Coppner
Joined 10 August 2024
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'''[DRAFT] Non-octave / generalized (?) overtone scale'''<br> | '''[DRAFT] Non-octave / generalized (?) overtone scale'''<br> | ||
TODO: research if a generalized form like this already exists<br> | |||
COS - constrained otonal sequence<nowiki><br></nowiki> | |||
in comparison to<nowiki><br></nowiki> | |||
OS: COS is constrained, OS is open ended, | |||
<br> | |||
Non-octave overtone scales are an approach to describe [[Overtone scale|overtone scales]] without the need of the [[octave]] as the period.<br> | Non-octave overtone scales are an approach to describe [[Overtone scale|overtone scales]] without the need of the [[octave]] as the period.<br> | ||
Therefore, they are [[non-octave]]-repeating scales based on a generating sequence which itself is a subset of the [[harmonic series]].<br> | Therefore, they are [[non-octave]]-repeating scales based on a generating sequence which itself is a subset of the [[harmonic series]].<br> | ||
They can also be viewed as a form of [[ | They can also be viewed as a form of [[generator sequence]].<br> | ||
Non-octave overtone scales are described by the form '''n...p:s'''<br> | Non-octave overtone scales are described by the form '''n...p:s'''<br> | ||
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etc. | etc. | ||
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 | |||
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 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? | |||
I feel like with every interval being present only once it somehow defeats the 'generator' aspect of GS. | |||
What do you think? | |||
.scl file | |||
! 5_7_8_10_11_12.scl | |||
! | |||
Otonal pentatonic 5:7:8:10:11:12 | |||
! | |||
5 | |||
! | |||
7/5 | |||
8/5 | |||
10/5 | |||
11/5 | |||
12/5 | |||