Mike Sheiman's Alternative Interval Categorizations: Difference between revisions

<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

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

**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...)

**Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.**

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...?

(8/7) is a minor **second-half**

**(15/13) is a** neutral **second-half**

(7/6) is a major **second-half**

(4/3) is a **minor fourth** **(not a perfect 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")**

(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

**(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**

**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.

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.**</pre></div>

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;

Here's a proposal for a &lt;u&gt;&lt;strong&gt;major/minor/neutral-only system&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;