[CAUT] temperament for Schubert

[Alan McCoy]

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
> 
>