Fwd: Marchetto

Uh, sorry about the mixup. Here is the correct whole tone division:

0: 1/1 C unison, perfect prime
1: 41/40 C/ Db\
2: 21/20 C#\ Db minor semitone (enharmonic semitone, whose half is a diesis or made up of 2 dieses)
3: 43/40 C# Db/ major diatonic semitone (3 dieses, larger than 18:17. Plus diesis makes chromatic semitone)
4: 11/10 C#/ D\ 4/5-tone (chromatic semitone or chroma, completes to whole tone when diesis is added)
5: 9/8 D major whole tone

And here is a 29-tone scale that may be attributed to Marchetto from what I gleaned:

0: 1/1 C unison, perfect prime
1: 41/40 C/ Db\
2: 21/20 C#\ Db minor semitone
3: 43/40 C# Db/
4: 11/10 C#/ D\ 4/5-tone, Ptolemy's second
5: 9/8 D major whole tone
6: 369/320 D/ Eb\
7: 189/160 D#\ Eb
8: 387/320 D# Eb/
9: 99/80 D#/ E\
10: 81/64 E Pythagorean major third
11: 3321/2560 E/ F\
12: 4/3 F perfect fourth
13: 41/30 F/ Gb\
14: 7/5 F#\ Gb septimal or Huygens' tritone, BP fourth
15: 43/30 F# Gb/
16: 22/15 F#/ G\ undecimal diminished fifth
17: 3/2 G perfect fifth
18: 123/80 G/ Ab\
19: 63/40 G#\ Ab narrow minor sixth
20: 129/80 G# Ab/
21: 33/20 G#/ A\
22: 27/16 A Pythagorean major sixth
23: 1107/640 A/ Bb\
24: 567/320 A#\ Bb
25: 1161/640 A# Bb/
26: 297/160 A#/ B\
27: 243/128 B Pythagorean major seventh
28: 9963/5120 B/ C\
29: 2/1 C octave

Highest deviation from 29-ET is 7.5 cents. It seems Margo Schulter's observations were correct. Marchetto does appear to advocate a 29-tone Pythagorean cyclic setup:

/tuning/topicId_11873.html#11873

Oz.

Begin forwarded message:

> From: Ozan Yarman <ozanyarman@...>
> Date: August 14, 2008 5:14:00 PM GMT+03:00
> To: Tuning List <tuning@yahoogroups.com>
> Subject: Marchetto
>
> I was just re-reading monz' article on Marchetto on Padua:
>
> http://sonic-arts.org/monzo/marchet/marchet.htm
>
> Following the first diagram showing the division of the whole tone > into 9 parts, monz states that Marchetto advocated a wide variety of > small intervals. However, I think the passage:
>
> Any fifth part as it is desired, may be called a diesis, whether the > lowest (smallest?) or the highest (largest?) division, this is the > most important division that can be obtained in singing a tone."
>
> should be understood to mean the arithmetical division of 9:8 into > five parts:
>
> 40:41:42:43:44:45
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 45/44 38.906 1/5-tone
> 2: 45/43 78.706 (enharmonic semitone, whose > half is a diesis or made up of 2 dieses)
> 3: 15/14 119.443 major diatonic semitone (3 > dieses, larger than 18:17. Plus diesis makes chromatic semitone)
> 4: 45/41 161.161 (chromatic semitone or chroma, > completes to whole tone when diesis is added)
> 5: 9/8 203.910 major whole tone
>
> This should clear up much issues! How about the neutral second > peculiar to maqams then?
>
> Oz.