musical tunings --------------- german: Musikalische Stimmungen I collected some of the most used tunings in the western music and added some of the (on western key instruments) playable world tunings to that. I hope I did not put anywhere wrong numbers in. Such errors would be hard to find. You'll find most of this tunings in german and english wikipedia and from there you have to follow some of the links to gether those informations.
Hope you can use the table-form I did chose. If you miss some important, just tell me. Hanno --------------------------------------------- http://www.fres.ch/bd/content/music/bach.html http://www.robertschroeter.de/diplom.pdf http://www.robertschroeter.de/stimmungen.html http://www.sengpielaudio.com/Rechner-centfrequenz.htm http://www.xs4all.nl/~huygensf/scala/ base=<freq> basekey=<central key> 1) just intonation in german: reine Stimmung (Natürlich-harmonische Stimmung) http://de.wikipedia.org/wiki/Reine_Stimmung 1a) diatonic scale interval[12]= {1, 16/15, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 16/9, 15/8}; octave=int((key-basekey)/12); note=(key-basekey)%12; freq=(base*2^octave)*interval[note]; 1b) indian scale http://en.wikipedia.org/wiki/Just_intonation interval[12]= {1, 16/15, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 27/16, 15/8}; 1c) pythagorean tuning german: Pythagoreische Stimmung (quintenrein) http://en.wikipedia.org/wiki/Just_intonation http://en.wikipedia.org/wiki/Pythagorean_tuning http://de.wikipedia.org/wiki/Pythagoreische_Stimmung interval[12]= {1, 256/243, 9/8, 32/27, 81/64, 4/3, 729/512, 3/2, 128/81, 27/16, 16/9, 243/128}; algorithm see 1) 1d) 5-limit pentatonic http://en.wikipedia.org/wiki/Pentatonic#Tuning interval[12]= {1, 256/243, 9/8, 32/27, 5/4, 4/3, 729/512, 3/2, 128/81, 5/3, 16/9, 243/128}; 1e) 5-limit pentatonic with blue notes (2+2) http://en.wikipedia.org/wiki/Pentatonic#Tuning interval[12]= {1, 256/243, 9/8, 7/6, 21/16, 4/3, 7/5, 3/2, 128/81, 7/4, 16/9, 243/128}; 1f) 5-limit pentatonic of gogo people in tansania http://en.wikipedia.org/wiki/Pentatonic#Tuning interval[12]= {1, 256/243, 9/8, 32/27, 5/4, 4/3, 729/512, 3/2, 128/81, 7/4, 16/9, 243/128}; 2) meantone temperament german: Mitteltönige Stimmungen http://en.wikipedia.org/wiki/Meantone_temperament 2a) 1/4 comma meantone http://de.wikipedia.org/wiki/Mitteltönige_Stimmung for 1/4 meantime tuning interval[12]= { 1, (2187/128)/(81/80)^1.75/16, (9/4)/(81/80)^.5/2, (8/27)*(81/80)^.75*4, (81/16)/(81/80)/4, (2/3)*(81/80)^.25*2, (729/64)/(81/80)^1.5/8, (3/2)/(81/80)^.25, 25/16, (27/8)/(81/80)^.75/2, (4/9)*(81/80)^.5*4, (243/32)/(81/80)^1.25/4 }; 2b) Silbermann-Sorge Temperatur http://de.wikipedia.org/wiki/Silbermann-Sorge-Temperatur I couldn't find better values than this. But a cent value should do it, cause the detune of a cent value is below the hearing level. interval[12]={ 2^(0/1200*1), 2^(86/1200*1), 2^(196/1200), 2^(306/1200), 2^(392/1200), 2^(502/1200), 2^(588/1200), 2^(698/1200), 2^(784/1200), 2^(894/1200), 2^(1004/1200), 2^(1090/1200) }; 3) Wohltemperierte Stimmungen 3a) Werckmeister-Stimmung http://de.wikipedia.org/wiki/Werckmeister-Stimmung 3a-3) Werckmeister III http://www.groenewald-berlin.de/text/text_T016.html interval[12]={ 1, 256/243, 64*2^.5/81, 32/27, 256*2^.25/243, 4/3, 1024/729, 8*8^.25/9, 128/81, 1024*2^.25/729, 16/9, 128*2^.25/81 }; 3a-4) Werckmeister IV http://www.groenewald-berlin.de/text/text_T017.html interval[12]={ 1, 16384*2^(1/3)/19683, 8*2^(1/3)/9, 32/27, 64*4^(1/3)/81, 4/3, 1024/729, 32*2^(1/3)/27, 8192*2^(1/3)/6561, 256*4^(1/3)/243, 9/4*2^(1/3), 4096/2187 }; 3a-5) Werckmeister V http://www.groenewald-berlin.de/text/text_T018.html interval[12]={ 1, 8*2^.25/9, 9/8, 2^.25, 8*2^.5/9, 9/4*8^.25, 2^.5, 3/2, 128/81, 8^.25, 3/8^.25, 4*2^.5/3 }; 3a-6) Werckmeister VI http://www.groenewald-berlin.de/text/text_T019.html interval[12]={ 1, 256/243, 1024*16^(1/7)/(792*81^(1/7)), 4*4^(1/7)/(3*3^(1/7)), 16*64^(1/7)/(9*729^(1/7)), 4/3, 16*16^(1/7)/(9*81^(1/7)), 2*2^(1/7)/3^(1/7), 128/81, 64*64^(1/7)/(27*729^(1/7)), 2*4^(1/7)/9^(1/7), 8*64^(1/7)/(3*729^(1/7)) }; 3b) Kirnberger-Stimmung http://de.wikipedia.org/wiki/Kirnberger-Stimmung 3b-1) Kirnberger II http://groenewald-berlin.de/text/text_T023.html interval[12]={ 1, 256/243, 9/8, 32/27, 5/4, 4/3, 45/32, 3/2, 128/81, 3*5^.5/4, 16/9, 15/8 }; 3b-2) Kirnberger III http://groenewald-berlin.de/text/text_T032.html interval[12]={ 1, 25/24, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 25/16, 5/3, 16/9, 15/8 }; 3c) Young http://en.wikipedia.org/wiki/Young_temperament interval[12]={ 2^(0/1200), 2^(106/1200), 2^(198/1200), 2^(306/1200), 2^(400/1200), 2^(502/1200), 2^(604/1200), 2^(698/1200), 2^(806/1200), 2^(898/1200), 2^(1004/1200), 2^(1102/1200) }; 4) equal temperamented german: Gleichstufige Stimmung http://en.wikipedia.org/wiki/Equal_temperament http://de.wikipedia.org/wiki/Gleichstufige_Stimmung 4a) 12-tone (12-TET) 2^(1/1200*halvetones*100) interval[12]={ 2^(0/1200), 2^(100/1200), 2^(200/1200), 2^(300/1200), 2^(400/1200), 2^(500/1200), 2^(600/1200), 2^(700/1200), 2^(800/1200), 2^(900/1200), 2^(1000/1200), 2^(1100/1200) }; 4b) 7-tone (7-TET) ethnic interval[12]={ 2^(0/1200), 2^(100/1200), /* Not available */ 2^(1*171/1200), 2^(300/1200), /* NA */ 2^(2*171/1200), 2^(3*171/1200), 2^(600/1200), /* NA */ 2^(4*171/1200), 2^(800/1200), /* NA */ 2^(5*171/1200), 2^(1000/1200), /* NA */ 2^(6*171/1200) }; 4c) 5-tone (5-TET) ethnic interval[12]={ 2^(0/1200), 2^(100/1200), /* Not available */ 2^(1*240/1200), 2^(300/1200), /* NA */ 2^(2*240/1200), 2^(500/1200), /* NA */ 2^(600/1200), /* NA */ 2^(3*240/1200), 2^(800/1200), /* NA */ 2^(4*240/1200), 2^(1000/1200), /* NA */ 2^(1100/1200) /* NA */ }; EOF _______________________________________________ beast mailing list [email protected] http://mail.gnome.org/mailman/listinfo/beast
