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Scale 2743: "Staptyllic"

Scale 2743: Staptyllic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

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Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Staptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,5,7,9,11}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3499
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1391
Deep Scaleno
Interval Vector465562
Interval Spectrump6m5n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC{0,4,7}341.9
F{5,9,0}242.1
G{7,11,2}242.3
A{9,1,4}341.9
Minor Triadsdm{2,5,9}242.1
em{4,7,11}242.1
am{9,0,4}341.9
Augmented TriadsC♯+{1,5,9}341.9
Diminished Triadsc♯°{1,4,7}242.1
{11,2,5}242.3
Parsimonious Voice Leading Between Common Triads of Scale 2743. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em am am C->am A A c#°->A C#+ C#+ dm dm C#+->dm F F C#+->F C#+->A dm->b° Parsimonious Voice Leading Between Common Triads of Scale 2743. Created by Ian Ring ©2019 G em->G F->am G->b° am->A

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2743 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3419
Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
3rd mode:
Scale 3757
Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
4th mode:
Scale 1963
Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
5th mode:
Scale 3029
Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
6th mode:
Scale 1781
Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
7th mode:
Scale 1469
Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
8th mode:
Scale 1391
Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllicThis is the prime mode

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [2743, 3419, 3757, 1963, 3029, 1781, 1469, 1391] (Forte: 8-22) is the complement of the tetratonic modal family [149, 673, 1061, 1289] (Forte: 4-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2743 is 3499

Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2743 is chiral, and its enantiomorph is scale 3499

Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel

Transformations:

T0 2743  T0I 3499
T1 1391  T1I 2903
T2 2782  T2I 1711
T3 1469  T3I 3422
T4 2938  T4I 2749
T5 1781  T5I 1403
T6 3562  T6I 2806
T7 3029  T7I 1517
T8 1963  T8I 3034
T9 3926  T9I 1973
T10 3757  T10I 3946
T11 3419  T11I 3797

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 2741Scale 2741: Major, Ian Ring Music TheoryMajor
Scale 2739Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2807Scale 2807: Zylygic, Ian Ring Music TheoryZylygic
Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian
Scale 1719Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.