Ptolemy's Scale Catalog

112

386

498

204

702

765

814

386

1200

1263

1312

1698

1902

1965


Repeat Ratio:	2:1
Scale Pattern:	28/27 36/35 5/4 9/8 28/27 36/35 5/4
Author:	Archytas of Tarentum
Created On:	ca. 400-347 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 16

► 02. Aristoxenus' Enharmonic

409

498

204

702

746

791

409

1200

1244

1289

1698

1902

1946


Repeat Ratio:	2:1
Scale Pattern:	120/120 120/117 120/114 120/90 120/80 120/78 120/76
Author:	Aristoxenus of Tarentum
Created On:	ca. 335 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 16

► 03. Eratosthenes' Enharmonic

112

386

498

204

702

740

814

386

1200

1238

1312

1698

1902

1940


Repeat Ratio:	2:1
Scale Pattern:	46/45 24/23 5/4 9/8 46/45 24/23 5/4
Author:	Eratosthenes
Created On:	ca. 250-195 BC
Keywords:	ancient greek tetrachord, beautiful, somber
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 16
Notes:	Eratosthenes accurately measured the circumference of the Earth with only 1% error. He also invented the first algorithm for discovering prime numbers.

► 04. Archytas' Chromatic

141

204

294

498

204

702

765

141

906

294

1200

1263

1404

1698

1902

1965


Repeat Ratio:	2:1
Scale Pattern:	28/27 243/224 32/27 9/8 28/27 243/224 32/27
Author:	Archytas of Tarentum
Created On:	ca. 400-347 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 17

► 05. Aristoxenus' Chromatic Malakon (soft)

119

379

498

204

702

761

821

379

1200

1259

1319

1698

1902

1961


Repeat Ratio:	2:1
Scale Pattern:	120/120 120/116 120/112 120/90 120/80 120/77.3333333 120/74.6666667
Waffle Iron:	[120] x [120 116 112 90 80 77.3333333 74.6666667]
Author:	Aristoxenus of Tarentum
Created On:	ca. 335 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 17

► 06. Aristoxenus' Chromatic Hemiolion (1/2 more)

135

363

498

204

702

768

837

363

1200

1266

1335

1698

1902

1968


Repeat Ratio:	2:1
Scale Pattern:	120/120 120/115.5 120/111 120/90 120/80 120/77 120/74
Waffle Iron:	[120] x [120 115.5 111 90 80 77 74]
Author:	Aristoxenus of Tarentum
Created On:	ca. 335 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 17

► 07. Aristoxenus' Chromatic Tonikon

182

316

498

204

702

791

884

316

1200

1289

1382

1698

1902

1991


Repeat Ratio:	2:1
Scale Pattern:	120/120 120/114 120/108 120/90 120/80 120/76 120/72
Waffle Iron:	[120] x [120 114 108 90 80 76 72]
Author:	Aristoxenus of Tarentum
Created On:	ca. 335 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 17
Notes:	Same as #08, Eratosthenes' Chromatic

► 08. Eratosthenes' Chromatic

182

316

498

204

702

791

884

316

1200

1289

1382

1698

1902

1991


Repeat Ratio:	2:1
Scale Pattern:	20/19 19/18 6/5 9/8 20/19 19/18 6/5
Author:	Eratosthenes
Created On:	ca. 250-195 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 18
Notes:	Same as #07, Aristoxenus' Chromatic Tonikon. Eratosthenes accurately measured the circumference of the Earth with only 1% error. He also invented the first algorithm for discovering prime numbers.

► 09. Didymus' Chromatic

112

182

316

498

204

702

112

814

884

316

1200

1312

1382

1698

1902


Repeat Ratio:	2:1
Scale Pattern:	16/15 25/24 6/5 9/8 16/15 25/24 6/5
Author:	Didymus
Created On:	1st century AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 18

► 10. Ptolemy's Chromatic Malakon (soft)

119

182

316

498

204

702

765

119

884

316

1200

1263

1382

1698

1902

1965


Repeat Ratio:	2:1
Scale Pattern:	28/27 15/14 6/5 9/8 28/27 15/14 6/5
Author:	Claudius Ptolemaeus
Created On:	ca. 120-160 AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 18

► 11. Ptolemy's Chromatic Syntonon (tense)

151

231

267

498

204

702

782

151

933

267

1200

1281

1431

1698

1902

1982


Repeat Ratio:	2:1
Scale Pattern:	22/21 12/11 7/6 9/8 22/21 12/11 7/6
Author:	Claudius Ptolemaeus
Created On:	ca. 120-160 AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 18

► 12. Archytas' Diatonic

231

294

204

498

204

702

765

231

996

204

1200

1263

1494

1698

1902

1965


Repeat Ratio:	2:1
Scale Pattern:	28/27 8/7 9/8 9/8 28/27 8/7 9/8
Author:	Archytas of Tarentum
Created On:	ca. 400-347 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 19

► 13. Aristoxenus' Diatonic Malakon (soft)

142

231

267

498

204

702

791

142

933

267

1200

1289

1431

1698

1902

1991


Repeat Ratio:	2:1
Scale Pattern:	120/120 120/114 120/105 120/90 120/80 120/76 120/70
Waffle Iron:	[120] x [120 114 105 90 80 76 70]
Author:	Aristoxenus of Tarentum
Created On:	ca. 335 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 19

► 14. Aristoxenus' Diatonic Syntonon (tense)

193

281

217

498

204

702

791

193

983

217

1200

1289

1481

1698

1902

1991


Repeat Ratio:	2:1
Scale Pattern:	120/120 120/114 120/102 120/90 120/80 120/76 120/68
Waffle Iron:	[120] x [120 114 102 90 80 76 68]
Author:	Aristoxenus of Tarentum
Created On:	ca. 335 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 19

► 15. Eratosthenes' Diatonic

204

294

204

498

204

702

792

204

996

204

1200

1290

1494

1698

1902


Repeat Ratio:	2:1
Scale Pattern:	256/243 9/8 9/8 9/8 256/243 9/8 9/8
Author:	Eratosthenes
Created On:	ca. 250-195 BC
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 19
Notes:	Same as #19, Ptolemy's Diatonic Ditoniaion. Eratosthenes accurately measured the circumference of the Earth with only 1% error. He also invented the first algorithm for discovering prime numbers.

► 16. Didymus' Diatonic

112

182

294

204

498

204

702

112

814

182

996

204

1200

1312

1494

1698

1902

2014


Repeat Ratio:	2:1
Scale Pattern:	16/15 10/9 9/8 9/8 16/15 10/9 9/8
Author:	Didymus
Created On:	1st century AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 20
Notes:	See also similar #20, Ptolemy's Diatonic Syntonon

► 17. Ptolemy's Diatonic Malakon (soft)

182

267

231

498

204

702

786

182

969

231

1200

1284

1467

1698

1902

1986


Repeat Ratio:	2:1
Scale Pattern:	21/20 10/9 8/7 9/8 21/20 10/9 8/7
Author:	Claudius Ptolemaeus
Created On:	ca. 120-160 AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 20

► 18. Ptolemy's Diatonic Toniaion

231

294

204

498

204

702

765

231

996

204

1200

1263

1494

1698

1902

1965


Repeat Ratio:	2:1
Scale Pattern:	28/27 8/7 9/8 9/8 28/27 8/7 9/8
Author:	Claudius Ptolemaeus
Created On:	ca. 120-160 AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 20

► 19. Ptolemy's Diatonic Ditoniaion

204

294

204

498

204

702

792

204

996

204

1200

1290

1494

1698

1902


Repeat Ratio:	2:1
Scale Pattern:	256/243 9/8 9/8 9/8 256/243 9/8 9/8
Author:	Claudius Ptolemaeus
Created On:	ca. 120-160 AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 20
Notes:	Same as #15, Eratosthenes' Diatonic

► 20. Ptolemy's Diatonic Syntonon (tense)

112

204

316

182

498

204

702

112

814

204

1018

182

1200

1312

1516

1698

1902

2014


Repeat Ratio:	2:1
Scale Pattern:	16/15 9/8 10/9 9/8 16/15 9/8 10/9
Author:	Claudius Ptolemaeus
Created On:	ca. 120-160 AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 20
Notes:	See also similar #16, Didymus' Diatonic

► 21. Ptolemy's Diatonic Hemiolion (1/2 more)

151

165

316

182

498

204

702

151

853

165

1018

182

1200

1351

1516

1698

1902

2053


Repeat Ratio:	2:1
Scale Pattern:	12/11 11/10 10/9 9/8 12/11 11/10 10/9
Author:	Claudius Ptolemaeus
Created On:	ca. 120-160 AD
Keywords:	ancient greek tetrachord
References:	Tuning and Temperament, A Historical Survey, J. Murray Barbour, p 21