Lhearne

::::::::::::::::::: Ok cool I see now. So the pythagorean axis is still the basis. I worried about using M and m for 4th and 5th where is means something different, but since it isn't defined at all for 4th and 5ths, I think that might be ok, though I still worry that the difference between major and minor fourths and fifths to augmented and diminished fourths and fifths would not be the same as for 2nds, 3rds, 6ths, and 7ths. The logic I was using from the diatonic system was that A - P = P - d = A - M = m - d = A1 = 2187/2048, where 1sts, 4ths, 5ths, and 8ths use P and 2nds, 3rds, 6ths, and 7ths use M and m. Although M4 - m4 = (33/32)^2 is similar in size to 2187/2048, the rastma separates them, and we are not tempering it in the naming system. What's more, major and minor come from the specific interval sizes of each generic interval of the diatonic scale. This is an integral basis to extended diatonic interval names. Another idea I had was to call 11/8 a neutral fourth, where for neutrals, using your N and n, which I like actually, we would have

::::::::::::::::::: regarding the disachisma, don't worry, your suggestion of the septimal kleisma was not what led me to suggest the diaschisma. The diaschisma is actually useful for intervals of 2.5 the same way the rastma is for intervals of 2.11. I thought that if defined based 2.3 and now extended to support 2.11, we should also aim to support 2.5, 2.7, and 2.13. The magic comma - the small dieses, is analogous to the Nexus comma in this way. 5 5/4 major thirds represents a tempered 3/2. 25/24 is important in 2.5, and in many 5-limit temperaments, not as a type of Augmented unison, as it can be defined as ccA1, but as a type of minor second, in Magic[7] and Hanson[7], for example. 225/224 then connects this to the 7-limit, but we don't need 225/224 if we have the diaschisma.  

::::::::::::::::::: Magic[7] 6|0 is our 'diatonic' scale -