User:Vector/Vector's interval naming scheme: Difference between revisions

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Created page with "Each interval name consists of a ''quality'' and an ''ordinal.'' Note that this is not the same as VJN, which names intervals based on commatic alterations, or ADIN, which names intervals based on their position in edos. == Process == To name an interval: === 1. Octave-reduce and determine closest ordinal. === The ordinals are as follows: {| class="wikitable" |+ !Ordinal !Neutral location !Cents |- |Unison |sqrt(2048/2187) | -57 |- |Seco..."
 
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Each interval name consists of a ''quality'' and an ''ordinal.'' Note that this is not the same as [[Vector's just notation|VJN]], which names intervals based on commatic alterations, or [[ADIN]], which names intervals based on their position in edos.
'''Vector's interval naming scheme''' begins as a simple formal-comma-based scheme. However, the direction of alteration is defined as towards the neutral ("in") or away from the neutral ("out"). The formal commas are those from FJS, specifically FloraC's version.


== Process ==
To name an interval:


=== 1. Octave-reduce and determine closest ordinal. ===
The basic set of adjectives are  
The ordinals are as follows:
{| class="wikitable"
{| class="wikitable"
|+
|+
!Ordinal
!Prime
!Neutral location
!Adjectives
!Cents
!Prefixes
!Alteration direction
|-
|-
|Unison
|5
|sqrt(2048/2187)
|classical
| -57
|penta-
|in
|-
|-
|Second
|7
|sqrt(32/27)
|septimal
|147
|septi-
|out
|-
|-
|Third
|11
|sqrt(3/2)
|undecimal
|351
|undeci-
|in
|-
|-
|Fourth
|13
|sqrt(243/128)
|tridecimal
|555
|trideci-
|in
|-
|-
|Fifth
|17
|sqrt(512/243)
|septendecimal
|645
|sede-
|in
|-
|-
|Sixth
|19
|sqrt(8/3)
|undevicesimal
|849
|devi-
|in
|-
|-
|Seventh
|23
|sqrt(27/8)
|vicesimotertial
|1053
|vice-
|out
|-
|-
|Octave
|29
|sqrt(2187/512)
|vicesimononal
|1257
|vine-
|in
|-
|31
|tricesimoprimal
|trice-
|in[a]
|}
|}
The unusual placement of the "unison" and "octave" are simply in order to make it so that the perfect unison has the same priority as a Pythagorean major or minor interval. Since intervals outside of the octave are not being considered, this is its only effect. The closest neutral ordinal to the interval's cent value defines the interval's ordinal.
[a] for octaves and unisons, "in" always flattens and "out" always sharpens, except for augmented/diminished unisons/octaves. Chromatic semitones and octaves can't use ADIN labels.
 
Other elements:
 
* retro- : Reverses the direction of alteration. Applies to all following elements.
* para- : Changes the diatonic interval referenced to the simplest one a Pythagorean comma away. (So, a paraclassical diminished fourth and a classical major third are the same interval, and "paraclassical" functions as a term meaning "inflect inwards by a schisma".
* trans- : Changes the diatonic interval referenced to the simplest one a diatonic semitone away. (So, a transclassical perfect fourth and a classical major third are the same interval.)
* alter- : Changes the diatonic interval referenced to the simplest one a chromatic semitone away. (So, an alterclassical minor third and a classical major third are the same interval.)
 
para-, trans-, and/or alter- all go at the beginning of an interval name. Stacking multiple of the same one works like warts do, where it successively uses more and more complex offsets by multiples of its relevant comma.
 
Under this scheme, 14/11 may be called the transeptiretroundecimal major third.
 
But that sounds stupid.


=== 2. Determine quality. ===
Fortunately, the scheme provides elements for certain composite formal commas as well:
Intervals "in the vicinity" of each of these offsets from their neutral ordinal's location get their corresponding qualities. "In the vicinity" is kept vague. "Priority" here means something different than in ADIN: if you are being non-specific, it determines which offsets to use and which ones to skip, with lower-priority interval categories being more important.
{| class="wikitable"
{| class="wikitable"
|+
|+
!Offset
!Number
!Priority 1
!Primes
!Priority 2
!Adjectives
!Priority 3
!Prefixes
!Priority 4
!Alteration direction
|-
|-
| -102
|5
|
|paraclassical
|
|schismic
|inframinor
|schi-
|inframinor
|in
|-
|-
| -95
|25
|
|paradiclassical
|
|diaschismic
|
|diaschi-
|sensaminor
|out
|-
|-
| -85
|125
|
|paratriclassical
|subminor
|dietic
|subminor
|dieti-
|subminor
|out
|-
|-
| -75
|7/5
|
|septiclassical
|
|aberschismic
|
|argi-
|gothminor
|out
|-
|-
| -65
|7/5
|
|parasepticlassical
|
|schismean
|neominor
|schimi-
|neominor
|in
|-
| -55
|minor
|triminor
|triminor
|triminor
|-
| -45
|
|
|
|novaminor
|-
| -35
|
|pentaminor
|pentaminor
|pentaminor
|-
| -25
|
|
|
|magiminor
|-
| -20
|
|
|supraminor
|supraminor
|-
| -10
|
|
|
|subneutral
|-
|0
|neutral
|neutral
|neutral
|neutral
|-
|10
|
|
|
|supraneutral
|-
|20
|
|
|submajor
|submajor
|-
|25
|
|
|
|magimajor
|-
|-
|35
|35
|
|pentaretroseptimal
|pentamajor
|minty
|pentamajor
|minti-
|pentamajor
|in
|-
|45
|
|
|
|novamajor
|-
|55
|major
|trimajor
|trimajor
|trimajor
|-
|65
|
|
|neomajor
|neomajor
|-
|75
|
|
|
|gothmajor
|-
|85
|
|supermajor
|supermajor
|supermajor
|-
|95
|
|
|
|sensamajor
|-
|-
|102
|11/7
|
|transeptiretroundecimal
|
|pentacircle
|ultramajor
|neo-
|ultramajor
|out
|}
 
=== 3. Apply special rules ===
Apply the following replacements:
{| class="wikitable"
|+
!Target
!Replacement
|-
|-
|novamajor unison
|11/5
|unison
|alterundeciclassical
|pine
|tardi-
|in
|-
|-
|novaminor fifth
|13/5
|diminished fifth
|transtrideciclassical
|barbados
|barba-
|out
|-
|-
|novamajor fifth
|19/5
|fifth
|paradeviclassical
|eratosthenean
|erato-
|out
|-
|-
|novaminor fourth
|17/5
|fourth
|parasedeclassical
|diatismic
|tismi-
|out
|-
|-
|novamajor fourth
|7/25
|augmented fourth
|schimiretroclassical, diaschiretroseptimal
|marvel
|marvi-
|in
|-
|-
|novaminor octave
|49/5
|octave
|paraargiseptimal
|-
|greenwoodmic
|major unison
|grewi-
|unison
|in
|-
|minor fifth
|diminished fifth
|-
|major fifth
|fifth
|-
|minor fourth
|fourth
|-
|major fourth
|augmented fourth
|-
|minor octave
|octave
|}
|}
== Example ==
What is the interval 462c?
Well, it is closest to the neutral ordinal 555c, so it is a kind of fourth. Additionally, its offset is -93, which places it in the sensaminor category. However, "sensaminor fourth" contains "minor fourth", which gets replaced to "fourth". So it is a ''sensafourth,'' or more broadly a ''subfourth''.
What is the interval 71c?
Well, it is closest to the neutral ordinal 147c (remember the neutral unison is -57c) so it is a kind of second. Additionally, its offset is -76, which places it in the "gothminor" category. So it is a ''gothminor second'', or more broadly a ''subminor second''.

Latest revision as of 06:16, 23 April 2026

Vector's interval naming scheme begins as a simple formal-comma-based scheme. However, the direction of alteration is defined as towards the neutral ("in") or away from the neutral ("out"). The formal commas are those from FJS, specifically FloraC's version.


The basic set of adjectives are

Prime Adjectives Prefixes Alteration direction
5 classical penta- in
7 septimal septi- out
11 undecimal undeci- in
13 tridecimal trideci- in
17 septendecimal sede- in
19 undevicesimal devi- in
23 vicesimotertial vice- out
29 vicesimononal vine- in
31 tricesimoprimal trice- in[a]

[a] for octaves and unisons, "in" always flattens and "out" always sharpens, except for augmented/diminished unisons/octaves. Chromatic semitones and octaves can't use ADIN labels.

Other elements:

  • retro- : Reverses the direction of alteration. Applies to all following elements.
  • para- : Changes the diatonic interval referenced to the simplest one a Pythagorean comma away. (So, a paraclassical diminished fourth and a classical major third are the same interval, and "paraclassical" functions as a term meaning "inflect inwards by a schisma".
  • trans- : Changes the diatonic interval referenced to the simplest one a diatonic semitone away. (So, a transclassical perfect fourth and a classical major third are the same interval.)
  • alter- : Changes the diatonic interval referenced to the simplest one a chromatic semitone away. (So, an alterclassical minor third and a classical major third are the same interval.)

para-, trans-, and/or alter- all go at the beginning of an interval name. Stacking multiple of the same one works like warts do, where it successively uses more and more complex offsets by multiples of its relevant comma.

Under this scheme, 14/11 may be called the transeptiretroundecimal major third.

But that sounds stupid.

Fortunately, the scheme provides elements for certain composite formal commas as well:

Number Primes Adjectives Prefixes Alteration direction
5 paraclassical schismic schi- in
25 paradiclassical diaschismic diaschi- out
125 paratriclassical dietic dieti- out
7/5 septiclassical aberschismic argi- out
7/5 parasepticlassical schismean schimi- in
35 pentaretroseptimal minty minti- in
11/7 transeptiretroundecimal pentacircle neo- out
11/5 alterundeciclassical pine tardi- in
13/5 transtrideciclassical barbados barba- out
19/5 paradeviclassical eratosthenean erato- out
17/5 parasedeclassical diatismic tismi- out
7/25 schimiretroclassical, diaschiretroseptimal marvel marvi- in
49/5 paraargiseptimal greenwoodmic grewi- in
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