Timbral Tunings
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Timbral Tuning Systems

Most musical instruments vibrate the air at many frequencies simultaneously - even when sounding a single note! The pattern of frequencies that a given instrument excites when a single note is played is called its harmonic spectrum.  Strings and woodwinds have a simple spectrum called the harmonic series where the lowest note or fundamental is the loudest, and the higher frequencies or "harmonics" are progressively quieter.  The harmonic spectra of cymbals, gongs, and percussion instruments don't follow any regular pattern.

Some ethnic music such as Balinese Gamelan, and modern composers such as Wendy Carlos, Matt Samolis, and Peter Warren have based tuning systems on the harmonic spectra of the instruments they used.  Gamelan orchestras are frequently tuned differently from one another depending on the harmonic spectra of the specific instruments in that orchestra.  William Sethares wrote a very interesting book discussing tuning systems based on the harmonic spectrum of a given sound or instrument.  In it he lists the tunings of several gamelan orchestras.

Excerpt from, William Sethares, "Tuning, Timbre, Spectrum, Scale."

There are more charts of gamelan tunings in the book, (including another slendro chart) plus lots of great information.  Buy it at: Barnes and Noble or at Amazon. The table below is reproduced with permission of the author.

Table H.4. (abbreviated)

Tuning of each slendro instrument of Gamelan Kyai Kaduk Manis.  All values are rounded to the nearest Hz.

Gamelan Kyai Kaduk Manis: Slendro
    I II III  
Instrument 6 1 2 3 5 6 1 2 3 5 6 1 2 3 5 6 1 2
gender 120 140 160 183 210 241 279 320 367 420 480 557 639 733  
gender   241 279 320 366 420 482 556 638 733 838 968 1114 1279
gender 120 139 159 182 209 240 277  
saron   241 280 322 367 421 482 557  
saron   244 281 322 369 423 482 557  
saron   482 559 651 738 840 968 1113  
The table in the book is continued here showing two more sarons, 2 bonangs, a kenong, and a gambang.
median 120 140 159 182 209 241 279 320 367 421 482 557 641 738 840 968 1114 1278

Quick scan of whole chart from book

Suggested Listening

Wendy Carlos, Beauty in the Beast - Powerful compositions in the style of buddhist chanting and other intense ethnic genres.

Matt Samolis and Peter Warren, Bowed Metal Music - A sound art sculpture comes alive with haunting sustained tones. Beautiful, sometimes relaxing, sometimes eerie.

A field recording: Morning Of The World-The Balinese Gamelan - Just what it says. The Balinese performers play all kinds of original percussion instruments tuned to match the timbre of the notes they play. Most of this music was written to support dances that tell spiritual stories of love and war and death.