Mike Sheiman's Alternative Interval Categorizations - Revision history

BudjarnLambeth: Added links to dead end pg

2024-01-09T06:11:14Z

Added links to dead end pg

← Older revision		Revision as of 06:11, 9 January 2024
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	People often say xenharmonic intervals like 16/11 are "sour" and mathematically similar intervals (e.g. octave inverses like		People often say xenharmonic intervals like [[16/11]] are "sour" and mathematically similar intervals (e.g. octave inverses like

	1/(16/11) or 11/8) are "sweet". Doesn't that seem a bit counter intuitive?		1/(16/11) or [[11/8]] are "sweet". Doesn't that seem a bit counter intuitive?

	We've been told via standard music theory to accept everything, '''even xenharmonic/microtonal intervals, be''' '''pigeon-holed into some sort of diatonic category'''.		We've been told via standard music theory to accept everything, '''even xenharmonic/microtonal intervals, be''' '''pigeon-holed into some sort of [[diatonic]] category'''.

	In 12EDO C is the tonic/"first".		In [[12EDO]] C is the [[tonic]]/"first".

	C# (apx. 17/16) is a minor second		C# (apx. 17/16) is a minor second
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	'''Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.'''		'''Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.'''

	So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like 14/9, between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels "sour" while an 11/8 slightly below it feels upbeat/sweet?		So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like [[14/9]], between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels "sour" while an 11/8 slightly below it feels upbeat/sweet?

	Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a '''diminished''' fifth. Around 14/9? That's upbeat because it's an '''augmented''' fifth. Why not just stick with major ('''more upbeat''') and minor ('''more downbeat''') and neutral ('''in-between upbeat and downbeat and a bit sour''')...equally distributed among 4ths, 5ths, 6ths...?		Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a '''diminished''' fifth. Around 14/9? That's upbeat because it's an '''augmented''' fifth. Why not just stick with major ('''more upbeat''') and minor ('''more downbeat''') and neutral ('''in-between upbeat and downbeat and a bit sour''')...equally distributed among 4ths, 5ths, 6ths...?

BudjarnLambeth: Categorised this uncategorised page

2023-04-27T00:32:35Z

Categorised this uncategorised page

← Older revision		Revision as of 00:32, 27 April 2023
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	At a quick glance...the point is '''with the latter system, you can hopefully quickly/easily tell which intervals to use to get upbeat (major), downbeat and a tad tense (minor), somewhat tense and mixed-mooded (neutral), or relatively sour (fourth-half) intervals.'''		At a quick glance...the point is '''with the latter system, you can hopefully quickly/easily tell which intervals to use to get upbeat (major), downbeat and a tad tense (minor), somewhat tense and mixed-mooded (neutral), or relatively sour (fourth-half) intervals.'''
			[[Category:Interval naming]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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Wikispaces>mikesheiman: Imported revision 491212770 - Original comment:

2014-02-22T11:17:31Z

**Imported revision 491212770 - Original comment: **

Wikispaces>mikesheiman: Imported revision 491212466 - Original comment:

2014-02-22T11:14:07Z

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Wikispaces>mikesheiman: Imported revision 491209524 - Original comment:

2014-02-22T10:44:09Z

**Imported revision 491209524 - Original comment: **

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference: 
: This revision was by author [[User:mikesheiman|mikesheiman]] and made on <tt>2014-02-22 10:44:09 UTC</tt>. 
: The original revision id was <tt>491209524</tt>. 
: The revision comment was: <tt></tt> 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. 
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">People often say xenharmonic intervals like 16/11 are "sour" and mathematically similar intervals (e.g. octave inverses like
1/(16/11) or 11/8) are "sweet". Doesn't that seem a bit counter intuitive?
We've been raised in music theory to accept everything, even xenharmonic/microtonal intervals, be pigeon-holed into some sort of diatonic category.

In 12EDO C is the tonic/"first".
C# (apx. 17/16) is a minor second
D (apx. 9/8) is a major second
D# (apx. 6/5) is a minor third
E (apx. 5/4) is a major third
**F (apx 4/3) is a perfect fourth** (Why not a major or minor? Inconsistency...)
**F# (apx. 7/5) is on the borderline between a fourth and fifth**
**G (apx. 3/2) is a perfect fifth** (Again, no major or minor. Inconsistency...)
G# (apx. 8/5)is a minor sixth
A (apx. 5/3) is a major sixth
A# (apx. 9/5) is a minor seventh
B (apx 15/8) is a major seventh
**Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.**
So how, then, to you categorize something like an **11/8 or 16/11 between a fourth and a fifth?** Or an interval like 14/9, between a fifth and a sixth? **Furthermore, how do explain when, for example, a 16/11 feels "sour" while an 11/8 slightly below it feels upbeat/sweet?**

Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a **diminished** fifth. Around 14/9? That's upbeat because it's an **augmented** fifth. Why not just stick with major (**more upbeat**) and minor (**more downbeat**) and neutral (**in-between upbeat and downbeat and a bit sour**)...equally distributed among 4ths, 5ths, 6ths...?

Here's a proposal
C is the tonic/"first".
(15/14 and less) is a minor second
(13/12 to 11/10) is a neutral second
(10/9 to 9/8) is a major second
(7/6) is a minor **second-half**
**(15/13) is a** neutral **second-half**
(8/7) is a major **second-half**

(apx. 9/8) is a major second
D# (apx. 6/5) is a minor third
E (apx. 5/4) is a major third
**F (apx 4/3) is a perfect fourth** (Why not a major or minor? Inconsistency...)
**F# (apx. 7/5) is on the borderline between a fourth and fifth**

**G (apx. 3/2) is a perfect fifth** (Again, no major or minor. Inconsistency...)
G# (apx. 8/5)is a minor sixth

A (apx. 5/3) is a major sixth

A# (apx. 9/5) is a minor seventh

B (apx 15/8) is a major seventh</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Mike Sheiman's Alternative Interval Categorizations</title></head><body>People often say xenharmonic intervals like 16/11 are &quot;sour&quot; and mathematically similar intervals (e.g. octave inverses like 
1/(16/11) or 11/8) are &quot;sweet&quot;. Doesn't that seem a bit counter intuitive? 
We've been raised in music theory to accept everything, even xenharmonic/microtonal intervals, be pigeon-holed into some sort of diatonic category. 
 
In 12EDO C is the tonic/&quot;first&quot;. 
C# (apx. 17/16) is a minor second 
D (apx. 9/8) is a major second 
D# (apx. 6/5) is a minor third 
E (apx. 5/4) is a major third 
F (apx 4/3) is a perfect fourth (Why not a major or minor? Inconsistency...) 
F# (apx. 7/5) is on the borderline between a fourth and fifth 
G (apx. 3/2) is a perfect fifth (Again, no major or minor. Inconsistency...) 
G# (apx. 8/5)is a minor sixth 
A (apx. 5/3) is a major sixth 
A# (apx. 9/5) is a minor seventh 
B (apx 15/8) is a major seventh 
Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent. 
So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like 14/9, between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels &quot;sour&quot; while an 11/8 slightly below it feels upbeat/sweet? 
 
 
Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a diminished fifth. Around 14/9? That's upbeat because it's an augmented fifth. Why not just stick with major (more upbeat) and minor (more downbeat) and neutral (in-between upbeat and downbeat and a bit sour)...equally distributed among 4ths, 5ths, 6ths...? 
 
Here's a proposal 
C is the tonic/&quot;first&quot;. 
(15/14 and less) is a minor second 
(13/12 to 11/10) is a neutral second 
(10/9 to 9/8) is a major second 
(7/6) is a minor second-half 
(15/13) is a neutral second-half 
(8/7) is a major second-half 
 
(apx. 9/8) is a major second 
D# (apx. 6/5) is a minor third 
E (apx. 5/4) is a major third 
F (apx 4/3) is a perfect fourth (Why not a major or minor? Inconsistency...) 
F# (apx. 7/5) is on the borderline between a fourth and fifth 
 
G (apx. 3/2) is a perfect fifth (Again, no major or minor. Inconsistency...) 
G# (apx. 8/5)is a minor sixth 
 
A (apx. 5/3) is a major sixth 
 
A# (apx. 9/5) is a minor seventh 
 
B (apx 15/8) is a major seventh</body></html></pre></div>

← Older revision		Revision as of 11:17, 22 February 2014
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:mikesheiman\|mikesheiman]] and made on <tt>2014-02-22 11:14:07 UTC</tt>.<br>		: This revision was by author [[User:mikesheiman\|mikesheiman]] and made on <tt>2014-02-22 11:17:31 UTC</tt>.<br>
	: The original revision id was <tt>~~491212466~~</tt>.<br>		: The original revision id was <tt>491212770</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	(13/12 to 11/10) is a neutral second		(13/12 to 11/10) is a neutral second
	(10/9 to 9/8) is a major second		(10/9 to 9/8) is a major second
	(7/6) is a minor second-half		(8/7) is a minor second-half
	(15/13) is a neutral second-half		(15/13) is a neutral second-half
	(8/7) is a major second-half		(7/6) is a major second-half
	(19/16 to 6/5) is a minor third		(19/16 to 6/5) is a minor third
	(11/9) is a neutral third		(11/9) is a neutral third
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	(13/12 to 11/10) is a neutral second<br />		(13/12 to 11/10) is a neutral second<br />
	(10/9 to 9/8) is a major second<br />		(10/9 to 9/8) is a major second<br />
	(7/6) is a minor <strong>second-half</strong><br />		(8/7) is a minor <strong>second-half</strong><br />
	<strong>(15/13) is a</strong> neutral <strong>second-half</strong><br />		<strong>(15/13) is a</strong> neutral <strong>second-half</strong><br />
	(8/7) is a major <strong>second-half</strong><br />		(7/6) is a major <strong>second-half</strong><br />
	(19/16 to 6/5) is a minor third<br />		(19/16 to 6/5) is a minor third<br />
	(11/9) is a neutral third<br />		(11/9) is a neutral third<br />