Topic: Gizmo 14 for 4:6:7:9:11:13 (Parapyth)

3 scales

Thread (1 messages)

From: Margo Schulter (2012-11-05)
Subject: Gizmo 14 for 4:6:7:9:11:13 (Parapyth)

Hello, all.

Here's a curious kind of 14-note tuning set found within Parapyth
(POTE, MET-24, or whatever) called Gizmo -- with that name
subject to revision if it duplicates something I haven't yet
found in a quick search of tuning and tuning-math.

The definition of Gizmo is that it's the smallest Parapyth set
including three 4:6:7:9:11:13 hexads, on the 1/1, 9/8. and 3/2.
Here's a JI transversal, and versions of Gizmo in MET-24 and POTE
Parapyth.


! gizmo14-ji_transversal.scl
!
Possible JI transversal of gizmo14.scl or gizmo14-pote.scl
  14
!
  91/88
  9/8
  11/9
  14/11
  21/16
  11/8
  3/2
  14/9
  13/8
  22/13
  7/4
  11/6
  63/32
  2/1


! gizmo14-pote.scl
!
Gizmo in Parapyth POTE, three ~4:6:7:9:11:13 hexads on 1/1, 9/8, 3/2
  14
!
  58.33900
  207.71200
  346.77100
  415.42400
  473.76300
  554.48300
  703.85600
  762.19500
  842.91500
  911.56800
  969.90700
  1050.62700
  1177.61900
  2/1


! gizmo14.scl
!
Parapyth set, three ~4:6:7:9:11:13 hexads on 1/1, 9/8, 3/2 (MET-24 version)
  14
!
  57.42187
  207.42187
  346.28906
  414.84375
  472.26562
  553.71094
  703.71094
  761.13281
  842.57812
  911.13281
  968.55469
  1050.00000
  1175.97656
  2/1


While the 4:6:7:9:11:13 hexads give Gizmo 14 a mostly harmonic
definition, it abounds in varied step sizes, and is a lot of fun
for maqam or dastgah.

Peace and love,

Margo