temperaments and tunings_a guide for lute players

7/29/2019 Temperaments and Tunings_A Guide for Lute Players

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Temperaments and Tunings: A Guide for Lute Players

This is a guide of advice and articles having to do with how to understand temperaments and fret p lacement

for fretted string instruments -- in particular the lute. This page, its opinions and recommendations, and any

mistakes or omissions are the sole responsibility of me. for clarifications or additions, p lease contact me via

the Contact page of the Renaissance Cittern Site.

Books & Articles1.

Tuning Advice2.

Tables of Cent Values3.

Formula for Converting Cent Values into Fret Factors4.

Links to Online Sources About Temperaments5.

1. Books & Articles

The following is a list of books and articles dealing with tuning and temperament with the specific concern ofplucked string instruments such as the lute. for lute players wishing to discover the joys of meantone

temperament with a minimum of theory, Damiani's chapter or Dolata's article, "Lute Tuning with Meantone

Temperaments" are highly recommended and both contain tables of factors for theoretical fret p lacement.

(But see note about differences in factor numbers below in "Tuning Advice.")

The following list is sorted chronologically, with older articles appearing first:

Dombois, Eugen. "Corret and Easy Fret Placement."Journal of the Lute Society of America VI (1973),

pp.30-33.

Dombois, Eugen. "Varieties of Meantone Temperament Realized on the Lute."Journal of the Lute

Society of America VII (1974), pp .82-89.

Lindley, Mark.Lutes, Viols and Temperaments. (Cambridge Univ. Press: 1984).

Crum, Alison and Sonia Jackson. "Appendix 1: Tuning (by Elizabeth Liddle)."Play the Viol. (Oxford

Univ. Press: 1989), pp.155-164.

Dolata, David. "Lute Tuning with Harmonics: A Square Peg in a Round Hole."LSA Quarterly (Feb.

1993), pp.7-9.

Dolata, David. "Lute Tuning with Meantone Temperaments."LSA Quarterly (Feb. 1993), pp.12-15.

Robiczek, Bonnie. "A Method for Tuning the Lute."Lute Society of America Newsletter, XVI, No. 1

(1981), reprinted inLSA Quarterly (May/Aug. 1993), pp .28-29.

Dolata, David. "An Introduction to Tuning and Temperaments."LSA Quarterly, (May/August 1993),

pp.30-31. [Note: cent values for Perfect 4th and Perfect 5th for 1/4 Comma Meantone in Table I are


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reversed. Should read: Perfect 4th: 503.5 and Perfect 5th: 696.5. -A:H]

Dolata, David. "The Secret of Tuning by Harmonics." GFA Soundboard(Spring 1993), pp.27-37,

Dolata, David. "An Introduction to Tuning and Temperaments, Part II."LSA Quarterly"(Feb. 1994),

pp.20-23.

Damiani, Andrea. "Chapter 19: Temperament." Method for Renaissance Lute. (Ut Orpheus Edizioni,

Bologna: 1999), pp.190-192. English Translation by Doc Rossi. [Book originally published in Italian.]

Anotherhighly interesting and recommended book that looks at the debate between pure tuning versus

meantone and equal temperaments is Temperament: How music became a battleground for the great minds of

Western Civilization, by Stuart Isacoff. I would recommend getting the later edition of this book which

contains an afterword that addresses some of the criticisms Isacoff received for his book as well as his

explanation of his views of temperaments.

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2. Tuning Advice

It should be pointed out that exact mathematical values for factors for fret p lacement do differ slightly from

article to article, perhaps in part due to the number of decimal places available on calculators used for

calculations. Despite this discrepancy, the factors are within an acceptable range when one considers that

precise adjustment of the frets is near impossible due to the nature of strings and their elasticity, variance in

the height of action from instrument to instrument, and differences in percept ion of hearing from person to

person. The mathematical and theoretical placement of frets is really just a guide to follow, after which one

may decide to alter this fret or that in order to please one's own aesthetic sense.

It should also be noted that for those who are interested in trying temperaments or tunings other than equal

for the first time, it is recommended that one rethink one's method of tuning. A tuning menthod such as the

following described by Stewart McCoy, and posted by Leonard Williams to the Lutenet (Ap ril, 2000), is

recommended:

I think you should be able to manage to tune the lute well without a sophisticated tuning box.

After all, the "old" guys didn't have one. The important thing is to be sure that you have the frets

in the correct position for the temperament you want. The exact spacing can be measured easily

enough, of course. The important thing to bear in mind with measuring is to ensure that your

calculations involve the vibrating length of the string, not the full length from nut to bridge,

because the string doesn't effectively vibrate right up against the nut and bridge. So for a string-

length of 60 cm, the vibrating length will possibly be somewhere in the region of 59.8 cm.

Although my tuning box can give me all sorts of fancy temperaments, I use it most of the time

just to get me started. The rest I do by ear. If I have problems, and I just can't get the instrument

in tune, then I will use the box for every note. But that really is for emergency use only, when


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panic is starting to set in.

1) I start by tuning the 6th course to G. The habit many musicians have of tuning to a' is a

hangover from tuning violins and other instruments. Tuning to a' is literally the last thing you

want to do with a lute in g'. So I tune the lower string of the 6th course first (using the box),

followed by its octave.

Sometimes it helps to have the octave of the 6th course tuned very slightly on the flat side,because the differences of thickness between the strings causes discrepancies higher up the neck.

When you press down say the 6th course at the 7th fret, the thinner string has further to go

before it reaches the fingerboard, so it will be pulled down further and thus stretched further,

increasing its p itch. This discrepancy will affect all stoppable octave courses to some extent, but

the fatter the string the more noticeable will be the discrepancy.

Anyway, once tuned, that course stays put, and I tune everything else to the lower octave of it,

come what may.

2) Next I tune the 1st course to the 6th course, if need be using a harmonic at the 5th fret.

3) Next I tune the 2nd course (as always to the lower string of the 6th course) using a harmonic at

the 7th fret. I aim to get the 2nd course the tiniest bit flat to that harmonic. I don't count beats

like piano tuners do. That's unnecessarily sophisticated. The main thing is for the 2nd course not

to be sharp to the harmonic on the 6th course.

If I feel unsure, I check f2 against a1 (i.e. 5th fret 2nd course against open 1st course), and a2

against h1. If it is impossible to get those two checks to work, the frets must be incorrectly

placed, probably because of using an incorrect vibrating length, or the strings are FALSE and need

replacing.

I play the following chord, which must sound good before I can proceed:

___a___

___a___

_______

_______

_______

___a___

4) Now that 3 courses are well in tune, I tune the 4th course. I do this by tuning it at the 2nd fret,

again to match the 6th course. If need be, I use the harmonic at the 12th fret of the 6th course.Again I sound a chord, which must sound well in tune:

___a___

___a___

_______

___c___

_______

___a___

If it is not in tune, it must be the 4th course which needs fiddling with, because I know that the


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other three were OK before.

Next I check the 4th course against the 2nd, if need be using a harmonic at the 12th fret of the 4th

course, but I can usually cope tuning notes an octave apart.

_______

___d___

_______

___a__________

_______

5) Four down, two to go. The fifth course comes next. Actually I usually begin by tuning this

course in 5ths to the 1st course, going for a slightly narrow fifth. That may do the trick, but even

if I get it spot on (which is not often), I still have numerous checks. The main one is c5 against

a2. I may also stick to my original plan of always checking against the lower string of the 6th

course, so I check a5 against f6. I don't bother with a6 against h5.

6) Last comes the 3rd course, which is always the hardest to get right. That's why it's suicide to

start tuning the lute to a'. I begin by tuning a3 to c6. This should be an octave. Then I check a5

against d3. Then I test a few chords:

___a____a____c___

___a____c____d___

___c____d____d___

_____________a___

________a________

___a_____________

Last comes my ultimate check. If the following two chords sound well in tune, I know I've made

it:

___c____d____

___e____d____

___f____f____

___e____f____

___c____f____

________d____

The commonest difficulty I have at the very end is that the 3rd course is sometimes a bit on the

sharp side. That's why I use those last two chords. If need be, I flatten the 3rd course very

slightly, even though that may not give me a perfect octave with c6. It 's a compromise which

often needs making.

One last point. If frets are correctly placed, and you always use octaves and unisons, it doesn't

matter what temperament y ou go for. the difficulties arise when you TRY to judge tuning with

intervals like major thirds, because the ear allows for greater tolerance with thirds than it does

with octaves and unisons.

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3. Tables of Cent Values

Note: All values assume a standard "G" tuning with a wolf 5th between G# and Eb (an enharmonically spelled

5th). Most common fret placements for meantone temperaments are dentoed by an asterisk (*).

TABLE 1: Comparison of Cent Values for 1/4 Comma, 1/6 Comma, and Pythagorean Tuning

Pure 1/4 Comma 1/6 Comma Pythagorean

Major 3rd 386 c. 386 c. 393.3 c. 408 c.

Perfect 4th 498 c. 503.5 c. 501.6 c. 498 c.

Perfect 5th 702 c. 696.5 c. 698.3 c. 702 c.

TABLE 2: Cent Values for Various Temperaments and Tunings

fret notePythagorean

Tuning

1/4

Comma

1/5

Comma

1/6

Comma

1/8

Comma

1/11 Comma

(Equal

Temperament)

"396" "Gerle"

a

[open]G 0 0 0 0 0 0 0 0

b1

* b2

G#

Ab

114

90

75.5

117.5

83.2

112

88.3

108.3

94.75

103.75100

93

105

88.8

108

c A 204 193 195.2 196.6 198.5 200 198 196.8

d1

* d2

A#

Bb

318

214

268.5

310.5

278.4

307.2

285

305

293.25

302.25300

291

303

285.6

304.8

* e1

e2

B

Cb408

386

428

390.4

419.2

393.3

413.3

397

406400

396

408

393.6

412.8

f C 498 503.5 502.4 501.6 500.75 500 501 501.6

g1

* g2

C#

Db

612

588

579

621

585.6

614.4

590

610

595.5

604.5600

594

606

590.4

609.6

h D 702 696.5 697.6 698.3 699.25 700 699 698.4

i1

* i2

D#

Eb

816

792

772

814

780.8

809.6

786.6

806.6

794

803800

792

804

787.2

806.4

k E 906 889.5 892.8 895 897.75 900 897 895.2

l1

* l2

E#

F

1020

996

965

1007

976

1004.8

983.3

1003.3

992.5

1001.51000

990

1002

984

1003.2

* m1

m2

F#

Gb

1110

1086

1082.5

1124.5

1088

1116.81091.6 1111.6 1100

1095

1107

1092

1111.2


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n G 1200 1200 1200 1200 1200 1200 1200 1200

TABLE 3: Comaprison of the sizes of Pure and Equal Intervals *

Interval Pure Equal Difference

Chromatic semitone 90 c. 100 c. +10 c.

Diatonic semitone 112 c. 100c. -12 c.

Major second 204 c. 200 c. -4 c.

Minor third 316 c. 300 c. -16 c.

Major third 386 c. 400 c. +24 c.

Fourth 498 c. 500 c. +2 c.

Tritone 590 c. 600 c. +10 c.

Fifth 702 c. 700 c. -2 c.

Minor sixth 814 c. 800 c. -14 .Major sixth 884 c. 900 c. +16 c.

Minor seventh 996 c. 1000 c. +4 c.

Major seventh 1088 c. 1100 c. +12 c.

Octave 1200 c. 1200 c. 0 c.

*taken from "An Introduction to Tuning and Temperaments, Part II" by David Dolata

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4. Formula for Converting Cent Values into Fret Factors

In the equation below,y=factorandx=cent value.

y = 1 - 0.5(x/1200)

This formula can be used to convert cents into a fret factor for any kind of string instrument. Once you have

determined the fret factors for all of the fret locations (based on cents) that you wish, simply multiply the

vibrating string length by the factor in order to obtain the location of the fret as measured from the nut. It maybe helpful to inscribe all of the fret locations onto a p iece of grid or graph p aper, then use this paper as a

template which can be conveniently stored in one's lute case. In this way it is possible to have a number of

different temperaments prepared for a single lute: all one needs to do is use the templates to quickly switch

fret p osition.

It should be noted, however, that the actual vibrating string length may differ slightly from the lute's mensur:

the vibrating length should be measured between the free end of the st ring at the nut to the location where the

string passes under itself near the bridge. One may also wish, depending upon the action of one's instrument,

to make the vibrating string length slightly smaller than what is measured in order to account for "bending" of


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the string when depressed.

An "easy" way to calculate the "actual" vibrating string length to use for calculations is simply to measure the

distance between the bridge-end of the nut and the center of the 12th fret (which is fixed on most instruments)

-- assuming, of course, that this fret was originally p laced in the correct position for a perfect octave.

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5. Links to Online Sources About Temperaments

(Just a start!)

David van Ooijen's do-It-Yourself Article

A History of Temperaments and Tunings

The Just Intonation Network

Tuning Forum/Digest

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Last updated Sep. 10, 2005

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