Re: [tuning] 19 tone notation

Georg Hajdu <HAJDU@UNI-MUENSTER.DE> wrote:

"I notated the music in Finale using eighth-tone notation. While this type of
notation leads to a maximum deviation of 12 cents only, I was wondering
whether anyone is experienced with writing for string instruments in 19TET
or other temperaments, and what kind of (probably more idealized) notation
systems would also be advisable (besides Joseph Yasser's system which I
always found outlandish)."

I would suggest notating 19 as a cycle of tempered fifths, in scalar order C,C#, Db/Cx, D, D#, Eb, E, Fb/E#, F, F#, Gb/Fx, G, G#, Ab/Gx, A, A#/Bbb, Bb, B, Cb/B#. The best approximation of the odd members of a harmonic series on C would the be: C G E D Bbb (orA#) D F# A B.

If you wish to give the player more exact intonational information, I've indicated a simple set of accidentals below, based on approximating a 5-limit lattice (++ and = could be replaced by up and down arrows, for example). An alternative would be to adding cent deviations from 12tet pitches to the pythagorean notation. I general, however, I prefer the elegance of the plain pythagorean notation; it seems equally good for tonal and non-tonal collections.

It might be advantageous to find a violinist with experience in playing early music with meantone continuo; tuning the violin to the 694.737 cent fifths should at least be a familiar place from which to depart.

Daniel Wolf
Budapest

17tet
cents/lattice notation/pythagorean notation and major scale

0 C C CDEFGABC
63.158 C#= C# C#D#E#F#G#A#B#
126.316 Db+ Db/Cx DbEbFGbAbBbC
189.474 D- D DEF#GABC#D
252.632 D#= D# D#E#FxG#A#B#Cx
315.789 Eb+ Eb EbFGAbBbCDEb
378.947 E- E EF#G#ABC#D#E
442.105 Fb++ Fb/E# FbGbAbBbbCbDbEbFb
505.263 F F FGABbCDEF
568.421 F#= F# F#G#A#BC#D#E#F#
631.579 Gb++ Gb/Fx GbAbBbCbDbEbFGb
694.737 G G GABCDEF#G
757.895 G#= G# G#A#B#C#D#E#FxG#
821.053 Ab+ Ab/Gx AbBbCDbEbFGAb
884.211 A- A ABC#DEF#G#A
947.368 Bbb++ A#/Bbb A#B#CxD#E#F#Gx
1010.526 Bb+ Bb BbCDEbFGABb
1073.684 B- B BC#D#EF#G#A#B
1136.842 Cb++ Cb/B# CbDbEbFbGbAbBbCb

Daniel Wolf wrote,

> 17tet
> c ents/lattice notation/pythagorean notation and major scale

> 0 C C CDEFGABC
>63.158 C#= C# C#D#E#F#G#A#B#

I think Daniel meant 19tET, not 17tET!