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Scale 3801: "Maptyllic"

Scale 3801: Maptyllic, 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
Maptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,4,6,7,9,10,11}
Forte Number8-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 879
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 879
Deep Scaleno
Interval Vector546553
Interval Spectrump5m5n6s4d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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}342
D♯{3,7,10}342.08
B{11,3,6}342.08
Minor Triadscm{0,3,7}441.92
d♯m{3,6,10}342.15
em{4,7,11}342.08
am{9,0,4}342.23
Augmented TriadsD♯+{3,7,11}441.85
Diminished Triads{0,3,6}242.31
d♯°{3,6,9}242.38
{4,7,10}242.46
f♯°{6,9,0}242.46
{9,0,3}242.31
Parsimonious Voice Leading Between Common Triads of Scale 3801. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ cm->a° em em C->em am am C->am d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° D# D# d#m->D# d#m->B D#->D#+ D#->e° D#+->em D#+->B e°->em f#°->am a°->am

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 3801 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 987
Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
3rd mode:
Scale 2541
Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
4th mode:
Scale 1659
Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
5th mode:
Scale 2877
Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic
6th mode:
Scale 1743
Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
7th mode:
Scale 2919
Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
8th mode:
Scale 3507
Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz

Prime

The prime form of this scale is Scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Complement

The octatonic modal family [3801, 987, 2541, 1659, 2877, 1743, 2919, 3507] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3801 is 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3801 is chiral, and its enantiomorph is scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Transformations:

T0 3801  T0I 879
T1 3507  T1I 1758
T2 2919  T2I 3516
T3 1743  T3I 2937
T4 3486  T4I 1779
T5 2877  T5I 3558
T6 1659  T6I 3021
T7 3318  T7I 1947
T8 2541  T8I 3894
T9 987  T9I 3693
T10 1974  T10I 3291
T11 3948  T11I 2487

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 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 3737Scale 3737: Phrocrian, Ian Ring Music TheoryPhrocrian
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
Scale 2777Scale 2777: Aeolian Harmonic, Ian Ring Music TheoryAeolian Harmonic
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major

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.