Historic tuning modes

Jason Kanter jkanter@rollingball.com
Wed, 27 Mar 2002 21:09:26 -0800


Newton said: 
> Maybe the final version should have a "significant" category to help
> determine it's historical significant.  Obviously 200 HTs would have
> quite a few that were less significant than others in terms of who, when
> and where they were used.

I'd greatly welcome any educated opinions about which are significant. Also,
there is a good bit of overlap (e.g. 2 versions of Werckmeister III. One of
them is 7.8 cents lower than the other, but the offset pattern is
identical... see the numbers immediately below. I could discard the one that
has A at -7.8 cents...)

C +3.9    +11.7
C# -5.9    +2.0
D -3.9    +3.9
D# -2.0    +5.9
E -5.9    +2.0
F +1.9    +9.8
F# -7.8    0.0
G 0.0    +7.8
G# -3.9    +3.9
A -7.8    0.0
A# 0.0    +7.8
B -3.9    +3.9

Here are the temperaments I have now (names only); this is a "splice" of the
TuneLab files, which are themselves mostly taken from Jorgensen, and the
Chip Miller/Avery Todd website, which has about 175 temperaments. I had
Excel run comparisons and have combined the names where the offsets are
identical (e.g. Broadwood Best is identical to Ellis Tuner Well 4, and
Tuner's Guide Marsh Q-E is identical to Johann Nepomuk Hummel Q-E). I am
working at a disadvantage since I have not yet located a copy of Jorgensen
and must rely on the help of you folks. I also know that the 75-HT file I
have built is already too large for some, so I will want to break the next
release into several files, and would like suggestions about how to group
them.  Pythagoreans, Means, Wells? By century? ... thanks in advance,
comments welcome.

1/10 - Comma Meantone
1/7 - Comma Meantone
1/8 - Comma Meantone
1/9- Comma Meantone
14th Century Pythagorean
1797 Meantone
1799 Meantone
17th Century Meantone
A Merrick Q-E
Agricola's Altered Pythagorean Tuning
Agricola's Monochord (Just)
Agricola's Pythagorean-type Monochord (Irregular)
Alexander John Ellis 1875 Q-E
Alexander John Ellis 1885 Q-E
Alexander Metcalf Fisher
Anton Bemetzrieder Pythagorean
Aron's 1/4 Syntonic Comma Meantone - equal beating
Aron's 1/4 Syntonic Comma Meantone - theoretically correct
Aron-Neidhart Well Temperament - theoretically correct
Artusi's Monochord #1 (Irregular)
Artusi's Monochord #2 (Irregular)
Artusi's Monochord #3 (Irregular)
Augustus De Morgan unequal
Barbour Murray - Well Temperament by Regularly Varied Fifths
Barbour/Bermudo    
Barbour/Galilei #1 (also called Galilei's Temperament with Linear Correction
No. 2 (Equal) )
Barbour/Galilei #2 
Barbour/Grammateus 
Barbour/Pythagorean
Bendeler's #1 (1/3 - comma) (Irregular)
Bendeler's #2 (1/3 - comma) (Irregular)
Bendeler's #3 (1/4 - comma) (Irregular)
Bermudo's Equal Semi-tones
Bermudo's Vihuela Temperament (1/6- 1/2-Comma)
Boulliau's Equal Temperament
Bremmer EBVT
Broadwood Best       Ellis Tuner Well 4
Broadwood Usual    
Charles E Moscow Pythagorean
Christiaan Huygens 31
Coleman 11
Coleman 16
Coleman 4
Coleman Balanced 16
Colonna's Irregular Just #1 (Irregular)
Colonna's Irregular Just #2 (Irregular)
De Morgan Unequal  
DeCaus's Monochord (Just)
Dechales' 'Guidonian' 1/5 comma Meantone
Dowland's Lute Tuning (Irregular)
Early 18th Century Well
Ellis Tuner 5 Q-E
Ellis Tuner Well 2
Ellis' Fractional Approximations (Equal)
Equal Beating Charles Earl Stanhope
Equal beating J.Preston Well
Equal Beating Prinz Well
Equal Temperament  
Equal-beating JJ Rousseau
Erlangen Monochord (Just)
Erlangen Monochord (Revised) (Just)
Euler's Monochord (Just)
FACTORY TUNERS 1840 Q-E
Fogliano's Just Meantone - 1529
Fogliano's Monochord #1 (Just)
Fogliano's Monochord #2 (Just)
Fogliano's Tempered Just Intonation (Just)
Fogliano's Tempered Just Intonation (Revised) (Just)
Fogliano-Aron Just Meantone - equal-beating
Fogliano-Aron Just Meantone - non-tempered
Fogliano-Aron Just Meantone - theoretically correct
Francesco AntonioVallotti well
Galilei / Pythagorean (Equal)
Galilei's Equal Temperament
Galilei's Temperament with Linear Correction No. 1 (Equal)
Galilei/Nassarre (Equal)
Gallimard's Modified Meantone #1 (Irregular)
Gallimard's Modified Meantone #2 (Irregular)
Ganassi's Monochord (Approximation) (Equal)
Ganassi's Monochord (Irregular)
Geometric Approsimation (19:12 for Minor Sixth) (Equal)
George Frederick Handel Well
Gioseffo Zarlino 2 7th
Gottfried Keller 1 5th ditonic
Grammateus/Pythagorean Monochord (Irregular)
Hammond's Fractional Approximations (Equal)
Harrison Well Temperament - equal beating
Harrison Well Temperament - theoretically correct
Harrison's 3/10-Comma Meantone
Hawkes' Modified 1/5 - Comma (Irregular)
Henderson's Empirical Adaptation of the Barbour Well Temperament
Henricus Grammateus Pythagorean
Hô Tchhêng-thyen's Approximation (Equal)
Hô Tchhêng-thyen's Temperament Improved (Equal)
Howard Willet Pyle Q-E
Improved Wm Hawkes meantone
Jean Jousse well
Jean-Baptiste Romieu 1/7 Comma Meantone of 1755
Jean-Le Rond D'Alembert well
Jean-Le Rond Dalembert
Johann C Gottlieb Graupner Q-E
Johann George Neidhardt Pythag
Johann Philipp Kimberger well
John Holden 1 5th syntonic
John Marsh 4 25th syntonic
Jousse's Well Temperament
Just Intonation (Jorgenson)      (same as Marpurg Monochord #1)
Just Intonation - Marpurg/Ptolemy
Kellner Wohltemperirt/Bach
Kepler's Monochord #1 (Just)
Kepler's Monochord #2 (Just)
Kirnberger III
Kirnberger III - Avery
Kirnberger Well Temperament (1779)
Kirnberger's 1/2 - Comma (Irregular)(also called Unequal)(same as Von
Wiese's #2)
Levens' Monochord (Altered from) (Irregular)
Levens' Monochord (linear divisions) (Irregular)
Malcolm's Monochord (Irregular)
Malcolm's Monochord (Just)
Mark Wicks Q-E
Marpurg Temperament #1 - 1/3 Diatonic Comma -1776
Marpurg's Monochord #3 (Just)
Marpurg's Monochord #4 (Just)
Marpurg's Temperament #1 (1/12 1/6 - comma) (Irregular)
Marpurg's Temperament #3 (1/12 5/24 - comma) (Irregular)
Marpurg's Temperament A (1/12 1/6 - comma) (Irregular)
Marpurg's Temperament B (1/12 1/6 - comma)
Marpurg's Temperament C (1/12 1/6 - comma) (Irregular)
Marpurg's Temperament D (1/12 1/6 - comma) (Irregular)
Marpurg's Temperament E (1/12 1/6 - comma) (Irregular)
Marpurg's Temperament G (1/5 - comma) (Irregular)
Marpurg's Temperament I (1/3 - comma) (Irregular)
Meantone Temperament with Two Sharp Fifths (Irregular)
Meckenheuser's Division of the Syntonic Comma (Equal)
Mercadier (1/12 1/6 - comma) (Irregular)
Merrick's Equal Temperament
Mersenne's First (and Second) Geometrical Approximation (Equal)
Mersenne's First Geometrical Method for Equal Temperament
Mersenne's Improved Meantone #1 (Irregular)
Mersenne's Improved Meantone #2 (Irregular)
Mersenne's Lute Tuning #1 (Just)
Mersenne's Lute Tuning #2 (Just)
Mersenne's Practical Equal Temperament (Equal)
Mersenne's Second Geometrical Approximation (Equal)
Mersenne's Spinet Tuning #1 (Just)
Mersenne's Spinet Tuning #2 (Just)
Metius Adrian - Mean-Tone Tuning
Montvallon's Monochord (Just)
Nassarre's Equal Semitones (Equal)
Nassarre's Temperament Idealized (Equal)
Neidhardt's Circulating #1 (1/12 1/6 comma) (Irregular)
Neidhardt's Circulating #2 (1/12 1/6 - comma) (Irregular)
Neidhardt's Circulating #3 (1/12 1/6 - comma) (Irregular)
Neidhardt's Fifth Circle #10 (1/6 1/4 - comma)
Neidhardt's Fifth Circle #10 (Idealized) (Irregular)
Neidhardt's Fifth Circle #11 (1/12 1/6 35798 - comma)
Neidhardt's Fifth Circle #12 (1/12 1/6 35798 - comma)
Neidhardt's Fifth Circle #5 (1/12 1/6 - comma) (Irregular)
Neidhardt's Fifth Circle #6 (1/12 1/4 - comma) (Irregular)
Neidhardt's Fifth Circle #7 (1/6 1/4 - comma) (Irregular)
Neidhardt's Fifth Circle #9 (1/12 1/4 - comma) (Irregular)
Neidhardt's Fifth-Circle #2 (1/6 - comma) (Irregular)
Neidhardt's Fifth-circle #3 (1/6 - comma) (Irregular)(also called Unequal
#1)
Neidhardt's Fifth-circle #4 (1/4 - comma) (Irregular)
Neidhardt's Sample Temperament #2 (1/12 1/6 35798 - comma)
Neidhardt's Sample Temperament #3 (1/12 1/6 35798 - comma)
Neidhardt's Third Circle #1 (1/12 1/6 35798 - comma)
Neidhardt's Third Circle #3 (1/12 1/6 - comma) (Irregular)
Neidhardt's Third Circle #4 (1/12 1/6 - comma)
Neidhardt's Third Circle #5 (1/12 1/6 - comma) (Irregular)
Neidhardt-MarpurgDeMorganPythag
Neidhart Unequal #2
Neidhart's Division of the Syntonic Comma (Equal)
Paul Bailey 1993
Paul Bailey Well 2002
Peter Prelleur well
Pietro Aaron quarter syntonic
Prelleur Well-Temperament
Prinz Well-Temeperament
Pythagorean Just (Just Intonation - 12 tones)
Pythagorean Just Intonation - Diatonic Scale - Ionian Mode
Ramarin-Beer 1/6 Syntonic Comma - Meantone
Rameau's Modified Meantone (Irregular)
Ramis' Monochord (Just)
Reinhard's Monochord (Irregular)
Rep 18th cent well
Rep Victorian well
ROBERT SMITH 50
Romieu's Monochord (Just)
Rossi's 2/9-Comma Meantone
Rousseau Equal Beating
Rousseau's Monochord (Just)
Salinas' 1/3 Comma Meantone
Sauveur's 1/5 Comma System
Schlick's Irregular Good Temperament
Schlick's Tuning (Hypothetical #1)
Schlick's Tuning (Hypothetical #2)
Schröter's Approximation No. 1 (Equal)
Schröter's Approximation No. 2 (Equal)
Schröter's Column of Differences No. 1 (Equal)
Schröter's Column of Differences No. 2 (Equal)
Silbermann's 1/6-Comma Meantone
Silbermann's 1/6-Comma Tuning
Smith's 5/18-Comma Meantone
Stanhope - Equal Beating
Stanhope Equal Beating
Stanhope's Temperament (1/3 - comma) (Irregular)
Stevin's Equal Temperament
Strähle's Temperament (Corrected by Barbour) (Equal)
Strähle's Temperament (given by Faggot) (Equal)
Symmetric Septenarium Temperament (1/7 - comma) (Irregular)
Tchheng-thyen's Unequal Temperament
Theoretical ChasEarl Stanhope
Theoretical JJ Rousseau
Theoretical JohnPreston well
Theoretical Prinz well
Tuner's Guide      
Tuner's Guide Becket quasi-equal (also Jean Jousse q-e)
Tuner's Guide Marsh Q-E (same as Johann Nepomuk Hummel Q-E)
Tuner's Guide well 1
Tuner's Guide well 2
Tuner's Guide well 3
Tuner's Guide Well-Temperament # 3 (1840) (Theoretically Correct)
Vallotti Well Temperament
Vallotti's Well Temperament (c. 1750)
Vallotti-Young well
Verheijen Rossi - 1/5 Comma Meantone
Victorian Moore, year 1885
Viennese Q-E
Von Wiese's #1 (1/2 - comma) (Irregular)
Von Wiese's #3 (1/2 - comma) (Irregular)
Wâng Phó's Pythagorean-type Monochord (Irregular)
Wâng Phó's Unequal Temperament
Well temperament - 1/4 Diatonic Comma
Wendell 2002 Lite (Victorian) WT
Werckmeister III
Werckmeister III - Avery
Werckmeister's 'Correct' #1 (1/4 - comma) -1691 (Irregular)
Werckmeister's 'Correct' #2 (1/3 - comma) (Irregular)
Werckmeister's 'Correct' #3 (1/4 - comma) (Irregular)
Werckmeister's Septenarium (1/7 - comma) (Irregular)
Young - Avery      
Young's #1 (1/12 3/16 - comma) (Irregular)
Young's #2 (1/6 - comma) (Irregular)
Young's Well Temperament #2 (1800) - equal beating
Young's Well Temperament #2 (1800) - theoretically correct
Zarlino's 2/7 Comma Meantone (Barbour)
Zarlino's 2/7 Comma Meantone (Henderson)
Zarlino's Pure Diatonic   and   Just Intonation - Ptolemy's Diatonic
Syntonon
Zarlino/symmetrical - 12-tone

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jason kanter * piano tuning * piano teaching
bellevue, wa * 425 562 4127 * cell 425 831 1561
orcas island * 360 376 2799
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> From: Newton Hunt <nhunt@optonline.net>
> Reply-To: pianotech@ptg.org
> Date: Wed, 27 Mar 2002 22:36:53 -0500
> To: pianotech@ptg.org
> Subject: Re: Historic tuning modes
> 
> Hi Jason,
> 
> I downloaded the .pdf file and have looked at it but not studied it.
> Maybe the final version should have a "significant" category to help
> determine it's historical significant.  Obviously 200 HTs would have
> quite a few that were less significant than others in terms of who, when
> and where they were used.
> 
> I just love making more work for others. :)
> 
> Newton



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