John Dowland's Lute Fretting

[Joe Monzo]

© 1998 by Joe Monzo

(This page is accompanied by a MIDI file of the first section of Dowland's famous Lachrimae, in his preferred tuning. I also provide a faster version. The slow one shows the tuning better.)

John Dowland's lute piece Lachrimae was wildly popular around the turn of the 17th century, even being referred to by Shakespeare in some of his plays. Here is the opening section (as heard in my mp3) of Dowland's tablature manuscript:

Dowland's lute fretboard had only ten frets. A diagram of the complete fretting is given below, in an excerpt from my book.

The exact string measurements which produce this fretting are given by Dowland in his son Robert's book.1 They are also quoted in Diana Poulton's John Dowland -- His Life and Works2, and a drawing of the fretboard with cents values appeared on the cover of the first issue of Johnny Reinhard's journal Pitch3.

For each string I give the Letter-name, my JustMusic prime-factor notation, the absolute ratio, and absolute Semitones (which are cents divided by 100); each line indicates the fret, on the right by number, and on the left with Dowland's letter tablature:

 open string G n0 1/1 0.00 C 3-1 4/3 4.98 F 3-2 16/9 9.96 A 2132 9/8 12+2.04 D 2131 3/2 12+7.02 G 22(3...n)0 1/1 24+0.00 a ========== ========== ========== ========== ========== ========== 1st fret G#/Ab 3111131-1 33/31 1.08 C#/Db 11131-1 44/31 6.06 F#/Gb 3-111131-1 176/93 11.04 A#/Bb 213311131-1 297/248 12+3.12 D#/Eb 213211131-1 99/62 12+8.10 G#/Ab 223111131-1 33/31 24+1.08 b 2nd fret A 32 9/8 2.04 D 31 3/2 7.02 G 21(3...n)0 1/1 12+0.00 B 2134 81/64 12+4.08 E 2133 27/16 12+9.06 A 2232 9/8 24+2.04 c 3rd fret A#/Bb 317-1111 33/28 2.84 D#/Eb 7-1111 11/7 7.82 G#/Ab 213-17-1111 22/21 12+0.81 C 21337-1111 297/224 12+4.88 F 21327-1111 99/56 12+9.86 A#/Bb 22317-1111 33/28 24+2.84 d 4th fret B 31111211-1 264/211 3.88 E 111211-1 352/211 8.86 A 213-1111211-1 704/633 12+1.84 C#/Db 2133111211-1 297/211 12+5.92 F# 2132111211-1 396/211 12+10.90 B 2231111211-1 264/211 24+3.88 e 5th fret C 3-1 4/3 4.98 F 3-2 16/9 9.96 A#/Bb 213-3 32/27 12+2.94 D 2131 3/2 12+7.02 G 22(3...n)0 1/1 24+0.00 C 223-1 4/3 24+4.98 f 6th fret C#/Db 3117-1 24/17 5.97 F#/Gb 17-1 32/17 10.95 B 213-117-1 64/51 12+3.93 D#/Eb 213317-1 27/17 12+8.01 G#/Ab 223217-1 18/17 24+0.99 C#/Db 223117-1 24/17 24+5.97 g 7th fret D 31 3/2 7.02 G 21(3...n)0 1/1 12+0.00 C 213-1 4/3 12+4.98 E 2133 27/16 12+9.06 A 2232 9/8 24+2.04 D 2231 3/2 24+7.02 h 8th fret D#/Eb 3211131-1 99/62 8.10 G#/Ab 213111131-1 33/31 12+1.08 C#/Db 2111131-1 44/31 12+6.06 F 213411131-1 891/496 12+10.14 A#/Bb 223311131-1 297/248 24+3.12 D#/Eb 223211131-1 99/62 24+8.10 i 9th fret E 33 27/16 9.06 A 2132 9/8 12+2.04 D 2131 3/2 12+7.02 F# 2135 243/128 12+11.10 B 2234 81/64 24+4.08 E 2233 27/16 24+9.06 k 10th fret F 327-1111 99/56 9.86 A#/Bb 21317-1111 33/28 12+2.84 D#/Eb 217-1111 11/7 12+7.82 G 21347-1111 891/448 12+11.90 C 22337-1111 297/224 24+4.88 F 22327-1111 99/56 24+9.86 l

The complete scale or "gamut" is tabulated as follows (from the top down):

 letter-name prime-factor ratio Semitones tablature HIGHEST"OCTAVE" F 327-1111 99/56 9.86 10th fret, 6th string (6l) E 33 27/16 9.06 9th fret, 6th string (6k) D#/Eb 3211131-1 99/62 8.10 8th fret, 6th string (6i) D 31 3/2 7.02 7th fret, 6th string (6h) C#/Db 3117-1 24/17 5.97 6th fret, 6th string (6g) C 3-1 4/3 4.98 5th fret, 6th string (6f) C 337-1111 297/224 4.88 10th fret, 5th string (5l) B 34 81/64 4.08 9th fret, 5th string (5k) B 31111211-1 264/211 3.88 4th fret, 6th string (6e) A#/Bb 3311131-1 297/248 3.12 8th fret, 5th string (5i) A#/Bb 317-1111 33/28 2.84 3rd fret, 6th string (6d) A 32 9/8 2.04 2nd fret, 6th string (6c) & 7th fret, 5th string (5h) G#/Ab 3111131-1 33/31 1.08 1st fret, 6th string (6b) G#/Ab 3217-1 18/17 0.99 6th fret, 5th string (5g) G n0 1/1 0.00 open 6th string (6a) & 5th fret, 5th string (5f) MIDDLE"OCTAVE" G 347-1111 891/448 11.90 10th fret, 4th string (4l) F# 35 243/128 11.10 9th fret, 4th string (4k) F# 32111211-1 396/211 10.90 4th fret, 5th string (5e) F 3411131-1 891/496 10.14 8th fret, 4th string (4i) F 327-1111 99/56 9.86 3rd fret, 5th string (5d) E 33 27/16 9.06 2nd fret, 5th string (5c) & 7th fret, 4th string (4h) D#/Eb 3211131-1 99/62 8.10 1st fret, 5th string (5b) D#/Eb 3317-1 27/17 8.01 6th fret, 4th string (4g) D#/Eb 7-1111 11/7 7.82 10th fret, 3rd string (3l) D 31 3/2 7.02 open 5th string (5a) & 5th fret, 4th string (4f) & 9th fret, 3rd string (3k) C#/Db 11131-1 44/31 6.06 8th fret, 3rd string (3i) C#/Db 33111211-1 297/211 5.92 4th fret, 4th string (4e) C 3-1 4/3 4.98 7th fret, 3rd string (3h) C 337-1111 297/224 4.88 3rd fret, 4th string (4d) B 34 81/64 4.08 2nd fret, 4th string (4c) B 3-117-1 64/51 3.93 6th fret, 3rd string (3g) A#/Bb 3311131-1 297/248 3.12 1st fret, 4th string (4b) A#/Bb 3-3 32/27 2.94 5th fret, 3rd string (3f) A#/Bb 317-1111 33/28 2.84 10th fret, 2nd string (2l) A 32 9/8 2.04 open 4th string (4a) & 9th fret, 2nd string (2k) A 3-1111211-1 704/633 1.84 4th fret, 3rd string (3e) G#/Ab 3111131-1 33/31 1.08 8th fret, 2nd string (2i) G#/Ab 3-17-1111 22/21 0.81 3rd fret, 3rd string (3d) G n0 1/1 0.00 2nd fret, 3rd string (3c) & 7th fret, 2nd string (2h) LOWEST"OCTAVE" F#/Gb 3-111131-1 176/93 11.04 1st fret, 3rd string (3b) F#/Gb 17-1 32/17 10.95 6th fret, 2nd string (2g) F 3-2 16/9 9.96 open 3rd string (3a) & 5th fret, 2nd string (2f) F 327-1111 99/56 9.86 10th fret, 1st string (1l) E 33 27/16 9.06 9th fret, 1st string (1k) E 111211-1 352/211 8.86 4th fret, 2nd string (2e) D#/Eb 3211131-1 99/62 8.10 8th fret, 1st string (1i) D#/Eb 7-1111 11/7 7.82 3rd fret, 2nd string (2d) D 31 3/2 7.02 2nd fret, 2nd string (2c) & 7th fret, 1st string (1h) C#/Db 11131-1 44/31 6.06 1st fret, 2nd string (2b) C#/Db 3117-1 24/17 5.97 6th fret, 1st string (1g) C 3-1 4/3 4.98 open 2nd string (2a) & 5th fret, 1st string (1f) B 31111211-1 264/211 3.88 4th fret, 1st string (1e) A#/Bb 317-1111 33/28 2.84 3rd fret, 1st string (1d) A 32 9/8 2.04 2nd fret, 1st string (1c) G#/Ab 3111131-1 33/31 1.08 1st fret, 1st string (1b) G n0 1/1 0.00 open 1st string (1a)

Below is a graph of the pitches of the entire fretboard.

As can be seen from the diagrams, some pitches are represented on two strings, and one (the "D" in the middle octave) is represented on three strings.

The ratios derived from this fretting utilize the prime numbers 3, 7, 11, 17, 31, and 211. The strings are tuned (from the bottom up) 1/1 - 4/3 - 16/9 - 9/8 - 3/2 - 1/1. The 1st, 3rd, 4th, 8th and 10th frets all incorporate 111. The 6th fret uses 17-1, the 1st and 8th frets both use 31-1, and the 4th fret uses 211-1. Prime number 5 (giving the standard just-intonation "3rds" and "6ths") is notably absent.

Dowland wrote his pieces in tablature, as did most other composers of lute music, so there was no question as to which ratio would be played for a pitch where there was a choice available (for example, there are three different D#/Eb's within a range of 28 cents (each about 9 cents apart) in the middle octave).

This fretting is a well-temperament which gives each key its own characteristic "color", and it is eminently suitable for Elizabethan-era lute music.

Dowland's tablature for Lachrimae reveals that he specifically required some very strange harmonic structures, which are entirely lost in the many 12-EDO versions of this pieces that most Dowland fans have heard.

One glaring example of these unusual intervals is the Eb chord which appears on the first beat of the 2nd measure. The score calls for a high Bb on the last beat of the 1st measure which is 15 5/9 cents flatter than 12-tET Bb. Then on the first beat of the next measure comes an Eb-Bb-Eb trine with pitches deviating from 12-tET by +10 1/6, +12 1/6, and -17 1/2 cents, respectively. So we have:

```
frequency ratios

Bb -15.6 Â¢  |                 372  |
| Eb +10.2 Â¢           |  252
| Bb +12.2 Â¢           |  189
| Eb -17.5 Â¢           |  124

```

Man, listen to *those* holwin' wolves!

The top Bb forms a 3:1 ratio with the bottom Eb, and the middle Eb:Bb is a 4:3, so there are a Pythagorean "12th" ("8ve"+"5th") on the outside and "4th" on the inside. But the "4th" on the inside is made of different pitches from the "12th" on the outside. The higher Eb forms a 31:21 ratio with the top Bb, and the lower Bb forms a 189:124 ratio with the bottom Eb.

Wim Hoogewerf's playing of the Dowland pieces at the 1997 AFMM was outstanding. He performs them on a Vogt guitar whose fretboard has six grooves running the length of it, one under each string, with 24 (at least, possibly more) slideable frets in each groove, each fret long enough for just one string. This guitar is capable of retuning to any possible scale within the space limitations of the frets and fingers.

Hoogewerf repeated this performance at the AFMM in New York in May of 1999, and continues to play these pieces all over the world. His performances were the inspiration for my presentation on Dowland's tuning at the ISMA conference in Perugia, Italy, on September 11, 2001.

updated:

1998.11.23
1999.04.30
2001.07.04

REFERENCES

1Robert Dowland, 1610.
Varietie of Lute Lessons. London.

2Diana Poulton, 1972.
John Dowland -- His Life and Works.
University of California Press.
Appendix 2, page 458.

3Johnny Reinhard, 1986.
Pitch, for the International Microtonalist [Autumn].
New York.
Front cover.