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Mike Sheiman's Alternative Interval Categorizations: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
People often say xenharmonic intervals like [[16/11]] are "sour" and mathematically similar intervals (e.g. octave inverses like
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 10:44:09 UTC</tt>.<br>
1/(16/11) or [[11/8]] are "sweet". Doesn't that seem a bit counter intuitive?
: The original revision id was <tt>491209524</tt>.<br>
 
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We've been told via standard music theory to accept everything, '''even xenharmonic/microtonal intervals, be''' '''pigeon-holed into some sort of [[diatonic]] category'''.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
In [[12EDO]] C is the [[tonic]]/"first".
<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?
C# (apx. 17/16) is a minor second
We've been raised in music theory to accept everything, even xenharmonic/microtonal intervals, be pigeon-holed into some sort of diatonic category.
 
D (apx. 9/8) is a major second


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
D# (apx. 6/5) is a minor third
E (apx. 5/4) is a major 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**
'''F (apx 4/3) is a perfect fourth''' (Why not a major or minor? Inconsistency...)
**G (apx. 3/2) is a perfect fifth** (Again, no 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
G# (apx. 8/5)is a minor sixth
A (apx. 5/3) is a major sixth
A (apx. 5/3) is a major sixth
A# (apx. 9/5) is a minor seventh
A# (apx. 9/5) is a minor seventh
B (apx 15/8) is a major 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?**


'''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 for a <u>'''major/minor/neutral-only system'''</u>


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...?
C is the tonic/"first".


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


(apx. 9/8) is a major second
(8/7) is a minor '''second-half'''
D# (apx. 6/5) is a minor third
 
E (apx. 5/4) is a major third
'''(15/13) is a''' neutral '''second-half'''
**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**
(7/6) is a major '''second-half'''
 
(19/16 to 6/5) is a minor third
 
(11/9) is a neutral third
 
(5/4-9/7) is a major third
 
(4/3) is a '''minor fourth''' '''(not a perfect fourth)'''
 
(15/11) is a neutral fourth
 
(11/8) is a '''major fourth (a more upbeat fourth)'''
 
(7/5) is a '''minor fourth-half (not the usual tritone)'''
 
'''(10/7)''' is a '''neutral fourth-half (not the usual tritone)'''
 
(13/9) is a '''major fourth-half (a "more upbeat tritone")'''
 
(16/11) is a minor fifth
 
(22/15) is a neutral fifth
 
(3/2) is a '''major fifth (not a perfect fifth)'''
 
(17/11) is a '''minor fifth-half'''
 
'''---------------------'''
 
'''(14/9-11/7)''' is a '''major fifth-half'''
 
'''(8/5)''' is a minor sixth
 
(13/8-18/11) is a neutral sixth
 
'''(5/3)''' is a major sixth
 
(12/7) is a '''minor sixth-half'''
 
'''(26/15)''' is a '''neutral sixth-half'''
 
(7/4) is a '''major sixth-half'''
 
(16/9-9/5) is a minor seventh


**G (apx. 3/2) is a perfect fifth** (Again, no major or minor. Inconsistency...)
(11/6) is a neutral seventh
G# (apx. 8/5)is a minor sixth


A (apx. 5/3) is a major sixth
(15/8) is a major seventh


A# (apx. 9/5) is a minor seventh
'''Note there is only one gap where there isn't an equal minor/neutral/major sub-type categorization for every interval number/type!''' Only the fifth-half isn't perfectly even with two parts instead of 3.


B (apx 15/8) is a major seventh</pre></div>
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.'''
<h4>Original HTML content:</h4>
[[Category:Interval naming]]
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Mike Sheiman's Alternative Interval Categorizations&lt;/title&gt;&lt;/head&gt;&lt;body&gt;People often say xenharmonic intervals like 16/11 are &amp;quot;sour&amp;quot; and mathematically similar intervals (e.g. octave inverses like &lt;br /&gt;
1/(16/11) or 11/8) are &amp;quot;sweet&amp;quot;. Doesn't that seem a bit counter intuitive?&lt;br /&gt;
We've been raised in music theory to accept everything, even xenharmonic/microtonal intervals, be pigeon-holed into some sort of diatonic category.&lt;br /&gt;
&lt;br /&gt;
In 12EDO C is the tonic/&amp;quot;first&amp;quot;. &lt;br /&gt;
C# (apx. 17/16) is a minor second &lt;br /&gt;
D (apx. 9/8) is a major second &lt;br /&gt;
D# (apx. 6/5) is a minor third&lt;br /&gt;
E (apx. 5/4) is a major third&lt;br /&gt;
&lt;strong&gt;F (apx 4/3) is a perfect fourth&lt;/strong&gt; (Why not a major or minor? Inconsistency...)&lt;br /&gt;
&lt;strong&gt;F# (apx. 7/5) is on the borderline between a fourth and fifth&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;G (apx. 3/2) is a perfect fifth&lt;/strong&gt; (Again, no major or minor. Inconsistency...)&lt;br /&gt;
G# (apx. 8/5)is a minor sixth&lt;br /&gt;
A (apx. 5/3) is a major sixth&lt;br /&gt;
A# (apx. 9/5) is a minor seventh&lt;br /&gt;
B (apx 15/8) is a major seventh&lt;br /&gt;
&lt;strong&gt;Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.&lt;/strong&gt;&lt;br /&gt;
So how, then, to you categorize something like an &lt;strong&gt;11/8 or 16/11 between a fourth and a fifth?&lt;/strong&gt; Or an interval like 14/9, between a fifth and a sixth? &lt;strong&gt;Furthermore, how do explain when, for example, a 16/11 feels &amp;quot;sour&amp;quot; while an 11/8 slightly below it feels upbeat/sweet?&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a &lt;strong&gt;diminished&lt;/strong&gt; fifth. Around 14/9? That's upbeat because it's an &lt;strong&gt;augmented&lt;/strong&gt; fifth. Why not just stick with major (&lt;strong&gt;more upbeat&lt;/strong&gt;) and minor (&lt;strong&gt;more downbeat&lt;/strong&gt;) and neutral (&lt;strong&gt;in-between upbeat and downbeat and a bit sour&lt;/strong&gt;)...equally distributed among 4ths, 5ths, 6ths...?&lt;br /&gt;
&lt;br /&gt;
Here's a proposal&lt;br /&gt;
C is the tonic/&amp;quot;first&amp;quot;. &lt;br /&gt;
(15/14 and less) is a minor second&lt;br /&gt;
(13/12 to 11/10) is a neutral second&lt;br /&gt;
(10/9 to 9/8) is a major second&lt;br /&gt;
(7/6) is a minor &lt;strong&gt;second-half&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;(15/13) is a&lt;/strong&gt; neutral &lt;strong&gt;second-half&lt;/strong&gt;&lt;br /&gt;
(8/7) is a  major &lt;strong&gt;second-half&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
(apx. 9/8) is a major second&lt;br /&gt;
D# (apx. 6/5) is a minor third&lt;br /&gt;
E (apx. 5/4) is a major third&lt;br /&gt;
&lt;strong&gt;F (apx 4/3) is a perfect fourth&lt;/strong&gt; (Why not a major or minor? Inconsistency...)&lt;br /&gt;
&lt;strong&gt;F# (apx. 7/5) is on the borderline between a fourth and fifth&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;G (apx. 3/2) is a perfect fifth&lt;/strong&gt; (Again, no major or minor. Inconsistency...)&lt;br /&gt;
G# (apx. 8/5)is a minor sixth&lt;br /&gt;
&lt;br /&gt;
A (apx. 5/3) is a major sixth&lt;br /&gt;
&lt;br /&gt;
A# (apx. 9/5) is a minor seventh&lt;br /&gt;
&lt;br /&gt;
B (apx 15/8) is a major seventh&lt;/body&gt;&lt;/html&gt;</pre></div>
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