On Jan 9, 2009, at 3:08 PM, Fred Sturm wrote: > The historical question - what would be historically appropriate - > is a tough one. At a guess, one of Neidhardt's or Peter Prelleur's > would be more plausible. Thought I ought to elaborate a wee bit. Below I have pasted offsets for Neidardt's various temperaments as well as Prelleur's (the very last). My source is Chip Miller's website. I didn't count, but I think there are about 20 different temperaments by Neidardt. What does that tell you? It tells _me_ that there is a pretty wide range of what can be considered acceptable. Unfortunately, I don't know for sure what much of the descriptive title terminology means. I think "1/12 1/6 comma" means that there is a mix of 5ths, some of them 1/12 comma, some 1/16 comma. And similarly with other descriptions. But some of the other terms - "Fifth circle", "Third Circle", etc - don't mean anything to me. I guess I need to find Neidardt's theoretical treatise <G>. Neidhardt's Circulating #1 (1/12 1/6 comma) (Irregular) C: 6 C#: 0 D: 2 Eb: 2 E: -2 F: 4 F#: -2 G: 4 Ab: 2 A: 0 Bb: 2 B: -2 Neidhardt's Circulating #2 (1/12 1/6 - comma) (Irregular) C: 6 C#: 2 D: 2 Eb: 4 E: 0 F: 6 F#: 2 G: 4 Ab: 2 A: 0 Bb: 6 B: 2 Neidhardt's Circulating #3 (1/12 1/6 - comma) (Irregular) C: 6 C#: 2 D: 2 Eb: 4 E: 0 F: 4 F#: 2 G: 2 Ab: 2 A: 0 Bb: 4 B: 2 Neidhardt's Fifth Circle #10 (1/6 1/4 - comma) C: 6 C#: 0 D: 4 Eb: 4 E: -2 F: 4 F#: 2 G: 2 Ab: 2 A: 0 Bb: 2 B: 0 Neidhardt's Fifth Circle #10 (Idealized) (Irregular) C: 4 C#: -2 D: 2 Eb: 2 E: 2 F: 2 F#: 2 G: 0 Ab: 0 A: 0 Bb: 0 B: 0 Neidhardt's Fifth Circle #11 (1/12 1/6 1/4 - comma) (Irregular) C: 6 C#: 2 D: 4 Eb: 2 E: 0 F: 6 F#: 4 G: 6 Ab: 6 A: 0 Bb: 2 B: 4 Neidhardt's Fifth Circle #12 (1/12 1/6 1/4 - comma) (Irregular) C: 0 C#: 0 D: -2 Eb: 0 E: -4 F: -2 F#: 0 G: 0 Ab: -2 A: 0 Bb: -4 B: -2 Neidhardt's Fifth Circle #5 (1/12 1/6 - comma) (Irregular) C: 2 C#: 2 D: 2 Eb: 0 E: 4 F: 4 F#: 2 G: 2 Ab: 2 A: 0 Bb: 4 B: 4 Neidhardt's Fifth Circle #6 (1/12 1/4 - comma) (Irregular) C: 0 C#: 0 D: -4 Eb: 0 E: 0 F: -4 F#: 0 G: 0 Ab: -4 A: 0 Bb: 0 B: -4 Neidhardt's Fifth Circle #7 (1/6 1/4 - comma) (Irregular) C: 8 C#: 2 D: 2 Eb: 6 E: 8 F: 2 F#: 4 G: 4 Ab: 8 A: 0 Bb: 4 B: 6 Neidhardt's Fifth Circle #9 (1/12 1/4 - comma) (Irregular) C: 2 C#: 0 D: -2 Eb: 2 E: 2 F: 0 F#: -2 G: 2 Ab: 2 A: 0 Bb: -2 B: 2 Neidhardt's Fifth-Circle #2 (1/6 - comma) (Irregular) C: -2 C#: 0 D: 2 Eb: -4 E: -2 F: 0 F#: 2 G: -4 Ab: -2 A: 0 Bb: 2 B: -4 Neidhardt's Fifth-circle #3 (1/6 - comma) (Irregular) C: -2 C#: 0 D: -2 Eb: 0 E: -2 F: 0 F#: -2 G: 0 Ab: -2 A: 0 Bb: -2 B: 0 Neidhardt's Fifth-circle #4 (1/4 - comma) (Irregular) C: 0 C#: -4 D: -2 Eb: 0 E: -4 F: -2 F#: 0 G: -4 Ab: -2 A: 0 Bb: -4 B: -2 Neidhardt's Sample Temperament #2 (1/12 1/6 1/4 - comma) (Irregular) C: 10 C#: 0 D: 4 Eb: 4 E: -4 F: 6 F#: 0 G: 8 Ab: 2 A: 0 Bb: 4 B: -2 Neidhardt's Sample Temperament #3 (1/12 1/6 1/4 - comma) (Irregular) C: 8 C#: 0 D: 4 Eb: 4 E: -4 F: 6 F#: 0 G: 6 Ab: 2 A: 0 Bb: 4 B: -2 Neidhardt's Third Circle #1 (1/12 1/6 1/4 - comma) (Irregular) C: 6 C#: 0 D: 4 Eb: 2 E: -4 F: 4 F#: -2 G: 6 Ab: 0 A: 0 Bb: 4 B: -2 Neidhardt's Third Circle #3 (1/12 1/6 - comma) (Irregular) C: 4 C#: 0 D: 0 Eb: 0 E: -2 F: 4 F#: 2 G: 2 Ab: 0 A: 0 Bb: 6 B: -4 Neidhardt's Third Circle #4 (1/12 1/6 - comma) C: 6 C#: 2 D: 2 Eb: 2 E: 2 F: 4 F#: 2 G: 4 Ab: 2 A: 0 Bb: 6 B: 0 Neidhardt's Third Circle #5 (1/12 1/6 - comma) (Irregular) C: 0 C#: 0 D: 0 Eb: 0 E: -2 F: 2 F#: -2 G: 0 Ab: 0 A: 0 Bb: 0 B: -2 Neidhart Unequal #1 C: -2 C#: 0 D: -2 Eb: 0 E: -2 F: 0 F#: -2 G: 0 Ab: -2 A: 0 Bb: -2 B: 0 Neidhart Unequal #2 C: 0 C#: 0 D: 0 Eb: 0 E: -2 F: 2 F#: -2 G: 0 Ab: 0 A: 0 Bb: -900 B: -2 Neidhart's Division of the Syntonic Comma (Equal) C: -.5 C#: -1.40000000000001 D: -.199999999999989 Eb: -1 E: .100000000000023 F: -.600000000000023 F#: .5 G: -.299999999999955 Ab: -1.20000000000005 A: 0 Bb: -.799999999999955 B: .299999999999955 Prelleur Well-Temperament C: 4 C#: 0 D: 2 Eb: 3 E: 0 F: 5 F#: -1 G: 2 Ab: 1 A: 0 Bb: 4 B: -2 Regards, Fred Sturm University of New Mexico fssturm at unm.edu -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/caut_ptg.org/attachments/20090112/61e455c3/attachment-0001.html>
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