User:BudjarnLambeth/Oclock

The oclock scale^{[idiosyncratic term]} is a 9-tone scale created by including all the intervals from the following three MOS scales:

• The 3-tone MOS with generator 5\31, period 31\31, with 2 generators up and 0 generators down.
• The 5-tone MOS with generator 11\31, period 31\31, with 0 generators up and 4 generators down.
• The 3-tone MOS with generator 13\31, period 31\31, with 1 generator up and 3 generators down.

It is the following octave-repeating subset of 31edo: 5 4 1 3 5 2 3 6 2.

It belongs to a collection of scales called the wijzerplaat scales.^{[idiosyncratic term]}

It is full of many useful consonances in the 11-limit. It has 9 modes.

History and construction

The oclock scale was devised by Budjarn Lambeth in January 2025, after he had a dream featuring a disc inscribed with numbers - 31 in the middle, and 5, 11 and 13 around the outside.

Intending to make music based on these numbers, Lambeth created a few possible scales for that purpose, one of which was the oclock scale.

In the oclock scale, the percentage of generators up versus down for each MOS was determined by its numeral's vertical position on the disc.

The number of tones generated by each MOS was decided by the MOS's numeral (5, 11 or 13) minus the clockwise position of the numeral on the disc (1, 2, 3... 10, 11, or 12). (The number of generators is by definition one less than the number of tones.)

A recreation of the disc from the dream.

Mode 1

1. 193.5
2. 348.4
3. 387.1
4. 503.2
5. 696.8
6. 774.2
7. 890.3
8. 1122.6
9. 1200.0

Mode 2

1. 154.9
2. 193.6
3. 309.7
4. 503.3
5. 580.7
6. 696.8
7. 929.1
8. 1006.5
9. 1200.0

Subsets

Oclock hexatonic blues

1. 309.7
2. 503.3
3. 580.7
4. 696.8
5. 1006.5
6. 1200.0

Oclock heptatonic blues

1. 309.7
2. 503.3
3. 580.7
4. 696.8
5. 929.1
6. 1006.5
7. 1200.0

Oclock Dorian

1. 193.6
2. 309.7
3. 503.3
4. 696.8
5. 929.1
6. 1006.5
7. 1200.0

Mode 3

1. 38.7
2. 154.8
3. 348.4
4. 425.8
5. 541.9
6. 774.2
7. 851.6
8. 1045.1
9. 1200.0

Mode 4

1. 116.1
2. 309.7
3. 387.1
4. 503.2
5. 735.5
6. 812.9
7. 1006.4
8. 1161.3
9. 1200.0

Mode 5

1. 193.6
2. 271.0
3. 387.1
4. 619.4
5. 696.8
6. 890.3
7. 1045.2
8. 1083.9
9. 1200.0

Mode 6

1. 77.4
2. 193.5
3. 425.8
4. 503.2
5. 696.7
6. 851.6
7. 890.3
8. 1006.4
9. 1200.0

Subsets

Oclock Mixolydian

1. 193.5
2. 425.8
3. 503.2
4. 696.7
5. 890.3
6. 1006.4
7. 1200.0

Oclock inverse harmonic

1. 77.4
2. 425.8
3. 503.2
4. 696.7
5. 890.3
6. 1006.4
7. 1200.0

Oclock fennec

1. 77.4
2. 425.8
3. 503.2
4. 696.7
5. 851.6
6. 1006.4
7. 1200.0

Mode 7

1. 116.1
2. 348.4
3. 425.8
4. 619.3
5. 774.2
6. 812.9
7. 929.0
8. 1122.6
9. 1200.0

Mode 8

1. 232.3
2. 309.7
3. 503.2
4. 658.1
5. 696.8
6. 812.9
7. 1006.5
8. 1083.9
9. 1200.0

Mode 9

1. 77.4
2. 270.9
3. 425.8
4. 464.5
5. 580.6
6. 774.2
7. 851.6
8. 967.7
9. 1200.0