**Roshan Kakiya's Well Temperament Completely Solves the Just Intonation Dilemma**

**Roshan Kakiya's Well Temperament (created by correcting the Pythagorean comma):**

http://my.ptg.org/communities/community-home/digestviewer/viewthread?GroupId=43&MessageKey=db956071-2c21-439d-8ae5-be761bfbf01e&CommunityKey=6265a40b-9fd2-4152-a628-bd7c7d770cbf&tab=digestviewer&ReturnUrl=%2fcommunities%2fcommunity-home%2fdigestviewer%3fcommunitykey%3d6265a40b-9fd2-4152-a628-bd7c7d770cbf%26tab%3ddigestviewer
**Just Intonation Dilemma (partially solved by correcting the Syntonic comma):**

http://my.ptg.org/communities/community-home/digestviewer/viewthread?GroupId=43&MessageKey=3ce711a8-1939-4ab8-9f88-c85435a71885&CommunityKey=6265a40b-9fd2-4152-a628-bd7c7d770cbf&tab=digestviewer&ReturnUrl=%2fcommunities%2fcommunity-home%2fdigestviewer%3fCommunityKey%3d6265a40b-9fd2-4152-a628-bd7c7d770cbf

**Steps Required to Completely Solve the Just Intonation Dilemma**

**1. Correct the Syntonic comma:**The Syntonic comma can be corrected by keeping C-G (Fifth) pure, narrowing C-D (Major Second) by 1/3 Syntonic comma, narrowing F-G (Major Second) by 1/3 Syntonic comma and widening D-F (Minor Third) by 2/3 Syntonic comma. **2. Establish the Fifth-Fourth relationship and the Fourth-Fifth relationship:**Fifth-Fourth relationship = Pure Fifth-Tempered Fourth = C-G-D-A-E-B-F#Pure Fifth = 701.96 centsTempered Fourth = 505.21 centsFourth-Fifth relationship = Pure Fourth-Tempered Fifth = F#-C#-G#-D#-A#-F-CPure Fourth = 498.04 centsTempered Fifth = 694.79 cents**3. Use the relationships established in Step 2 to create a temperament:**C-G (Pure Fifth)G-D (Tempered Fourth)D-A (Pure Fifth)A-E (Tempered Fourth)E-B (Pure Fifth)B-F# (Tempered Fourth)F#-C# (Pure Fourth)C#-G# (Tempered Fifth)G#-D# (Pure Fourth)D#-A# (Tempered Fifth)A#-F (Pure Fourth)F-C (Tempered Fifth)
C |
0.00 |

C# |
92.18 |

D |
196.74 |

D# |
288.92 |

E |
393.48 |

F |
485.66 |

F# |
590.22 |

G |
701.96 |

G# |
786.96 |

A |
898.70 |

A# |
983.71 |

B |
1095.44 |

C |
1180.45 |

The Octave should have a value of 1200 cents. However, the correction of the Syntonic comma has led to the creation of another comma called the Diaschisma which has a value of 19.55 cents (1200 cents - 1180.45 cents).**4. Correcting the Diaschisma:**Pure Fifth = 701.96 centsTempered Fifth = 694.79 centsThere are 6 Pure Fifths and 6 Tempered Fifths. The Circle of Fifths is not complete because of the Diaschisma. The 6 Pure Fifths can remain intact. Each of the 6 Tempered Fifths must be widened in order to correct the Diaschisma. The Diaschisma can be corrected by widening each Tempered Fifth by 1/6 Diaschisma.Revised Tempered Fifth = 698.04 cents**5. Producing the Final Temperament:**Here is a list of all the intervals that are needed to produce the Final Temperament: Pure Fifth = 701.96 centsRevised Tempered Fifth = 698.04 centsPure Fourth = 498.04 centsRevised Tempered Fourth = 501.96 centsC-G (Pure Fifth)G-D (Revised Tempered Fourth)D-A (Pure Fifth)A-E (Revised Tempered Fourth)E-B (Pure Fifth)B-F# (Revised Tempered Fourth)F#-C# (Pure Fourth)C#-G# (Revised Tempered Fifth)G#-D# (Pure Fourth)D#-A# (Revised Tempered Fifth)A#-F (Pure Fourth)F-C (Revised Tempered Fifth)
C |
0.00 |

C# |
101.96 |

D |
200.00 |

D# |
301.96 |

E |
400.00 |

F |
501.96 |

F# |
600.00 |

G |
701.96 |

G# |
800.00 |

A |
901.96 |

A# |
1000.00 |

B |
1101.96 |

C |
1200.00 |

The Final Temperament is Roshan Kakiya's Well Temperament!

Conclusion: Roshan Kakiya's Well Temperament Completely Solves the Just Intonation Dilemma.

------------------------------Roshan Kakiya------------------------------