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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
=> is actually not harmonotonic


What do you think?


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
in MTS-ESP Master I'd use the same semantics


!! comparisons irrelevant because not harmonotonic !!
.scl file
in comparison to OS
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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