OTC 2L 10s

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Omnitetrachordal MODMOS scales

2L+10s

This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form 2L+ns are known to have this property.

temperaments: injera ?


Class 1

12 tones (5+2+5)

Dual of OTC 10L+2s. Probably only useful for small values of L/s.

P = 0.8849491924

Q = 3.8274237885 (4/3 = L+3.5s)

L = 100.00 to 600.00 cents (260.15 cents @ Q)

s = 0.00 to 100.00 cents (67.97 cents @ Q)

9/8 = 2s (0.00 to 200.00 cents)

4/3 = L+4s (500.00 to 600.00 cents)

MOS generator = s (0.00 to 100.00 cents)

MOS period = 1/2 octave (600.00 cents)

notable EDOs: 14, 16, 26, 38

LsssssLsssss (MOS, not OTC)

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LssssLssssss (OTC MODMOS) - gen chains 7,5

symmetric modes:

sssLssssLsss

ssLssssssLss

all modes:

ssLss ss ssLss
sLsss ss sLsss
Lssss ss Lssss
ss ssssL ssssL
ss sssLs sssLs
ss ssLss ssLss ssssL ssssL ss
ss sLsss sLsss sssLs sssLs ss
ss Lssss Lssss ssLss ssLss ss
sLsss sLsss ss
Lssss Lssss ss
ssssL ss ssssL
sssLs ss sssLs

12_02_10_ssLss_ss_ssLss.png


Class 2

12 tones (4+4+4)

Only works at high values of L/s.

Q2 = 3.8274237885 (4/3 = L+3.5s)

P = 6.7698983847

Q1 = 9.7123729809 (4/3 = L+2.5s)

L = 100.00 to 600.00 cents (260.15 cents @ Q2, 345.11 cents @ P, 396.09 cents @ Q1)

s = 0.00 to 100.00 cents (67.97 cents @ Q2, 50.98 cents @ P, 40.78 cents @ Q1)

9/8 = 4s (0.00 to 400.00 cents)

4/3 = L+3s (400.00 to 600.00 cents)

MOS generator = s (0.00 to 100.00 cents)

MOS period = 1/2 octave (600.00 cents)

notable EDOs: 20, 22, 24

LsssssLsssss (MOS, not OTC)

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LsssLsssssss (OTC MODMOS) - gen chains 8,4

all modes:

Lsss Lsss ssss
sssL ssss sssL
ssLs ssss ssLs
sLss ssss sLss
Lsss ssss Lsss
ssss sssL sssL
ssss ssLs ssLs
ssss sLss sLss
ssss Lsss Lsss
sssL sssL ssss
ssLs ssLs ssss
sLss sLss ssss

See also