7 tone equal in elementary school

This is neat:

http://gothamist.com/2008/04/11/video_of_the_da_188.php

This is way better than School of Rock; over in Mr. R's class in
Brooklyn, the little ones are becoming luthiers. Mr. R, Paul
Rubenstein, works for Working Playground and teaches high school and
middle school kids how to make electric guitars and amplifiers, a
program he started 5 years ago. He tells us:

"We make them entirely from scratch (except for the tuning
machines) including the pickups. It has just grown since then... now
we make amplifiers and square wave oscillators too."

"We are setting the frets to an unconventional tuning system:
7-tone equal temperament. This means that instead of having the
standard 12 notes (A, A#, B, etc.) we will have a seven-note scale
with notes that don't correspond to the usual notes-- they fall
in-between those notes, giving the scale a distinctive sound."

There's a video too.

Prent Rodgers

Paul's posted about this a fair bit over the years on the
tuning list. Good to see he's still getting press! -Carl

At 03:17 PM 5/9/2008, you wrote:
>This is neat:
>
>http://gothamist.com/2008/04/11/video_of_the_da_188.php
>
>This is way better than School of Rock; over in Mr. R's class in
>Brooklyn, the little ones are becoming luthiers. Mr. R, Paul
>Rubenstein, works for Working Playground and teaches high school and
>middle school kids how to make electric guitars and amplifiers, a
>program he started 5 years ago. He tells us:
>
> "We make them entirely from scratch (except for the tuning
>machines) including the pickups. It has just grown since then... now
>we make amplifiers and square wave oscillators too."
>
> "We are setting the frets to an unconventional tuning system:
>7-tone equal temperament. This means that instead of having the
>standard 12 notes (A, A#, B, etc.) we will have a seven-note scale
>with notes that don't correspond to the usual notes-- they fall
>in-between those notes, giving the scale a distinctive sound."
>
>There's a video too.
>
>Prent Rodgers

--- In MakeMicroMusic@yahoogroups.com, "Prent Rodgers"
<prentrodgers@...> wrote:
>
> This is neat:
>
> http://gothamist.com/2008/04/11/video_of_the_da_188.php
>
> This is way better than School of Rock; over in Mr. R's class in
> Brooklyn, the little ones are becoming luthiers. Mr. R, Paul
> Rubenstein, works for Working Playground and teaches high school and
> middle school kids how to make electric guitars and amplifiers, a
> program he started 5 years ago. He tells us:
>
> "We make them entirely from scratch (except for the tuning
> machines) including the pickups. It has just grown since then... now
> we make amplifiers and square wave oscillators too."
>
> "We are setting the frets to an unconventional tuning system:
> 7-tone equal temperament. This means that instead of having the
> standard 12 notes (A, A#, B, etc.) we will have a seven-note scale
> with notes that don't correspond to the usual notes-- they fall
> in-between those notes, giving the scale a distinctive sound."
>
> There's a video too.
>
> Prent Rodgers
>
From Robert. Sounds a bit like Thai music!

As I posted before I've been working on my own scale designed to enable easy harmony within over 7 notes per octave.

I recently read an article saying

1) 31 is the next series up from 19 which is the next up from 12 in the fibonacci series, thus making 31TET it an ideal step up from 12TET...
2) 31-TET is also clearer than 19TET and 19TET is less clear than 12 thus explaining in part why that scale never gained full acceptance over 12TET
3) Human psychology dictates the human mind separates tone into "colors" and can only differentiate between 7 plus or minus 2 colors clearly...thus making 9 the maximum number of tones able to be identified with perfect "clarity" rather than just the usual 7.

Here is the scale I came up with as a subset of 31-TET

A (1st note)
C (3rd note...)
F (6)
I (9)
-----
O (15)
S (19)
W (23)
Y (25)
-------
[ (27)

Is there any one else who in history has used this scale or something near it?

That and....how do you think it sounds?

[Non-text portions of this message have been removed]

Hi Michael,

>Here is the scale I came up with as a subset of 31-TET
>
> A (1st note)
> C (3rd note...)
> F (6)
> I (9)
>-----
> O (15)
> S (19)
> W (23)
> Y (25)
>-------
> [ (27)
>
>Is there any one else who in history has used this scale or something
>near it?
>
>That and....how do you think it sounds?

We'll need to know what C is before we can answer that.
Also, theory discussion is supposed to be better off on the
main tuning list
/tuning
if you want to repost there.

-Carl

if the numbers correspond to 31 steps, it looks like he is calling the first pitch 1 instead of 0 or 31
5 steps would be a whole tone but 10 a 5/4,t he 3/2 is 18 etc.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> Hi Michael,
>
> >Here is the scale I came up with as a subset of 31-TET
> >
> > A (1st note)
> > C (3rd note...)
> > F (6)
> > I (9)
> >-----
> > O (15)
> > S (19)
> > W (23)
> > Y (25)
> >-------
> > [ (27)
> >
> >Is there any one else who in history has used this scale or something
> >near it?
> >
> >That and....how do you think it sounds?
>
> We'll need to know what C is before we can answer that.
> Also, theory discussion is supposed to be better off on the
> main tuning list
> /tuning > </tuning>
> if you want to repost there.
>
> -Carl
>
>

Kraig Grady wrote:
> if the numbers correspond to 31 steps, it looks like he is calling the > first pitch 1 instead of 0 or 31
> 5 steps would be a whole tone but 10 a 5/4,t he 3/2 is 18 etc.

If I'm interpreting this right, the scale is something like:

C C# D Eb F^ G Av A^ Bb (with ^ and v as the semisharp and semiflat)

It certainly sounds interesting, but I don't quite get how it all fits together. The C# could be an approximate 7/4 above Eb, and F^ could be 11/8 above C. Or A^ could be Bbb, a diminished fifth above Eb.

Scala doesn't find a close match.

Scales with the same size and same key:
closest average absolute: mixed9_6.scl diff. 18.9964 cents
closest root mean square: mixed9_6.scl diff. 25.7392 cents
closest highest absolute: kayolonian_t.scl diff. 45.9391 cents
Scales with the same size and other key:
closest average absolute: pentatetra3.scl diff. 16.7157 cents in key 1
closest root mean square: pentatetra3.scl diff. 22.0261 cents in key 1
closest highest absolute: helmholtz_hd.scl diff. 44.6735 cents in key 5
Scales with any size:
closest average absolute: dimisept12.scl diff. 12.9032 cents
closest root mean square: dimisept12.scl diff. 15.4319 cents
closest highest absolute: dimisept12.scl diff. 24.0368 cents

mixed9_6.scl is just a subset of 12-equal.
pentatetra3.scl isn't very close either.
dimisept12.scl is just the first 3 notes of the scale, so that doesn't count.

There are many different properties you might want to look for in a 9-note subset of 31-tET. Here's just one possibility to consider:

mode /equal 5 3 4 3 3 3 4 3 3

C D Eb E# F# G Ab A# B

First of all I agree with Carl and subscribed to the Tuning group and put it on their thread.
But for the sake of discussion I'll at least try to tie some of this up here... :-)

Herman,

Secondly, yes, the first note would be 1/1 IE "A" in my scale = "C" IE the root note.
I am not too surprised Scala didn't find a close match b/c I started with a 7-note dorian mode scale (mostly based on an 8-note scale Dr. Oak-root suggested on here though I forget the exact specs...) and built up on that to 12-tones by
1) ear
2) trying to avoid getting closer than the critical band between each note and/or so close that the dissonance level between the notes would drop and sound fairly unison (IE from Bill Sethares's tuning/timber/consonance theories)
Then I chose the 9 of those 12 that sounded most consonant to my ears vis a vis each other...not using Harry Partch's tonal diamond or anything related.
-------------------------------------------------------------

BTW about your suggested scale of C D Eb E# F# G Ab A# B...

I'm new to this and thank you for the advice... If I read it correctly your suggested scale is essential C,D,F#,G,A#,B from 12TET plus Eb and Ab as the notes in 31-TET just below E and A?
Also, does the above scale you mentions have anything to do with the "African" blues scale between the major and minor keys (IE a note between d,d# and a note virtually between b and a#)?

[Non-text portions of this message have been removed]

Michael Sheiman wrote:

> BTW about your suggested scale of C D Eb E# F# G Ab A# B...
> > I'm new to this and thank you for the advice... If I read it correctly your suggested scale is essential C,D,F#,G,A#,B from 12TET plus Eb and Ab as the notes in 31-TET just below E and A? > Also, does the above scale you mentions have anything to do with the "African" blues scale between the major and minor keys (IE a note between d,d# and a note virtually between b and a#)?

This would actually make a pretty good blues-type scale, I think, if you can get by without a "iv" chord.

In 31-ET the sharps and flats are two steps each. So from C to D you have:

C C^ C# Db Dv D

The pattern continues:

D D^ D# Eb Ev E

then with a smaller interval between E and F:

E E^ Fv F

and so on. This all follows from the chain of fifths in traditional notation with a perfect fifth being 18 steps in 31-tET. You can get by without semisharp and semiflat symbols if you use double sharps and double flats, but I think that can get a little confusing.

C Dbb C# Db Cx D Ebb D# Eb Dx E Fb E# F Gbb F# Gb Fx G ....