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Scale 3235: "Pothimic"

Scale 3235: Pothimic, 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
Pothimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,5,7,10,11}
Forte Number6-Z41
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2215
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 335
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,4,5,6}
<3> = {3,5,6,7,9}
<4> = {6,7,8,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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
Minor Triadsa♯m{10,1,5}110.5
Diminished Triads{7,10,1}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3235. Created by Ian Ring ©2019 a#m a#m g°->a#m

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3235 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3665
Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
3rd mode:
Scale 485
Scale 485: Stoptimic, Ian Ring Music TheoryStoptimic
4th mode:
Scale 1145
Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
5th mode:
Scale 655
Scale 655: Kataptimic, Ian Ring Music TheoryKataptimic
6th mode:
Scale 2375
Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic

Prime

The prime form of this scale is Scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Complement

The hexatonic modal family [3235, 3665, 485, 1145, 655, 2375] (Forte: 6-Z41) is the complement of the hexatonic modal family [215, 1475, 1805, 2155, 2785, 3125] (Forte: 6-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3235 is 2215

Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3235 is chiral, and its enantiomorph is scale 2215

Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic

Transformations:

T0 3235  T0I 2215
T1 2375  T1I 335
T2 655  T2I 670
T3 1310  T3I 1340
T4 2620  T4I 2680
T5 1145  T5I 1265
T6 2290  T6I 2530
T7 485  T7I 965
T8 970  T8I 1930
T9 1940  T9I 3860
T10 3880  T10I 3625
T11 3665  T11I 3155

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 3233Scale 3233, Ian Ring Music Theory
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 3203Scale 3203, Ian Ring Music Theory
Scale 3219Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
Scale 3267Scale 3267, Ian Ring Music Theory
Scale 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3107Scale 3107, Ian Ring Music Theory
Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic
Scale 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 2211Scale 2211: Raga Gauri, Ian Ring Music TheoryRaga Gauri
Scale 2723Scale 2723: Raga Jivantika, Ian Ring Music TheoryRaga Jivantika
Scale 1187Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi

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.