Search found 268 matches

by Dave Keenan
Thu Feb 13, 2020 11:12 am
Forum: Just Intonation notations
Topic: Generalisation of the terms "epimoric" and "superparticular" as applied to ratios
Replies: 5
Views: 198

Re: Generalisation of the terms "epimoric" and "superparticular" as applied to ratios

Examples shown with the Latin-derived names. . . . . . . . . . . . . . . . +-----------+----------------------+----------------------+----------------------+ | subtriple | subtriple | subtriple | subtriple | | | superparticular | superbiparticular | supertriparticular | . . . | 1/3 | 2/7 3/10 4/13 5...
by Dave Keenan
Thu Feb 13, 2020 10:47 am
Forum: Just Intonation notations
Topic: Generalisation of the terms "epimoric" and "superparticular" as applied to ratios
Replies: 5
Views: 198

Re: Generalisation of the terms "epimoric" and "superparticular" as applied to ratios

Examples shown with the Greek-derived names. . . . . . . . . . . . . . . . +-----------+----------------------+----------------------+----------------------+ | subtriple | subtriple | subtriple | subtriple | | | epimoric | epidimoric | epitrimoric | . . . | 1/3 | 2/7 3/10 4/13 5/16 … | 3/11 5/17 7/2...
by Dave Keenan
Thu Feb 13, 2020 9:18 am
Forum: Just Intonation notations
Topic: Generalisation of the terms "epimoric" and "superparticular" as applied to ratios
Replies: 5
Views: 198

Re: Generalisation of the terms "epimoric" and "superparticular" as applied to ratios

cmloegcmluin , Thank you for the examples. Assuming you have consciously adopted my suggested anglicised "super<n>particular" in place of the strict Latin "super<n>partient" for n>1, then you have them all correct except the first four. With those, you seem to have confused mod=0 with div=0. When m...
by Dave Keenan
Wed Feb 12, 2020 10:48 pm
Forum: Just Intonation notations
Topic: Generalisation of the terms "epimoric" and "superparticular" as applied to ratios
Replies: 5
Views: 198

Generalisation of the terms "epimoric" and "superparticular" as applied to ratios

This arose as a question from cmloegcmluin on facebook. And is a summary of information gleaned from the reference he found thanks to Google Books: Theoretic Arithmetic, in Three Books by Thomas Taylor, 1816. The relevant information begins on page 34. "Superparticular" and "epimoric" are terms of L...
by Dave Keenan
Wed Feb 12, 2020 11:07 am
Forum: 12-edo-relative notations
Topic: The boundaries between the Trojan symbols
Replies: 0
Views: 84

The boundaries between the Trojan symbols

In Figure 10 of http://sagittal.org/sagittal.pdf we give a number-line marked in cents showing the approximate boundaries between the Trojan symbols, but we do not give precise numerical values. Here they are as fractions of a semitone plus or minus epsilon, where epsilon stands for an infinitesimal...
by Dave Keenan
Tue Feb 11, 2020 11:03 pm
Forum: 12-edo-relative notations
Topic: Extending Trojan notation to finer resolution
Replies: 4
Views: 107

Re: Extending Trojan notation to finer resolution

cmloegcmluin , You certainly have been prolific on topics xenharmonic recently. I am glad that you like the theory behind the Sagittal system. As you have probably read, it was designed to notate both EDOs and JI, right from the beginning, and was designed with the help of an online community of xe...
by Dave Keenan
Tue Feb 11, 2020 11:40 am
Forum: 12-edo-relative notations
Topic: Extending Trojan notation to finer resolution
Replies: 4
Views: 107

Re: Extending Trojan notation to finer resolution

Elsewhere in that facebook thread I wrote:
Dave Keenan
Cmloegcmluin, I have no problem with cents. You could even do both. i.e. Sagittal Trojan symbols /on/ the staff, with the cents for any such symbols stacked /above/ the staff.
by Dave Keenan
Tue Feb 11, 2020 11:19 am
Forum: 12-edo-relative notations
Topic: Extending Trojan notation to finer resolution
Replies: 4
Views: 107

Re: Extending Trojan notation to finer resolution

Here's my proposed multi-Trojan 12-relative 768-edo notation. Symbol Degrees Cents Tones Unicode in up down of 768 SMuFL fonts --------------------------------------------- :#: :b: 64 100 1/2 U+E262 U+E260 :/|\: :\!/: 32 50 1/4 U+E30A U+E30B :|~: :!~: 16 25 1/8 U+E370 U+E371 :/|: :\!: 8 12 1/16 U+E3...
by Dave Keenan
Tue Feb 11, 2020 9:48 am
Forum: 12-edo-relative notations
Topic: Extending Trojan notation to finer resolution
Replies: 4
Views: 107

Extending Trojan notation to finer resolution

This began with the following new thread post by Cmloegcmluin Xenharmonic Feisbeuk on facebook . I've moved it here so that (a) it doesn't get lost, and (b) in subsequent posts I can show the actual symbols by using the forum "smilies". Cmloegcmluin Xenharmonic Feisbeuk Can anyone recommend a notati...
by Dave Keenan
Tue Dec 03, 2019 5:04 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 59
Views: 10682

Re: A proposal to simplify the notation of EDOs with bad fifths

This text-only version of the periodic table of EDOs is for Margo ( mschulter ). I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX +98.0 +48.0 +28.5 +18.0 +11.6 +7.1 +3.9 +1.5 -0.4 -2.0 -3.4 -5.2 -7.2 -9.6 -12.6 -16.2 -20.9 -27.0 -35.3 -47.4 +36.5 +9.2 +0.5 -4.3 -11.0 -23.7 CG ...