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Kite's thoughts on pergens: Difference between revisions

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==Naming very large intervals==
==Naming very large intervals==


So far, the largest multigen has been a 12th. As the multigen fractions get bigger, the multigen can get quite large. To avoid cumbersome degree names like 16th or 22nd, for degrees above 12, adding an 8ve is indicated by "c" for '''compound''' (a conventional music theory term). Thus 10/3 = cM6 = compound major 6th, 9/2 = ccM2 or cM9, etc. For a pergen with an unsplit octave, the multigen is some voicing of the fifth that is less than n/2 octaves. For (P8, M/6), the multigen M is less than 3 octaves, and can be P4, P5, P11, P12, ccP4 or ccP5.
So far, the largest multigen has been a 12th. As the multigen fractions get bigger, the multigen can get quite large. To avoid cumbersome degree names like 16th or 22nd, for degrees above 12, adding an 8ve is indicated by "c" for '''compound''' (a conventional music theory term). Thus 10/3 = cM6 = compound major 6th, 9/2 = ccM2 or cM9, etc. For a pergen with an unsplit octave, the multigen is some voicing of the fifth that is less than n/2 octaves. For (P8, M/6), the multigen M is less than 3 octaves, and can be P4, P5, P11, P12, ccP4 or ccP5. The last one can be spoken as "coco-fifth".


==Secondary splits==
==Secondary splits==
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===Notation guide PDF===
===Notation guide PDF===


This PDF is a rank-2 notation guide that shows the full lattice for the first 32 pergens, up through the quarter-splits block. It includes alternate enharmonics for many pergens.
This PDF is a rank-2 notation guide that shows the full lattice for the first 32 pergens, up through the quarter-splits block. It also includes the single-split pergens from the fifth-split, sixth-split and seventh-split blocks. It includes alternate enharmonics for many pergens.


[http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf tallkite.com/misc_files/notation guide for rank-2 pergens.pdf]
[http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf '''tallkite.com/misc_files/notation guide for rank-2 pergens.pdf''']


Screenshots of the first 2 pages:
{| class="wikitable" style="text-align:center;"
|+Table of contents for the N'''otation Guide for Rank-2 Pergens''' (* means true double)
|-
! colspan="3" |unsplit
!  colspan="3"| quarter-splits
! colspan="3" |single-split fifth-splits
! colspan="3" |single-split seventh-splits
|-
!1
| | (P8, P5)
| | unsplit
| | 16
|(P8/4, P5)
|quarter-8ve
!33
|(P8/5, P5)
|fifth-8ve
!96
|(P8/7, P5)
|seventh-8ve
|-
! colspan="3" |half-splits
! | 17
|(P8, P4/4)
|quarter-4th
!34
|(P8, P4/5)
|fifth-4th
!97
|(P8, P4/7)
|seventh-4th
|-
!2
| | (P8/2, P5)
| | half-8ve
| | 18
|(P8, P5/4)
|quarter-5th
!35
|(P8, P5/5)
|fifth-5th
!98
|(P8, P5/7)
|seventh-5th
|-
!3
| | (P8, P4/2)
| | half-4th
| | 19
|(P8, P11/4)
|quarter-11th
!36
|(P8, P11/5)
|fifth-11th
!99
|(P8, P11/7)
|seventh-11th
|-
!4
| | (P8, P5/2)
| | half-5th
| | 20
|(P8, P12/4)
|quarter-12th
!37
|(P8, P12/5)
|fifth-12th
!100
|(P8, P12/7)
|seventh-12th
|-
!5
| | (P8/2, P4/2) *
| | half-everything *
| | 21
|(P8/4, P4/2) *
|quarter-8ve, half-4th *
!38
|(P8, ccP4/5)
|fifth-coco-4th
!101
|(P8, ccP4/7)
|seventh-coco-4th
|-
! colspan="3" |third-splits
! | 22
|(P8/2, M2/4)
|half-8ve, quarter-tone
! colspan="3" |single-split sixth-splits
!102
|(P8, ccP5/7)
|seventh-coco-5th
|-
!6
| | (P8/3, P5)
| | third-8ve
| | 23
|(P8/2, P4/4) *
|half-8ve, quarter-4th *
!64
|(P8/6, P5)
|sixth-8ve
!103
|(P8, c<sup>3</sup>P4/7)
|seventh-trico-4th
|-
!7
| | (P8, P4/3)
| | third-4th
| | 24
|(P8/2, P5/4) *
|half-8ve, quarter-5th *
!65
|(P8, P4/6)
|sixth-4th
| colspan="3" rowspan="9" |
|-
!8
| | (P8, P5/3)
| | third-5th
| | 25
|(P8/4, P4/3)
|quarter-8ve, third-4th
!66
|(P8, P5/6)
|sixth-5th
|-
!9
| | (P8, P11/3)
| | third-11th
| | 26
|(P8/4, P5/3)
|quarter-8ve, third-5th
!67
|(P8, P11/6)
|sixth-11th
|-
!10
| | (P8/3, P4/2)
| | third-8ve, half-4th
| | 27
|(P8/4, P11/3)
|quarter-8ve, third-11th
!68
|(P8, P12/6)
|sixth-12th
|-
!11
| | (P8/3, P5/2)
| | third-8ve, half-5th
| | 28
|(P8/3, P4/4)
|third-8ve, quarter-4th
!69
|(P8, ccP4/6)
|sixth-coco-4th
|-
!12
| | (P8/2, P4/3)
| | half-8ve, third-4th
| | 29
|(P8/3, P5/4)
|third-8ve, quarter-5th
!70
|(P8, ccP5/6)
|sixth-coco-5th
|-
!13
| | (P8/2, P5/3)
| | half-8ve, third-5th
| | 30
|(P8/3, P11/4)
|third-8ve, quarter-11th
| colspan="3" rowspan="3" |
|-
!14
| | (P8/2, P11/3)
| | half-8ve, third-11th
| | 31
|(P8/3, P12/4)
|third-8ve, quarter-12th
|-
!15
| | (P8/3, P4/3) *
| | third-everything *
| | 32
|(P8/4, P4/4) *
|quarter-everything *
|}Screenshots of the first 2 pages:


[[File:pergens_1.png|alt=pergens 1.png|704x948px|pergens 1.png]]
[[File:pergens_1.png|alt=pergens 1.png|704x948px|pergens 1.png]]
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