RE: Recent Archive Contributions

Yes, that looks more like it! Nice to see the correspondence comments in the
right column, too.

It is important to remember though, that this scale is a matrix of harmonic
series (used as scales and chord materials) and subharmonic series (also
used as scales and chord materials). The matrix allows for close
relationships among the tonalities (individual series) for modulation among
them. The linear representation should be usefull for melodic instruments
(and perhaps harmonic as well) that would be expected to move fluidly among
the changes in tonality. Of course, numerous modes exist both within the
individual tonalities and the composit scale as well and various subsets of
these can be very useful.



On Thu, 5 Sep 1996, Manuel Op de Coul wrote:

> Denny,
>
> Maybe it's this scale. You get it when the INVERT is done with
> respect to 2/1 instead of 17/8. Or it's created with SQUARE and then
> entering the 10 factors of 8 to 17, and then REDUCE 2/1 and UNIQUE.
>
> Manuel
> 1: 18/17 98.95463 Arabic lute index finger
> 2: 17/16 104.9554 17th harmonic
> 3: 16/15 111.7313 minor diatonic semitone
> 4: 15/14 119.4428 major diatonic semitone
> 5: 14/13 128.2983 2/3-tone
> 6: 13/12 138.5727 tridecimal 2/3-tone
> 7: 12/11 150.6371 3/4-tone
> 8: 11/10 165.0043 4/5-tone
> 9: 10/9 182.4038 minor whole tone
> 10: 9/8 203.9100 major whole tone
> 11: 17/15 216.6867
> 12: 8/7 231.1741 septimal whole tone
> 13: 15/13 247.7411
> 14: 7/6 266.8710 septimal minor third
> 15: 20/17 281.3584
> 16: 13/11 289.2098
> 17: 6/5 315.6414 minor third
> 18: 17/14 336.1296 supraminor third
> 19: 11/9 347.4080 undecimal neutral third
> 20: 16/13 359.4725 tridecimal neutral third
> 21: 5/4 386.3139 major third
> 22: 14/11 417.5081
> 23: 9/7 435.0843 septimal major third
> 24: 22/17 446.3627
> 25: 13/10 454.2141
> 26: 17/13 464.4279
> 27: 4/3 498.0452 perfect fourth
> 28: 15/11 536.9509
> 29: 11/8 551.3181 harmonic augmented fourth
> 30: 18/13 563.3825
> 31: 7/5 582.5125 septimal diminished fifth
> 32: 24/17 596.9998 1st septendecimal tritone
> 33: 17/12 603.0007 2nd septendecimal tritone
> 34: 10/7 617.4880 septimal augmented fourth, Euler's tritone
> 35: 13/9 636.6179
> 36: 16/11 648.6823 harmonic diminished fifth
> 37: 22/15 663.0495
> 38: 3/2 701.9553 perfect fifth
> 39: 26/17 735.5726
> 40: 20/13 745.7864
> 41: 17/11 753.6378
> 42: 14/9 764.9162 septimal minor sixth
> 43: 11/7 782.4924
> 44: 8/5 813.6866 minor sixth
> 45: 13/8 840.5280 tridecimal neutral sixth
> 46: 18/11 852.5924 undecimal neutral sixth
> 47: 28/17 863.8709
> 48: 5/3 884.3591 major sixth
> 49: 22/13 910.7907
> 50: 17/10 918.6421
> 51: 12/7 933.1295 septimal major sixth
> 52: 26/15 952.2593
> 53: 7/4 968.8264 harmonic seventh
> 54: 30/17 983.3137
> 55: 16/9 996.0905 Pythagorean minor seventh
> 56: 9/5 1017.596 just minor seventh
> 57: 20/11 1034.996
> 58: 11/6 1049.363 21/4-tone
> 59: 24/13 1061.427
> 60: 13/7 1071.702 16/3-tone
> 61: 28/15 1080.557 grave major seventh
> 62: 15/8 1088.269 classic major seventh
> 63: 32/17 1095.045
> 64: 17/9 1101.045
> 65: 2/1 1200.000 octave
>
>

Denny Genovese
Director

Southeast Just Intonation Center

World Harmony Project Inc.
PO Box 15464
Gainesville, FL 32604

Email: sejic@afn.org Web Page: http://www.afn.org/~sejic



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