One thing is certain. Mr. Neidardt had way too much time on his hands. <G> Alan -- Alan McCoy, RPT Eastern Washington University amccoy at mail.ewu.edu 509-359-4627 509-999-9512 > From: Fred Sturm <fssturm at unm.edu> > Reply-To: "College and University Technicians <caut at ptg.org>" <caut at ptg.org> > Date: Mon, 12 Jan 2009 08:58:38 -0700 > To: "College and University Technicians <caut at ptg.org>" <caut at ptg.org> > Subject: Re: [CAUT] temperament for Schubert > > 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 > >
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