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Coppner

Joined 10 August 2024
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Hi all!
I have a - what seems like a fairly simple - question which I am unable to answer.
How would you categorize the following subset of the harmonic series as a tuning


5:7:8:10:11:12


5:7:8:10:11:12
Some observations
- its pentatonic
- its period is 12/5 (its a non-octave tuning)
- its a subset of the harmonic series
- its arithmetic
- its non-equal, the (arithmetic) step sizes are 2/5, 1/5, 2/5, 1/5, 1/5
- every interval is unique (in cents: 528, 231, 386, 165, 150)
- its not harmonotonic
- its not a over-n scale: period is not the octave, therefore, its not a AFDO (arithmetic frequency division of octave) either
- its not a OS (otonal sequence): OS has one step size (interval p) and does not care about the end of the sequence/the period, rather, it's approach is 'take the first n in the sequence'
I could do 2-OS2/5 but that would generate 5:7:9:11:13:...
- its not a OD (otonal division), but could be viewed as one specific scale/subset of 7-OD12/5 [5:6:7:8:9:10:11:12]


- is pentatonic
Is it a generator sequence? Every interval is unique, therefore it has as many generators as it does intervals (5) - does calling it a quinary GS even make sense here?
- period is 12/5
I feel like with every interval being present only once it somehow defeats the 'generator' aspect of GS.
- is arithmetic
- is non-equal, (arithmetic) step sizes: 2/5, 1/5, 2/5, 1/5, 1/5
- is still harmonotonic though? by nature of being a subset of the harmonic series


in my own semantics, I'd refer to it by 5->12[2,1,2,1,1] (from including overtone 5 to including overtone 12
What do you think?
in MTS-ESP Master I'd use the same semantics




in comparison to OS
.scl file
    OS has one step size (interval p) and does not care about the end of the sequence/ the period, rather, it's approach is 'take the first n in the sequence'
    I could do 2-OS2/5 but that would generate 5:7:9


in comparison to OD
! 5_7_8_10_11_12.scl
    could be one specific scale/subset of 6-OD5/4 [5:6:7:8:9:10:11]
!
Otonal pentatonic 5:7:8:10:11:12
!
5
!
7/5
8/5
10/5
11/5
12/5
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