names for 7-limit intervals

Greetings.

I recently proposed some alterative names for 7-limit intervals, and
Gene Smith suggested that I post my proposals to this list.

Moving to 7-limit harmony adds six intervals to our repertoire, for
which Gene supplied the following existing names -- not all consistent:

7/4: harmonic seventh,
septimal seventh,
blue seventh,
septimal augmented sixth

12/7: septimal major sixth,
supermajor sixth,
septimal diminished seventh

10/7: Eulerian tritone,
septimal diminished fifth

7/5: septimal tritone,
septimal augmented fourth

7/6: septimal minor third,
subminor third,
septimal augmented second

8/7: septimal whole tone,
septimal diminished third

I like the name "blue seventh" for 7/4. It suggests to me that we have
enriched the standard list of modifiers

diminished, minor, major, augmented

with "blue", where "blue" means about a third of the way from minor to
diminished, a "shrunken minor". If we introduce "red" as a natural
opposite of "blue", we can define it to mean about a third of the way
from major to augmented, a "swollen major". The enriched modifier
sequence

diminished, blue, minor, major, red, augmented

would give us the names "red sixth" for 12/7, "blue third" for 7/6, and
"red second" for 8/7:

7/4 - 969 cents - blue seventh, septimal augmented sixth
12/7 - 933 cents - red sixth, septimal diminished seventh
10/7 - 617 cents - septimal diminished fifth
7/5 - 583 cents - septimal augmented fourth
7/6 - 267 cents - blue third, septimal augmented second
8/7 - 231 cents - red second, septimal diminished third

Are these good names?

Lyle Ramshaw

--- In tuning@yahoogroups.com, "Ramshaw, Lyle" <lyle.ramshaw@...> wrote:

> 7/4 - 969 cents - blue seventh, septimal augmented sixth
> 12/7 - 933 cents - red sixth, septimal diminished seventh
> 10/7 - 617 cents - septimal diminished fifth
> 7/5 - 583 cents - septimal augmented fourth
> 7/6 - 267 cents - blue third, septimal augmented second
> 8/7 - 231 cents - red second, septimal diminished third

One comment about these names is that if you assume Pythagorean tuning,
then "red" always means 64/63, and "blue" always means 63/64. So, for
instance, take the Pythagorean major six of 27/16, and the "red"
verdion will be (27/16)*(64/63) = 12/7. Now 10/7 is the red version,
not of the Pythagorean tritone, but of the classic diatonic tritone of
45/32. 7/5 is the blue version of 64/45.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Ramshaw, Lyle" <lyle.ramshaw@>
wrote:
>
> > 7/4 - 969 cents - blue seventh, septimal augmented sixth
> > 12/7 - 933 cents - red sixth, septimal diminished seventh
> > 10/7 - 617 cents - septimal diminished fifth
> > 7/5 - 583 cents - septimal augmented fourth
> > 7/6 - 267 cents - blue third, septimal augmented second
> > 8/7 - 231 cents - red second, septimal diminished third
>
> One comment about these names is that if you assume Pythagorean
tuning,
> then "red" always means 64/63, and "blue" always means 63/64.

Here's a thought: red and green are complementary colors, as are blue
and orange. We could use red to mean 81/80, green to mean 80/81,
orange to mean 64/63, and blue to mean 63/64. We now have:

10/9: green tone
9/8: tone
8/7: orange tone
7/6: blue minor third
27/16: minor third
6/5: red minor third
5/4: green major third
81/64: major third
9/7: orange major third
21/16: blue fourth
4/3: fourth
27/20: red fourth
40/27: green fifth
3/2: fifth
32/21: orange fifth
14/9: blue minor sixth
128/81: minor sixth
8/5: red minor sixth
5/3: green major sixth
27/16: major sixth
12/7: orange major sixth
7/4: blue seventh
16/9: seventh
9/5: red seventh

I suggest emerald for Pythagorean, ruby for 5-limit, azure for 7-limit,
sapphire for 11-limit, amethyst for 13-limit intervals. Quad erat
demonstrandum:

> 10/9: ruby tone
> 9/8: (emerald) tone
> 8/7: azure tone
> 7/6: azure minor third
> 32/27: emerald third (corrected Gene's mistake. Well, I never!)
> 6/5: ruby minor third
> 5/4: ruby major third
> 81/64: emerald major third
> 9/7: azure major third
> 21/16: azure fourth
> 4/3: fourth
> 27/20: ruby fourth
> 40/27: emerald fifth
> 3/2: fifth
> 32/21: azure fifth
> 14/9: azure minor sixth
> 128/81: emerald minor sixth
> 8/5: ruby minor sixth
> 5/3: ruby major sixth
> 27/16: emerald major sixth
> 12/7: azure major sixth
> 7/4: azure seventh
> 16/9: emerald seventh
> 9/5: ruby seventh

Oz.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 16 Mart 2007 Cuma 12:08
Subject: [tuning] Re: names for 7-limit intervals

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "Ramshaw, Lyle" <lyle.ramshaw@>
> wrote:
> >
> > > 7/4 - 969 cents - blue seventh, septimal augmented sixth
> > > 12/7 - 933 cents - red sixth, septimal diminished seventh
> > > 10/7 - 617 cents - septimal diminished fifth
> > > 7/5 - 583 cents - septimal augmented fourth
> > > 7/6 - 267 cents - blue third, septimal augmented second
> > > 8/7 - 231 cents - red second, septimal diminished third
> >
> > One comment about these names is that if you assume Pythagorean
> tuning,
> > then "red" always means 64/63, and "blue" always means 63/64.
>
> Here's a thought: red and green are complementary colors, as are blue
> and orange. We could use red to mean 81/80, green to mean 80/81,
> orange to mean 64/63, and blue to mean 63/64. We now have:
>
> 10/9: green tone
> 9/8: tone
> 8/7: orange tone
> 7/6: blue minor third
> 27/16: minor third
> 6/5: red minor third
> 5/4: green major third
> 81/64: major third
> 9/7: orange major third
> 21/16: blue fourth
> 4/3: fourth
> 27/20: red fourth
> 40/27: green fifth
> 3/2: fifth
> 32/21: orange fifth
> 14/9: blue minor sixth
> 128/81: minor sixth
> 8/5: red minor sixth
> 5/3: green major sixth
> 27/16: major sixth
> 12/7: orange major sixth
> 7/4: blue seventh
> 16/9: seventh
> 9/5: red seventh
>
>

Why not "go all the way" with:

7/4, 7/5, 7/6, and

8/7, 9/7, 10/7, 11/7, 12/7 and 13/7 ?

Anything less seems incomplete.

Mark Rankin

--- "Ramshaw, Lyle" <lyle.ramshaw@hp.com> wrote:

> Greetings.
>
> I recently proposed some alterative names for
> 7-limit intervals, and
> Gene Smith suggested that I post my proposals to
> this list.
>
> Moving to 7-limit harmony adds six intervals to our
> repertoire, for
> which Gene supplied the following existing names --
> not all consistent:
>
> 7/4: harmonic seventh,
> septimal seventh,
> blue seventh,
> septimal augmented sixth
>
> 12/7: septimal major sixth,
> supermajor sixth,
> septimal diminished seventh
>
> 10/7: Eulerian tritone,
> septimal diminished fifth
>
> 7/5: septimal tritone,
> septimal augmented fourth
>
> 7/6: septimal minor third,
> subminor third,
> septimal augmented second
>
> 8/7: septimal whole tone,
> septimal diminished third
>
> I like the name "blue seventh" for 7/4. It suggests
> to me that we have
> enriched the standard list of modifiers
>
> diminished, minor, major, augmented
>
> with "blue", where "blue" means about a third of the
> way from minor to
> diminished, a "shrunken minor". If we introduce
> "red" as a natural
> opposite of "blue", we can define it to mean about a
> third of the way
> from major to augmented, a "swollen major". The
> enriched modifier
> sequence
>
> diminished, blue, minor, major, red, augmented
>
> would give us the names "red sixth" for 12/7, "blue
> third" for 7/6, and
> "red second" for 8/7:
>
> 7/4 - 969 cents - blue seventh, septimal
> augmented sixth
> 12/7 - 933 cents - red sixth, septimal diminished
> seventh
> 10/7 - 617 cents - septimal diminished fifth
> 7/5 - 583 cents - septimal augmented fourth
> 7/6 - 267 cents - blue third, septimal augmented
> second
> 8/7 - 231 cents - red second, septimal
> diminished third
>
> Are these good names?
>
> Lyle Ramshaw
>

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In my proposal for using "blue" and "red" as names for 7-limit
intervals, Mark Rankin asks why I did not also discuss the ratios 9/7,
11/7, and 13/7.

Answer: I didn't want to tackle, say, 11/7 until I was ready to also
tackle 14/11, its octave-complement.

I suggest measuring the "complexity" of an interval by expressing that
interval as some power of two times the ratio of two odd numbers and
then taking the max of those odd numbers. (Factors of two get special
treatment in this definition because the octave is so basic.) Under
this measure,

the unison and octave have "complexity" 1;

the fifth and fourth have "complexity" 3;

the major and minor thirds and sixths have "complexity" 5;

the six intervals that I discussed in my email have "complexity" 7;

but complexity(9/7) = 9, complexity(11/7) = 11, and complexity(13/7) =
13.

Lyle

Ramshaw, Lyle wrote:

> I suggest measuring the "complexity" of an interval by expressing that
> interval as some power of two times the ratio of two odd numbers and
> then taking the max of those odd numbers. (Factors of two get special
> treatment in this definition because the octave is so basic.) Under
> this measure,
> > the unison and octave have "complexity" 1;
> > the fifth and fourth have "complexity" 3;
> > the major and minor thirds and sixths have "complexity" 5;
> > the six intervals that I discussed in my email have "complexity" 7;
> > but complexity(9/7) = 9, complexity(11/7) = 11, and complexity(13/7) =
> 13.

Then you're using an odd limit. Welcome to the club!

http://tonalsoft.com/enc/l/limit.aspx

Graham