Recorded at the home of Dr. Made Hood in Singapadu, Bali, on June 27, 2012.
Notes for Bali Alloy Overture [based on Dr. Made Bandem's Gamelan Gong Kebyar in Singapadu, Bali]:
Fundamental Pitch (ding):
1/1 = 278.73 hz [concert C# +9.7 cents]
Pentatonic Pelog Scale Adapted for Strings:
Cents from 1/1= 0, 120.8, 298, 701.955, 778.9
Equivalent Ratios from 1/1= 1/1, 15/14, 19/16, 3/2, 11/7
(Ding) = D [1/1]
(Dong) = Eb +20.8 cents [15/14]
(Deng) = F -2 cents [19/16]
(Dung) = A +2 cents [3/2]
(Dang) = Bb -21 cents [11/7]
The tuning for the Overture is derived from several different avenues based on the tuning of the gamelan. The main goal in developing a system of tuning that would work well with any conceivable gamelan tuning was to discover a 3/2 equivalent in the fundamental pitches of the gamelan, and assign two open strings of the quartet to tune to that 3/2. In this case, since Ding to Dung on the gamelan was a narrow fifth where Ding is around 280 hz, it seemed feasible that the quartet could tune a 3/2 on their D and A strings starting just flat of Ding and going just sharp of Dung, and then finger the rest of the pitches with the gamelan.
The rest of the pitches used are based on multiplications of 3/2, 4/3, or 5/4 from the standing gamelan pitches. These pitches derived from the gamelan scale are:
*4/3, 10/7, 19/12, 2/1, 44/21 (parallel 4/3 above gamelan selisir pitches)
*3/2, 45/28, 57/32, 9/4, 33/14 (parallel 3/2 above gamelan selisir pitches)
*1/1, 15/14, 19/16, 5/4, 75/56, 3/2, 11/7, 57/32, 15/8 (mix of 5/4 and 3/2 parallels to create stepwise 9 tone scale)
The purpose of deriving a system of tuning like this is so that notationally, all of the pitches can be described through the tuning of the gamelan by using accidentals that refer to the pitches of the gamelan. Therefore, instead of thinking of the tuning as a just intonation based around a fixed 1/1, the tuning works as a series of just relationships revolving around the fixed tuning of the gamelan. Therefore, in tuning fingered pitches in the string quartet, the player should always be listening to the gamelan pitch that is referred to by the gamelan accidental. In most cases, the accidental sits next to the equivalent tone of the gamelan. But in cases where there are parallel relationships between the string pitch and the gamelan pitch, the gamelan accidental serves as a guide as to what tone to be in tune with.
This system of intonation technique should serve to allow to string players to conform with the gamelan as one unified ensemble.
- New Music