McClain toy piano tuning: Difference between revisions

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McClain toy piano tuning was discovered by [[Levi McClain]], who found a toy [[:Category:Piano|piano]] which had been accidentally tuned to it instead of to the intended [[12edo]] diatonic scale.  
McClain toy piano tuning was discovered by [[Levi McClain]], who found a toy [[:Category:Piano|piano]] which had been accidentally tuned to it instead of to the intended [[12edo]] diatonic scale.  


He measured the tuning of each key and described the [[scale]] he measured.  
He measured the tuning of each key on the piano and described the [[scale]] he measured. He documented his findings in the video ''[https://www.youtube.com/watch?v=8eOCLohjgOQ Discovering a NEW MODE Through This Microtonal Defect]'' (Jan 2024). It includes audio examples.


He documented his findings in the video ''[https://www.youtube.com/watch?v=8eOCLohjgOQ Discovering a NEW MODE Through This Microtonal Defect]'' (Jan 2024). It includes audio examples.
== Table of intervals ==
{| class="wikitable"
|+
!Interval ([[cents]])
!Note name
![[17-limit]] approximation
|-
| -819
|C‡
| -8/5
|-
| -689
|D
| -3/2
|-
| -499
|E
| -4/3
|-
| -290
|F#
| -13/11
|-
| -95
|G#
| -18/17
|-
|'''0'''
|'''A'''
|'''1/1'''
|-
|215
|B
|17/15
|-
|400
|C#
|5/4
|-
|509
|D
|4/3
|-
|700
|E
|3/2
|-
|912
|F#
|5/3
|-
|1100
|G#
|17/9
|-
|'''1158'''
|'''Ad'''
|'''35/18, 39/20'''
|-
|1358
|Bd
|11/5
|-
|1561
|C‡
|22/9
|-
|1665
|Dd
|13/5
|-
|1874
|Ed
|44/15
|-
|2131
|F⩩
|24/7
|}


== List of intervals ==
== Relationship to other tunings ==
* -819 C#
 
* -689 D
=== 31edo ===
* -499 E
The McClain toy piano tuning can be closely approximated using a [[heptatonic]] subset of [[31edo]], repeating on the 30\31 (30th degree of 31edo).
* -290 F#
 
* -95 G#
This reminded McClain of the 31edo double Lydian scale, described by [[Zhea Erose]].
* 0 A
 
* 215 B
McClain was then inspired to describe the double Phrygian scale - the McClain toy piano tuning tempered to 31edo - along with the entire family of [[Erose-McClain double mode]]s.
* 400 C#
 
* 509 D
=== Ed11/2s ===
* 700 E
The entire width of McClain's toy piano tuning (2950 cents) is almost exactly [[11/2]] (2951 cents).
* 912 F#
 
* 1100 G#
This lends itself to the use of [[ed11/2]] tunings to approximate it.
* 1158 A
 
* 1358 B
Some ed11/2s with outstanding approximations (for their size) of McClain's toy piano tuning are:
* 1561 C#
* [[72ed11/2]] (19c error)
* 1665 D
* [[89ed11/2]] (13c error)
* 1874 E
* [[118ed11/2]] (9c error)
* 2131 F#
* [[197ed11/2]] (7c error)
* [[252ed11/2]] (5c error)
 
For comparison, 31edo’s approximation has 20c error.
 
== Scala files ==
Made with [[Scale Workshop]]. Work with any instrument or software that supports [[Scala]].
 
 
; Original:


== Scala file ==
<pre>
<pre>
! McClainToyPiano.scl
! McClainToyPiano.scl
Line 56: Line 142:
</pre>
</pre>


== Relationship to other tunings ==


=== 31edo ===
; Tempered to 31edo
The McClain toy piano tuning can be closely approximated using a [[heptatonic]] subset of [[31edo]], repeating on the 30\31 (30th degree of 31edo).


This reminded McClain of the 31edo double Lydian scale, described by [[Zhea Erose]].  
<pre>
 
! 31edoMcClainToyPiano.scl
McClain was then inspired to describe the double Phrygian scale - the McClain toy piano tuning tempered to 31edo - along with the entire family of [[Erose-McClain double mode]]s.
! Created using Scale Workshop 3.0.2
!
! https://scaleworkshop.plainsound.org/scale/zbmiWVXV7
!
31edo McClain toy piano tuning
17
!
116.1
309.7
541.9
735.5
812.9
1045.2
1200.0
1316.1
1509.7
1703.2
1935.5
1974.2
2167.7
2361.3
2477.4
2709.7
2941.9
</pre>


=== Ed11/2s ===
The entire width of McClain's toy piano tuning is almost exactly [[11/2]]. Less than 2 cents off.


This lends itself to the use of [[ed11/2]] tunings to approximate it.
; Tempered to 118ed11/2


Some ed11/2s with outstanding approximations for their size of McClain's toy piano tuning are:
<pre>
* [[72ed11/2]]
! 118_ed_11_2_McClainToyPiano.scl
* [[83ed11/2]]
! Created using Scale Workshop 3.0.2
* [[89ed11/2]]
!
* [[94ed11/2]]
! https://scaleworkshop.plainsound.org/scale/zbmiWVXV7
* [[118ed11/2]]
!
* [[183ed11/2]]
118ed11over2 McClain toy piano tuning
* [[197ed11/2]]
17
* [[228ed11/2]]
!
* [[252ed11/2]]
125.1
325.1
525.2
725.3
825.4
1025.5
1225.5
1325.6
1525.7
1725.8
1925.9
1975.9
2176.0
2376.1
2476.1
2701.2
2951.3
</pre>


== Music ==
== Music ==
Line 87: Line 210:


[[Category:17-tone scales]]
[[Category:17-tone scales]]
[[Category:Empirical scales]]
[[Category:Empirical tuning]]
[[Category:Ed11/2|Category:Ed11/]]
[[Category:Pages with Scala files]]
[[Category:Pages with Scala files]]
[[Category:Piano]]

Latest revision as of 09:55, 11 December 2024

The McClain toy piano tuning is an empirical tuning with flat pseudo-octaves.

McClain toy piano tuning was discovered by Levi McClain, who found a toy piano which had been accidentally tuned to it instead of to the intended 12edo diatonic scale.

He measured the tuning of each key on the piano and described the scale he measured. He documented his findings in the video Discovering a NEW MODE Through This Microtonal Defect (Jan 2024). It includes audio examples.

Table of intervals

Interval (cents) Note name 17-limit approximation
-819 C‡ -8/5
-689 D -3/2
-499 E -4/3
-290 F# -13/11
-95 G# -18/17
0 A 1/1
215 B 17/15
400 C# 5/4
509 D 4/3
700 E 3/2
912 F# 5/3
1100 G# 17/9
1158 Ad 35/18, 39/20
1358 Bd 11/5
1561 C‡ 22/9
1665 Dd 13/5
1874 Ed 44/15
2131 F⩩ 24/7

Relationship to other tunings

31edo

The McClain toy piano tuning can be closely approximated using a heptatonic subset of 31edo, repeating on the 30\31 (30th degree of 31edo).

This reminded McClain of the 31edo double Lydian scale, described by Zhea Erose.

McClain was then inspired to describe the double Phrygian scale - the McClain toy piano tuning tempered to 31edo - along with the entire family of Erose-McClain double modes.

Ed11/2s

The entire width of McClain's toy piano tuning (2950 cents) is almost exactly 11/2 (2951 cents).

This lends itself to the use of ed11/2 tunings to approximate it.

Some ed11/2s with outstanding approximations (for their size) of McClain's toy piano tuning are:

For comparison, 31edo’s approximation has 20c error.

Scala files

Made with Scale Workshop. Work with any instrument or software that supports Scala.


Original
! McClainToyPiano.scl
! Created using Scale Workshop 3.0.2
!
! https://scaleworkshop.plainsound.org/scale/zbmiWVXV7
!
The McClain toy piano tuning
 17
!
 130.0
 320.0
 529.0
 724.0
 819.0
 1034.0
 1219.0
 1328.0
 1519.0
 1721.0
 1919.0
 1977.0
 2177.0
 2380.0
 2484.0
 2693.0
 2950.0


Tempered to 31edo
! 31edoMcClainToyPiano.scl
! Created using Scale Workshop 3.0.2
!
! https://scaleworkshop.plainsound.org/scale/zbmiWVXV7
!
31edo McClain toy piano tuning
 17
!
 116.1
 309.7
 541.9
 735.5
 812.9
 1045.2
 1200.0
 1316.1
 1509.7
 1703.2
 1935.5
 1974.2
 2167.7
 2361.3
 2477.4
 2709.7
 2941.9


Tempered to 118ed11/2
! 118_ed_11_2_McClainToyPiano.scl
! Created using Scale Workshop 3.0.2
!
! https://scaleworkshop.plainsound.org/scale/zbmiWVXV7
!
118ed11over2 McClain toy piano tuning
 17
!
 125.1
 325.1
 525.2
 725.3
 825.4
 1025.5
 1225.5
 1325.6
 1525.7
 1725.8
 1925.9
 1975.9
 2176.0
 2376.1
 2476.1
 2701.2
 2951.3

Music

JUMBLE
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