
Across Java, Bali, Sunda, and other regions, gamelan instruments do not aim for harmonic partials. Instead, their spectra are shaped to produce characteristic timbres and to reinforce the tuning systems (sléndro and pélog).
But the type of inharmonicity varies strongly by instrument and region.
🥁 Metallophones (Saron, Gender, Slenthem, Demung, Peking)
These are the core “bar” instruments of gamelan.
Spectral Pattern
Their partials follow the physics of stiff metal bars, not strings or air columns.
This produces strongly stretched partials.
Typical partial ratios for a rectangular bar are around:
(varies with bar shape, undercutting, and material)
Regional Variation
Central Javanese gamelan: bars are often undercut to reduce inharmonicity slightly, but still far from harmonic.
Balinese gamelan: bars are intentionally tuned to emphasize beating between paired instruments (ombak), so partials are often more stretched and more irregular.
Research
Yes—quite a lot. Key researchers include:
Wayne B. Morrison & John R. Pierce (classic studies on bar inharmonicity)
Andrew McGraw, Michael Tenzer, William Sethares (spectral analysis and tuning)
UCLA and MIT acoustics labs have published detailed measurements
🔔 Gongs (Gong Ageng, Kempul, Kenong, Kethuk)
Gongs are the most complex acoustically.
Spectral Pattern
Large Javanese gongs have quasi-harmonic low partials:
Often something like
But the pattern is not a stretched or compressed harmonic series.
Instead, they follow vibrational modes of circular plates with a raised boss, which produce:
Some near-harmonic relationships
Some wildly inharmonic modes
Strong regional and maker-specific variation
Regional Variation
Javanese gong ageng: more controlled, stable partials; makers aim for a deep, slow “wah” beating.
Balinese gongs: brighter, more complex spectra; often more inharmonic.
Research
Extensive measurements by Fletcher & Rossing, Sethares, and Indonesian acousticians.
Gong acoustics are a major topic in ethnomusicology.
🥁 Bonang (Kettle Gongs)
Bonang pots are small bossed gongs arranged in rows.
Spectral Pattern
Highly inharmonic, but with some partials intentionally tuned to reinforce the scale degrees.
Makers adjust the boss height and wall thickness to shape partials.
Regional Variation
Balinese bonang-like instruments (reyong) have even more complex spectra due to paired tuning.
🎼 Rebab, Suling, and Vocals
These are the non-metal parts of the ensemble.
Rebab (bowed spike fiddle): nearly harmonic partials, like other bowed strings.
Suling (bamboo flute): nearly harmonic.
Vocals: harmonic.
These contrast intentionally with the inharmonic metallophones.
🧭 Summary Table
| Instrument | Harmonic? | Stretched? | Compressed? | Completely Inharmonic? | Notes |
|---|---|---|---|---|---|
| Saron / Gender / Slenthem | No | Yes | No | Partially | Stiff bar modes |
| Bonang | No | Mixed | Mixed | Yes | Bossed gong modes |
| Gong Ageng | No | Mixed | Mixed | Yes | Some near-harmonic low modes |
| Kempul / Kenong | No | Mixed | Mixed | Yes | Complex plate modes |
| Rebab | Yes-ish | Slight | No | No | Bowed string |
| Suling | Yes | No | No | No | Air column |
| Vocals | Yes | Slight | No | No | Human voice |
📚 Has There Been Much Research?
Yes—gamelan acoustics is one of the most studied non-Western instrument families. Major contributors include:
Fletcher & Rossing – The Physics of Musical Instruments (detailed gong and bar measurements)
William Sethares – spectral tuning and inharmonicity analysis
Andrew McGraw, Michael Tenzer – ethnomusicological acoustics
UCLA Gamelan Research Group
Numerous Indonesian researchers from ISI Surakarta, ISI Yogyakarta, and Udayana University
There are dozens of published spectral analyses, especially of Balinese instruments.
🎤 If you want, I can also map out how gamelan tuning systems (sléndro/pélog) interact with these inharmonic partials.
Gamelan tuning and gamelan acoustics are deeply intertwined. The tuning systems don’t just sit on top of the instruments — they emerge from, reinforce, and are shaped by the inharmonic partials of the instruments themselves. This is one of the reasons gamelan music sounds so unlike Western ensembles: the tuning and the timbre are co‑designed.
Below is a clear map of how this interaction works.
🎼 1. The Core Idea: Gamelan scales are built to sound good with inharmonic spectra
Western tuning systems assume harmonic partials (1:2:3:4…). Gamelan instruments do not have harmonic partials — especially the metallophones and gongs.
So instead of forcing the instruments to match a theoretical scale, Indonesian makers historically shaped the scale to fit the timbre.
This is why sléndro and pélog vary from ensemble to ensemble: the tuning is optimized for the specific partials of that set of instruments.
🥁 2. Metallophone partials shape the tuning of sléndro and pélog
Metallophones (saron, gender, demung, peking, slenthem) have strongly stretched partials because they are stiff metal bars.
Typical bar partials look like:
These are nowhere near harmonic. But here’s the key: the second partial (≈2.7× fundamental) often lies near a musically meaningful interval.
For example:
2.7× ≈ 2.7/2 = 1.35 octaves above the fundamental
1.35 octaves ≈ 14 semitones (a major seventh)
In many gamelan tunings, one of the scale degrees sits near this region. Makers exploit this by adjusting bar shape so that the partials reinforce specific scale tones.
Result:
Sléndro and pélog intervals are chosen partly to minimize roughness between:
fundamentals of one note
partials of another note
This is exactly the kind of analysis William Sethares formalized in his work on “tuning–timbre matching.”
🔔 3. Gongs reinforce the tonal centers of the tuning
Large Javanese gongs (gong ageng, kempul, kenong) have complex spectra, but their lowest modes often cluster around near-harmonic relationships:
1 : 2 : ~2.8 : 4 : ~5.2
The near‑octave and near‑fifth relationships help the gong ageng act as a tonic marker.
How tuning interacts with gong partials:
The gong ageng’s lowest partials define the “home” pitch.
Other instruments are tuned so that their fundamentals and partials avoid clashing with the gong’s strongest modes.
This is why the gong ageng is the reference point for tuning an entire gamelan.
Balinese gongs, with brighter and more inharmonic spectra, push the tuning toward more brilliant, beating-rich intervals.
🥣 4. Bonang (kettle gongs) shape the contour of the scale
Bonang pots have partials that are:
highly inharmonic
strongly influenced by boss height and wall thickness
intentionally shaped to reinforce certain scale degrees
Makers often tune the bonang first, then tune the metallophones to match the bonang’s spectral “landscape.”
Why?
Because the bonang:
articulates melodic patterns
outlines the scale
has partials that strongly color the tuning
So the tuning system is literally built around the bonang’s inharmonicity.
🌊 5. Balinese ombak (paired tuning) interacts with partials
Balinese gamelan instruments come in male–female pairs tuned slightly apart to create ombak (waves/beating).
This beating happens not just between fundamentals but between partials.
Because the partials are stretched:
beating rates increase at higher partials
the timbre becomes “shimmering” and “shocking”
the tuning must be adjusted so that the beating is aesthetically balanced across registers
Thus, Balinese tuning is shaped by:
desired beating rates
partial stretching
the interaction of paired instruments
🧭 6. Summary: How tuning and partials interact
| Instrument | Partial Structure | How It Shapes Tuning |
|---|---|---|
| Metallophones | Strongly stretched bar partials | Scale degrees chosen to minimize roughness between partials |
| Gong Ageng | Some near-harmonic low modes | Defines tonal center; tuning avoids clashing with gong modes |
| Bonang | Highly inharmonic kettle-gong modes | Scale contour shaped around bonang partials |
| Balinese pairs | Stretched partials create complex beating | Tuning adjusted to produce desired ombak across partials |
| Rebab, Suling, Voice | Nearly harmonic | Provide contrast; help stabilize pitch perception |
📚 7. Has this been studied?
Yes — extensively. Key contributors include:
William Sethares (tuning–timbre matching theory)
Fletcher & Rossing (instrument acoustics)
Andrew McGraw, Michael Tenzer (ethnomusicology + acoustics)
UCLA Gamelan Research Group
Indonesian researchers at ISI Surakarta, ISI Yogyakarta, and Udayana University
There are dozens of spectral analyses of Javanese and Balinese instruments, including full partial charts for individual gamelan sets.
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