## Search found 23 matches

Sun Oct 30, 2016 12:30 pm
Forum: Equal Division notations
Topic: EDOs with multiple prime mappings
Replies: 42
Views: 3385

### Re: EDOs with multiple prime mappings

Alright, I've banged my head against the wall long enough. I'm officially giving up on my endeavor, and recommending the use of Kite's ups and downs for most ETs up to and including 31edo, with the exception of 30edo, and Standard Sagittal as it is for 30edo and everything above 31edo. I note that w...
Wed Oct 19, 2016 10:57 am
Forum: Equal Division notations
Topic: EDOs with multiple prime mappings
Replies: 42
Views: 3385

### Re: EDOs with multiple prime mappings

So, after spending some time on this, I have indeed discovered that by dividing 9/8 (the one consistent with the best 3/2, provided the best 3/2 is no sharper than 720¢) instead of the limma and apotome, I can accomplish exactly the same results as my original proposal with one fewer symbol pair, an...
Sat Oct 15, 2016 4:55 pm
Forum: Equal Division notations
Topic: EDOs with multiple prime mappings
Replies: 42
Views: 3385

### Re: EDOs with multiple prime mappings

It looks like ETs that fit this bill would be: 17, 22, 24, 29, 31, 36, 38, 43, 50, and 57 (12 and 19 need zero additional symbols). 45/44 is the only comma I have found so far that works for these ETs; being the difference between 11/9 and 5/4 (or 9/4 and 11/5, or 15/11 and 4/3), I'd say it carries...
Sat Oct 15, 2016 10:14 am
Forum: Equal Division notations
Topic: EDOs with multiple prime mappings
Replies: 42
Views: 3385

### Re: EDOs with multiple prime mappings

I've been working on this post for 2 days, so apologies if you've already covered some stuff in replies during the time I've been writing this. . I don't think there's any question that 6 should be notated as a subset of 12, and 18 as a subset of 36. But it's arguable whether 8 should be notated as ...
Thu Oct 13, 2016 3:34 pm
Forum: Equal Division notations
Topic: EDOs with multiple prime mappings
Replies: 42
Views: 3385

### Re: EDOs with multiple prime mappings

I fear that in not replying to everything, I'm just burying certain points under continued discussion of others. So I'm going to endeavor to address all of your points I have not yet addressed in one marathon post. This discussion has spawned a lot of off-shoots! 1. (Mentioned above) When the limma ...
Sun Oct 09, 2016 3:59 pm
Forum: Equal Division notations
Topic: EDOs with multiple prime mappings
Replies: 42
Views: 3385

### Re: EDOs with multiple prime mappings

Okay, going to try to work my way through your replies. I have no idea how any sensible and usable EDO notation could actually reflect the presence of _all_ the well-approximated primes. Please explain. If by "all", you mean "to the infinite limit" then of course, it would be abs...
Sun Oct 09, 2016 1:16 pm
Forum: Equal Division notations
Topic: EDOs with multiple prime mappings
Replies: 42
Views: 3385

### Re: EDOs with multiple prime mappings

I have yet to catch up on your latest replies in this thread, as I've been traveling for business this weekend and have elected to focus on actually finishing the list of enharmonic equivalents in my proposal. I have finally completed it, although I confess much of it was typed out on airplanes, in ...
Sun Oct 09, 2016 12:51 pm
Forum: Equal Division notations
Topic: OT: Subgroups & Small EDOs
Replies: 6
Views: 560

### Re: OT: Subgroups & Small EDOs

By "larger ET" here, I was referring to your "generally considered decently accurate superset-ETs". So for each of the EDOs you have listed, you need to tell me what superset EDO you are referring to -- I would expect it to be something like: the smallest multiple whose best fif...
Sun Oct 09, 2016 12:22 am
Forum: Equal Division notations
Topic: OT: Subgroups & Small EDOs
Replies: 6
Views: 560

### Re: OT: Subgroups & Small EDOs

Okay, here is my unweighted error calculation. What I did was to calculate the errors of each basis interval, then take the minimum and maximum. If the minimum is negative and the max is positive, adding abs(min) to maximum gives the largest error on the coprime grid (aka tonality diamond) formed by...
Wed Oct 05, 2016 9:47 am
Forum: Equal Division notations
Topic: OT: Subgroups & Small EDOs
Replies: 6
Views: 560

### Re: OT: Subgroups & Small EDOs

Can you tell me what the maximum absolute error is for each of those larger ETs on the stated subgroup, assuming untempered octaves, so I can decide whether I find them sufficiently accurate? It would be interesting to see them as decimal fractions of the step of the larger ET, as well as in cents....