User:Ganaram inukshuk/Diagrams: Difference between revisions
→Family Tree of MOSses: Given the knowledge provided by others on the xen Discord, I uploaded another version of the MOS family tree that includes multi-period MOSses. |
m Found that Erv Wilson described the mos family tree so I linked to the relevant source. |
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Personal note: <s>I don't think I've ever seen a scale tree organized like this, but I'd be curious to know if it's been conceived elsewhere. The fact that it only contains single-period scales makes it unusual compared to other scale trees.</s> It turns out this is a [[wikipedia:Stern–Brocot_tree|Stern-Brocot tree]] adapted to show the relationship between MOSses. SB trees only ever show ratios in their reduced form, hence why the MOS family tree only shows single-period MOSses. | Personal note: <s>I don't think I've ever seen a scale tree organized like this, but I'd be curious to know if it's been conceived elsewhere. The fact that it only contains single-period scales makes it unusual compared to other scale trees.</s> It turns out this is a [[wikipedia:Stern–Brocot_tree|Stern-Brocot tree]] adapted to show the relationship between MOSses. SB trees only ever show ratios in their reduced form, hence why the MOS family tree only shows single-period MOSses. | ||
Update (2022-07-28): This type of diagram was already by described by Erv Wilson, with connections to Fibonacci's "rabbit sequence". http://anaphoria.com/RabbitSequence.pdf | |||
=== Single-period MOSses only === | === Single-period MOSses only === | ||
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=== Including Multi-period MOSses === | === Including Multi-period MOSses === | ||
By including multi-period MOSses, the family tree's similarity to the Stern-Brocot tree becomes more apparent. | By including multi-period MOSses, the family tree's similarity to the Stern-Brocot tree becomes more apparent. | ||
[[File:Family tree of mv2 scales with multi period scales.svg|frameless|1500x1500px]] | [[File:Family tree of mv2 scales with multi period scales.svg|frameless|1500x1500px]] | ||
== MOS Diagrams for a Specific EDO == | |||
I've found it easier to conceptualize the relationship between scales with a given generator pair if it's represented rectangularly instead of circularly. Here's an example of a "rectangular horogram" for 17edo. | |||
[[File:17edo Rectangular Horograms.png|2000x2000px]] | |||