This is a concert presented by 2:1 and Bohemian In Exile inaugurating a new art space at 1464 Gratiot Ave. Thollem is playing a solo concert on three pianos each tuned differently by Clem Fortuna in tuning systems of his own design.
Following is a brief description by Clem followed by further notes:
In 2010 I had the opportunity to tune for Thollem McDonas at a recital for the Bohemian National Home. I wanted to try something more adventurous than the usual equal temperament, and tuned the piano to seventh comma meantone. Thollem liked the sound, but wanted to try something more radical for a future recital. The three tunings I have invented for this concert are so far removed from conventional tunings that one would be hard pressed to play conventional music on them. One is forced to create something new, which is something at which Thollem excels.
The 1903 Chickering grand piano is tuned to a simple form of Just Intonation. A mathematically perfect ratio between certain notes creates maximum consonance. This requires other notes to be more out of tune, creating a nice contrast. This particular Just Intonation does not center on any one key, but rather on a chain of contiguous perfect minor thirds (a ratio of 6:5). Six perfect minor and six perfect major triads are available, in very unrelated keys.
The Krakauer baby grand is tuned to 12 selected notes taken from a scale of 41 tones per octave. Seven perfect fifths are used. This tuning was used by the Xenharmonic Gamelan group, which I founded in 1998. The naturals (white keys) on the piano are tuned to a quasi Siamese scale, and the sharps are tuned to a quasi Javanese scale. The tuning is similar to the 5-7 temperament created by Professor Owen Jorgensen, but is derived from a 41 note temperament instead of 70 note.
The 2003 Steinway M is tuned to another more radical form of Just Intonation. All fifths are a perfect 3:2 ratio. All major and minor thirds are a perfect ratio of 5:4, 6:5, 7:6, or 9:7, with an occasional 11:9. However, as a result, none of the fourths, sixths, or even octaves are in tune, making it very challenging to work with. Normally, repeated octaves form the basis for all tuning systems, whether historic or microtonal.
Regards
Clem
Further information from Clem:
The Chickering is pretty straightforward. C, Eb, F# and A are tuned in contiguous 6:5 minor thirds. G, Bb, Db and E are tuned the same, a fifth above, and a fifth above that is D, F, Ab and B. The diagram I gave you shows it graphically: D F Ab B
G Bb Db E
C Eb F# A
where all triangles are perfect triads. I believe 12 perfect triads are the maximum possible with 12 notes.
The Krakauer used 12 notes from a 41 note (slightly unequal) temperament. Every sixth note creates the seven naturals, with B and C only 5 notes apart. F# is 1 tone above F, C# 2 tones above C, G# 3 tones above G, D# 4 tones above D and A# 5 tones above A. This puts the naturals in a Siamese scale and the sharps in a Javenese Slendro type scale. The cents values are:
C + 13
Db -18
D -6
Eb +8
E -24
F +44
F# -20
G +14
Ab +6
A -4
Bb +40
B -22
The Steinway tuning uses perfect fifths throughout. The cents between semitones is 119, 78, 119, 119, 119, 78, 70. Contiguous major thirds run 386, 435, 386, 435, 345, 435, 386. Contiguous minor thirds run 316, 267, 357, 267, 316, 267, 316. These make all major thirds 5:4 or 9:7 and minor thirds 6:5 or 7:6, except the odd one third out of seven, which is close to 11:9. This works out so 3 out of every 7 sevenths is a 7:4. I won't type out the complete cents value for each note, but I did type it all into my tunelab program.
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7:24
Metal Sculpture on Rosa Parks in Detroitby thollem84 views
Too short! I want to hear more! :)
tmaysfr 10 months ago