User:VectorGraphics/Augmented and diminished intervals - Revision history

Lériendil: Lériendil moved page User:VectorGraphics/Augmented and dimininshed intervals to User:VectorGraphics/Augmented and diminished intervals without leaving a redirect: fixed a typo

2025-04-24T03:24:49Z

Lériendil moved page User:VectorGraphics/Augmented and dimininshed intervals to User:VectorGraphics/Augmented and diminished intervals without leaving a redirect: fixed a typo

← Older revision	Revision as of 03:24, 24 April 2025
(No difference)

VectorGraphics at 07:26, 19 December 2023

2023-12-19T07:26:11Z

← Older revision		Revision as of 07:26, 19 December 2023
Line 97:		Line 97:
	Yup. That's right. According to the definition of augmented, all these different intervals - varying by over 200 cents - are augmented thirds. Yes, even that large tritone (which is extra cursed). The theoretical maximum and minimum within diatonic scales vary by 378 cents (interestingly, a major third) and overlap with major thirds, supermajor thirds, and even perfect fifths.		Yup. That's right. According to the definition of augmented, all these different intervals - varying by over 200 cents - are augmented thirds. Yes, even that large tritone (which is extra cursed). The theoretical maximum and minimum within diatonic scales vary by 378 cents (interestingly, a major third) and overlap with major thirds, supermajor thirds, and even perfect fifths.

	Now, it might be a little unfair to compare augmented thirds specifically given how much ~~they~~ can already vary across diatonic scales, so let's instead take a peek at augmented fifths:		Now, it might be a little unfair to compare augmented thirds specifically given how much thirds can already vary across diatonic scales, so let's instead take a peek at augmented fifths:
	{\| class="wikitable"		{\| class="wikitable"
	!ratio		!ratio

VectorGraphics: Created page with "I find the words "augmented" and "diminished" not that useful. Let's step through some major thirds: {| class="wikitable" |+ !ratio !edosteps !cents |- | |4/12 |400 |- |5/4..."

2023-12-19T07:25:29Z

Created page with "I find the words "augmented" and "diminished" not that useful. Let's step through some major thirds: {| class="wikitable" |+ !ratio !edosteps !cents |- | |4/12 |400 |- |5/4..."

New page

I find the words "augmented" and "diminished" not that useful.

Let's step through some major thirds:
{| class="wikitable"
|+
!ratio
!edosteps
!cents
|-
|
|4/12
|400
|-
|5/4
|
|386
|-
|81/64
|
|409
|-
|24/19
|
|404
|-
|
|6/19
|378
|}
All about the same size, right?

Now let's look at supermajor thirds:
{| class="wikitable"
!ratio
!edosteps
!cents
|-
|
|6/17
|423
|-
|9/7
|
|435
|-
|
|11/31
|425
|-
|
|7/19
|442
|}
Also about the same size.

Now, let's take a look at the augmented thirds of all the scales we've looked at so far that have them defined, and a few more:
{| class="wikitable"
!ratio
!edosteps
!cents
|-
|
|8/17
|564
|-
|177147/131072
|
|522
|-
|
|12/31
|464
|-
|
|7/19
|442
|-
|125/96
|
|456
|-
|
|5/12
|500
|-
|
|9/26
|415
|-
|
|14/27
|622
|}
Yup. That's right. According to the definition of augmented, all these different intervals - varying by over 200 cents - are augmented thirds. Yes, even that large tritone (which is extra cursed). The theoretical maximum and minimum within diatonic scales vary by 378 cents (interestingly, a major third) and overlap with major thirds, supermajor thirds, and even perfect fifths.

Now, it might be a little unfair to compare augmented thirds specifically given how much they can already vary across diatonic scales, so let's instead take a peek at augmented fifths:
{| class="wikitable"
!ratio
!edosteps
!cents
|-
|
|8/17
|847
|-
|6561/4096
|
|815
|-
|
|20/31
|774
|-
|
|12/19
|757
|-
|25/16
|
|772
|-
|
|8/12
|800
|-
|
|16/26
|738
|-
|
|20/27
|888
|}
Not much better - that's still a variation of 150 cents!

"Augmented", along with its partner "diminished", simply don't fit in a brightness-based system. They're scale-specific. And it's also rather hard to know exactly what interval one is talking about when using "augmented" and "diminished" - even between pythagorean and classical here, that's still about a diesis apart. And if we bring in ARCHY, then that comma grows to over 100 cents.

Simply put, I don't find "augmented" or "diminished" useful for naming intervals. Chords, maybe.