User:Ganaram inukshuk/TAMEX: Difference between revisions

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6,211 edits
kth-descendant -> kth-order descendant
Line 20: Line 20:
!Base mos
!Base mos
!Chromatic mosses
!Chromatic mosses
(1st descendants)
(1st-order descendants)
!Enharmonic mosses
!Enharmonic mosses
(2nd descendants)
(2nd-order descendants)
!Subchromatic mosses
!Subchromatic mosses
(3rd descendants)
(3rd-order descendants)
!''k''th descendant mosses
!''k''th-order descendant mosses
|-
|-
|''mos-name''
|''mos-name''
Line 31: Line 31:
|enharmonic ''mos-name''
|enharmonic ''mos-name''
|subchromatic ''mos-name''
|subchromatic ''mos-name''
|(''k''th) ''mos-name'' descendant
|(''k''th-order) ''mos-name'' descendant
|-
|-
|''mos-name''
|''mos-name''
Line 37: Line 37:
|''mosprefix''-monic
|''mosprefix''-monic
|''mosprefix''-subchromatic
|''mosprefix''-subchromatic
|(''k''th) ''mosprefix''-descendant
|(''k''th-order) ''mosprefix''-descendant
|}
|}
=== Step ratio descriptions ===
=== Step ratio descriptions ===
Optionally, the names for a step ratio range, describing the step ratio of the root mos, can be added before these descriptions, either as a single word or prefix. Any step ratio range can be used for 4th descendants and beyond, as context allows.
Optionally, the names for a step ratio range, describing the step ratio of the root mos, can be added before these descriptions, either as a single word or prefix. Any step ratio range can be used for 4th-order descendants and beyond, as context allows.
{| class="wikitable"
{| class="wikitable"
|+Step ratio descriptions
|+Step ratio descriptions
Line 46: Line 46:
! colspan="2" |Base mos
! colspan="2" |Base mos
! colspan="4" |Chromatic mosses
! colspan="4" |Chromatic mosses
(1st descendants)
(1st-order descendants)
! colspan="4" |Enharmonic mosses
! colspan="4" |Enharmonic mosses
(2nd descendants)
(2nd-order descendants)
! colspan="4" |Subchromatic mosses
! colspan="4" |Subchromatic mosses
(3rd descendants)
(3rd-order descendants)
|-
|-
!Mos
!Mos
Line 139: Line 139:
|+Descendant mosses of 5L 2s
|+Descendant mosses of 5L 2s
!Base mos
!Base mos
!1st descendants
!1st-order descendants
!2nd descendants
!2nd-order descendants
!3rd descendants
!3rd-order descendants
!4th descendants
!4th-order descendants
!5th descendants
!5th-order descendants
|-
|-
| rowspan="16" |5L 2s
| rowspan="16" |5L 2s
Line 205: Line 205:
Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:
Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:


* There are 16 4th descendants, or '''4th diadescendant''' scales''.''
* There are 16 4th-order descendants, or '''4th-order diadescendant''' scales''.''
* There are 32 5th descendants, or '''5th diadescendant''' scales.
* There are 32 5th-order descendants, or '''5th-order diadescendant''' scales.
* There are 2 to the ''k''th power ''k''th descendants, or '''''k''th diadescendant''' scales.
* There are 2 to the ''k''th power ''k''th-order descendants, or '''''k''th-order diadescendant''' scales.
Step ratios ranges can be added to these descriptions, as shown.
Step ratios ranges can be added to these descriptions, as shown.
{| class="wikitable"
{| class="wikitable"
|+Descendant mosses of 5L 2s
|+Descendant mosses of 5L 2s
! colspan="2" |Base mos
! colspan="2" |Base mos
! colspan="2" |1st descendants
! colspan="2" |1st-order descendants
! colspan="2" |2nd descendants
! colspan="2" |2nd-order descendants
! colspan="2" |3rd descendants
! colspan="2" |3rd-order descendants
! colspan="2" |4th descendants
! colspan="2" |4th-order descendants
|-
|-
!Mos
!Mos
Line 237: Line 237:
| rowspan="2" |ultrasoft diasubchromatic
| rowspan="2" |ultrasoft diasubchromatic
|7L 26s
|7L 26s
| rowspan="2" |ultrasoft 4th diadescendants
| rowspan="2" |ultrasoft 4th-order diadescendants
|-
|-
|26L 7s
|26L 7s
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| rowspan="2" |parasoft diasubchromatic
| rowspan="2" |parasoft diasubchromatic
|26L 19s
|26L 19s
| rowspan="2" |parasoft 4th diadescendants
| rowspan="2" |parasoft 4th-order diadescendants
|-
|-
|19L 26s
|19L 26s
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| rowspan="2" |quasisoft diasubchromatic
| rowspan="2" |quasisoft diasubchromatic
|19L 31s
|19L 31s
| rowspan="2" |quasisoft 4th diadescendants
| rowspan="2" |quasisoft 4th-order diadescendants
|-
|-
|31L 19s
|31L 19s
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| rowspan="2" |minisoft diasubchromatic
| rowspan="2" |minisoft diasubchromatic
|31L 12s
|31L 12s
| rowspan="2" |minisoft 4th diadescendants
| rowspan="2" |minisoft 4th-order diadescendants
|-
|-
|12L 31s
|12L 31s
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| rowspan="2" |minihard diasubchromatic
| rowspan="2" |minihard diasubchromatic
|12L 29s
|12L 29s
| rowspan="2" |minihard 4th diadescendants
| rowspan="2" |minihard 4th-order diadescendants
|-
|-
|29L 12s
|29L 12s
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| rowspan="2" |quasisoft diasubchromatic
| rowspan="2" |quasisoft diasubchromatic
|29L 17s
|29L 17s
| rowspan="2" |quasihard 4th diadescendants
| rowspan="2" |quasihard 4th-order diadescendants
|-
|-
|17L 29s
|17L 29s
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| rowspan="2" |parahard diasubchromatic
| rowspan="2" |parahard diasubchromatic
|17L 22s
|17L 22s
| rowspan="2" |parahard4th diadescendants
| rowspan="2" |parahard4th-order diadescendants
|-
|-
|22L 17s
|22L 17s
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| rowspan="2" |ultrahard diasubchromatic
| rowspan="2" |ultrahard diasubchromatic
|22L 5s
|22L 5s
| rowspan="2" |ultrahard 4th diadescendants
| rowspan="2" |ultrahard 4th-order diadescendants
|-
|-
|5L 22s
|5L 22s
|}
|}
== Additional temperament-agnostic mos names ==
== Additional temperament-agnostic mos names ==

Revision as of 05:25, 26 November 2023

Work-in-progress

This page assumes the reader is familiar with TAMNAMS mos names, mos prefixes, and step ratios.

TAMEX (from Temperament-Agnostic Moment-of-Symmetry Scale Extension Description System), originally devised by Frostburn and Ganaram inukshuk as two separate naming schemes, is an extension to the mos pattern names provided by TAMNAMS. This scheme is a means of describing how descendant scales (namely, chromatic and enharmonic mosses) with more than 10 steps relate back to smaller mosses and, to a lesser extent, what step ratios of the original mos is needed to produce that descendant mos. Additionally, it is a means of generalizing the notion of a chromatic scale to nondiatonic mosses.

Despite looking like a naming system, what TAMEX provides are descriptions of descendant mosses that relate to a single, TAMNAMS-named mos. Hence, "names" for mosses are meant to be as general as possible and can refer to more than one mos.

Description scheme for TAMNAMS-named mosses

Base descriptions

To describe mosses that have more than 10 notes, descriptions are based on how they're related to another, named mos, based on how many generations apart the two are:

  • The immediate child of a mos is a chromatic mos.
  • The grandchild scale of a mos is an enharmonic mos.
  • The great-grandchild scale of a subchromatic mos.
  • In general, a mos that is a kth descendant of a named mos is a kth descendant.

Descriptions can take on one of two forms: a description as two words, or a single word bearing the mos's prefix. Which one to be used is up the user and whichever form is best depending on context. In the case of kth descendants, the ordinal value kth can be omitted to refer to any or all descendant mosses, depending on context.

Base descriptions
Base mos Chromatic mosses

(1st-order descendants)

Enharmonic mosses

(2nd-order descendants)

Subchromatic mosses

(3rd-order descendants)

kth-order descendant mosses
mos-name chromatic mos-name enharmonic mos-name subchromatic mos-name (kth-order) mos-name descendant
mos-name mosprefix-chromatic mosprefix-monic mosprefix-subchromatic (kth-order) mosprefix-descendant

Step ratio descriptions

Optionally, the names for a step ratio range, describing the step ratio of the root mos, can be added before these descriptions, either as a single word or prefix. Any step ratio range can be used for 4th-order descendants and beyond, as context allows.

Step ratio descriptions
Base mos Chromatic mosses

(1st-order descendants)

Enharmonic mosses

(2nd-order descendants)

Subchromatic mosses

(3rd-order descendants)

Mos L:s range Mos L:s range Range name Prefix Mos L:s range Range name Prefix Mos L:s range Range name Prefix
xL ys 1:1 to 1:0 (x+y)L xs 1:1 to 2:1 soft s- (x+y)L (2x+y)s 1:1 to 3:2 soft s- (x+y)L (3x+2y)s 1:1 to 4:3 ultrasoft us-
(3x+2y)L (x+y)s 4:3 to 3:2 parasoft ps-
(2x+y)L (x+y)s 3:2 to 2:1 hyposoft hs- (3x+2y)L (2x+y)s 3:2 to 5:3 quasisoft qs-
(2x+y)L (3x+2y)s 5:3 to 2:1 minisoft ms-
xL (x+y)s 2:1 to 1:0 hard h- (2x+y)L xs 2:1 to 3:1 hypoard hh- (2x+y)L (3x+y)s 2:1 to 5:2 minihard mh-
(3x+y)L (2x+y)s 5:2 to 3:1 quasihard qh-
xL (2x+y)s 3:1 to 1:0 hard h- (3x+y)L xs 3:1 to 4:1 parahard ph-
xL (3x+y)s 4:1 to 1:0 ultrahard uh-

Example: descendants of 5L 2s

The descendants of 5L 2s can be organized as a scale tree, as shown.

Descendant mosses of 5L 2s
Base mos 1st-order descendants 2nd-order descendants 3rd-order descendants 4th-order descendants 5th-order descendants
5L 2s 7L 5s 7L 12s 7L 19s 7L 26s 7L 29s
26L 7s . . .
19L 7s 26L 19s
19L 26s
12L 7s 19L 12s 19L 31s
31L 19s
12L 19s 31L 12s
12L 31s 12L 43s
5L 7s 12L 5s 12L 17s 12L 29s 12L 41s
29L 12s . . .
17L 12s 29L 17s
17L 29s
5L 12s 17L 5s 17L 22s
22L 17s
5L 17s 22L 5s
5L 22s 5L 29s

With 5L 2s as the root mos:

  • There are 2 chromatic descendants, or diachromatic scales: 7L 5s and 5L 7s
  • There are 4 enharmonic descendants, or diamonic scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s
  • There are 8 subchromatic descendants, or diasubchromatic scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.

Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:

  • There are 16 4th-order descendants, or 4th-order diadescendant scales.
  • There are 32 5th-order descendants, or 5th-order diadescendant scales.
  • There are 2 to the kth power kth-order descendants, or kth-order diadescendant scales.

Step ratios ranges can be added to these descriptions, as shown.

Descendant mosses of 5L 2s
Base mos 1st-order descendants 2nd-order descendants 3rd-order descendants 4th-order descendants
Mos Description Mos Description Mos Description Mos Description Mos Descriptions
5L 2s diatonic 7L 5s soft diachromatic 7L 12s soft diamonic 7L 19s ultrasoft diasubchromatic 7L 26s ultrasoft 4th-order diadescendants
26L 7s
19L 7s parasoft diasubchromatic 26L 19s parasoft 4th-order diadescendants
19L 26s
12L 7s hyposoft diamonic 19L 12s quasisoft diasubchromatic 19L 31s quasisoft 4th-order diadescendants
31L 19s
12L 19s minisoft diasubchromatic 31L 12s minisoft 4th-order diadescendants
12L 31s
5L 7s hard diachromatic 12L 5s hypohard diamonic 12L 17s minihard diasubchromatic 12L 29s minihard 4th-order diadescendants
29L 12s
17L 12s quasisoft diasubchromatic 29L 17s quasihard 4th-order diadescendants
17L 29s
5L 12s hard diamonic 17L 5s parahard diasubchromatic 17L 22s parahard4th-order diadescendants
22L 17s
5L 17s ultrahard diasubchromatic 22L 5s ultrahard 4th-order diadescendants
5L 22s

Additional temperament-agnostic mos names

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