Timbre and the suitable tuning and temperament

 People prefer piano to use equal temperament and string instruments to use just intonation. It can be understood that the mechanics of the instruments: the piano is hard to adjust during a performance and strings are good at their agility. It can have the same conclusion when we examine the timbre of the instruments.

Here is the harmonic series comparison between a piano and a violin playing on the same note A2.



In the piano, the harmonic strength is strong on the first 3 harmonics but decays rapidly after 1kHz; the violin carries a more spread of harmonic strength. It maintains strength even over 1kHz until 4kHz. In other words, the strings instruments have louder upper harmonic partials compared to the piano. In real practice, the string instruments are often played with vibrato, which generates even more complex harmonics compare to a piano.

I use Pure Data to generate the purer sound for clearer comparison and easier to switch between different temperaments and tuning as well as timbre. The examples demonstrate the timbre and harmonic series affect the sonority in a different tuning. According to Lindley (2001), a pronounced degree of inharmonicity in the timbre, as in a set of chimes or a xylophone, eliminates the qualitative difference, except in the case of unison or octave, between the sound of a pure concord and that of a slightly impure or tempered one. The timbre of the piano recalls this quality.

For fifth, just intonation is the purest and most stable system to go no matter less or more harmonic contest.



In equal temperament and just intonation, the tuning of major 3rd is quite different, 13 cents lower in JI. With one pure sine tone, the use of ET and JI does not have a big difference. With less harmonic context like piano, the JI sounds a little bit dull while ET sounds richer. However, with more harmonic context like strings, JI sounds harmonious while ET sounds harsh and interfering.


The tuning of minor 3rd in JI is 16 cents higher than ET. With less harmonic context, the JI sounds a little bit richer while ET sounds duller. It is a matter of taste of choosing each system. I would prefer ET since JI sounds higher and closer to the sonority natural third and the duller sound matches the affective of minor keys. With more harmonic context, ET sounds harmonious while JI sounds harsher.

The tuning of minor 7th in ET is different from 30 cents higher than JI.  With less harmonic context, between JI and ET, it is hard to tell which one is better. It is a matter of taste of choosing each system. However, with more harmonic context, ET sounds a little more harmonious while JI sounds a little harsher, but it is hard to judge which one sounds better. I would prefer ET.

Lindley, M. (2001) Temperaments. Grove Music Online. Retrieved 28 Feb. 2022, from https://www-oxfordmusiconline-com.ezproxy.bcu.ac.uk/grovemusic/view/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000027643.

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