23edo and octave stretching: Difference between revisions

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Lookalikes: [[36edt]], [[68edo|68ed8]], [[159edo|159ed128]], [[227edo|227ed1024]]

Pianos typically have stretched octaves due to the inharmonicity of the strings. This stretch is concentrated at the low and high octaves of the piano. As a result, while the standard 88-key piano covers over seven octaves, only the middle four octaves or so are commonly used, because the treble and bass registers have so much stretch and do not sound as good. Ordinary pianos are tuned with 12 keys per octave, and 12edo is ideal for perfect octaves, but does not work as well for stretched ones. The total amount of stretch depends on the size of the piano but typically is around 70 cents (across the tuning range of the whole piano), although this stretch is unequally distributed as stated before.

Alternatively, it might be possible to design a piano in which the stretch is evenly distributed. Stretched 23edo would be ideal for such a piano. A piano covering between four and five octaves would be ideal; such a piano would have around 100 keys (versus 88 for a standard piano) and the total amount of stretch across the entire tuning range would be about the same as on a standard piano. While the range is narrower (4-5 octaves rather than 7-8), the effective ''usable'' range is about the same (since the low and high ranges of a standard piano are usually avoided due to the extreme stretch and dissonance in those regions, whereas in a stretched-23 piano, the stretch is evenly distributed and the entire range sounds equally well).

Guitars, unlike pianos, typically do not have much stretch since the strings are not as stiff. Thus, stretched-23 is not as natural an option for them. However, it might be possible to design a guitar-like instrument using stiffer wire (more akin to piano wire). Such a "guitar" could only be played with a stiff plectrum; attempting to play it with just the fingers would be very painful. Other families of stringed instruments could be adapted in a similar manner.

Brass and wind instruments should work well if the air column is suitably shaped.

Stretched 23edo provides a good option for those seeking to combine Western-style instruments like piano and guitar (which have nearly harmonic spectra) with more obviously inharmonic ones (idiophones) from other cultures. In particular, the natural fifth in stretched-23 is almost halfway between the very flat fifth of 9edo (which is used, for example, in Indonesian pelog) and the harmonic perfect fifth. As for slendro, it may be approximated as 5-5-4-5-4, or (if we use the ''diminished'' octave as our repeat unit instead) 5-4-5-4-4.

== See also ==

* [[33/32 equal step tuning|33/32 equal-step tuning]] - can be considered a stretched 23edo.

* [[Quartkeenlig]] - a regular temperament interpretation of 23edo octave stretching.

[[Category:23edo]]