Pythagorean tuning is derived from the 3/2 frequency ratio, and has been believed by some to be the basis of many historical scales.

Pythagorean tuning uses steps of the frequency ratios 3/2 (702 cents) to generate steps of fifths;
and 4/3 (498 cents) to generate steps of fourths. This results in a spiral tuning yet the resultant harmony is generally agreed to be unsatisfactory.

Some authorities claim that this is the basis of all Indian tunings, and that North Indian scales are derived from steps of fifths in the sa - ma pattern; whilst the South Indian tuning uses steps of fourths in the sa - pa pattern. As Indian musical practice tends to contain many ornamentations, much vibrato, and glissando, this is doubtful.

Steps of Fifths

Indian

Name

Position Western

Equivalent

Ratio Cents
Sa

I

C 2/1 1200.0
Ma

V

G 3/2 702.0
Kai. N

II

D 9/8 203.9
Sadh G

VI

A 27/16 905.9
Sudh D

III

E 81/64 407.8
Sudh R

VII

B 243/128 1109.8
Pra M

#IV

F# 729/512 611.7
Kak N

#I

C# 2187/2048 113.7
Antara G

#V

G# 6561/4096 815.6
Sadh G

#II

D# 19683/16384 317.6
Ch D

#VI

A# 59049/32768 1019.6
Ch R

#III

E# 177147/131072 521.5
Pa (a comma

flatter)

#VII

B# 531441/524288 23.5


Steps of Fourths

Indian

Name

Position Western

Equivalent

Ratio Cents
Sa

I

C 2/1 1200.0
Pa

IV

F 4/3 498.0
Ch.R

bVII

Bb 16/9 996.1
Ch. D

bIII

Eb 32/27 294.1
Ant G

bVI

Ab 128/81 792.2
Kakali N

bII

Db 256/243 90.2
Pra M

bV

Gb 1024/729 588.3
Sud R

bVIII

Cb 4096/2187 1086.3
Sud D

bIV

Fb 8192/6561 384.4
Sadh G bbVII Bbb 32768/19683 882.4
Kaisiki N bbIII Ebb 65536/59049 180.5
Sud M bbVI Abb 262144/177147 678.5
Pa (a comma

sharper)

bbII Dbb 1048576/531441 1176.5

LucyTuning homepage

Compare to LucyTuned values (Pythagorean flats are flatter and sharps are sharper)

Equal temperaments

Meantone Tunings

Hybrid tunings mapped using L & s

Download Microsoft Works 4.0 Spreadsheet (includes adjustable cent values and fretting positions for Pythagorean Tuning)- worksfret.zip

Integer frequency ratio and Just Intonation tunings

back to Pitch, Pi,..... Chapter One


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