Joachim Mohr   Mathematik Musik Delphi

Die Eulerschreibweise


Modulationen in Eulerschreibweise

Angegeben werden 12 Töne pro Tonart (Dur/Moll+2) in der der reinen Stimmung, zum Beispiel:
c 'des d 'es ,e f ,fis g 'as ,a 'b ,h c 'des d 'es ,e f ,fis g 'as ,a 'b ,h c mit den 12 reinen Dur- und Molldreiklängen:
1. Stufe: c 'es g (moll) c e g (dur)
2. Stufe: 'des f 'as (dur)
3. Stufe: 'es g 'b (dur) ,e g ,h (moll)
4. Sufe: f ,a c (dur) f 'as c (moll)
5. Stufe: g ,h d (dur) g 'b d (moll)
6. Stufe: 'as c 'es (dur) ,a c ,e (moll)
7.Stufe: ,h d ,fis (moll)
Um besser vergleichen zu können: gleiche Töne untereinander
Die quintverwandten Tonarten:
des: ,c  des 'eses  es 'fes ,f  ges ,g  as 'heses  ,b 'ces  ,c  des 'eses  es 'fes  ,f   ges ,g  as 'heses  ,b 'ces ,c 
as:  ,c  des ,d     es 'fes ,f 'ges ,g  as 'heses  b  'ces  ,c  des ,d     es 'fes  ,f  'ges ,g  as 'heses  b  'ces ,c 
                                        ↑          ——               —————                ———     ↑  

as: ,c  des ,d  es 'fes ,f 'ges ,g  as 'heses  b 'ces  ,c  des ,d  es 'fes  ,f  'ges ,g  as 'heses  b 'ces ,c 
es: ,c 'des ,d  es 'fes  f 'ges ,g  as ,a      b 'ces  ,c 'des ,d  es 'fes  f   'ges ,g  as ,a      b 'ces ,c 
                ↑       ——             ————                ———     ↑

es: ,c 'des ,d  es 'fes f 'ges ,g  as ,a  b 'ces  ,c 'des ,d  es 'fes  f  'ges ,g  as ,a  b 'ces ,c 
b:   c 'des ,d  es ,e   f 'ges ,g 'as ,a  b 'ces   c 'des ,d  es ,e    f  'ges ,g 'as ,a  b 'ces  c 
                                          ↑       ——             ————              ———    ↑

b: c 'des ,d  es ,e f 'ges ,g 'as ,a  b 'ces  c 'des ,d  es ,e  f  'ges ,g 'as ,a  b 'ces c 
f: c 'des ,d 'es ,e f 'ges g  'as ,a  b ,h    c 'des ,d 'es ,e  f  'ges  g 'as ,a  b ,h   c 
                    ↑      ——           ————            ———     ↑

f: c 'des ,d 'es ,e f 'ges g 'as ,a  b ,h c 'des ,d 'es ,e  f  'ges g 'as ,a  b ,h c 
c: c 'des d  'es ,e f ,fis g 'as ,a 'b ,h c 'des  d 'es ,e  f  ,fis g 'as ,a 'b ,h c
   ↑      ——          ————          ——    ↑ 

c: c 'des d 'es ,e f ,fis g 'as ,a 'b ,h c 'des d 'es ,e f ,fis g 'as ,a 'b ,h c g: c ,cis d 'es ,e f ,fis g 'as a 'b ,h c ,cis d 'es ,e 'f ,fis g 'as a 'b ,h c ↑ —— ———— —— ↑ g: c ,cis d 'es ,e 'f ,fis g 'as a 'b ,h c ,cis d 'es ,e 'f ,fis g 'as a 'b ,h c d: 'c ,cis d 'es e 'f ,fis g ,gis a 'b ,h 'c ,cis d 'es e 'f ,fis g ,gis a 'b ,h 'c ↑ —— ———— —— ↑ d: 'c ,cis d 'es e 'f ,fis g ,gis a 'b ,h 'c ,cis d 'es e 'f ,fis g ,gis a 'b ,h 'c a: 'c ,cis d ,dis e 'f ,fis 'g ,gis a 'b h 'c ,cis d ,dis e 'f ,fis 'g ,gis a 'b h 'c ↑ —— ———— —— ↑ a: 'c ,cis d ,dis e 'f ,fis 'g ,gis a 'b h 'c ,cis d ,dis e 'f ,fis 'g ,gis a 'b h 'c e: 'c ,cis 'd ,dis e 'f fis 'g ,gis a ,ais h 'c ,cis 'd ,dis e 'f fis 'g ,gis a ,ais h 'c ↑ ——— ———— —— ↑ e: 'c ,cis 'd ,dis e 'f fis 'g ,gis a ,ais h 'c ,cis 'd ,dis e 'f fis 'g ,gis a ,ais h 'c h: 'c cis 'd ,dis e ,eis fis 'g ,gis 'a ,ais h 'c cis 'd ,dis e ,eis fis 'g ,gis 'a ,ais h 'c ↑ ——— ———— —— ↑ h: 'c, cis 'd ,dis e ,eis fis 'g ,gis 'a ,ais h 'c cis 'd ,dis e ,eis fis 'g ,gis 'a ,ais h 'c fis: ,his cis 'd ,dis 'e ,eis fis 'g gis 'a ,ais h ,his cis 'd ,dis 'e ,eis fis 'g gis 'a ,ais h ,his ↑ ——— ———— —— ↑ fis: ,his cis 'd ,dis 'e ,eis fis 'g gis 'a ,ais h ,his cis 'd dis 'e ,eis fis 'g gis 'a ,ais h ,his cis: ,his cis 'd dis 'e ,eis fis ,fisis gis 'a ,ais 'h ,his cis 'd ,dis 'e ,eis fis ,fisis gis 'a ,ais 'h ,his ↑ ——— ———— —— ↑
Terzverwandte Tonarten:
,a: c ,,cis ,d ,,dis ,e f ,,fis g ,,gis ,a  b ,h c ,,cis ,d ,,dis ,e f ,,fis g ,,gis ,a  b ,h c 
 c: c 'des   d  'es  ,e f  ,fis g 'as   ,a 'b ,h c  'des  d  'es  ,e f  ,fis g  'as  ,a 'b ,h c 
                                         ↑ ——       ———— ——  ————      —————   —————  ↑ 

Vergleich der Abweichungen der Tonhöhen

[,a a]=k=syntonisches Komma=21,51 Cent
[des cis]=pythagoreisches Komma=23,46 Cent
[c ,his]=p-k=1,95 Cent=Schischma
[,cis 'des]=2k-p=19,55 Cent=Diaschisma
[,,cis 'des]=3k-p=41,06 Cent=kleine Diesis