Stretched octave guitar

An stretched octave guitar was evaluated today.

* Open string length---- 650 mm.

* Twelfth fret positioned at 323.5 mm, measured from the lower bridge.

* Major, minor triads and all sorts of chords sounded very expressive and bright.

2.00904851441 (1207.815 cents)

Semitone factor--1.05986170875

0.94351932119

OPEN STRING LENGHT = 650 mm.

Fret measurements from the lower bridge to the fret.

Fret (Toctave)

position---- 650 mm. ... E.Tempered---------------- E.Tempered - Toctave fret position

T1-- 613.3 ...... 613.5 ........ 0.2 mm

T2-- 578.6 ...... 579 ......... 0.4

T3-546 ........ 546.6 ....... 0.6

T4-515 ........ 516 .......... 1

T5-486 ........ 487 .......... 1

T6-- 458.6 ....... 459.6 ......... 1

T7-- 432.7 ....... 433.8 ......... 1.1

T8-- 408.3 ....... 409.5 ......... 1.2

T9-- 385.2 ...... 386.5 ......... 1.3

T10-- 363.5 ...... 364.8 ........ 1.3

T11-343 ...... 344.3 ........1.3

T12-- 323.5 .......325..........1.5

T13-- 305.3 .......306.7..........1.4

T14-288 .......289.5..........1.5

T15-- 271.7 .......273.3..........1.6

T16-- 256.4 .......258..........1.6

T17-242 .......243.5..........1.5

T18-- 228.3 .......229.8..........1.5

T19-- 215.4 .......217..........1.6

T20-203.2 ......204.7......... 1.5

Mario Pizarro

January 1, 2012

Yeah, stretched octaves are good sometimes. They're good for 12edo, but other temperaments are just crying out for them, for example mavila and 16edo. A 10 cent octave stretch goes a hell of a long way toward making 16edo sound palatable. Judging 16edo by its sound with pure 2/1s is practically criminal.

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
>
>
> An stretched octave guitar was evaluated today.
>
> * Open string length---- 650 mm.
>
> * Twelfth fret positioned at 323.5 mm, measured from the lower bridge.
>
> * Major, minor triads and all sorts of chords sounded very expressive and bright.
>
>
> 2.00904851441 (1207.815 cents)
>
> Semitone factor--1.05986170875
>
> 0.94351932119
>
> OPEN STRING LENGHT = 650 mm.
>
> Fret measurements from the lower bridge to the fret.
>
>
>
> Fret (Toctave)
>
> position---- 650 mm. ... E.Tempered---------------- E.Tempered - Toctave fret position
>
>
>
> T1-- 613.3 ...... 613.5 ........ 0.2 mm
>
>
>
> T2-- 578.6 ...... 579 ......... 0.4
>
>
>
> T3-546 ........ 546.6 ....... 0.6
>
>
>
> T4-515 ........ 516 .......... 1
>
>
>
> T5-486 ........ 487 .......... 1
>
>
>
> T6-- 458.6 ....... 459.6 ......... 1
>
>
>
> T7-- 432.7 ....... 433.8 ......... 1.1
>
>
>
> T8-- 408.3 ....... 409.5 ......... 1.2
>
>
>
> T9-- 385.2 ...... 386.5 ......... 1.3
>
>
>
> T10-- 363.5 ...... 364.8 ........ 1.3
>
>
>
> T11-343 ...... 344.3 ........1.3
>
>
>
> T12-- 323.5 .......325..........1.5
>
>
>
> T13-- 305.3 .......306.7..........1.4
>
>
>
> T14-288 .......289.5..........1.5
>
>
>
> T15-- 271.7 .......273.3..........1.6
>
>
>
> T16-- 256.4 .......258..........1.6
>
>
>
> T17-242 .......243.5..........1.5
>
>
>
> T18-- 228.3 .......229.8..........1.5
>
>
>
> T19-- 215.4 .......217..........1.6
>
>
>
> T20-203.2 ......204.7......... 1.5
>
>
>
> Mario Pizarro
>
> January 1, 2012
>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> Yeah, stretched octaves are good sometimes. They're good for 12edo, but other temperaments are just crying out for them, for example mavila and 16edo. A 10 cent octave stretch goes a hell of a long way toward making 16edo sound palatable. Judging 16edo by its sound with pure 2/1s is practically criminal.

If I want to adjust the octave stretch of a guitar I can do that to pretty high accuracy just by adjusting the bridge position, right?

People make "11edo" or "13edo" guitars this way, which is really inaccurate, especially in the second octave worth of frets, but if you just want to adjust the stretch by 10 cents/octave or less it seems like the error in that approximation would be quite small.

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> If I want to adjust the octave stretch of a guitar I can do that to pretty high accuracy just by adjusting the bridge position, right?
>
> People make "11edo" or "13edo" guitars this way, which is really inaccurate, especially in the second octave worth of frets, but if you just want to adjust the stretch by 10 cents/octave or less it seems like the error in that approximation would be quite small.
>

Right. That relates to my proposal for a guitar with movable or lace-up frets having positions based on 154-EDO where the bridge is movable so it makes approximations of 152-EDO thru 156-EDO (which are multiples of 19 17 22 31 and 12 EDOs respectively). Changing from 154 to 156 is like a 16 cent stretch, and in that case the maximum error in the first octave of frets is only 1.3 cents.

But I'm still trying to figure out the best thing to do with that abyssmal second octave of fret positions. As well as the aforementioned extreme inaccuracy of the stretched or compressed cases, 154-EDO positions become too close together there anyway.

-- Dave Keenan

Keenan:

Since the fret distribution table given in my message takes 2.00904851441 as the value of the stretched octave, the equal fret interval becomes (2.00904851441)^(1/12) = 1.05986170875.

For an open string length of 650 millimeters, the first fret is positioned at (650/1.05986..... ) = 613.3 mm.

The second fret is positioned at (613.3/1.05986..... ) = 578.6 mm.

The third one is positioned at (578.6/1.05986..... ) = 546 mm. and so forth.

What I did was to buy a 12Edo guitar, 650 mm. open string length, then I retired its equal tempered frets and placed the stretched frets according to the table.

------------------------------------------

I worked with 12edo. Other temperaments would imply more calculations.

You wrote: > If I want to adjust the octave stretch of a guitar I can do that to pretty high accuracy just by adjusting the bridge position, right?.

<<In my message I stated 2.00904851441 for the toctave frequency, (From 0 to the 12th fret).

If we assume some frequency like 330 Hz for the open first string, its toctave frequency in Hz equals

2.00904851441* 330 = 662.986009755 Hz. The rule of three gives and confirms the toctave string length stated in the table:

650 mm-----330 Hz

X ------------ 662.98600... -------------------- X = 323.5 mm

Semitone factor = 2.00904851441^(1/12) = 1.05986170875

The bridge position is placed 650 - 323.5 = 326.5** mm below the toctave (323.5 mm**.).

If you want to adjust the octave stretch by adjusting the bridge position, OK, you only need to calculate (**).

I hope this explanation helps you.

Mario

January, 2.

----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>

To: <tuning@yahoogroups.com>

Sent: Sunday, January 01, 2012 11:24 PM

Subject: [tuning] Re: Stretched octave guitar

> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>>
>> Yeah, stretched octaves are good sometimes. They're good for 12edo, but >> other temperaments are just crying out for them, for example mavila and >> 16edo. A 10 cent octave stretch goes a hell of a long way toward making >> 16edo sound palatable. Judging 16edo by its sound with pure 2/1s is >> practically criminal.
>
> If I want to adjust the octave stretch of a guitar I can do that to pretty > high accuracy just by adjusting the bridge position, right?
>
> People make "11edo" or "13edo" guitars this way, which is really > inaccurate, especially in the second octave worth of frets, but if you > just want to adjust the stretch by 10 cents/octave or less it seems like > the error in that approximation would be quite small.
>
> Keenan
>
>
>
>
> ------------------------------------
>

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, January 01, 2012 11:24 PM
Subject: [tuning] Re: Stretched octave guitar

> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>>
>> Yeah, stretched octaves are good sometimes. They're good for 12edo, but >> other temperaments are just crying out for them, for example mavila and >> 16edo. A 10 cent octave stretch goes a hell of a long way toward making >> 16edo sound palatable. Judging 16edo by its sound with pure 2/1s is >> practically criminal.
>
> If I want to adjust the octave stretch of a guitar I can do that to pretty > high accuracy just by adjusting the bridge position, right?
>
> People make "11edo" or "13edo" guitars this way, which is really > inaccurate, especially in the second octave worth of frets, but if you > just want to adjust the stretch by 10 cents/octave or less it seems like > the error in that approximation would be quite small.
>
> Keenan
>
>
>
>
> ------------------------------------
>
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